Welcome to the World of
Material Science
Preface: What is Material Science?
Welcome to the World of Materials
Welcome to the world of science and engineering, and the application of discoveries in the
world we live. Look around your environment and what is it that you see and experience. Can
you identify any of these materials? Do you notice any tables, chairs, flooring, trash cans,
books, or computers? There are items made of wood, metals, plastics, ceramics and
combinations of these materials. If we are inclined to stay in a society where status quo is a way
of life, many of the products we surround ourselves with would not be in existence. Are there
any ideas on what have been major causes that have resulted in the in materials we have
today?
In addition to new materials, society need understanding on how we implement these
materials and what benefits do these materials give to our society?
Let’s look at a presentation by Ken Robinson. Sir Ken Robinson (born 4 March 1950) is an
author, speaker, and international advisor on education in the arts to government, non-profits,
education, and arts bodies. He was Director of The Arts in Schools Project (1985–89), Professor
of Arts Education at the University of Warwick (1989–2001), and was knighted in 2003 for
services to education.
http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity.html
Notice the comment regarding the ability of educators to prepare student to a society that is
unknown. We are to school the students to materials that haven’t been discovered yet.
Did you know….
http://www.youtube.com/watch?v=pMcfrLYDm2U
Material Science is an engineering course and is the only engineering course that is defined as
both a science and engineering. There is Civil Engineering, Mechanical Engineering, Chemical
Engineering, and now consider Material Science and Engineering.
Before we begin our journey into Material Science, we need to review some basic safety rules.
Let’s look at the first power point found day one of week one. Once we complete the journey
into safety we can then venture into the world of materials. The order found in the semester
course or the year long course, are suggested paths to travel. Depending on the time allocated
in the school year adjustments can be made. It is recommended to closely follow the suggested
path until you have gone through the course entirely. Some activities may be omitted due to
the lack of materials or costs. Note it may be necessary to annotate the missing/used
material(s) so they can be placed on the inventory list for future classes. Remember to also
keep current the amount of supplies you have so they can be replenished.
Journal
Introduction:
Welcome to the Science and Technology Journal. This document is a living text to be
created by the students under the guidance of the instructor, who are taking the Science and
Technology of Materials course. The students will create this Journal throughout the year by
adding articles, presentation, free writes, lab reports and weekly reviews to the documents. To
assist the students in the creation of this Journal, you the teacher must guide and instruct the
students on the techniques that should be followed in each section. As you travel through the
journal, notice the explanations associated in each section. As you touch the tab you will be
directed to that page. That page will have a narrative description of the content to be found in
that section. If needed, an explanation may be found describing the template to be followed.
Let’s begin our investigation into the Science and Technology Journal.
Science and Technology Journal
Journal Prompts
1. What did this article make you think of?
2. What did you read that you did not understand?
3. What did you learn from the article?
4. What puzzles you about this article?
5. Do you agree or disagree with this article?
6. If you had one question to ask the author, what would it be and why?
7. What made sense to you about this article?
Language for learning is:
 personal exploratory for the purpose of thinking, not testing incomplete a
process, not a final product informal non-graded in the traditional sense
Journal Prompts:
1. I observed ........
2. My idea worked because ........
3. My goal in this project is to ........
4. Next time I’ll ........
5. My modification was to ........
6. The experiment was successful (unsuccessful) because ........
7. I wonder what would happen if ........
8. What did you do? think? feel?
9. What did you observe?
10.What was the most useful thing you heard in the last 30 minutes?
11. Write down what is bugging you.
12. What could the “stuff” be used for?
13. What was the “stuff” (material) like? What are its properties?
14. How did its behavior change/remain stable?
15. How is it different from similar “stuff”?
16. How would its properties be useful?
17. What did the “stuff” do?
18. Why do you think it does what it does?
It must be remembered there are NO WRONG ANSWERS! You intent should be to
express your understanding of the topic being questioned. At times your free write will be
based on your past experiences before any additional explanation is given. Other times it may
be based on, what was taught it, and determine the level of understanding obtained.
Each Lab write up should
have the name of all
participants and the date of
the lab
Name_______ Lab Partners_____________________
Date________________
Title the lab… This may seem
simple but it is essential to
identify the lab
Objective: What is the purpose of this lab?
All Lab write ups should have:
Objective
Procedure
Data
Conclusion
The conclusion is the most
import part of the write up. It
should include whether the
TITLE OF LAB
Procedure: How was the lab performed? Make sure
to include the steps you performed. By reading this,
an individual should be able to repeat the lab.
Graphics and explanations may be included in this
section. Graphics without explanations are NOT
acceptable.
Data: This portion of the lab write-up includes any
data collected during the experiment. The data may
be included as tables, making sure to label all values
with appropriate units. In addition, any and all
calculations and/or observations are located in this
section.
Conclusion: The conclusion is an important section of the
objective has been met or not.
Use the information from the
data portion of the write up to
support your decisions. This
write up should be factual.
Remember to ask “why?” did something occur and why you did what was done, and let
this support your conclusive argument.
Articles
Throughout the semesters, articles will be distributed to the students and it is their
responsibility to
1) Place the article in the Journal and
2) READ THE ARTICLE! These articles are support materials to the information
presented, and the students are responsible for knowing what the articles
contained. The articles can be included in the tests of the material to be graded.
Scientific Content
Scientific Content This section is for students to record the scientific content from the
class. This will help them when working on weekly reviews and for reviewing for exams.
Important Concepts should be placed in this section, including some worksheets that are
distributed throughout the class.
Presentations
If the instructor chooses, they can distribute copies of the presentations to students
prior to class. Depending on instructor preference, presentations can be distributed
immediately before class or after the material has been presented. Students can take notes on
the presentations. The presentations will be presented to the students with an option to with
an area to the right where the students are able to take personal notes. These presentations
with notes should be included in this section
Weekly Review
The purpose of the Weekly Review is to have the students integrate everything that has
occurred throughout the week. Suggested outline of this weekly report can be:
Week _____
Topic ______________
Monday_________________________
________________________________
________________________________
Tuesday_________________________
________________________________
________________________________
Wednesday_______________________
________________________________
________________________________
Thursday ________________________
________________________________
________________________________
Friday ___________________________
_________________________________
_________________________________
General Review____________________________
_________________________________________
_________________________________________
Week 1: Introduction to Safety?
Safety
It is essential to prepare all science classes with a review of safety. A power point
presentation is available covering the topic. It must be stressed that clothing, safety glasses,
and hair are a few points of discussion that could be listed as general safety procedures.
Glassware can result in cuts let alone injecting solutions into an open wound as a result
of the cuts. Pouring materials into glassware is also a point to be considered. Prevention of
“splashing,” drips, and thermal shock are major issues of considerations that can be prevented
by simply erroring on the side of caution.
When dealing with chemicals, protective goggles is a must, as well as the usage of the
safety techniques established in your previous chemistry classes such as waffling as oppose to
smelling into a vial or test tube.
Heating is a common property that will be used throughout the course. We will be using
various heating devices and it is essential that we maintain all levels of safety that are referred
to in the power point presentation.
A safety quiz will be administered to verify awareness of the safety procedures
established in this class.
Safety Power point
Safety Quiz
Let’s begin the investigation of materials.
Oobleck Experiment.
Purpose of the activity:
1. making observations
2. being open to the unexpected
3. looking at properties
Materials:
1.
2.
3.
4.
5 oz. Dixie cups or plastics cups
wood craft sticks
water
white powder (cornstarch)
Procedure:
1. Fill the Dixie cup approximately 1/3 to 1/2 full with white powder (cornstarch).
2. Add 1/3 as much water.
3. Stir with craft stick.
4. Consistency should be sort of like thick toothpaste or putty.
5. Go outside and experiment with the material.
Experiment with the substance:
1.
2.
3.
4.
5.
6.
7.
stir slow
stir fast
push the stick down through it – slowly and quickly
squeeze it in your hand
roll it into a ball and pull it apart
hit a ball with a hammer
play catch with
Journal:
1.
2.
3.
4.
Describe the material
How did you make it?
What did you do to it?
How did it respond/behave?
Teacher Information to describe to the students after the experiment is completed
This activity demonstrates
1. a non-Newtonian material. It does NOT “obey” the laws of Newtonian physics.
2. Oobleck displays a property known as dilatancy which is the tendency to become
more rigid (solid) when it is stirred or subjected to a shear force or pressure.
3. Therefore, Oobleck is known as a shear-thickening fluid (STF). Let the students
experiment with the mixture before telling them that the white powder is
cornstarch. This is a good opening day or first week activity to introduce journaling.
Class Discussion after experimentation and journaling:
What happened?
1. A “correctly-made” batch of Oobleck should move like a fluid (liquid) when slowly
stirred. It will be thick and viscous but “still flow”.
2. When stirred quickly (more shear force applied), the mixture should “lock up” and
behave like a solid. Upon sitting still, the mixture will return to its fluid state.
3. If the craft stick is slowly pushed down through the mixture, little resistance will be felt
and the stick will reach the bottom of the cup.
4. If the craft stick is quickly rammed onto the surface of the mixture it will not be able to
penetrate into the mixture which has become rigid due to the added energy (force).
Explanation?
1. Cornstarch is a polymer which means it is made up of long molecules.
2. Water and cornstarch do not mix real well. The starch doesn’t fully dissolve; it is
more of a suspension.
3. The starch molecule “rolls up” from both ends and becomes somewhat of a
spherical shape that might resemble BB’s.
a. Students seem to understand this when an analogy is made to a “slap
bracelet”.
b. When slowly stirred, the starch “balls” roll around each other and the
mixture has fluid properties.
c. When a larger amount of shear force is applied, the molecule uncurls and
becomes more linear.
d. These long molecules then entangle and the mixture becomes rigid like a
solid.
e. When the shear force is removed, the molecules move more freely and “roll”
back up into balls which allows the mixture to flow like a liquid again.
-cornstarch in water without shear force
-cornstarch in water with shear force
-like BB’s (spheres)
-molecules uncoil and stretch out
-roll around and move like a fluid
-chains become entangled and lock
.
up
Cornstarch does not mix well and will separate. This activity can be tied into a Forensic activity
simply by adding some food coloring into the mix. Both physical and chemical properties can be
illustrated in the Oobleck activity and an extension of the Oobleck activity can be made
discussing the effects of Kevlar
Vocabulary:
Non-Newtonian - does NOT follow the laws of physics as described by Newton
Dilatant - adding energy (shear force) makes a liquid thicker or more rigid – more viscous
examples – oobleck (cornstarch-water mixture), liquid body armor
Thixotropic - adding energy (shear force) makes a solid thinner or liquefy – less viscous
examples – catsup, concrete, some paint Ralph Lauren, printer’s ink
Viscosity resistance or opposition to flow of a liquid
Options:
Have 3 different bowls of “powder” in separate areas of the room. Use cornstarch, flour, and
plaster of Paris. Do not tell the students that the powders are different. Let them discover that
the batches are not all the same and hypothesize and investigate why.
Make large batches of Oobleck and place it in shallow pans. Have students slap it with their
hands or young children step on it.
Have students experiment to determine the “perfect” recipe for Oobleck while making and
recording all measurements.
Another thixotropy and dilatancy lab may be found in the Battelle MS&T Handbook or CD
beginning on page 4.4
Watch the YouTube video “A pool filled with non-Newtonian fluid” at
http://www.youtube.com/watch?v=f2XQ97XHjVw&mode=related&search
The students can read an article about liquid body armor and then write a short summary
paragraph that relates it to the Oobleck lab they did in class.
Body Armor Fit for a Superhero –
http://www.businessweek.com/magazine/content/06_32/b3996068.htm
Liquid Body Armor –
http://usmilitary.about.com/cs/armyweapons/a/liquidarmor.htm
There are also several video clips about liquid body armor that students find interesting.
http://www.metacafe.com/watch/159764/liquid_armor/
http://www.nanooze.org/english/articles/article20_liquidarmor.html
There is a Dr. Seuss book about oobleck called “Bartholomew and the Oobleck”.
Articles are available to support the points on:
http://www.scientificamerican.com/article.cfm?id=enhanced-armor&print=true
Liquid Body Armor
Journal entries:
Describe the material.
+3 – white, thick, hard to stir and mix
How did you make it?
+3 – half cup of white powder (cornstarch) in a cup and added enough water to make a
thick paste
Stirred with a craft stick until mixed.
What did you do to it?
+4 – stirred slow, stirred fast, pushed stick down slowly, pushed stick down quickly,
played with it in my hands and rolled it into a ball, let it ooze between my fingers
How did it respond/behave?
+4 – flowed like a liquid when little or no pressure was applied – became stiff and hard
like a solid when force or pressure was applied – shattered when hit with a hammer Reflect
+4 – one point for each specific idea
+2 – method completed
Total: +20 points
Week 2: Classification of Materials and
Atomic Structure
Introduction to Material Science
An introduction of the course can be centered on the topic of “STUFF”. As
previously discussed let’s review some materials found within the classroom. Let’s look a
metals, plastics, composites and chrome. Why do we use these materials?
Well, can we make an attempt to define “Material Science?”
Materials Science is the science of all materials –
 including ceramics, composites, electronic materials, metals and polymers
 Emphasis on the study of the physical and chemical properties of matter
 interdisciplinary –uses knowledge of physics, chemistry and biology applied to
materials
The Materials Scientist

develops new materials

determines what materials to use

how to process the material into a useful component

***this is a critical part of all manufacturing processes!***
As we investigate the world of Material Science one major point must be discussed….Where
does the material come from?
If we believe that other factories or manufacturers are the source of the materials, we may be
partially correct but there is another area that is more accurate…. The Earth.
Once we have the materials why do we need to further research the use of the materials?
Advancements in nearly every field of science and manufacturing depend upon the
improvement and development of new materials.
So we can see that Material Science is an area of study whose findings are shared with many
areas, such as the medical field, other engineering areas such as Metallurgy, Civil Engineering
and Mechanical Engineering, and construction to name a few.
And what new discoveries does the Material Scientist use? The knowledge is based on Biology,
Chemistry, Physics and Mathematics. Material Scientists investigate areas of metals, ceramics,
polymers, composites and semiconductors, using applied knowledge previously learned.
Material Scientists investigate the relationship between Structure, properties and processing.
http://www.strangematterexhibit.com/whatis.html
Let’s take time to rewrite our comments regarding Material Science after the power point
presentation and discussion on the NASA Article.
Power Point Introduction to Material Science
NASA article What is Material Science?
Classification of Materials
Our objective in this simple activity is to access student’s prior knowledge of materials.
The students will be given a sample of material and they are to determine whether the material
is a metal, ceramic, composite, or polymer. They are to defend their decisions. At no time is the
student to be corrected.
Purpose:
 To assess prior knowledge of students.
 To generate interest in types and properties of materials.
 To help students develop their own definition/description of each material category.
 Practice Critical Thinking Skills: evaluating the materials and classifying and justifying the
materials categories
Procedure
1. Hand out or have students choose an object(s) until all are taken
2. Each student’s task is to classify their object by putting it into one of the material
categories and justify (give reasons) for their choice.
3. Generate lists on the board or overhead as students classify their object and give their
reasoning. Be encouraging but do not indicate if their placement is correct or incorrect.
4. After all the objects have been classified, ask the students to count up how many objects
they think have been put into the wrong category.
5. Go through the lists and make corrections.
6. As a class, generate a list of properties or descriptions for each category.
Notes and Suggestions:
• Students generally feel uncomfortable with this at first. They are not used to thinking out loud
or having to give reasons for their answers.
• Rephrase what the student says so they can hear their thoughts
 Do not give any indication if their answer is correct. The students start listening to each
other and it is interesting to see how they are accepting of each other’s “opinions” as
“facts”.
• Do not accept “because” as a reason. Insist that they give you more. Give them lead-in
questions if they need help.
• If a student places an item into the polymer category and gives their reason as “because it
isn’t a metal” – request more information, ask “how do you know it isn’t a metal?”
• If a student gives a response along the line of “because it looks like a metal” – request
more information, “what does a metal look like?”
• Following is a list of sample items. Use whatever you find sitting around the classroom or
home. It is a good idea to include some simple items along with some that are “ringers” (have
no correct answer).
• Follow up with a discussion about the history of materials use. (see handout)
• Alternative method:
 assign each material category a different location in the room
 give each student an object to classify
 have the students take their object to the material location they think their
object belongs in
 have the students at each material location decide who belongs/stays and who
needs to go to a different category
 have each group write a description and/or list of properties for their material
category
 share group results with entire class
• Alternative method:
 spread the objects around the room
 have the students classify each object on their own
 place the students in small groups to discuss their “answers” and develop a
description and/or list of properties for each material category
 have a class discussion to develop a consensus on the classification of each
object and to develop a final description for each material category
Sample Items: (make an ID Box)
Metals
Ceramics/Glass
stainless steel foil
glass stirring rod
metal scoopula
brick
copper wire
aluminum wire
steel wool
Light Bulb - Assembly
glass bottle
Polymers
latex balloon
Fed Ex envelope
(Tyvek)
preform
PVC pipe
rubber stopper
Styrofoam cup
Composites
plywood
cardboard
cotton cloth
Candle
Candle – polymer or
composite
Light bulb – this isn’t a single material, it is an “assembly”. It is made up of more than one
material and each material has its own function. The different materials are joined together but
still are separate unlike a composite.
***candle – the students will want to place it under composite because of the wick. Remove
the wick if possible or tell them just to consider the wax. Some scientists would not classify the
wax as a polymer because the chains are too short. This is a good point of discussion.
Examples of student generated lists of properties for each category:
Metals
hard)
Ceramics/Glass
not conductors
Polymers
plastics
Shiny Luster
variable melt T°
flexible
malleable
ductile
good conductors
heavy (dense)
most are dense
opaque
undergo oxidation
bendable
strong
can be elements
some are magnetic
fairly high melt T°
impermeable
workable
High Melting T
brittle
some are transparent
fragile
breakable
not workable
formed by heat
sand or clay based
fairly high density
poor conductors
can be formed
includes minerals
can be recycled
Some are Natural
some are absorbent
flexible
low melt T°
low density
many are recyclable
stretchable
not brittle
bendable
rubbery
expandable
shrinkable
elasticity
some are transparent
poor conductors
can be easily formed
long molecules
Composites
combination of 2 or
more
corrode easily
come from ores
can be mixtures
(alloys)
some are hard
variety of properties
made of compounds
Classification of Materials
Types of matter: element, compound, mixture
Types of elements: metals, nonmetals, semimetals
Types of structure: crystalline, amorphous
Types of bonding: metallic, ionic, covalent, intermolecular forces
Metals
Type of Matter
Type of Elements
Element or mixture
Metallic elements
Type of Structure
Crystalline
Type of Bonding
Metallic bonding
Ceramics/Glass
Compound or
Mixture of
compounds
Metals with
nonmetals
OR
Semimetals with
nonmetals
Ceramics = crystalline
Glass = amorphous
Ionic bonding and
network covalent
bonding
Polymers
Mostly compounds
Nonmetals
Mostly amorphous
with some regions of
crystallinity
Covalent bonding and
weak intermolecular
forces
Classification of Matter
When classifying matter we begin with the defining matter and introduce the
atom. Expanding the discussion we investigate solids, liquids, gases and plasma looking at their
molecular structure.
Let’s fill in the table in the next slide based on what we just learned about the
states of matter… (red indicate the answers)
What happens when heat is applied to the mass of various states of matter? If the solid state is
below its freezing point and heat is applied, the temperatures rises following the behavior of
Q= mcT. When it reaches its freezing point and heat is applied, the material begins to melt,
however there is no temperature increase Q = mLf. A transition from the solid state to the
liquid state occurs (fusion) at this point all of the material will become a liquid and only then
can the temperature increase, once again using Q= mcT. When the boiling point is reached,
and heat is applied, the material once again goes through a phase change, transitioning from a
liquid to a gas and following Q = mLv. Finally when the transition is complete and the material is
totally gaseous in nature, the temperature of the gas can increase using Q = mcT.
Atomic Structure and Bonding
What do we know about atoms and the periodic table? Take about 10 minutes, no
more, to do a free write in the journal about your perception of atoms and the periodic table.
Discussions centers on the atom, discussing the nucleus, protons and electrons, and
how each affects the mass of the atoms. The creation of ions and isotopes must be explained
and associated with the bonding properties taught in chemistry.
Bohr Atomic Model :
Bohr proposed his quantized shell model of the atom to explain how electrons can have stable
orbits around the nucleus in 1913. According to classical mechanics and electromagnetic
theory, any charged particle moving on a curved path emits electromagnetic radiation,
subsequently, in the Rutherford model the electrons were unstable; the electrons would lose
energy and spiral into the nucleus. Bohr modified the Rutherford model by requiring that the
electrons move in orbits of fixed size and energy. The size of the orbit controls the energy of an
electron and is lower for smaller orbits. When electrons jump from one orbit to another
radiation can occur. The atom will be completely stable in the state with the smallest orbit,
since there is no orbit of lower energy into which the electron can jump.
Because an electron is continually accelerating in a curved path in orbit,
according to
classical physics, it should emit electromagnetic radiation (photons) continously. The resulting
loss of energy implies that the electron should spiral into the nucleus in a very short time (i.e.
atoms can not exist)
Bohr modified the Rutherford model by requiring that the electrons move in orbits of fixed size
and energy. The size of the orbit controls the energy of an electron and is lower for smaller
orbits
Bohr understood that classical mechanics by itself could never explain the atom's stability. A
stable atom can be described by certain constants. The classical fundamental constants-namely, the charges and the masses of the electron and the nucleus--cannot be combined to
make a length. Bohr noticed that the quantum constant formulated by the German physicist
Max Planck, has dimensions when combined with the mass and charge of the electron, produce
a measure of length. The measure is close to the known size of atoms. Bohr was encouraged to
use Planck's constant in searching for a theory of the atom.
Planck’s constant was introduced in 1900 in a formula explaining the light radiation emitted
from heated bodies. Classical theory states comparable amounts of light energy should be
produced at all frequencies. This is not only contrary to observation but also implies the absurd
result that the total energy radiated by a heated body should be infinite. Planck’s postulation
was that energy can only be emitted or absorbed in discrete amounts, which he called quanta
(the Latin word for "how much"). The energy quantum is related to the frequency of the light
by a new fundamental constant, ħ. Heated bodies heated, radiate energy in a particular
frequency range, according to classical theory, proportional to the temperature of the body.
The radiation can occur only in quantum amounts of energy. If the radiant energy is less than
the quantum of energy, the amount of light in that frequency range will be reduced. Planck's
formula correctly describes radiation from heated bodies. Planck's constant has the dimensions
of action, which may be expressed as units of energy multiplied by time, units of momentum
multiplied by length, or units of angular momentum. Planck's constant can be written as h =
6.6x10-34 Joule seconds.
Bohr obtained an accurate formula for the energy levels of the hydrogen atom while using
Planck’s constant. He theorized that the angular momentum of the electron is quantized--i.e., it
can have only discrete values. He rationalized that electrons obey the laws of classical
mechanics by traveling around the nucleus in circular orbits. The electron orbits have fixed sizes
and energies. The orbits are labeled by an integer, the quantum number n.
Bohr explained how electrons could jump from one orbit to another only by emitting or
absorbing energy in fixed quanta. If an electron jumps one orbit closer to the nucleus, it must
emit energy equal to the difference of the energies of the two orbits. When the electron jumps
to a larger orbit, it must absorb a quantum of light equal in energy to the difference in orbits.
Week 3: Atomic Structure and Periodic Table
The Periodic Table
Article based on an article by Dr. Doug Stewart
The periodic table is based on the one devised and published by Dmitri Mendeleev in 1869.
Mendeleev found he could arrange the 65 elements then known in a grid or table so that each
element had:
1. A higher atomic weight than the one on its left. For example,
Calcium (atomic weight 40) is placed to the right of Potassium (atomic
weight 39):
2. Similar chemical properties to other elements in the same column - in
other words similar chemical reactions. Magnesium, for example, is
placed in the alkali earths' column:
Mendeleev realized that the table in front of him lay at the very heart of
chemistry. And more than that, Mendeleev saw that his table was incomplete
- there were spaces where elements should be, but no-one had discovered
them.
Mendeleev had made a crucial breakthrough, he made little further progress.
With the benefit of hindsight, we know that Mendeleev's periodic table was
underpinned by false reasoning. Mendeleev believed, incorrectly, that
chemical properties were determined by atomic weight. Of course, this was
perfectly reasonable when we consider scientific knowledge in 1869.
In 1869, the electron had not been discovered - that happened 27 years later,
in 1896. It took 44 years for the correct explanation of the regular patterns in
Mendeleev's periodic table to be found
Clarity came in 1913 from Henry Moseley, who fired electrons at atoms, resulting in the
emission of x-rays. Moseley found that each element he studied emitted x-rays at a
unique frequency. When observing the frequencies emitted by a series of elements, he
determined that a pattern was best explained if the positive charge in the nucleus
increased by exactly one unit from element to element.
Today the chemical elements are still arranged in order of increasing atomic number (Z) as we
look from left to right across the periodic table. We call the horizontal rows periods. For
example, here is Period 4:
We call the vertical rows groups.
an element's chemistry is determined by the way its electrons are arranged - its electron
configuration.
Electrons in atoms can be pictured as occupying layers or shells surrounding the atomic
nucleus. Picture electrons as little planets whizzing around a sun-like nucleus, which is where
the protons and neutrons are located, this is called a Bohr representation of an atom. This is
actually an approximation, but it's a good starting point for understanding the chemical
properties of the elements. Atoms which occupy the same group of the periodic table have the
same number of outer electrons.
These outer electrons are called valence electrons. It is the valence electrons which cause
chemical reactivity.
The noble gases are unreactive, because their outer electron shells are full. A
full shell of outer electrons is a particularly stable arrangement. This means that
noble gas atoms neither gain nor lose electrons easily; they react with other
atoms with great difficulty, or not at all.
Other atoms lose electrons, gain electrons or share electrons to achieve the
same electron configuration as a noble gas - in doing so, they form chemical
bonds, and make new substances.
The number of valence electrons in atoms is the basis of the regular patterns
observed by Mendeleev in 1869, patterns which ultimately have given us our
modern periodic table.
Week 4: Properties of Materials
Properties of Matter
Investigations into the properties of matter are divided into two major areas: the
Physical Properties and the Chemical Properties.

Physical properties - properties that do not change the chemical nature of matter

Chemical Properties - properties that do change the chemical nature of matter
Examples of physical properties are: color, smell, freezing point, boiling point, melting point,
infra-red spectrum, magnetism, opacity, viscosity, and density. Notice that measuring any of
these properties will not alter the basic structure of the matter.
Examples of chemical properties are: heat combustion, reactivity with water, PH and
electromotive forces.
The more properties we can identify in a substance, the better knowledge we have about the
nature of the material.
One of the first experiments we have is in the mechanical properties of the materials.
Looking at one of thermal properties of matter, we discover the property of expansion is
associated with heat (Linear Expansion). The fact that this property exists can be demonstrated
by the ring and ball demonstration. An additional example of a bimetallic material, when
heated and cooled, can lead to the discussion of a switch in a thermostat.
Workability is a major issue when we investigate metals. (distribute copper wire to students
having the “work”(malleability and ductility) the material.)
Remember to leave time for students to update their Journals with the material covered for the
week.
Continuing our discussion into the mechanical properties of metals, we find ourselves in the
basic world of physics. We are examining stresses and strains, shearing and twisting. As a result,
we may need to review or actually define these concepts to the students depending on the
level that the materials class is offered.
Tension
The forces involved in supporting a ball by a rope. Tension is the force of the rope on the
scaffold, the force of the rope on the ball, and the balanced forces acting on and produced by
segments of the rope.
Tension is (magnitude of) the pulling force exerted by a string, cable, chain, or similar solid
object on another object. It results from the net electrostatic attraction between the particles
in a solid when it is deformed so that the particles are further apart from each other than when
at equilibrium, where this force is balanced by repulsion due to electron shells; as such, it is the
pull exerted by a solid trying to restore its original, more compressed shape. Tension is the
opposite of compression.
As tension is the magnitude of a force, it is measured in Newtons (or sometimes pounds-force)
and is always measured parallel to the string on which it applies. There are two basic
possibilities for systems of objects held by strings: Either acceleration is zero and the system is
therefore in equilibrium, or there is acceleration and therefore a net force is present. Note that
a string is assumed to have negligible mass.
Compression Force
Compressive strength is the capacity of a material or structure to withstand axially directed
pushing forces. When the limit of compressive strength is reached, materials are
crushed. Concrete can be made to have high compressive strength, e.g. many concrete
structures have compressive strengths in excess of 50 MPa, whereas a material such as
soft sandstone may have a compressive strength as low as 5 or 10 MPa.
Measuring the compressive strength of a steel can
Compressive strength is often measured on a universal testing machine; these range from very
small table top systems to ones with over 53 MN capacity. Measurements of compressive
strength are affected by the specific test method and conditions of measurement. Compressive
strengths are usually reported in relationship to a specific technical standard.
Torsion
A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that
stores mechanical energy when it is twisted. The amount of force (actually torque) it exerts is
proportional to the amount it is twisted.
There are two types. A torsion bar is a straight bar of metal or rubber that is subjected to
twisting (shear stress) about its axis by torque applied at its ends. A more delicate form used in
sensitive instruments, called a torsion fiber consists of a fiber of silk, glass, or quartz under
tension, that is, twisted about its axis. The other type, a helical torsion spring, is a metal rod or
wire in the shape of a helix (coil) that is subjected to twisting about the axis of the coil by
sideways forces (bending moments) applied to its ends, twisting the coil tighter. This
terminology can be confusing because in a helical torsion spring the forces acting on the wire
are actually bending stresses, not torsional (shear)
Shearing
A shear stress, denoted (Greek: tau), is defined as the
component of stress coplanar with a material cross section.
Shear stress arises from the force vector component parallel
to the cross section. Normal stress, on the other hand, arises
from the force vector component perpendicular or anti-parallel
to the material cross section on which it acts.
A shear stress, is applied to
the top of the square while the
bottom is held in place. This
stress results in a strain, or
deformation, changing the square
into aparallelogram. The area
http://www.youtube.com/watch?v=W5A8gU37wGg&feature=related
involved would be the top of the
parallelogram.
Continuing our excursion into mechanical properties of matter, we look at the effects of forces
placed on a material. Work hardening, strain hardening, or cold work is the strengthening of a
material by increasing the material's dislocation density. In metallic crystals, irreversible
deformation is usually carried out on a microscopic scale by defects called dislocations, which
are created by fluctuations in local stress fields within the material culminating in a lattice
rearrangement as the dislocations propagate through the lattice. At normal temperatures the
dislocations are not annihilated by annealing. Instead, the dislocations accumulate, interact
with one another, and serve as pinning points or obstacles that significantly impede their
motion. This leads to an increase in the yield strength of the material and a subsequent
decrease in ductility.
Work hardening is a consequence of plastic deformation, or a permanent deformity to a
material
Point defects
The simplest point defects are as follows:
Vacancy – missing atom at a certain crystal lattice position;
Interstitial impurity atom – extra impurity atom in an interstitial position;
Self-interstitial atom – extra atom in an interstitial position;
Substitution impurity atom – impurity atom, substituting an atom in crystal lattice;
Frenkel defect – extra self-interstitial atom, responsible for the vacancy nearby.
Increase in the number of dislocations is a quantification of work hardening. Plastic
deformation occurs as a consequence of work being done on a material; energy is added to the
material. In addition, the energy is almost always applied fast enough and in large enough
magnitude to not only move existing dislocations, but also to produce a great number of new
dislocations by jarring or working the material sufficiently enough.
A simple illustration of the effects of annealing, quenching and tempering can be illustrated in a
simple experiment:
Heat-Treating Steel Lab
Work Hardening – to strengthen a material by reshaping it while the part is cold
Forging – Shape or form materials by beating or hammering it
Annealing –
Heat to red hot, air cool
Metal is heated and cooled to allow crystals to form
Softens metals by relieving stress
Quenching/Hardening
Heat until red hot and quench into cold water
Rapid cooling of metals locks atoms into place in an unstable crystal structure
Strengthens metals but brittle
Tempering –
Heat to red hot, quench in cool water
Heating materials so atoms re-orient themselves
Removes brittleness but keeps strength
Heat-Treating Steel
Materials:





4 bobby pins
4 large paperclips
Heat source – Bunsen burner or propane torch
Container of water for quenching
Tongs or pliers
Procedure:
1. Set aside one bobby pin and one paperclip for comparison. (Control)
2. Heat the loop of one bobby pin and a loop of one paperclip red hot and slowly lift out of flame.
Slow cool. (Anneal)
3. Heat 2 of each red hot and quench in ice water. Quick cool. (Quench)
4. Take one of each from step #3 and heat again in the top of the flame for a few seconds and
then quench. Do NOT let it get red hot. (Temper)
5. Make a data table for comparison of properties when the heat-treated area is bent.
6. Test the bobby pins one at a time by slowly pulling the ends apart. Record observations.
7. Test the paperclips one at a time by pulling the heat-treated loop open. Record observations.
8. Propose reasons for any differences in results.
Notes:

Don’t heat beyond red hot – too much heat and you start burning out the carbon.



Bobby pins are high carbon steel and paper clips are low carbon steel.
This lab is usually done after the iron wire demo so that students have been exposed to the
idea of allotropes and solid state phase changes in regards to iron.
This lab is also usually done after the work-hardening and heat-treating of copper lab.
Typical Results:
bobby pin
control
anneal
quench
temper
“normal”
softer, easier to
snaps in two,
feels much like
bend, lost the
brittle
the control
softer, easier to
varies depending
doesn’t feel much
bend
on the paperclip,
different than
sometimes
the other
harder,
paperclips
springiness
paperclip
“normal”
sometimes more
like the control,
but is NOT
brittle, doesn’t
break
Why steel is affected differently by heat treating:






Iron is allotropic – BCC below 912° C and FCC above 912° C
Steel is an interstitial alloy – most other alloys are substitutional
FCC is more tightly packed than BCC but has larger individual gaps – carbon fits into FCC
better than it does BCC
Carbon can be in different locations and in different forms:
o Between grain boundaries
o In the interstices (gaps within the crystal)
o Bonded with iron as Fe3C (cementite) which is a ceramic
Annealing is like what happens with copper
o there is crystal regrowth and dislocations are decreased
o the metal is softened
o carbon has time to migrate to lowest energy positions
Quenching causes steel to become very strong but also very brittle
forms an intermediate crystal structure which is metastable (has extra energy
stored) – it is body-centered tetragonal
o Carbon does not have time to migrate out to lower energy positions
o Extra “stress” is in the crystal
Tempering is a secondary heat treatment
o Strength is maintained while improving toughness – removes some of the brittleness
o Carbon has time and energy to migrate to lower energy positions
o Remains body-centered tetragonal
o Called martensite
o

Bobby pin is high carbon steel – approximately 0.7%. Therefore, the carbon has a large effect on
the properties and greater differences are observed in the various heat treatments.
Paper clips are low carbon steel – approximately 0.2%. The strengthening of the steel during
quenching is mostly due to the solid state phase change from FCC to BCT. Therefore tempering
doesn’t alter the properties really – there isn’t enough carbon to cause brittleness during quenching.
Electrical and Thermal Properties of Materials
It is well known that one of the subatomic particles of an atom is the electron. The electrons
carry a negative electrostatic charge and under certain conditions can move from atom to
atom. The direction of movement between atoms is random unless a force causes the electrons
to move in one direction. This directional movement of electrons due to an electromotive force
is what is known as electricity.
Electrical Conductivity
Electrical conductivity is a measure of how well a material accommodates the movement of an
electric charge. It is the ratio of the current density to the electric field strength. Its SI derived
unit is the Siemens per meter, but conductivity values are often reported as percent IACS. IACS
is an acronym for International Annealed Copper Standard, which was established by the 1913
International Electrochemical Commission. The conductivity of the annealed copper (5.8001 x
107S/m) is defined to be 100% IACS at 20°C . All other conductivity values are related back to
this conductivity of annealed copper. Therefore, iron with a conductivity value of 1.04 x
107 S/m, has a conductivity of approximately 18% of that of annealed copper and this is
reported as 18% IACS. An interesting side note is that commercially pure copper products now
often have IACS conductivity values greater than 100% IACS because processing techniques
have improved since the adoption of the standard in 1913 and more impurities can now be
removed from the metal.
Conductivity values in Siemens/meter can be converted to % IACS by multiplying the
conductivity value by 1.7241 x10-6. When conductivity values are reported in
microSiemens/centimeter, the conductivity value is multiplied by 172.41 to convert to the %
IACS value.
Electrical conductivity is a very useful property since values are affected by such things as a
substances chemical composition and the stress state of crystalline structures. Therefore,
electrical conductivity information can be used for measuring the purity of water, sorting
materials, checking for proper heat treatment of metals, and inspecting for heat damage in
some materials.
Electrical Resistivity
Electrical resistivity is the reciprocal of conductivity. It is the is the opposition of a body or
substance to the flow of electrical current through it, resulting in a change of electrical energy
into heat, light, or other forms of energy. The amount of resistance depends on the type of
material. Materials with low resistivity are good conductors of electricity and materials with
high resistivity are good insulators.
The SI unit for electrical resistivity is the ohm meter. Resistivity values are more commonly
reported in micro ohm centimeters units. As mentioned above resistivity values are simply the
reciprocal of conductivity so conversion between the two is straightforward. For example, a
material with two micro ohm centimeter of resistivity will have ½ microSiemens/centimeter of
conductivity. Resistivity values in microhm centimeters units can be converted to % IACS
conductivity values with the following formula:
172.41 / resistivity = % IACS
Temperature Coefficient of Resistivity
As noted above, electrical conductivity values (and resistivity values) are typically reported at
20 oC. This is done because the conductivity and resistivity of material is temperature
dependant. The conductivity of most materials decreases as temperature increases.
Alternately, the resistivity of most material increases with increasing temperature. The amount
of change is material dependant but has been established for many elements and engineering
materials.
The reason that resistivity increases with increasing temperature is that the number of
imperfection in the atomic lattice structure increases with temperature and this hampers
electron movement. These imperfections include dislocations, vacancies, interstitial defects and
impurity atoms. Additionally, above absolute zero, even the lattice atoms participate in the
interference of directional electron movement as they are not always found at their ideal lattice
sites. Thermal energy causes the atoms to vibrate about their equilibrium positions. At any
moment in time many individual lattice atoms will be away from their perfect lattice sites and
this interferes with electron movement.
When the temperature coefficient is known, an adjusted resistivity value can be computed
using the following formula:
R1 = R2 * [1 + a * (T1–T2)]
Where: R1 = resistivity value adjusted to T1
R2 = resistivity value known or measured at temperature T2
a = Temperature Coefficient
T1 = Temperature at which resistivity value needs to be known
T2 = Temperature at which known or measured value was obtained
For example, suppose that resistivity measurements were being made on a hot piece of
aluminum. Normally when measuring resistivity or conductivity, the instrument is calibrated
using standards that are at the same temperature as the material being measured, and then no
correction for temperature will be required. However, if the calibration standard and the test
material are at different temperatures, a correction to the measured value must be made.
Presume that the instrument was calibrated at 20oC (68oF) but the measurement was made at
25oC (77oF) and the resistivity value obtained was 2.706 x 10-8 ohm meters. Using the above
equation and the following temperature coefficient value, the resistivity value corrected for
temperature can be calculated.
R1 = R2 * [1 + a * (T1–T2)]
Where: R1 = ?
R2 = 2.706 x 10-8 ohm meters (measured resistivity at 25 oC)
a = 0.0043/ oC
T1 = 20 oC
T2 = 25 oC
R1 = 2.706 x 10-8ohm meters * [1 + 0.0043/ oC * (20 oC – 25 oC)]
R1 = 2.648 x 10-8ohm meters
Note that the resistivity value was adjusted downward since this example involved calculating
the resistivity for a lower temperature.
Since conductivity is simply the inverse of resistivity, the temperature coefficient is the same for
conductivity and the equation requires only slight modification. The equation becomes:
s1 = s2 / [1 + a * (T1 –T2)]
Where: s1 = conductivity value adjusted to T1
s2 = conductivity value known or measured at temperature T2
a = Temperature Coefficient
T1 = Temperature at which conductivity value needs to be known
T2 = Temperature at which known or measured value was obtained
In this example let’s consider the same aluminum alloy with a temperature coefficient of 0.0043
per degree centigrade and a conductivity of 63.6% IACS at 25 oC. What will the conductivity be
when adjusted to 20 oC?
s1= 63.6% IACS / [1 + 0.0043 * (20 oC – 25 oC)]
s1= 65.0% IASC
The temperature coefficient for a few metallic elements is shown below.
Material
Temperature
Coefficient (/ oC)
Nickel
0.0059
Iron
0.0060
Molybdenum
0.0046
Tungsten
0.0044
Aluminum
0.0043
Copper
0.0040
Silver
0.0038
Platinum
0.0038
Gold
0.0037
Zinc
0.0038
Possible labs to consider to reinforce the theory: The Electrical Resistivity of Materials or the
Fruit Power (reference ASM Semester Materials Course, Part A, Lessons, Week 3, Day 2).
Introductions to Crystals
(CREETOWN GEM ROCK MUSEUM
Chain Road, Creetown, Newton Stewart
Dumfries & Galloway, Scotland, DG8 7HJ
01671 820 357)
Crystals are solid material in which the atoms are
arranged in regular geometrical patterns. The
crystal shape is the external expression of the
mineral's regular internal atomic structure.
Temperature, pressure, chemical conditions and
the amount of space available are some of the things
that affect their growth. Many crystallize from watery
solutions, some from molten rock as during volcanic eruptions when lava cools rapidly.
Each mineral will always form in a range of crystal shapes.
Although there are literally thousands of minerals, their crystal
shape can be grouped on the basis of their symmetry into seven
systems of three dimensional patterns.
Cubic
The outstanding macroscopic properties of crystalline solids are rigidity, incompressibility and
characteristic shape. All crystalline solids are composed of orderly arrangements of atoms, ions,
or molecules. The macroscopic result of the microscopic arrangements of the atoms, ions or
molecules is exhibited in the symmetrical shapes of the crystalline solids.
Solids are either amorphous, without form, or crystalline. In crystalline solid s the array of
particles are well ordered. Crystalline solids have definite, rigid shapes with clearly defined
faces. The arrangement of the atoms, ions or molecules, are very ordered and repeat in 3dimensions. Small, 3-dimensional, repeating units called unit cells are responsible for the order
found in crystalline solids.
The unit cell can be thought of as a box which when stacked together in 3-dimensions produces
the crystal lattice. There are a limited number of unit cells which can be repeated in an orderly
pattern in three dimensions. We will explore the cubic system in detail to understand the
structure of most metals and a wide range of ionic compounds.
In the cubic crystal system three types of arrangements are found;
Models of Crystals
Students do the “Models of Crystals” lab. They build 4 different unit cells using toothpicks and
polystyrene balls. A recommendation is to use 1 ½” diameter spheres – the smaller ones tend
to fall apart quickly after using just a few times. They build the most basic one (simple cubic)
and the 3 most commonly found in metals (BCC, FCC, HCP). See the lab sheet the students fill
out.
Permanent models made out of ping-pong balls and hot glue are very useful. These help the
students compare the different models in terms of packing and slip planes since they dismantle
their models before building the next one. It is also helpful to build planes of atoms and then
stack them. This helps the students to see that the layers are all actually the same in a model;
they are just “offset” when stacking them together to make the unit cell. This is also great to
see the overall 3-D pattern of the crystal shape. This works especially well with FCC and HCP. If
you make 3 planes for each, then the students can also try piecing them together into one layer
instead of stacking them into 3 layers to make a unit cell. By building a bigger plane from
smaller ones, the students can pick out the “section” that is used in each of the different layers
in the unit cell. The repeating pattern is much more noticeable.
After the students have finished building the models and writing in their journals, ask the
students the following question:

“Why do we care what particular crystal structure a metal has?”
o because crystal structure affects properties of the metal
Have the students rank the crystal models from “most closely packed” to “least closely packed”.
1. HCP - “most closely packed”
2. FCC
3. BCC
4. simple cubic “least - closely packed”
Consider the following scenario:
You are riding your 4-wheeler in the country and you come to a deep ditch that someone has
built a log bridge across. Which type of bridge would be easier to go across?
Then roll the single piece of chalk across the “chalk bridges” – first the one with gaps and then
the one without gaps. Which one is harder to do and requires more energy? They will all agree
that the one without gaps is easier.
Now reconsider the question AGAIN:


“Which type of crystal structure allows a metal to be more workable, one that is closely
packed or one that is loosely packed?”
“Which one is easier for the planes of atoms to slide past each other?”
Common sense wants to tell us that having more “open space” in a crystal makes it easier for
atoms to move around so the metal is more workable. But this isn’t the case with planes of
atoms. More ‘gappiness’ allows the atoms to fall into these spaces and makes it harder to keep
them moving to work the metal.


more tightly packed = more workable
more slip planes = more workable
Workable – changing the shape of a solid (while remaining a solid) without it cracking or
breaking (malleability and ductility)
Based on the above information, have the students reason out which crystal structure should
be the most workable. Since FCC is both tightly packed and has many slip planes, it is the most
workable.
Have the students fill in the following table:
Type of crystal
Closely-packed?
Many slip planes?
Workability
FCC
Yes
Yes
Highest
BCC
No
Yes
Medium
HCP
Yes
No
Lowest
structure
Is there a way to figure out if the packing and the slip planes have an equal effect on the
workability or if one of the two factors has more.
Since BCC and HCP both have a “yes” and a “no” and HCP is the least workable, reasoning
would dictate that the number of slip planes has more effect on the workability than how
closely packed the atoms are.
Predict which familiar metals should have an FCC crystal structure. They can usually correctly
name several such as gold, copper, aluminum, lead, etc…
Then compile a list of some common metals and their crystal shapes.
BCC
FCC
HCP
Other
chromium
aluminum
cobalt
tin
iron (<910 °C)
copper
magnesium
tungsten
gold
titanium
iron (>910 °C)
zinc
lead
platinum
silver
Iron appears in two different columns because it is allotropic. This concept will be further
developed in the Iron Wire Demo. But the students should be able to grasp the idea that
blacksmiths pound on a piece of iron when it is glowing red hot and stop when it loses its color
since FCC is a more workable crystal structure than BCC.
A sheet of copper and a sheet of titanium are also useful for demonstrating the difference in
the workability of an FCC metal and an HCP metal. Simply hold down one end of the metal
against the edge of a table, push down on the other end and release. The copper is very
workable and easy to bend and will not completely return to its original shape. The titanium
takes more force to bend and will spring back to its original shape.
Models of Crystals Lab
Terms:
crystal:
unit cell:
slip plane:
Name and abbreviation of unit cells that will be constructed:
Brief Method:
Construct the crystal models one at a time as pictured “a” through “d” in the figure on the
next page.
Journal the following for each model you build:



sketch of unit cell
label with name and abbreviation
describe the packing and slip planes
o examples: close, tight, loose, “gappiness”, many or few slip planes
Before dismantling a model and building the next one, as a class, try to assemble the
individual unit cells into a bigger crystal. The teacher will assist with this.




Pay close attention to spacing and alignment.
For example, the spheres in layer 1 of model C do not touch each other. The center
sphere in model C should touch all the spheres of the 1st and 3rd layers but none of
the other spheres should touch each other.
When stacking the layers to build each model, be sure the orientation is the same
as in the diagram.
Use the fewest number of toothpicks possible.
Models of Crystals Lab
Terms:
crystal: -an object with a regularly repeating arrangement of its atoms
-it often has external plane faces
unit cell: -the simplest and smallest arrangement of atoms that can be
repeated to form a particular crystal
slip plane: -a surface along which layers of atoms can slide
Name and abbreviation of unit cells that will be constructed:
Simple cubic
Body-centered cubic – BCC
Face-centered cubic – FCC
Hexagonal close packed - HCP
Brief Method:
We are going to make models of 4 different crystals using toothpicks and
Styrofoam balls.
Construct the crystal models one at a time as pictured “a” through “d” in the figure
on the next page.
Journal the following for each model you build:



sketch of unit cell
label with name and abbreviation
describe the packing and slip planes
o examples: close, tight, loose, “gappiness”, many or few slip planes
o (Hint: cubic structures have many slip planes)
Before dismantling a model and building the next one, as a class, try to assemble
the individual unit cells into a bigger crystal. The teacher will assist with this.
a. simple cubic
-loosely packed, lots of “gappiness”
-lots of slip planes
b. face-centered cubic
-tightly packed, much less “gappiness”
-lots of slip planes
c. body-centered cubic
-loosely packed, more “gappiness”
-lots of slip planes
d. hexagonal close-packed
-tightly packed, not much “gappiness”
-few slip planes
Type of
Closely
Many slip
Workability
crystal
packed?
planes?
FCC
Yes
Yes
Highest
BCC
No
Yes
Medium
HCP
Yes
No
Lowest
structure
BCC
FCC
HCP
Other
chromium
aluminum
cobalt
manganese
iron (<910 °C)
calcium
magnesium
tin
molybdenum
copper
titanium
sodium
gold
tungsten
iron (>910
zinc
°C)
lead
nickel
platinum
silver
Perhaps the simplest cubic system is the simple cubic structure. The unit cell for the simple
cubic structure contains one-eighth portions of eight corner atoms to make one complete
atom, molecule or ion in each unit cell. Given the radius of the atom or ion the edge length is
just; edge length (a) = 2r where r is the radius of the atom or ion.
The body-centered cubic structure is built up of body-centered cubic unit cell containing two
atoms in each unit cell, one atom from the eight, one-eighth portions of the eight corner atoms
and one from the atom located in the center of the unit cell. In this structure the relationship
between the edge length and the radius of the atom is more complicated; edge length (a) =
4r/SQRT(3)
The last unit cell is the face-centered cubic cell. This cell contains 4 atoms per unit cell. Three
atoms from the six faces, one-half of each face atom is contained in a particular unit cell, and
one atom from the eight, one-eighth portions of the eight corner atoms. The relationship of the
edge length to the atoms radius is; edge length (a) = 2*SQRT(2)r
Ionic crystals are composed of charged species and the ions of the compound have different
sizes. There are several ionic structures which you should be familiar.
The NaCl structure which is common to LiCl, KBr, RbI, MgO, CaO and AgCl. This structure can be
viewed two different ways: face-centered cubic in chloride ions with sodium ions in every
octahedral hole, or as two interpenetrating face-centered cubic structures.
Unit cell
The crystal structure of a material or the arrangement of atoms within a given type of crystal
structure can be described in terms of its unit cell. The unit cell is a small box containing one or
more atoms, a spatial arrangement of atoms. The unit cells stacked in three-dimensional space
describe the bulk arrangement of atoms of the crystal. The crystal structure has a threedimensional shape. The unit cell is given by its lattice parameters, which are the length of the
cell edges and the angles between them, while the positions of the atoms inside the unit cell
are described by the set of atomic positions (xi , yi , zi) measured from a lattice point.

Simple cubic (P)

Body-centered cubic (I)

Face-centered cubic (F)
Miller indices
Main article: Miller index
Planes with different Miller indices in cubic crystals
Vectors and atomic planes in a crystal lattice can be described by a three-value Miller index
notation (ℓmn). The ℓ, m, and n directional indices are separated by 90°, and are thus
orthogonal. In fact, the ℓ component is mutually perpendicular to the m and n indices.
By definition, (ℓmn) denotes a plane that intercepts the three points a1/ℓ, a2/m, and a3/n, or
some multiple thereof. That is, the Miller indices are proportional to the inverses of the
intercepts of the plane with the unit cell (in the basis of the lattice vectors). If one or more of
the indices is zero, it simply means that the planes do not intersect that axis (i.e., the intercept
is "at infinity").
Considering only (ℓmn) planes intersecting one or more lattice points (the lattice planes), the
perpendicular distance d between adjacent lattice planes is related to the (shortest) reciprocal
lattice vector orthogonal to the planes by the formula:
Atomic coordination
By considering the arrangement of atoms relative to each other, their coordination numbers (or
number of nearest neighbors), interatomic distances, types of bonding, etc., it is possible to
form a general view of the structures and alternative ways of visualizing them.
HCP lattice (left) and the FCC lattice (right)
Close packing
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch13/structure.php#structure
The principles involved can be understood by considering the most efficient way of packing
together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For
example, if plane A lies beneath plane B, there are two possible ways of placing an additional
atom on top of layer B. If an additional layer was placed directly over plane A, this would give
rise to the following series :
...ABABABAB....
This type of crystal structure is known as hexagonal close packing (hcp).
If however, all three planes are staggered relative to each other and it is not until the fourth
layer is positioned directly over plane A that the sequence is repeated, then the following
sequence arises:
...ABCABCABC...
This type of crystal structure is known as cubic close packing (CCP).
The unit cell of the CCP arrangement is the face-centered cubic (FCC) unit cell. This is not
immediately obvious as the closely packed layers are parallel to the {111} planes of the FCC unit
cell. There are four different orientations of the close-packed layers.
The packing efficiency could be worked out by calculating the total volume of the spheres and
dividing that by the volume of the cell as follows:
The 74% packing efficiency is the maximum density possible in unit cells constructed of spheres
of only one size. Most crystalline forms of metallic elements are HCP, FCC, or BCC (bodycentered cubic). The coordination number of hcp and fcc is 12 and its atomic packing factor
(APF) is the number mentioned above, 0.74. The APF of bcc is 0.68 for comparison.
Bravais lattices
When the crystal systems are combined with the various possible lattice centerings, we arrive
at the Bravais lattices. They describe the geometric arrangement of the lattice points, and
thereby the translational symmetry of the crystal. In three dimensions, there are 14 unique
Bravais lattices that are distinct from one another in the translational symmetry they contain.
All crystalline materials recognized until now (not including quasicrystals) fit in one of these
arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown
above. The Bravais lattices are sometimes referred to as space lattices.
The crystal structure consists of the same group of atoms, the basis, positioned around each
and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions
according to the arrangement of one of the 14 Bravais lattices. The characteristic rotation and
mirror symmetries of the group of atoms, or unit cell, is described by its crystallographic point
group.
Grain boundaries
Grain boundaries are interfaces where crystals of different orientations meet. A grain boundary
is a single-phase interface, with crystals on each side of the boundary being identical except in
orientation. The term "crystallite boundary" is sometimes, though rarely, used. Grain boundary
areas contain those atoms that have been perturbed from their original lattice sites,
dislocations, and impurities that have migrated to the lower energy grain boundary.
Treating a grain boundary geometrically as an interface of a single crystal cut into two parts,
one of which is rotated, we see that there are five variables required to define a grain
boundary. The first two numbers come from the unit vector that specifies a rotation axis. The
third number designates the angle of rotation of the grain. The final two numbers specify the
plane of the grain boundary (or a unit vector that is normal to this plane).
Grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite
size is a common way to improve strength, as described by the Hall–Petch relationship. Since
grain boundaries are defects in the crystal structure they tend to decrease the electrical and
thermal conductivity of the material. The high interfacial energy and relatively weak bonding in
most grain boundaries often makes them preferred sites for the onset of corrosion and for the
precipitation of new phases from the solid. They are also important to many of the mechanisms
of creep (Creep (deformation), the tendency of a solid material to slowly move or deform
permanently under the influence of stresses.)
Grain boundaries are in general only a few nanometers wide. In common materials, crystallites
are large enough that grain boundaries account for a small fraction of the material. However,
very small grain sizes are achievable. In nano-crystalline solids, grain boundaries become a
significant volume fraction of the material, with profound effects on such properties as
diffusion (Diffusion describes the spread of particles through random motion from regions of
higher concentration to regions of lower concentration. The time dependence of the statistical
distribution in space is given by the diffusion equation. The concept of diffusion is tied to that of
mass transfer driven by a concentration gradient) and plasticity (plasticity describes the
deformation of a material undergoing non-reversible changes of shape in response to applied
forces). In the limit of small crystallites, as the volume fraction of grain boundaries approaches
100%, the material ceases to have any crystalline character, and thus becomes an amorphous
solid (an amorphous (from the Greek a, without, morphé, shape, form) or non-crystalline solid
is a solid that lacks the long-range order characteristic of a crystal).
Defects and impurities
Real crystals feature defects (Point defects are defects that occur only at or around a single
lattice point. They are not extended in space in any dimension) or irregularities in the ideal
arrangements described above and it is these defects that critically determine many of the
electrical and mechanical properties of real materials.
Point Defects
3 Main Types of Defects
Ask the students what comes to mind when you hear the word “defect”. They usually say
something “bad” or “unwanted” or “negative”. When discussing that point defects can be used
to make alloys point out that we create “defects” on purpose because they result in useful
changes in properties. Reinforce the idea that defects can lead to positive changes when
discussing that line defects can increase the hardness or strength of metals.
1. Point Defects – single atom defects
Use overhead to illustrate the types of point defects – have students draw
them in their journal.
a. Vacancy – atom is missing (void)
-move around in crystal by diffusion
-use BB board to illustrate
b. Interstitial – extra atoms inserted in the gaps between the regular atoms
-used in making alloys – ex. steel
c. Substitutional – replace some of the original atoms with different atoms
-used in making alloys
2. Line Defects – dislocations
-regions in crystals where atoms are not perfectly aligned – use
overheads to illustrate
-can move
-a small number make a metal more workable – a large number make a
metal harder to work
-when working a metal, dislocations can get “jammed” or “pinned”. This
can make the metal harder = work-hardening
3. Interfacial Defects
-grain boundaries
-3-D
-affected by size of grains
“Working a metal”
-changing its shape while a solid
Ex. – pounding
bending
stretching
rolling
When one atom substitutes for one of the principal atomic components within the crystal
structure, alteration in the electrical and thermal properties of the material may ensue.
Impurities may also manifest as spin impurities in certain materials. Research on magnetic
impurities demonstrates that substantial alteration of certain properties such as specific heat
may be affected by small concentrations of an impurity, as for example impurities in
semiconducting ferromagnetic alloys may lead to different properties as first predicted in the
late 1960s. Dislocations in the crystal lattice allow shear at lower stress than that needed for a
perfect crystal structure.
Prediction of structure
Main article: Crystal structure prediction
Crystal structure of sodium chloride (table salt)
The difficulty of predicting stable crystal structures based on the knowledge of only the
chemical composition has long been a stumbling block on the way to fully computational
materials design. Now, with more powerful algorithms and high-performance computing,
structures of medium complexity can be predicted using such approaches as evolutionary
algorithms, random sampling, or metadynamics.
The crystal structures of simple ionic solids (e.g., NaCl or table salt) have long been rationalized
in terms of Pauling's rules (Pauling's rules are five rules published by Linus Pauling in 1929 for
determining the crystal structures of complex ionic crystals), first set out in 1929 by Linus
Pauling, referred to by many since as the "father of the chemical bond". Pauling also considered
the nature of the interatomic forces in metals, and concluded that about half of the five
d-orbitals in the transition metals are involved in bonding, with the remaining nonbonding dorbitals being responsible for the magnetic properties. He, therefore, was able to correlate the
number of d-orbitals in bond formation with the bond length as well as many of the physical
properties of the substance. He subsequently introduced the metallic orbital, an extra orbital
necessary to permit uninhibited resonance of valence bonds among various electronic
structures.
In the resonating valence bond theory, the factors that determine the choice of one from
among alternative crystal structures of a metal or intermetallic compound revolve around the
energy of resonance of bonds among interatomic positions. It is clear that some modes of
resonance would make larger contributions (be more mechanically stable than others), and that
in particular a simple ratio of number of bonds to number of positions would be exceptional.
The resulting principle is that a special stability is associated with the simplest ratios or "bond
numbers": 1/2, 1/3, 2/3, 1/4, 3/4, etc. The choice of structure and the value of the axial ratio
(which determines the relative bond lengths) are thus a result of the effort of an atom to use its
valency in the formation of stable bonds with simple fractional bond numbers.
After postulating a direct correlation between electron concentration and crystal structure in
beta-phase alloys, Hume-Rothery analyzed the trends in melting points, compressibilities and
bond lengths as a function of group number in the periodic table in order to establish a system
of valencies of the transition elements in the metallic state. This treatment thus emphasized
the increasing bond strength as a function of group number. The operation of directional forces
were emphasized in one article on the relation between bond hybrids and the metallic
structures. The resulting correlation between electronic and crystalline structures is
summarized by a single parameter, the weight of the d-electrons per hybridized metallic orbital.
The “d-weight” calculates out to 0.5, 0.7 and 0.9 for the fcc, hcp and bcc structures respectively.
The relationship between d-electrons and crystal structure thus becomes apparent.
Week 5: Properties of Materials
Crystal Iron Wire Lab
Purpose This demonstration is designed to show the student the following:
A. Abrupt solid-state phase changes can occur in allotropic materials.
B. Thermal expansion occurs when metals are heated.
C. Light is emitted when metals are heated hot enough.
D. Iron tends to oxidize more rapidly when it is heated.
E. Magnetic properties are lost when iron is heated beyond a certain temperature called
the Curie temperature.
Time Required 15 -20 minutes.
Material and Equipment
 Iron Wire, #24
 Variac, 110 V, 15 Amp
 Power Cord, Modified
 Ring Stands, 2
 Buret Clamps, 2
 Mass, 50-200 g
 Magnet, Small
 "C" Clamps
 Meter Stick
 Thermal Wire Adapters, 2
Safety Concerns
1. The wire gets extremely hot. Treat it with care. It also becomes brittle with repeated use
and can break unexpectedly.
2. The amount of electrical current is large enough to produce a substantial shock. Care should
be taken not to touch the wire when the electricity is turned on.
3. When the magnet drops from the wire it is very hot. You should have a fire resistant surface
for it to fall onto. Also, let it cool before picking it up.
Procedure
1. Use the "c" clamps or bench clamps to firmly mount the two ring stands on
nonconductive tables about ten feet apart. Place clamps on the stands and use the
thermal wire adapters to attach the wire. Adjust the distance between the ring stands
to make the wire fairly taut. You do not want to put any tension on the wire.
2. Hang the weight on the wire in the center between the stands
3. Attach a small magnet about half way between the weight and the end of the wire.
The placement is not really critical.
4. Attach the clamped ends of the electrical leads to each end of the iron wire. Do not
attach the electrical leads directly to the ring stand.
5. Have the students list observations they make during the next few minutes in their journals.
6. Use the Variac to slowly increase the voltage to the wire until the heat from the electrical
resistance causes the wire to expand noticeably. Reduce the voltage back to zero and discuss
the thermal expansion.
7. Dim the lights in the room.
8. Use the Variac to slowly increase the voltage to the wire until the wire glows bright
orange. The magnet should drop off during this interval
9. Rapidly reduce the voltage while carefully observing the weight
10. Repeat steps 8 and 9.This time put a meterstick vertically right behind the weight.
11. Have the students share their observations. Discuss these. Then repeat steps 8 and 9
once again.
This write-up was taken from:
Material Science Solids, Metals, Ceramics, Polymers. Composites Published by Energy
Concepts, Inc. By Len Booth ISBN: 1-55756-163-X, 1-55756-164-8, 1-55756-165-6, 1-55756166-4, 1-55756-167-2
The Iron Wire Demo IS an example of a solid state phase change. Examples of other labs and
demos that show a solid state phase change are:
•
Sulfur lab
•
Nitinol demo
•
Aluminum/Zinc alloy lab
Summary of observations made by students:
•
Heat makes metals expand -thermal expansion
•
Metals con get hot enough to give off light -incandescence
•
Heat increases the rate of oxidation (rusting)
•
Ferrous metals lose magnetism at a certain temperature -Curie temperature is -770°C
•
Solid state phase change occurred at 910°C. This was observed as a "dip' (bounce) by
the wire as it was contracting while cooling.
Iron at room temperature is BCC -more spread out
Iron above 910°C is FCC -closer packed
Dip was caused by changing from FCC to BCC at 910°C
After running the demo a couple of times, turn the power off (unplug the variac) and
• Use steel wool to "clean" an inch of the wire OR
• have a couple of volunteers bend the wire back and forth a few times. Turn the power
back on and redo the demo. The areas on the wire that were cleaned or bent will be visibly
brighter. Ask the students what is causing this phenomenon. The rate of oxidation is greatly
increased due to the heating of the wire. The oxidation is a ceramic material which insulates the
wire. Cleaning or bending the wire removes the oxidation which is brittle. This allows the wire
to glow brighter (hotter) the next time the demo is performed.
After the wire cools, cut it up into pieces approximately 4 to 5 inches long and give one to
each student. Have them bend it back and forth over a piece of white paper. The oxidation
that formed on the outside of the wire is a ceramic material and therefore very brittle and it
will readily flake off exposing malleable metal underneath.
This demonstration can also be found in the Battelle MS&T handbook (starting on page 4.22)
and the MAST modules (starting on page 41 in the metals unit).
Iron Phase
Temp.
Range, DC
< ~912
-Fe (ferrite)
770
Crystal Structure
Body-centered cubic
(BBC) less dense,
ferromagnetic at low
temperature, but
loses ferromagnetism
on heating
Temperature at which
Fe loses its
ferromagnetism
="Curie temperature"
 -Fe
(austenite)
-Fe
-912 - 1394
Face-centered cubic
(FCC) more dense,
paramagnetic
1394 - ~1538
Body-centered cubic
(BCC) less dense,
paramagnetic
Crystal Structure
In crystallography, atomic packing factor (APF) or packing fraction is the fraction of volume in a
crystal structure that is occupied by atoms. It is dimensionless and always less than unity. For
practical purposes, the APF of a crystal structure is determined by assuming that atoms are rigid
spheres. The radius of the spheres is taken to be the maximal value such that the atoms do not
overlap. For one-component crystals (those that contain only one type of atom), the APF is
represented mathematically by
where Natoms is the number of atoms in the unit cell, Vatom is the volume of an atom, and Vunit cell
is the volume occupied by the unit cell. It can be proven mathematically that for onecomponent structures, the most dense arrangement of atoms has an APF of about 0.74. In
reality, this number can be higher due to specific intermolecular factors. For multiplecomponent structures, the APF can exceed 0.74.
Body-centered cubic crystal structure
BCC structure
The primitive unit cell for the body-centered cubic (BCC) crystal structure contains several
fractions taken from nine atoms: one on each corner of the cube and one atom in the center.
Because the volume of each corner atom is shared between adjacent cells, each BCC cell
contains two atoms.
Each corner atom touches the center atom. A line that is drawn from one corner of the cube
through the center and to the other corner passes through 4r, where r is the radius of an atom.
By geometry, the length of the diagonal is a√3. Therefore, the length of each side of the BCC
structure can be related to the radius of the atom by
Knowing this and the formula for the volume of a sphere (
calculate the APF as follows:
 r3), it becomes possible to
Hexagonal close-packed crystal structure
HCP structure
For the hexagonal close-packed (HCP) structure the derivation is similar. The side length of the
hexagon will be denoted as a while the height of the hexagon will be denoted as c. Then:
It is then possible to calculate the APF as follows:
Quasicrystals:
The Discovery of an Impossible Crystal Structure?
Crystals
Crystallography is the science of studying the arrangements of atoms in solids. The traditional
definition of a crystal is a three-dimensional structure formed by a repeating pattern of atoms,
ions or molecules, called a lattice. Unit cells are the repeating unit in traditional crystal
structures that maintains the properties of the entire crystal lattice. In crystallography,
materials scientists use tools such as X-ray diffraction and electron diffraction to study the
atomic arrangement in crystals to better understand the properties of a material.
Figure 1. Crystal Structure of NaCl
Symmetry in Crystals
What is symmetry? Symmetry is observed in everyday life. If an object exhibits symmetry, it has
a visible repeating pattern. This pattern can be observed by rotating the object, imagining a
mirror plane in the object, or moving parts of the object a particular distance. Often objects
found in nature will have some symmetry present.
Figure 1. Examples of items in nature exhibiting symmetry.
In crystal structures, symmetry indicates a repeating pattern occurring through the crystal
lattice. In crystals, symmetry is an important property which reflects the crystal structure and
affects the different physical properties of that material. Three main types of symmetry are
translational symmetry, rotational symmetry and reflection symmetry. If a material has
rotational symmetry, it can be rotated to a specific angle, without a change in the material
being detected. If a material has reflection symmetry,
Translational symmetry: If a material has translational symmetry, a section of the material can
be shifted a fixed distance, resulting in a copy of the original pattern. The triangles below
exhibit translational symmetry in this pattern because the movement to the right generates a
new set of triangles that is a copy of the original.
Figure 2. Illustration of translational symmetry. All the atoms in the lattice are the same, one
atom is colored blue to identify the translation.
Rotational Symmetry: If a material has rotational symmetry, it can be rotated about an axis by
a certain angle and the crystal structure remains the same. For example, in the image below in
Figure 3, the structure can be rotated 60 degrees and the structure remains the same. This
structure has 6-fold symmetry because it can be rotated 6 times in a 360 degree period.
Figure 3. Illustration of rotational symmetry. All the atoms in the lattice are the same, one atom is colored blue to identify the rotation
operation.
Reflection symmetry: If a material has reflection symmetry, a mirror symmetry operation can
be performed to produce the same object. In this operation, a mirror plane is placed in the
material. If this mirror plane shows the reproduction of the structure on both sides, the
material has reflection symmetry.
Mirror Plane
Figure 4. Illustration of Reflection symmetry.
What are Quasicrystals?
The field of quasicrystals is a relatively new area in the field of crystallography. A quasicrystal is
a material that is ordered, but not periodic. What does this mean? A material with order is
arranged in a pattern. A material that is periodic has repeating patterns. A quasicrystal is a
material arranged in a pattern, but the pattern is not repeated throughout the material.
Scientists did not think these types of structures existed until their discovery in the 1980s.
Quasicrystals do not exhibit translational symmetry, but they might exhibit rotational or
reflection symmetry. Below is an example of a quasicrystal pattern along with a repeating
pattern which exhibits translational symmetry.
Figure 5. (a) Quasicrystal Pattern1 (b)Repeating Pattern
Similar patterns have been found in ancient tile patterns in medieval Islamic mosaics in
buildings such as the Alhambra in Spain and the Darb-i Imam Shrine in Iran. These structures
exhibit patterns that are regular, but do not repeat in the structure.
The discovery of Quasicrystals
In 1982 scientist Dan Schechtman was studying the structure of an aluminum-manganese alloy
at NIST(National Institute of Science and Technology) outside of Washington DC. Using electron
microscopy and diffraction, he observed a diffraction pattern with 10 concentric circles. The
presence of a diffraction pattern indicated that the material was ordered. However, the 10-fold
diffraction pattern observed was not observed previously and was not present in the Tables of
Crystallography. In traditional crystallography, this was thought impossible. Upon further
inspection, Schechtman identified the material to have five-fold rotational symmetry.
Why was this unexpected? Scientists were familiar with materials that exhibited 3-fold, 4-fold
and 6-fold symmetry, but a material with a structure that exhibited 5-fold symmetry was not
known. Intuitively, it is rather simple to fill a space with a material that has 3, 4 or 6-fold
symmetry. Each point is equidistant from each other. With 5-fold symmetry, it is not as simple
because gaps are observed, shown in Figure 7d.
Figure 7. Diagram showing space-filling of objects with different symmetry (a) 3-fold, (b) 4-fold,
(c) 6-fold, (d) 5-fold
The structure of quasicrystals can be explained using mathematical mosaics. In the 1970s,
Roger Penrose created a pattern called Penrose Tiling that does not repeat itself, but uses only
a combination of two shapes. While the Penrose Tiling does not exhibit translational symmetry,
it can be created to exhibit rotational symmetry and reflection symmetry.
Figure 8. Illustration of the construction of penrose tiles from two types of triangles.
The presence of two shapes allows the space to be filled appropriately and the material exhibits
5-fold symmetry. However, each point is no longer equidistant from the other points.
(a)
(b)
Figure 8. (a) Periodic Tiling (b) Penrose Tiling that is aperiodic.2
This subject was highly controversial until other scientists observed similar structures in other
materials. In 2011 Dan Shechtman won the Nobel Prize in chemistry for his discovery. Since
their discovery, many quasicrystals have been synthesized in the laboratory. However, only
recently scientists have discovered that there are quasicrystals that occur in nature. A new kind
of mineral was discovered in eastern Russia in 2009 called icosahedrite which exhibited 10-fold
symmetry. Quasicrystals were also observed in a new steel material developed in Sweden
where there existed hard steel quasicrystals embedded in a softer steel material. This was only
observed at the atomic level when investigation of the material was conducted. The purpose of
the quasicrystals was to act like armor and protect the softer steel regions.
Properties of Qua
Quasicrystals are hard and brittle materials. They are not good conductors of heat or electricity.
These properties have proved them useful in coatings, thermoelectric materials, thermal
insulation and components in LEDs (Light-emitting diodes). Recently, quasicrystals have been
used in nonstick surface coatings in commercially made frying pans.
References and additional links:
1 Image from http://www.jcrystal.com/steffenweber/qc.html
2 Image from http://en.wikipedia.org/wiki/Penrose_tiling
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/info_publ_eng_2011.pdf
http://www.spring8.or.jp/en/news_publications/press_release/2007/071203
http://www.goldennumber.net/penrose.htm
http://www.tau.ac.il/~ronlif/quasicrystals.html
http://mcs.open.ac.uk/ugg2/quasi_intro.shtml
Instructor guide:
This activity is designed for students who have been introduced to crystal structures and
properties of solids. However, this activity can be inserted into chemistry, physics or materials
science courses at the high school level. In addition, this activity can be placed in a geometry or
math course with adequate discussion. Accompanying this article is a hands-on activity where
the students can construct two 3-D shapes, a cube and a quasicrystal. They will observe
differences in the structures. Each student will be given the paper to construct their own
structure. The students should then combine their structures to see how the cubes can fill
space together to make a repeating pattern. They should find that the cube will easily to fill
space, but the quasicrystal cannot. For variation and possibly better explanation, the instructor
can print out the patterns in different colors.
This activity was adapted from the following website:
http://www.goldennumber.net/images/DIYquasicrystal.gif
Additional resources and links:
http://www.youtube.com/watch?v=k_VSpBI5EGM
http://www.youtube.com/watch?v=EZRTzOMHQ4s
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/sciback_2011.pdf
http://www.goldennumber.net/quasicrystal.htm
Free computer program to generate your own quasicrystal!
http://www.condellpark.com/kd/quasig.htm
Penrose Tile Puzzles
http://www.gamepuzzles.com/pentuniv.htm
Growing Crystals
Growing Sugar Crystals – Make your own Rock Candy!
It's easy to grow your own sugar crystals! Sugar crystals are also known as rock candy since the
crystallized sucrose (table sugar) resembles rock crystals and because you can eat your finished
product. You can grow beautiful clear sugar crystals with sugar and water or you can add food
coloring to get colored crystals. It's simple, safe, and fun.
Difficulty: Easy Time Required: a few days to a week
Objective: Grow Sugar Crystals
Materials:
• 1 cup water
• 3 cups table sugar (sucrose)
• clean glass jar
• pencils
• string
• pan or bowl for boiling water and making solution
• spoon or stirring rod
Here's How:
1. Gather your materials.
2. You may wish to grow a seed crystal, a small crystal to weight your string and provide a
surface for larger crystals to grow onto. A seed crystal is not necessary as long as you are
using a rough string or yarn. See seed crystal formation below.
3. Tie the string to a pencil. If you have made a seed crystal, tie it to the bottom of the
string. Set the pencil across the top of the glass jar and make sure that the string will
hang into the jar without touching its sides or bottom. However, you want the string to
hang nearly to the bottom. Adjust the length of the string, if necessary.
4. Creation of the saturated solution: Boil the water. Note: If you boil your water in the
microwave, be very careful removing it to avoid getting splashed! Stir in the sugar, a
teaspoonful at a time. Keep adding sugar until it starts to accumulate at the bottom of
the container and won't dissolve even with more stirring. This means your sugar
solution is saturated. If you don't use a saturated solution, then your crystals won't grow
quickly. On the other hand, if you add too much sugar, new crystals will grow on the
undissolved sugar and not on your string.
5. Pour your solution into the clear glass jar. Note: If you have undissolved sugar at the
bottom of your container, avoid getting it in the jar.
6. Place the pencil over the jar and allow the string to dangle into the liquid.
7. Set the jar somewhere where it can remain undisturbed. If you like, you can set a coffee
filter or paper towel over the jar to prevent dust from falling into the jar.
8. Check on your crystals after a day. You should be able to see the beginnings of crystal
growth on the string or seed crystal.
9. Let the crystals grow until they have reached the desired size or have stopped growing. At
this point, you can pull out the string and allow the crystal to dry. You can eat them or
keep them. Have fun!
Tips:
1. Crystals will form on a cotton or wool string or yarn, but not on a nylon line. If you use a
nylon line, tie a seed crystal to it to stimulate crystal growth.
2. If you are making the crystals to eat, please don't use a fishing weight to hold your string
down. The lead from the weight will end up in the water -- it's toxic. Paper clips are a
better choice, but still not great.
Seed Crystal formation:
Pour a small amount of your saturated solution onto a plate, let the drop evaporate, and scrape
the crystals formed on the bottom to use as seeds. Or pour saturated solution into a glass jar
and dangle a rough object (like a piece of string) into the liquid. Small crystals will start to grow
on the string, which can be used as seed crystals.
http://chemistry.about.com/od/growingcrystals/ht/blsugarcrystal.htm
Models of Crystals
Students do the “Models of Crystals” lab. They build 4 different unit cells using toothpicks and
polystyrene balls. A recommendation is to use 1 ½” diameter spheres – the smaller ones tend
to fall apart quickly after using just a few times. They build the most basic one (simple cubic)
and the 3 most commonly found in metals (BCC, FCC, HCP). See the lab sheet the students fill
out.
Permanent models made out of ping-pong balls and hot glue are very useful. These help the
students compare the different models in terms of packing and slip planes since they dismantle
their models before building the next one. It is also helpful to build planes of atoms and then
stack them. This helps the students to see that the layers are all actually the same in a model;
they are just “offset” when stacking them together to make the unit cell. This is also great to
see the overall 3-D pattern of the crystal shape. This works especially well with FCC and HCP. If
you make 3 planes for each, then the students can also try piecing them together into one layer
instead of stacking them into 3 layers to make a unit cell. By building a bigger plane from
smaller ones, the students can pick out the “section” that is used in each of the different layers
in the unit cell. The repeating pattern is much more noticeable.
After the students have finished building the models and writing in their journals, ask the
students the following question:
• “Why do we care what particular crystal structure a metal has?”
Have the students rank the crystal models from “most closely packed” to “least closely packed”.
1. HCP - “most closely packed”
2. FCC
3. BCC
4. simple cubic “least - closely packed”
• “Which type of crystal structure allows a metal to be more workable, one with many slip
planes or one with fewer slip planes?”
• “Which type of crystal structure allows a metal to be more workable, one that is closely
packed or one that is loosely packed?” (“One that has a lot of ‘gappiness’ or one that has little
‘gappiness’?”)
The students almost always get the answer to the first question right. It is logical that a crystal
structure with many slip planes will be more workable. However, the answer to the second
question isn’t as obvious. At least half of the students always say that more loosely packed
crystal structures (ones with more open space) make a metal more workable. By workable we
mean malleable or ductile. I then use the “chalk demo” to illustrate the answer.
Chalk demo:
Materials:
•
5 pieces of chalk laid side by side with an ~ ⅛” gap between each piece (use hot glue to
attach them to a piece of clear plastic)
•
5 pieces of chalk laid side by side with no gaps between them (attach to plastic)
•
one piece of chalk to roll across the top of the other pieces
Give the students the following scenario:
You are riding your 4-wheeler in the country and you come to a deep ditch that someone has
built a log bridge across. Which type of bridge would be easier to go across?
Then roll the single piece of chalk across the “chalk bridges” – first the one with gaps and then
the one without gaps. Which one is harder to do and requires more energy? They will all agree
that the one without gaps is easier.
Now tell the students you are going to ask them the original questions AGAIN:
•
“Which type of crystal structure allows a metal to be more workable, one that is closely
packed or one that is loosely packed?”
•
“Which one is easier for the planes of atoms to slide past each other?”
The students get it. Common sense wants to tell us that having more “open space” in a crystal
makes it easier for atoms to move around so the metal is more workable. But this isn’t the case
with planes of atoms. More ‘gappiness’ allows the atoms to fall into these spaces and makes it
harder to keep them moving to work the metal.
•
•
more tightly packed = more workable
more slip planes = more workable
Workable – changing the shape of a solid (while remaining a solid) without it cracking or
breaking (malleability and ductility)
Based on the above information, have the students reason out which crystal structure should
be the most workable. Since FCC is both tightly packed and has many slip planes, it is the most
workable.
Have the students fill in the following table:
Is there a way to figure out if the packing and the slip planes have an equal effect on the
workability or if one of the two factors has more.
Since BCC and HCP both have a “yes” and a “no” and HCP is the least workable, reasoning
would dictate that the number of slip planes has more effect on the workability than how
closely packed the atoms are.
Now ask the students to predict which familiar metals should have an FCC crystal structure.
They can usually correctly name several such as gold, copper, aluminum, lead, etc…
Then compile a list of some common metals and their crystal shapes.
BCC
FCC
HCP
Other
chromium
aluminum
cobalt
tin
iron (<910 °C)
copper
magnesium
tungsten
gold
titanium
iron (>910 °C)
zinc
lead
platinum
silver
Iron appears in two different columns because it is allotropic. This concept will be further
developed in the Iron Wire Demo. But the students should be able to grasp the idea that
blacksmiths pound on a piece of iron when it is glowing red hot and stop when it loses its color
since FCC is a more workable crystal structure than BCC.
A sheet of copper and a sheet of titanium are also useful for demonstrating the difference in
the workability of an FCC metal and an HCP metal. Simply hold down one end of the metal
against the edge of a table, push down on the other end and release. The copper is very
workable and easy to bend and will not completely return to its original shape. The titanium
takes more force to bend and will spring back to its original shape.
Week 6: Crystalline vs Amorphous
What are the differences between crystalline and amorphous compounds or elements?
Elements themselves are not crystalline or amorphous. Instead this describes the structure of
certain elements and compounds in the solid state. For instance, a single element can be found
in both a crystalline form as well as an amorphous form.
A crystalline solid is one in which there is a regular repeating pattern in the structure, or in
other words, there is long-range order. In fact, you can completely describe the entire crystal by
describing the single "repeat unit." For instance, as a simple example, if I have the pattern
ABCABCABCABCABC... (that repeats infinitely) I can completely describe it by just saying it is
"ABC" over and over again. In a 3-dimensional crystal, this repeat unit is called the "unit cell."
Some crystalline solids are diamond, table salt, and many types of minerals found in the earth.
An amorphous solid is one which does not have long-range order. In other words, there is no
repeat unit. To contrast the example above, it would now be: ABCBCABBCACBACBAC... where
there is no way to figure out what will be the next letter. Some examples of amorphous solids
are glass (in windows, for example), wax, and plastics. If a liquid cools very quickly, the
molecules will not have time to arrange themselves in the most favorable pattern (which will
almost always be crystalline), and so they are locked into a disordered solid.
Silicon is a common solid that can be found in both amorphous and crystalline forms,
depending on how it is manufactured. Crystalline silicon is much harder to grow, but it is what
is used in computer chips. Amorphous silicon is much cheaper and easier to grow, and is
commonly used in solar panels.
Diffusion
Diffusion is one of the fundamental processes by which material moves. It is thus important in
biology and medicine, chemistry and geology, engineering and physics, and in just about every
aspect of our lives. Diffusion is a consequence of the constant thermal motion of atoms,
molecules, and particles, and results in material moving from areas of high to low
concentration. Thus the end result of diffusion would be a constant concentration, throughout
space, of each of the components in the environment.
Of course there are also processes that generate inhomogeneity, even while diffusion is
smoothing things out, and the world we live in is the sum of both. The speed of mixing by
diffusion depends on three main parameters:
1. temperature
2. size (mass) of the diffusing particles
3. viscosity of the environment
The temperature of a system is a measure of the average kinetic energy, the energy due to
movement, of the particles in the system (the distinction between particles, molecules, and
atoms will not be important in our discussion). In most systems the energy is just equal to a
constant times the temperature. Since a higher kinetic energy means a higher velocity, it's clear
why the speed of diffusion
increases with temperature: everything is moving faster (in the formula below, E is the kinetic
energy, k Boltzmann's constant, T the temperature, m the mass, and v is the velocity).
A heavy particle has a lower velocity for a given kinetic energy, or temperature. A large particle
interacts more with its environment, which slows it down. Thus, heavy, large particles diffuse
more slowly than light, small ones.
The environment (the material the diffusing material is immersed in) is very important.
Diffusion is most rapid in a gas (because molecules can travel a considerable distance before
they hit another molecule, and even then they just bounce off), slower in a liquid (there is a lot
of movement, but all molecules remain weakly tied to each other as they move), and very slow
or sometimes zero in a solid (because the forces between molecules and atoms are so generally
so large that there are only infrequent exchanges of position).
Structure of Metals
A very high percentage of the elements are metals. However, only a few types of
structures occur for most elemental metals. This leads to the use of sphere packings to
models metal structures.
On this page, we give a brief discussion on metal structures. Namely, metals have closest
packing (FCC and HCP) structures, the body centered cubic (bcc), simple cubic (SC) and
complicated closest packing structures.
We will only scratch the surface on the subject on metal structures, but the basic concepts
presented here let you understand why metals behave they way they do (properties).
What metals have the closest packing structures?
In solids, two types of closest packing of spheres have been discussed. They are the facecentered closest packing (FCC (Swaddle called it cubic closest packing (CCP), and hexagonal
closest packing (HCP).
Since the periodic table is a useful tool for representing information, the structure types of metals
can be displayed using a period table.
In the above diagram, the CCP (FCC) structures are represented by a red circle, whereas the HCP
structures are represented by black hexagon.
Copper is the most common mentioned metal that has the FCC structure. This element is one of
the noble metals. It has been widely used for door knobs and other tools, and has been widely
recognized. Yet, most nobel metals, Cu, Ag, Au, Ni, Pd, Pt, Rh, and Ir have FCC type structures.
Among the group 2 elements, only Ca and Sr have the FCC structure, whereas Be and Mg have
HCP structures. So do Zn, Cd, Sc, Y, Lu, Ti, Zr, Hf, Tc, Re, Ru, Os and most rare earth
elements. These are mentioned to bring your attention to these two common types of structures,
and you are encouraged to at least be able to give a few examples for each type.
Amazingly, the HCP and FCC structure are very similar in many aspect, but nature knows best.
The structures adopted by various metals occur by their design. When crystallization takes place,
the atoms arrange themselves according to their structure types.
Example 1
Gold has a very high density, d, of 19.3 g/mL, and it has the FCC structure. If the gold
atoms were spheres as modeled by the FCC structure, what is the atomic radius?
Discussion
A handbook did give the radius of gold as 144 pm (1 pm = 1012).
Copper has a specific gravity of 8.92, evaluate its atomic radius.
The atomic radius of silver Ag is listed as 145 pm. Evaluate its density.
What metals have the body centered cubic structure?
Alkali metals, Li, Na, K, Rb, and Cs all have the body centered cubic (bcc) structure. In addition,
the vanadium and chromium groups also have the bcc structure. Furthermore, at room
temperature, iron has a bcc structure.
This type of structure has two atoms per unit cell, and it is slightly less densely packed as the
FCC or HCP types as shown by Example 1.
Example 2
What is the fraction of the volume occupied by spheres for a bcc type structure?
Discussion
The fraction of 0.68 is slightly less than those (0.74) of closest packed structures. Thus,
the bcc structures are less densely packed according to the hard sphere model.
Is there any metal adopting the simple cubic structure?
Yes, polonium (Po) has been reported to have a simple
cubic crystal structure. From packing point of view, this
type of arrangement is not stable, and this structure type
is not common.
The cubic unit cell contains only one sphere, and the edge
length is exactly equal to the diameter of the sphere. In the
diagram, we choose the origin to be the center of an atom,
but if you choose the origin to be the center among 8 spheres, your cube enclose a whole atom.
You can work out the fraction of space occupied by spheres in such an arrangement to be /6
(0.52), much less than the bcc structure type.
What are the features of rare earth metals?
If you go back to the periodic table of structure types, you will see that the rare earth elements
have FCC (CCP), HCP, BCC, and another type marked by hc (4 H). In other words, these 14
elements exemplify many types of structures. We have covered the other types than the hc (4
H) type pretty well.
Actually, the hc (4 H) type has a complicated packing sequence such as ABAC, ABCB, etc. That
is why they are designated as (4 H). Actually, the structure of Sm (samarium) has a very
complicated sequence of ACACBCBAB ACACBCBAB ....
Confidence Building Questions
What is the volume of a sphere with a radius of 1.0 cm?
Skill Give the formula of volume for a sphere with radius r.
What is the volume of a cube with an edge length of 2.0 cm?
Discussion
The fraction of space occupied by spheres in a simple cubic arrangement is 4.19/8.0 =
0.52.
What is the number of nearest neighbors in a bcc structure?
Skill Be prepared to answer simple "matter of fact" questions regarding structure types.
From the previous question, you know that there are 8 nearest neighbors in a bcc
structure. The next nearest neighbor is at a distance a (unit cell edge length). How
many neighbors have a distance a from an atom of the bcc type structure?
Skill Be prepared to answer simple "matter of fact" questions regarding structure types.
Give three metals that have the bcc structure?
Discussion
Give some examples for the CCP (FCC) and HCP types.
History of Metals
A Short History of Metals
By
Alan W. Cramb
Department of Materials Science and Engineering
Carnegie Mellon University
Process Metallurgy is one of the oldest applied sciences. Its history can be traced back to 6000
BC. Admittedly, its form at that time was rudimentary, but, to gain a perspective in Process
Metallurgy, it is worthwhile to spend a little time studying the initiation of mankind's
association with metals. Currently there are 86 known metals. Before the 19th century only 24
of these metals had been discovered and, of these 24 metals, 12 were discovered in the 18th
century. Therefore, from the discovery of the first metals - gold and copper until the end of the
17th century, some 7700 years, only 12 metals were known. Four of these metals, arsenic,
antimony , zinc and bismuth , were discovered in the thirteenth and fourteenth centuries,
while platinum was discovered in the 16th century. The other seven metals, known as the
Metals of Antiquity, were the metals upon which civilization was based. These seven metals
were:
(1) Gold (ca) 6000BC
(2) Copper,(ca) 4200BC
(3) Silver,(ca) 4000BC
(4) Lead, (ca) 3500BC
(5) Tin, (ca) 1750BC
(6) Iron, smelted, (ca) 1500BC
(7) Mercury, (ca) 750BC
These metals were known to the Mesopotamians, Egyptians, Greeks and the Romans. Of the
seven metals, five can be found in their native states, e.g., gold, silver, copper, iron (from
meteors) and mercury. However, the occurrence of these metals was not abundant and the
first two metals to be used widely were gold and copper. And, of course, the history of metals is
closely linked to that of coins and gemstones
After the seven metals of antiquity: gold, silver, copper, mercury, tin , iron and lead, the next
metal to be discovered was Arsenic in the 13th century by Albertus Magnus. Arsenicus
(arsenious oxide) when heated with twice its weight of soap became metallic. By 1641
arsenious oxide was being reduced by charcoal. Arsenic is steel gray, very brittle and crystalline;
it tarnishes in air and when heated rapidly forms arsenious oxide with the odor of garlic.
Arsenic compounds are poisonous. The symbol As is taken from the latin arsenicum. Arsenic
was used in bronzing and improving the sphericity of shot. The most common mineral is
Mispickel or Arsenopyrite (FeSAs) from which arsenic sublimes upon heating.
The next metal to be isolated was antimony. Stibium or antimony sulphide was roasted in an
iron pot to form antimony. Agricola reported this technique in 1560. Antimony whose name
comes from the Greek "anti plus monos"- a metal not found alone, has as its symbol Sb from
the latin stibium. It is an extremely brittle flaky metal. Antimony and its compounds are highly
toxic. Initial uses were as an alloy for lead as it increased hardness. Stibnite is the most common
ore. It was commonly roasted to form the oxide and reduced by carbon.
By 1595, bismuth was produced by reduction of the oxide with carbon , however, it was not
until 1753 when bismuth was classified as an element. Zinc was known to the Chinese in 1400;
however, it was not until 1738, when William Champion patented the zinc distillation process
that zinc came into common use. Before Champion's process, zinc, which was imported from
China, was known as Indian Tin or Pewter. A Chinese text from 1637 stated the method of
production was to heat a mixture of calamine (zinc oxide) and charcoal in an earthenware pot .
The zinc was recovered as an incrustation on the inside of the pot. In 1781 zinc was added to
liquid copper to make brass. This method of brass manufacture soon became dominant.
One other metal was discovered in the 1500's in Mexico by the Spaniards. This metal
was platinum. Although not 100% pure, it was the first metal to be discovered and sourced
from the "New World". The property which brought this metal to the prospector’s attention
was its lack of reactivity with known reagents. Early use of platinum was banned because it was
used as a blank for coins which were subsequently gold coated, proving that the early
metallurgists understood not only density but also economics. Although, platinum was known
to the western world, it was not until the 1800's that platinum became widely used.
Several other metals were isolated during the 1700's. These were Cobalt, Nickel, Manganese,
Molybdenum, Tungsten, Tellurium, Beryllium , Chromium, Uranium, Zirconium and Yttrium .
Only laboratory specimens were produced and all were reduced by carbon with the exception
of tungsten which became the first metal to be reduced by hydrogen.
Therefore, before 1800 there were 12 metals in common use:
Gold
Silver
Copper
Lead
Mercury
Iron
Tin
Platinum
Antimony
Bismuth
Zinc
Arsenic
Before 1805 all metals were reduced by either carbon or hydrogen , however, the majority of
the metals once smelted were not pure. Refining of gold, that is the separation of silver from
gold, has a very old history. During the second millennium it is clear that an amalgamation
process using molten lead was used to separate the metal from crushed quartz. The lead then
being cupelled to separate the gold and the silver. Purification was then carried further (but not
until the first millennium) by a cementing process where a mixture of the alloy was closely
mixed with common salt. The silver reacted, formed a chloride which was soluble and easily
rinsed off. The cementation process was used until about 1100 A.D. when other refining
processes became popular. One method used sulfur addition to the molten bullion to form
silver sulfide which was removed as "black" during gentle beating. Mineral acids were
developed by the alchemists. Nitric acid was used to dissolve silver in the 1200's as a
purification technique. By the end of the 15th century, Stibium (antimony sulfide) was also used
in the cementation process. Generally, a mixture of salt, stibium and sulfur was heated with the
gold foil.
Gold plating of silver was very popular and in 1250 Bartholommeus Anglicus gave the following
advice:
"And when a plate of gold shall be melded with a plate of silver, or joined there to, it needeth to
beware namely of three things, of powder, of winde and of moisture: for if any hereof come
between gold and silver, they may not be joined together,then one with another: and therefore
it needeth to meddle these two metals together in a full cleane place and quiet and when they
be joined in this manner, the joining is inseparable, so that they may not afterward be departed
asunder,"
This advice is good today. Amalgamation processes were also popular. The gold was dissolved
in mercury. The amalgam was coated onto the piece and then heated to drive off the mercury
leaving a gold coated piece. Gold could also be removed by the reverse process (1567).
Before 1807 all metals which had been separated had been reduced by either carbon or
hydrogen. The separation of other metals needed the invention of the galvanic cell. Sir
Humphrey Davy used the generating pile developed by Volta and demonstrated that water
could be decomposed into hydrogen and oxygen. Next he tried a solution containing potash
and again gained hydrogen and oxygen. Then he tried a piece of moistened potash which
produced at the negative electrode something that burned brightly. His next experiment was
decisive, he placed the potash on an insulated platinum dish which was connected to the
negative pole of the battery. He then connected the positive pole to the upper surface of the
potash and produced small metallic globules. In this manner he produced potassium and
sodium.
The Swedish chemist, Berzelius, found that the metals contained in lime and baryta (barium
oxide) could also be separated in this way. He used mercury as a cathode which caused the
separated metals to dissolve in the mercury. After electrolysis the mercury was distilled away
and Calcium and Barium were left behind. Later, Davy produced Strontium by the same
technique. By allowing the manufacture of sodium and potassium Davy and Berzelius had
opened the door to the reduction of many refractory materials.
In 1817 Cadmium was discovered. Stroymeyer noted that zinc carbonate had a yellowish tinge
not attributable to iron. Upon reduction he thought that the alloy contained two metals. The
metals were separated by fractional distillation. At 800 C, as cadmium's boiling point is lower
than zinc, the cadmium distilled first.
In 1841 Charles Askin developed a method of separating cobalt and nickel when both metals
are in solution. Using a quantity of bleaching powder he found that if the quantity of powder
was small enough only cobalt oxide was precipitated and separated. The nickel could then be
easily precipitated with lime and a source for pure cobalt and nickel was available. Pure cobalt
oxide revolutionized the pottery industry as the blues were now available.
Chromium although it had been produced by reduction with carbon was the first metal to be
extensively produced using another metal (zinc). Wohler in 1859 melted chromium chloride
under a fused salt layer and attracted the chromium with zinc. The resulting zinc chloride
dissolved in the fused salt and chromium produced. In 1828, Wohler produced beryllium by
reducing beryllium chloride with potassium in a platinum crucible.
Aluminium was first produced by Christian Oersted in 1825. However it was not until 20 years
later that significant quantities were produced. Wohler fused anhydrous aluminum chloride
with potassium to set free aluminum. Later Ste Claire Deville in 1854 put together a production
process using sodium instead of potassium.
The current from Galvanic cells were also used for electroplating. This was first practiced in the
1830's when silver was deposited on baser metals. After silver plating, copper and nickel plating
was developed. In the middle of the 18th century it was found that metallic separation could be
carried out by the application of galvanic electricity. The current was passed from an anode
made of an impure, crude metal into a suitable electrolyte and the pure material plated out
onto a resistant cathode. Impurities present in the crude cathode dropped to the bottom of the
vessel and formed a “sludge".
From this short review of metallurgical developments it can be seen that as the early
metallurgists became more sophisticated their ability to discover and separate all the metals
grew. However in all of their work it was necessary for all the basic steps to be carried out e.g.
the ore had to be identified, separated from gangue, sized, concentrated and reduced in a
manner which accomplished a phase separation.
Week 7: Introduction to Metals
Mechanics of Metals (http://www.virginia.edu/bohr/mse209/chapter6.htm)
Introduction
Often materials are subject to forces (loads) when they are used. Mechanical engineers
calculate those forces and material scientists how materials deform (elongate, compress, twist)
or break as a function of applied load, time, temperature, and other conditions.
Materials scientists learn about these mechanical properties by testing materials. Results from
the tests depend on the size and shape of material to be tested (specimen), how it is held, and
the way of performing the test. That is why we use common procedures, or standards, which
are published by the ASTM.
Concepts of Stress and Strain
To compare specimens of different sizes, the load is calculated per unit area, also called
normalization to the area. Force divided by area is called stress. In tension and compression
tests, the relevant area is that perpendicular to the force. In shear or torsion tests, the area is
perpendicular to the axis of rotation.
 = F/A0
tensile or compressive stress
 = F/A0
shear stress
The unit is the Megapascal = 106 Newtons/m2.
There is a change in dimensions, or deformation elongation, DL as a result of a tensile or
compressive stress. To enable comparison with specimens of different length, the elongation is
also normalized, this time to the length L. This is called strain, e.
e = L/L
The change in dimensions is the reason we use A0 to indicate the initial area since it changes
during deformation. One could divide force by the actual area, this is called true stress.
For torsional or shear stresses, the deformation is the angle of twist,  and the shear strain is
given by:
 = tg 
Stress—Strain Behavior
Elastic deformation. When the stress is removed, the material returns to the dimension it had
before the load was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent
Plastic deformation. When the stress is removed, the material does not return to its previous
dimension but there is a permanent, irreversible deformation.
In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:

That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In
some cases, the relationship is not linear so that E can be defined alternatively as the local
slope:
E = 
Shear stresses produce strains according to:
=G
where G is the shear modulus.
Elastic moduli measure the stiffness of the material. They are related to the second derivative of
the interatomic potential, or the first derivative of the force vs. internuclear distance (Fig. 6.6).
By examining these curves we can tell which material has a higher modulus. Due to thermal
vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger
ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances
depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single
crystals. For randomly oriented poli-crystals, E is isotropic.
Anelasticity
Here the behavior is elastic but the stress-strain curve is not immediately reversible. It takes a
while for the strain to return to zero. The effect is normally small for metals but can be
significant for polymers.
Elastic Properties of Materials
Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio of
lateral and axial strains is called the Poisson's ratio n.
lateral/axial
The elastic modulus, shear modulus and Poisson's ratio are related by E = 2G(1+n)
Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the stress.
The point at which this happens is the yield point because there the material yields, deforming
permanently (plastically).
Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is
called yield stress, and is an important measure of the mechanical properties of materials. In
practice, the yield stress is chosen as that causing a permanent strain of 0.002 (strain offset, Fig.
6.9.)
The yield stress measures the resistance to plastic deformation.
The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched
beyond repair, but the motion of dislocations, which involves breaking and reforming bonds.
Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes through a
maximum, called the tensile strength (sTS) , and then falls as the material starts to develop
a neck and it finally breaks at the fracture point (Fig. 6.10).
Note that it is called strength, not stress, but the units are the same, MPa.
For structural applications, the yield stress is usually a more important property than the tensile
strength, since once it is passed, the structure has deformed beyond acceptable limits.
Ductility is the ability to deform before breaking. It is the opposite of brittleness. Ductility can
be given either as percent maximum elongation emax or maximum area reduction.
%EL = max x 100 %
%AR = (A0 - Af)/A0
These are measured after fracture (repositioning the two pieces back together).
Resilience is the capacity to absorb energy elastically. The energy per unit volume is the area
under the strain-stress curve in the elastic region.
Toughness is the ability to absorb energy up to fracture. The energy per unit volume is
the total area under the strain-stress curve. It is measured by an impact test True
Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile
strength. The material starts necking (the transverse area decreases) but the stress cannot
increase beyond TS. The ratio of the force to the initial area, what we normally do, is called the
engineering stress. If the ratio is to the actual area (that changes with stress) one obtains
the true stress.
Elastic Recovery during Plastic Deformation
If a material is taken beyond the yield point (it is deformed plastically) and the stress is then
released, the material ends up with a permanent strain. If the stress is reapplied, the material
again responds elastically at the beginning up to a new yield point that is higher than the
original yield point (strain hardening, Ch. 7.10). The amount of elastic strain that it will take
before reaching the yield point is called elastic strain recovery (Fig. 6. 16).
Compressive, Shear, and Torsion Deformation
Compressive and shear stresses give similar behavior to tensile stresses, but in the case of
compressive stresses there is no maximum in the s-e curve, since no necking occurs.
Hardness
Hardness is the resistance to plastic deformation (e.g., a local dent or scratch). Thus, it is a
measure of plastic deformation, as is the tensile strength, so they are well correlated.
Historically, it was measured on an empirically scale, determined by the ability of a material to
scratch another, diamond being the hardest and talc the softer. Now we use standard tests,
where a ball, or point is pressed into a material and the size of the dent is measured. There are
a few different hardness tests: Rockwell, Brinell, Vickers, etc. They are popular because they are
easy and non-destructive (except for the small dent).
Variability of Material Properties
Tests do not produce exactly the same result because of variations in the test equipment,
procedures, operator bias, specimen fabrication, etc. But, even if all those parameters are
controlled within strict limits, a variation remains in the materials, due to uncontrolled
variations during fabrication, non homogenous composition and structure, etc. The measured
mechanical properties will show scatter, which is often distributed in a Gaussian curve (bellshaped), that is characterized by the mean value and the standard deviation (width).
Design/Safety Factors
To take into account variability of properties, designers use, instead of an average value of, say,
the tensile strength, the probability that the yield strength is above the minimum value
tolerable. This leads to the use of a safety factor N > 1 (typ. 1.2 - 4). Thus, a working value for
the tensile strength would be sW = sTS / N.
Important Terms:
Anelasticity
Ductility
Elastic deformation
Elastic recovery
Engineering strain
Engineering stress
Hardness
Modulus of elasticity
Plastic deformation
Poisson’s ratio
Proportional limit
Shear
Tensile strength
Toughness
Yielding
Yield strength
Drawing Wire
Wire drawing is a metal working process used to reduce the cross-section of a wire by pulling
the wire through a single, or series of, drawing die(s). There are many applications for wire
drawing, including electrical wiring, cables, tension-loaded structural components, springs,
paper clips, spokes for wheels, and stringed musical instruments. Although similar in process,
drawing is different from extrusion, because in drawing the wire is pulled, rather than pushed,
through the die. Drawing is usually performed at room temperature, thus classified as a cold
working process, but it may be performed at elevated temperatures for large wires to reduce
forces. More recently drawing has been used with molten glass to produce high quality optical
fibers.
The wire drawing process is quite simple in concept. The wire is prepared by shrinking the
beginning of it, by hammering, filing, rolling or swaging, so that it will fit through the die; the
wire is then pulled through the die. As the wire is pulled through the die, its volume remains
the same, so as the diameter decreases, the length increases. Usually the wire will require more
than one draw, through successively smaller dies, to reach the desired size. The American wire
gauge scale is based on this. This can be done on a small scale with a draw plate, or on a large
commercial scale using automated machinery. The process of wire drawing improves material
properties due to cold working.
The areal reduction of small wires, are 15–25% and larger wires are 20–45%. Very fine wires are
usually drawn in bundles. In a bundle, the wires are separated by a metal with similar
properties, but with lower chemical resistance so that it can be removed after drawing. If the
reduction in diameter is greater than 50%, the process may require annealing between the
process of drawing the wire through the dies. Commercial wire drawing usually starts with a
coil of hot rolled 9 mm (0.35 in) diameter wire. The surface is first treated to remove scales. It is
then fed into either a single block or continuous wire drawing machine.
Single block wire drawing machines include means for holding the dies accurately in position
and for drawing the wire steadily through the holes. The usual design consists of a cast-iron
bench or table having a bracket standing up to hold the die, and a vertical drum which rotates
and by coiling the wire around its surface pulls it through the die, the coil of wire being stored
upon another drum or "swift" which lies behind the die and reels off the wire as fast as
required. The wire drum or "block" is provided with means for rapidly coupling or uncoupling it
to its vertical shaft, so that the motion of the wire may be stopped or started instantly. The
block is also tapered, so that the coil of wire may be easily slipped off upwards when finished.
Before the wire can be attached to the block, a sufficient length of it must be pulled through
the die; this is effected by a pair of gripping pincers on the end of a chain which is wound
around a revolving drum, so drawing the wire until enough can be coiled two or three times on
the block, where the end is secured by a small screw clamp or vice. When the wire is on the
block, it is set in motion and the wire is drawn steadily through the die; it is very important that
the block rotates evenly and that it runs true and pulls the wire at a constant velocity,
otherwise "snatching" occurs which will weaken or even break the wire. The speeds at which
wire is drawn vary greatly, according to the material and the amount of reduction.
Continuous wire drawing machines differ from the single block machines in having a series of
dies through which the wire passes in a continuous manner. The difficulty of feeding between
each die is solved by introducing a block between each die. The speeds of the blocks are
increased successively, so that the elongation is taken up and any slip compensated for. One of
these machines may contain 3 to 12 dies. The operation of threading the wire through all the
dies and around the blocks is termed "stringing-up". The arrangements for lubrication include a
pump which floods the dies, and in many cases also the bottom portions of the blocks run in
lubricant.
Often intermediate anneals are required to counter the effects of cold working, and to allow
further drawing. A final anneal may also be used on the finished product to
maximize ductility and electrical conductivity.
An example of product produced in a continuous wire drawing machine is telephone wire. It is
drawn 20 to 30 times from hot rolled rod stock.
While round cross-sections dominate most drawing processes, non-circular cross-sections are
drawn. They are usually drawn when the cross-section is small and quantities are too low to
justify rolling. In these processes, a block or Turk's-head machine are used.
Lubrication
Lubrication in the drawing process is essential for maintaining good surface finish and long die
life. The following are different methods of lubrication:




Wet drawing: the dies and wire or rod are completely immersed in lubricant
Dry drawing: the wire or rod passes through a container of lubricant which coats the
surface of the wire or rod
Metal coating: the wire or rod is coated with a soft metal which acts as a solid lubricant
Ultrasonic vibration: the dies and mandrels are vibrated, which helps to reduce forces
and allow larger reductions per pass
Various lubricants, such as oil, are employed. Another lubrication method is to immerse the
wire in a copper(II) sulfate solution, such that a film of copper is deposited which forms a kind
of lubricant. In some classes of wire the copper is left after the final drawing to serve as a
preventive of rust or to allow easy soldering.
Mechanical Properties
The strength-enhancing effect of wire drawing can be substantial. The highest grule strengths
available on any steel have been recorded on small-diameter cold-drawn austenitic stainless
wire. Tensile strength can be as high as 400 ksi (3760 MPa).
Week 8: Properties of Metals
Corrosion
Corrosion is the gradual destruction of material, usually metal, by chemical reaction with its
environment. In the most common use of the word, this means electrochemical oxidation
of metals in reaction with an oxidant such as oxygen. Rusting, the formation of iron oxides, is a
well-known example of electrochemical corrosion. This type of damage typically
produces oxide(s) or salt(s) of the original metal. Corrosion can also occur in materials other
than metals, such as ceramics or polymers, although in this context, the term degradation is
more common.
Many structural alloys corrode merely from exposure to moisture in the air, but the process can
be strongly affected by exposure to certain substances. Corrosion can be concentrated locally
to form a pit or crack, or it can extend across a wide area more or less uniformly corroding the
surface. Because corrosion is a diffusion controlled process, it occurs on exposed surfaces. As a
result, methods to reduce the activity of the exposed surface, such
as passivation and chromate-conversion, can increase a material's corrosion resistance.
However, some corrosion mechanisms are less visible and less predictable.
Drawing dies
Diagram of a carbide wire drawing die
Drawing dies are typically made of tool steel, tungsten carbide, or diamond, with tungsten
carbide and manufactured diamond being the most common. For drawing very fine wire a
single crystal diamond die is used. For hot drawing, cast-steel dies are used. For steel wire
drawing, a tungsten carbide die is used. The dies are placed in a steel casing, which backs the
die and allow for easy die changes. Die angles usually range from 6–15°, and each die has at
least 2 different angles: the entering angle and approach angle. Wire dies usually are used with
power as to pull the wire through them. There are coils of wire on either end of the die which
pull and roll up the wire with a reduced diameter.
ReWriteNITINOL
Nickel-titanium alloys have been found to be the most useful of all Shape memory alloys
(SMAs). Other shape memory alloys include copper-aluminum-nickel, copper-zinc-aluminum,
and iron- manganese-silicon alloys.(Borden, 67) The generic name for the family of nickeltitanium alloys is Nitinol. In 1961, Nitinol, which stands for Nickel Titanium Naval Ordnance
Laboratory, was discovered to possess the unique property of having shape memory. William J.
Buehler, a researcher at the Naval Ordnance Laboratory in White Oak, Maryland, was the one
to discover this shape memory alloy. The actual discovery of the shape memory property of
Nitinol came about by accident. At a laboratory management meeting, a strip of Nitinol was
presented that was bent out of shape many times. One of the people present, Dr. David S.
Muzzey, heated it with his pipe lighter, and surprisingly, the strip stretched back to its original
form. (Kauffman and Mayo, 4)
Exactly what made these metals "remember" their original shapes was in question after the
discovery of the shape-memory effect. Dr. Frederick E. Wang, an expert in crystal physics,
pinpointed the structural changes at the atomic level which contributed to the unique
properties these metals have. (Kauffman and Mayo, 4)
He found that Nitinol had phase changes while still a solid. These phase changes, known as
martensite and austenite, "involve the rearrangement of the position of particles within the
crystal structure of the solid" (Kauffman and Mayo, 4). Under the transition temperature,
Nitinol is in the martensite phase. The transition temperature varies for different compositions
from about -50 ° C to 166 ° C (Jackson, Wagner, and Wasilewski, 1). In the martensite phase,
Nitinol can be bent into various shapes. To fix the "parent shape" (as it is called), the metal
must be held in position and heated to about 500 ° C. The high temperature "causes the atoms
to arrange themselves into the most compact and regular pattern possible" resulting in a rigid
cubic arrangement known as the austenite phase (Kauffman and Mayo, 5-6). Above the
transition temperature, Nitinol reverts from the martensite to the austenite phase which
changes it back into its parent shape. This cycle can be repeated millions of times (Jackson,
Wagner, and Wasilewski, 1).
ALLOYS
An alloy is a mixture or metallic solid solution composed of two or more elements. Complete
solid solution alloys give single solid phase microstructure, while partial solutions give two or
more phases that may or may not be homogeneous in distribution, depending on thermal (heat
treatment) history. Alloys usually have different properties from those of the component
elements.
Alloy constituents are usually measured by mass. Alloys are usually classified as substitutional
or interstitial alloys, depending on the atomic arrangement that forms the alloy. They can be
further classified as homogeneous, consisting of a single phase, heterogeneous, consisting of
two or more phases, or intermetallic, where there is no distinct boundary between phases.
(Notice how this information on alloys ties in with the topic of defects)
It is time to review for the mid-term exam
Week 9: Ceramics: Structure and Properties
Introduction to Ceramics
Introduction to
Design of Structural Ceramics
David Stienstra, Ph.D.
Rose-Hulman Institute of Technology
Copyright 1992 Revised 2003 Ceramics 2 1/21/2004
Permission for use given May 1, 2012
Goals and Overview
This goal of this work is to help the designer faced with the possible use of structural ceramics.
The intent is to:
• examine the advantages of ceramics in design
• describe how you can approach the special problems of designing with brittle
materials
• introduce you to some common structural ceramics
• describe how processing affects properties;
• provide you with sources of information when you need to know more
At the end of the course you will probably not be able to single handedly design and build an
all-ceramic gas turbine engine. You should, however, be better able to:
• understand manufacturer’s information
• discuss problems and desires with suppliers
• read the increasingly abundant information in the field
To accomplish these modest goals we will start by looking at reasons ceramics should be
considered for structural applications and the special challenges of working with ceramics. In
Section 1 we overview the most common structural ceramics and their manufacturing methods.
The last portion will address more
specific design issues including the statistical approach to design (Section 2), the problems of
thermal stress (Section 3), and joining ceramics (Section 4).
Why Use Ceramics for Structural Applications?
Consider the turbocharger rotor (Fig 1.1) for an automobile. The design criteria include
• high temperature resistance (hot exhaust gases)
• low coefficient of thermal expansion (small blade tip clearance)
• low mass (low polar moment of inertia for fast spin up)
• durability (survive over 100,000 miles)
• low cost (need willing purchasers)
Figure 1.1 Silicon Nitride turbocharger rotors (From www.kyocera.com)
A ceramic (sintered silicon nitride) turbocharger was first used in a production vehicle in the
Nissan Fairlady Z sports car in 1985 (Weidmann, et al., 1990). This was the result of work begun
by Garrett Company in the 1970's. In 1990 Garrett Automotive Division of Allied Signal
Automotive supplied ceramic turbochargers to Nissan Motors at a rate of more than 2000 per
month. These were used in the 1990 Nissan Skyline, the world's first production car with twin
ceramic turbocharger rotors. Toyota Motor Corporation also mass produces silicon nitride
ceramic rotors for turbochargers (Sheppard, 1990).
To see the reason for the switch to ceramics, we can look at some material properties that
relate to the design criteria. Table 1.1 shows a comparison of properties for silicon nitride and
a nickel alloy commonly used for turbocharger rotors. We see that the density of the ceramic is
significantly lower than the metal and the strength at temperature is comparable, so we can
expect that the rotating inertia of the ceramic rotor will be much smaller that for the metal.
This is indeed the case, with estimates of a 50-60% Ceramics 3 1/21/2004 decrease in inertia
for the ceramic rotor (Wachtman, 1989, Seppard, 1990). The result of this decrease in inertia is
a faster spin up time and increased acceleration at low speeds (Fig. 1.2.
Property
Silicon Nitride
Nickel Alloy
Specific Gravity
3.3
300
8-9
200
Weibull Modulus
10-20
>50
Young's Modulus (GPa)
304
200
Toughness, KIC(MPa√m)
4-6
60-75
Thermal Coef. of Exp.
(cm/cm per C)
3.1
13
Fracture Stress
(avg. at 1100 K)
Table 1.1 Turbocharger Rotor Materials (data from Callister)
Figure 1.2 Comparison of wide-open throttle acceleration for ceramic and metal
turbocharger rotors, 2.3 liter engine - Zephyr test vehicle. (Wachtman, 1989)
While this performance advantage is the major factor in the consideration of ceramics for the
rotors, the resistance of silicon nitride to the high temperature exhaust is also. Additionally, a
lower coefficient of expansion can mean a smaller air gap between rotor and housing and more
efficient performance.
The major disadvantages of ceramic in this application is the low fracture toughness and the
lower Weibull Modulus. A low Weibull modulus means that the strength data are more widely
scattered. Therefore, the designer is faced with a very brittle material with more poorly defined
strength.
An additional problem for the designer is thermal stress at the attachment of the low
coefficient of expansion ceramic to the high coefficient of expansion metal shaft. Finally, due to
low volume production and difficult manufacturing, the cost of ceramic parts remains relatively
high.
Overview of Advantages of Ceramics
The primary advantages of ceramics relate primarily to their temperature resistance, high
hardness, low density, and relative inertness. Temperature resistance-The higher temperature
resistance of ceramics interests designers of gas turbine engines (Mayer, et al., Gardner, 1991,
Sheppard, 1990) since efficiency and performance of gas turbines tends to increase with
increasing operating temperatures. While the same is not true for diesel engines, designers of
diesels are interested because use of ceramics may eliminate the need for a cooling system and
thereby increase efficiency and lower cost (Wachtman, 1989).
High hardness – Hardness is useful in impact resistance and wear resistance. The high wear
resistance of ceramics is important for design of automotive components such as rocker arm
pads (e.g. pressureless-sintered silicon nitride, Sialon Kubel, 1989), the design of ball and roller
bearings, and in the design of
artificial hips. Ceramic bearings (e.g. hot-pressed silicon nitride, HPSN (Anon, 1990, Wachtman,
1989)) are attractive not only for wear resistance but because of the high temperature
resistance can run longer in situations where there is a loss of lubrication. Alumina has been
shown to be a very low friction substitute for metals in hip implants and is inert in the hostile
environment of the human body. Other ceramics are described as bioactive, and interface
seamlessly with human bone (Hulbert, et al., 1987).
Ceramics have been used as cutting and shaping tools for many years. The wear and
temperature resistance are ideal for this application.
Low Density - The advantage of low density was developed with the example of the
turbocharger rotor. This property is also certainly important in high rpm gas turbines and other
rotating or reciprocating applications.
Relative inertness - The corrosion resistance of ceramics is important for the biomedical implant
applications mentioned earlier. It is also important for the high temperature applications where
high temperature oxidation may be a significant problem in competitive metals (Sheppard,
1991).
The special considerations of design with ceramics tend to center on their brittleness and the
difficulty of manufacture. Brittleness leads to large data scatter in strength, and to a marked
sensitivity to flaws. As a result, failure tends to be catastrophic rather than gradual and may
occur at stresses well below what the designer expects. This is not to imply that brittle
materials are weak or fragile. For example, cast iron is a very brittle material, yet a cast iron
engine block is very strong and durable. Likewise, structural ceramics can be both strong and
durable.
Because of the large scatter in data, a statistical approach to design is needed. Important
factors for the designer to know are the stresses in the part (particularly the volume of material
exposed to different stress levels) and the statistical distribution of strength for the material
used. These can be combined to determine the probability of failure for the part.
Because of the flaw sensitivity, some knowledge of fracture mechanics is needed and care
needs to be taken that stress concentrations are minimized in the part design. Likewise, the
manufacturing method should be such as to make the part as homogenous internally and as
smooth externally as possible.
Difficulty in manufacturing can limit the size and shape of the product and can exacerbate the
scatter in strength data. As you might expect, conventional casting, forging, cold forming, and
welding are not applicable to ceramics. Manufacturing methods are more similar to those used
in powder metals,
although extrusion and injection molding are also used. In addition, joining of ceramics to
metals presents problems because of the difference in thermal expansion between the two
materials. The lack of ductility and the mismatch in thermal expansion with metals make
thermal stress an important consideration.
Section 1 - Comparing Properties of Ceramics with Metals and Polymers
General Properties of Ceramics
Ceramics tend to be hard, stiff, brittle, electrical insulators with low coefficients of expansion.
These properties result from strong ionic and covalent atomic bonding. The following sections
describe the properties of the different types of ceramics and how they compare with metals
and polymers.
Melting Temperature
Melting temperature is very closely related to strength of atomic bonding and thus the melting
temperatures of ionic and covalently bonded ceramics tends to be higher than for metals and
polymers as shown in Table 1.2 below. Exceptions include the weakly bonded NaCl (table salt)
and strongly bonded metals like tungsten.
Table 1.2 Melting Temperatures of Selected Metals, Polymers, and Ceramics
Thermal expansion is also controlled by strength of atomic bonds since the amplitude of the
atom’s vibrations will be smaller at a given temperature if strength is high. Expansion is usually
measured by the coefficient of thermal expansion, a factor that represents how much the
material will increase in length for a given temperature increase. Linear coefficients of thermal
expansion are compared below in Table 1.3
(Because crystallographic orientation affects expansion, the data shown are for polycrystalline
materials). One can see a mismatch between metals, polymers, and ceramics. This can be
significant when a joint between a metal and ceramic must cycle through a temperature range.
Then the difference in expansion
can lead to significant thermal stresses and possible thermal fatigue.
The magnitude of the thermal coefficient of expansion is also important in cases of thermal
shock. Gas turbine components may see dramatic temperature changes on startup and shut
down. In that case materials with very low coefficients of expansion (like Pyrex) show small
thermal stresses. Note that a
ceramic with a very low coefficient can be good when used alone but may not be when mated
with a metal.
Table 1.3 Thermal Expansion Coefficients for Selected Metals, Polymers and Ceramics
(polycrystalline).
Modulus of Elasticity
The modulus of elasticity (Young's Modulus) is the ratio of stress to strain in the elastic region
and thus represents the elastic stiffness of the material. Since the source of elastic strain is
bond stretching, this too is a function of atomic bond strength.
As temperature increases and the material expands, average atom spacing increases and the
modulus of elasticity tend to decrease slightly. Modulus also varies with crystallographic
direction, but is considered to have a single value for polycrystalline materials. A comparison of
moduli at room temperature is shown
below in Table 1.4.
Table 1.4 Elastic Modulus for Selected Metals, Polymers, and Ceramics
Electrical Conductivity
Since charge is generally carried by electrons, metals, with their many "free electrons" tend to
be excellent conductors. Ceramics, due to their ionic or covalent bonding, have more tightly
held electrons and tend to be electrical insulators. There is a wide range of behavior among
ceramics however, and some transition metal oxides can approach the conductivity of metals.
The structural ceramics are poor conductors and are either semiconductors, like SiC, or
insulators like alumina and silicon nitride. Typical resistivities for the materials are shown below
in Table 1.5.
Table 1.5 Electrical Resistivities for Selected Metals, Polymers, and Ceramics
Thermal Conductivity
That ceramics can have good thermal conductivity is surprising to many people. In fact,
diamond is the best thermal conductor known (at room temperature) and materials like SiC and
BeO conduct heat better than iron (Figure 1.3, Table 1.6). Normally, we think that electrical and
thermal conductivity go hand in hand, and in metals they do. In the case of ceramics, however,
other mechanisms for conduction of heat are possible and ceramics can vary from relatively
good thermal conductors to excellent thermal insulators. Phonons or quantized vibrations of
the crystal lattice are the mechanism for efficient conduction of heat in ceramics.
Figure 1.3 Thermal Conductivity of Selected Metals and Ceramics (Richerson,1992)
Ceramics can have an advantage when electrical resistivity and thermal conductivity are
needed at the same time. One such application is in substrates for electronic circuitry where
heat dissipation is needed.
Thermal conductivity also depends upon temperature and this dependence is much stronger
for some materials than for others (as seen in fig 1.3). In addition, effective thermal
conductivity also depends upon processing because of the insulating effect of porosity.
Table 1.6 Room Temp thermal conductivities for Selected Metals, Polymers, and Ceramics
Ductility
Ductility in structural ceramics is very small at most temperatures, and thus they can be said to
be brittle materials for the purposes of design. This brittleness leads to a number of problems
including scatter in strength data and extreme flaw sensitivity. Because the ceramics can't
plastically deform to redistribute
stresses, stress concentrations and thermal gradients can cause much larger problems than
they would with metal
Table 1.7 Fracture Toughness, KIC for Selected Metals, Polymers, and Ceramics
Strength
Strength of ceramics is very dependent upon the flaw distribution in the materials. These
"flaws" can be of a microscopic nature and may not be flaws from a normal perspective. For
example, the strength of glass fibers is the highest immediately after manufacture, and simply
handling them with clean hands can cause sufficient surface damage to reduce strength by
30%. Because small flaws can have a very large effect, the strength data of ceramics tends to be
widely scattered.
The most practical way of dealing with widely scattered data is the use of statistics. In the case
of ceramic strength data, the standard statistical model is the Weibull distribution. A Weibull
parameter (Weibull slope, Shape parameter, Weibull Modulus) is often stated when describing
the strength of a ceramic. The
meaning and use of this parameter is discussed in Section 2.
Another result of flaw sensitivity is that ceramics are much stronger in compression than
tension (it is hard to open a crack in compression). Testing of ceramics is often done in bending
and the failure stress in bending is often called the Modulus of Rupture, MOR. Table 1.8 shows
the typical ranges of strengths for
a variety of ceramics. Tensile strengths are typically lower than MOR as explained in Section 2.
Table 1.8 Strength of ceramics Richerson,1992)
Because ceramics are used at high temperature, strength at temperature is also a concern.
Figure 1.4 shows the comparison of ceramics and competitor metals. Note that the oxides,
alumina and zirconia are not shown. They tend to be weaker at temperature and not
competitive with silicon nitride and silicon carbide for high temperature, high strength
applications.
Table 1.9 shows a comparison of a variety of properties of ceramics compared with metals.
Note the range of properties based on manufacturing method. Also note that properties
quoted from different sources for the same nominal material may be significantly different.
Part of this is inherent variation, part is different manufacturing, and part is different dates of
testing. In particular, Weibull modulus has changed over the past decades.
Table 1.9 Properties of Structural Ceramic Materials (ASM, 1989)
Atomic Bonding
(Metallic, Ionic, Covalent, and van der Waals Bonds)
From elementary chemistry it is known that the atomic structure of any element is made up of
a positively charged nucleus surrounded by electrons revolving
around it. An element’s atomic number indicates the number of
positively charged protons in the nucleus. The atomic weight of
an atom indicates how many protons and neutrons in the
nucleus. To determine the number of neutrons in an atom, the
atomic number is simply subtracted from the atomic weight.
Atoms like to have a balanced electrical charge. Therefore, they
usually have negatively charged electrons surrounding the
nucleus in numbers equal to the number of protons. It is also
known that electrons are present with different energies and it
is convenient to consider these electrons surrounding the
nucleus in energy “shells.” For example, magnesium, with an
atomic number of 12, has two electrons in the inner shell, eight in the second shell and two in
the outer shell.
All chemical bonds involve electrons. Atoms will stay close together if they have a shared
interest in one or more electrons. Atoms are at their most stable when they have no partiallyfilled electron shells. If an atom has only a few electrons in a shell, it will tend to lose them to
empty the shell. These elements are metals. When metal atoms bond, a metallic bond occurs.
When an atom has a nearly full electron shell, it will try to find electrons from another atom so
that it can fill its outer shell. These elements are usually described as nonmetals. The bond
between two nonmetal atoms is usually a covalent bond. Where metal and nonmetal atom
come together an ionic bond occurs. There are also other, less common, types of bond but the
details are beyond the scope of this material. On the next few pages, the Metallic, Covalent and
Ionic bonds will be covered in more detail.
Imperfections include point defects and impurities. Their formation is strongly affected by the
condition of charge neutrality (creation of unbalanced charges requires the expenditure of a
large amount of energy.
Non-stoichiometry refers to a change in composition so that the elements in the ceramic are
not in the proportion appropriate for the compound (condition known as stoichiometry). To
minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges (Fig.
13.1).
Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a vacancyinterstitial pair of cations (placing large anions in an interstitial position requires a lot of energy
in lattice distortion). A Schottky-defect is the a pair of nearby cation and anion vacancies.
Introduction of impurity atoms in the lattice is likely in conditions where the charge is
maintained. This is the case of electronegative impurities that substitute a lattice anions or
electropositive substitutional impurities. This is more likely for similar ionic radii since this
minimizes the energy required for lattice distortion. Defects will appear if the charge of the
impurities is not balanced.
Optical properties
Cermax xenon arc lamp with synthetic sapphire output window
Optically transparent materials focus on the response of a material to incoming lightwaves of a
range of wavelengths. Frequency selective optical filters can be utilized to alter or enhance the
brightness and contrast of a digital image. Guided lightwave transmission via frequency
selective waveguides involves the emerging field of fiber optics and the ability of certain glassy
compositions as a transmission medium for a range of frequencies simultaneously (multi-mode
optical fiber) with little or no interference between competing wavelengths or frequencies.
This resonant mode of energy and data transmission via electromagnetic (light) wave
propagation, though low powered, is virtually lossless. Optical waveguides are used as
components in Integrated optical circuits (e.g. light-emitting diodes, LEDs) or as the
transmission medium in local and long haul optical communication systems. Also of value to the
emerging materials scientist is the sensitivity of materials to radiation in the
thermal infrared (IR) portion of the electromagnetic spectrum. This heat-seeking ability is
responsible for such diverse optical phenomena as Night-vision and IR luminescence.
Thus, there is an increasing need in the military sector for high-strength, robust materials which
have the capability to transmit light (electromagnetic waves) in the visible (0.4 – 0.7
micrometers) and mid-infrared (1 – 5 micrometers) regions of the spectrum. These materials
are needed for applications requiring transparent armor, including next-generation highspeed missiles and pods, as well as protection against improvised explosive devices (IED).
In the 1960s, scientists at General Electric (GE) discovered that under the right manufacturing
conditions, some ceramics, especially aluminium oxide (alumina), could be made translucent.
These translucent materials were transparent enough to be used for containing the
electrical plasma generated in high-pressure sodium street lamps. During the past two decades,
additional types of transparent ceramics have been developed for applications such as nose
cones for heat-seeking missiles, windows for fighter aircraft, and scintillation counters for
computed tomography scanners.
In the early 1970s, Thomas Soules pioneered computer modeling of light transmission through
translucent ceramic alumina. His model showed that microscopic pores in ceramic, mainly
trapped at the junctions of microcrystalline grains, caused light to scatter and prevented true
transparency. The volume fraction of these microscopic pores had to be less than 1% for highquality optical transmission.
This is basically a particle size effect. Opacity results from the incoherent scattering of light at
surfaces and interfaces. In addition to pores, most of the interfaces in a typical metal or ceramic
object are in the form of grain boundaries which separate tiny regions of crystalline order.
When the size of the scattering center (or grain boundary) is reduced below the size of the
wavelength of the light being scattered, the scattering no longer occurs to any significant
extent.
In the formation of polycrystalline materials (metals and ceramics) the size of
the crystalline grains is determined largely by the size of the crystalline particles present in the
raw material during formation (or pressing) of the object. Moreover, the size of the grain
boundaries scales directly with particle size. Thus a reduction of the original particle size below
the wavelength of visible light (~ 0.5 micrometers for shortwave violet) eliminates any
light scattering, resulting in a transparent material.
Recently, Japanese scientists have developed techniques to produce ceramic parts that rival
the transparency of traditional crystals (grown from a single seed) and exceed the fracture
toughness of a single crystal. In particular, scientists at the Japanese firm Konoshima Ltd., a
producer of ceramic construction materials and industrial chemicals, have been looking for
markets for their transparent ceramics.
Livermore researchers realized that these ceramics might greatly benefit highpowered lasers used in the National Ignition Facility (NIF) Programs Directorate. In particular, a
Livermore research team began to acquire advanced transparent ceramics from Konoshima to
determine if they could meet the optical requirements needed for Livermore’s Solid-State Heat
Capacity Laser (SSHCL). Livermore researchers have also been testing applications of these
materials for applications such as advanced drivers for laser-driven fusion power plants.
[Examples of ceramics materials
Porcelain high-voltage insulator
Silicon carbide is used for inner plates of ballistic vests
Ceramic BN crucible
Until the 1950s, the most important ceramic materials were
1)pottery, bricks and tiles,
(2) cements and
(3) glass.
A composite material of ceramic and metal is known as cermet.
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Barium titanate (often mixed with strontium titanate) displays ferroelectricity, meaning
that its mechanical, electrical, and thermal responses are coupled to one another and also
history-dependent. It is widely used in electromechanical transducers, ceramic capacitors,
and data storage elements. Grain boundary conditions can create PTC effects in heating
elements.
Bismuth strontium calcium copper oxide, a high-temperature superconductor
Boron nitride is structurally isoelectronic to carbon and takes on similar physical forms:
a graphite-like one used as a lubricant, and a diamond-like one used as an abrasive.
Earthenware used for domestic ware such as plates and mugs.
Ferrite is used in the magnetic cores of electrical transformers and magnetic core
memory.
Lead zirconate titanate (PZT) was developed at the United States National Bureau of
Standards in 1954. PZT is used as an ultrasonic transducer, as its piezoelectric properties
greatly exceed those of Rochelle salt.
Magnesium diboride (MgB2) is an unconventional superconductor.
Porcelain is used for a wide range of household and industrial products.
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Sialon (Silicon Aluminium Oxynitride) has high strength; high thermal, shock, chemical
and wear resistance, and low density. These ceramics are used in non-ferrous molten metal
handling, weld pins and the chemical industry.
Silicon carbide (SiC) is used as a susceptor in microwave furnaces, a commonly used
abrasive, and as a refractory material.
Silicon nitride (Si3N4) is used as an abrasive powder.
Steatite (magnesium silicates) is used as an electrical insulator.
Titanium carbide Used in space shuttle re-entry shields and scratchproof watches.
Uranium oxide (UO2), used as fuel in nuclear reactors.
Yttrium barium copper oxide (YBa2Cu3O7-x), another high temperature superconductor.
Zinc oxide (ZnO), which is a semiconductor, and used in the construction of varistors.
Zirconium dioxide (zirconia), which in pure form undergoes many phase
changes between room temperature and practical sintering temperatures, can be
chemically "stabilized" in several different forms. Its high oxygen ion
conductivity recommends it for use in fuel cells and automotive oxygen sensors. In another
variant, metastable structures can impart transformation toughening for mechanical
applications; most ceramic knife blades are made of this material.
Partially stabilised zirconia (PSZ) is much less brittle than other ceramics and is used for
metal forming tools, valves and liners, abrasive slurries, kitchen knives and bearings subject
to severe abrasion.
Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion
of magnetic fields occurring in certain materials when cooled below a characteristic critical
temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like
ferromagnetism and atomic spectral lines, superconductivity is a quantum
mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection
of magnetic field lines from the interior of the superconductor as it transitions into the
superconducting state. The occurrence of the Meissner effect indicates that superconductivity
cannot be understood simply as the idealization of perfect conductivity in classical physics.
[A magnet levitating above a hightemperature superconductor, cooled
withliquid nitrogen. Persistent
electric current flows on the surface
of the superconductor, acting to
exclude the magnetic field of the
magnet (Faraday's law of induction).
This
current effectively
forms an is lowered.
.
The electrical resistivity of a metallic conductor decreases
gradually
as temperature
electromagnet that repels the
In ordinary conductors, such as copper or silver, this decrease
is limited by impurities and other
magnet.
defects. Even near absolute zero, a real sample of a normal conductor shows some resistance.
In a superconductor, the resistance drops abruptly to zero when the material is cooled below
its critical temperature. An electric current flowing in a loop of superconducting wire can persist
indefinitely with no power source.
In 1986, it was discovered that some cuprate-perovskite ceramic materials have a critical
temperature above 90 K (−183 °C).] Such a high transition temperature is theoretically
impossible for a conventional superconductor, leading the materials to be termed hightemperature superconductors. Liquid nitrogen boils at 77 K, facilitating many experiments and
applications that are less practical at lower temperatures. In conventional superconductors,
electrons are held together in pairs by an attraction mediated by lattice phonons. The best
available model of high-temperature superconductivity is still somewhat crude. There is a
hypothesis that electron pairing in high-temperature superconductors is mediated by shortrange spin waves known as paramagnons.
http://www.youtube.com/watch?v=pPBsxylW2Z0
Most of the physical properties of superconductors vary from material to material, such as
the heat capacity and the critical temperature, critical field, and critical current density at which
superconductivity is destroyed.
On the other hand, there is a class of properties that are independent of the underlying
material. For instance, all superconductors have exactly zero resistivity to low applied currents
when there is no magnetic field present or if the applied field does not exceed a critical value.
The existence of these "universal" properties implies that superconductivity is
a thermodynamic phase, and thus possesses certain distinguishing properties which are largely
independent of microscopic details.
Zero electrical DC resistance
Electric cables for accelerators at CERN.
Both the massive and slim cables are rated for 12,500 A. Top: conventional cables for
LEP; bottom: superconductor-based cables for the LHC
The simplest method to measure the electrical resistance of a sample of some material is to
place it in an electrical circuit in series with a current source I and measure the
resulting voltage V across the sample. The resistance of the sample is given by Ohm's
law as R = V/I. If the voltage is zero, this means that the resistance is zero.
Superconductors are also able to maintain a current with no applied voltage whatsoever, a
property exploited in superconducting electromagnets such as those found in MRI machines.
Experiments have demonstrated that currents in superconducting coils can persist for years
without any measurable degradation. Experimental evidence points to a current lifetime of at
least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed
the estimated lifetime of the universe, depending on the wire geometry and the temperature.
In a normal conductor, an electric current may be visualized as a fluid of electrons moving
across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice,
and during each collision some of the energy carried by the current is absorbed by the lattice
and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions. As
a result, the energy carried by the current is constantly being dissipated. This is the
phenomenon of electrical resistance.
The situation is different in a superconductor. In a conventional superconductor, the electronic
fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons
known as Cooper pairs. This pairing is caused by an attractive force between electrons from the
exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair
fluid possesses anenergy gap, meaning there is a minimum amount of energy ΔE that must be
supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the
lattice, given by kT, where k is Boltzmann's constant and T is the temperature, the fluid will not
be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow
without energy dissipation.
In a class of superconductors known as type II superconductors, including all known hightemperature superconductors, an extremely small amount of resistivity appears at
temperatures not too far below the nominal superconducting transition when an electric
current is applied in conjunction with a strong magnetic field, which may be caused by the
electric current. This is due to the motion of vortices in the electronic superfluid, which
dissipates some of the energy carried by the current. If the current is sufficiently small, the
vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny
compared with that of non-superconducting materials, but must be taken into account in
sensitive experiments. However, as the temperature decreases far enough below the nominal
superconducting transition, these vortices can become frozen into a disordered but stationary
phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance
of the material becomes truly zero.
Week 10: Ceramics: Structure and
Properties
GLASS
PDF Article Glass Article:
Glass is an amorphous (non-crystalline) solid material. Glasses are typically brittle and
optically transparent.
The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime
glass, composed of about 75% silica (SiO2) plus Na2O, CaO, and several minor additives. Often,
the term glass is used in a restricted sense to refer to this specific use.
In science, however, the term glass is usually defined in a much wider sense, including every
solid that possesses a non-crystalline (i.e., amorphous) structure and that exhibits a glass
transition when heated towards the liquid state. In this wider sense, glasses can be made of
quite different classes of materials: metallic alloys, ionic melts, aqueous solutions, molecular
liquids, and polymers. For many applications (bottles, eyewear) polymer glasses (acrylic
glass, polycarbonate, polyethylene terephthalate) are a lighter alternative to traditional silica
glasses.
Glass, as a substance, plays an essential role in science and industry. Its chemical, physical, and
in particular optical properties make it suitable for applications such as flat glass, container
glass, optics and optoelectronics material, laboratory equipment, thermal insulator (glass
wool), reinforcement materials (glass-reinforced plastic, glass fiber reinforced concrete),
and glass art (art glass, studio glass).
Silica (the chemical compound SiO2) is a common fundamental constituent of glass. In nature,
vitrification of quartz occurs when lightning strikes sand, forming hollow, branching rootlike
structures called fulgurite.
History
The history of creating glass can be traced back to 3500 BCE in Mesopotamia.[1] The term glass
developed in the late Roman Empire. It was in the Roman glassmaking center at Trier, now in
modern Germany, that the late-Latin term glesum originated, probably from a Germanic word
for a transparent, lustrous substance.
Glass ingredients
Quartz sand (silica) is the main raw material in commercial glass production
While fused quartz (primarily composed of SiO2) is used for some special applications, it is not
very common due to its high glass transition temperature of over 1200 °C (2192 °F). Normally,
other substances are added to simplify processing. One is sodium carbonate (Na2CO3), which
lowers the glass transition temperature. However, the soda makes the glass water soluble,
which is usually undesirable, so lime (calcium oxide [CaO], generally obtained from limestone),
some magnesium oxide (MgO) and aluminium oxide (Al2O3) are added to provide for a better
chemical durability. The resulting glass contains about 70 to 74% silica by weight and is called
a soda-lime glass. Soda-lime glasses account for about 90% of manufactured glass.
Most common glass has other ingredients added to change its properties. Lead glass or flint
glass is more 'brilliant' because the increased refractive index causes noticeably more specular
reflection and increased optical dispersion. Adding barium also increases the refractive
index. Thorium oxide gives glass a high refractive index and low dispersion and was formerly
used in producing high-quality lenses, but due to its radioactivity has been replaced
by lanthanum oxide in modern eye glasses. Iron can be incorporated into glass to
absorb infrared energy, for example in heat absorbing filters for movie projectors, while
cerium(IV) oxide can be used for glass that absorbs UV wavelengths.
1. Fused silica glass, vitreous silica glass: = silica (SiO2) 99% + water 1%. Has very low
thermal expansion, is very hard and resists high temperatures (1000-1500 º C). It is also
the most resistant against weathering (alkali ions leaching out of the glass, while
staining it). It is used for high temperature applications such as furnace tubes, melting
crucibles, etc.
2. Soda-lime-silica glass, window glass: Silica 72% + sodium oxide (Na2O) 14.2% + magnesia
(MgO) 2.5% + lime (CaO) 10.0% + alumina (Al2O3) 0.6%. Is transparent, easily formed
and most suitable for window glass. It has a high thermal expansion and can't stand
heat well (500-600ºC). Used for windows, containers, light bulbs, tableware.
3. Sodium borosilicate glass, Pyrex: = silica 81% + boric oxide (B2O3) 12% + soda (Na2O)
4.5% + alumina (Al2O3) 2.0%. Stands heat expansion three times better than window
glass. Used for chemical glassware, cooking glass, car head lamps, etc. Borosilicate
glasses (e.g.Pyrex) have as main constituents silica and boron oxide. They have fairly
low coefficients of thermal expansion (7740 Pyrex CTE is 3.25×10–6/°C[6] as compared to
about 9×10−6/°C for a typical soda-lime glass[7]), making them more dimensionally
stable. The lower CTE also makes them less subject to stress caused by thermal
expansion, thus less vulnerable to cracking from thermal shock. They are commonly
used for reagent bottles, optical components and household cookware.
4. Lead-oxide glass, crystal glass: = silica 59%+ soda (Na2O) 2.0% + lead oxide (PbO) 25% +
potassium oxide (K2O) 12% + alumina 0.4% + zinc oxide (ZnO) 1.5%. Has a high
refractive index, making the look of glassware more brilliant (crystal glass). It also has a
high elasticity, making glassware 'ring'. It is also more workable in the factory, but
cannot stand heating very well.
5. Alumino-silicate glass: = silica 57% + alumina 16% + boric oxide (B2O3) 4.0% + barium
oxide (BaO) 6.0% + magnesia 7.0% + lime 10%. Extensively used for fibreglass, used for
making glass-reinforced plastics (boats, fishing rods, etc.). Also for halogen bulb glass.
6. Oxide glass: = alumina 90% + germanium oxide (GeO2) 10%. Extremely clear glass, used
for fibre-optic wave guides in communication networks. Light loses only 5% of its
intensity through 1km of glass fibre.[8]
Another common glass ingredient is "cullet" (recycled glass). The recycled glass saves on raw
materials and energy; however, impurities in the cullet can lead to product and equipment
failure.
Fining agents such as sodium sulfate, sodium chloride, or antimony oxide may be added to
reduce the number of air bubbles in the glass mixture. Glass batch calculation is the method by
which the correct raw material mixture is determined to achieve the desired glass composition.
Candy Lab
Procedure
Thoughts on Glass Lab……………
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Look at clarity of mixture to the changing temperature
Look at the various amount of water
Liquidous
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Measuring out the concentration of sugar, corn starch and water, accuracy is
not essential. However keep station clean.
As it Boils the liquid clears ~ 310 F or 154 C
Using silicon or carbonate in glass is analogous the sugar in candy
Make sampling container
 Pour sample at various temperature to determine the formation of glass
and/or crystallization
 As the temperature is increasing what is happening to the clarity and to the
“glass” creation
 Recall we desire to have glass at room temperature
 We could look at the crystallization rate and observe the composition
 As the temperature increases and the water vaporizes, we can pull fibers…..Is
the temperature above or below Tg? Must be below because above would
imply the existence of glass.
 As you apply heat, if the solution changes color, such as yellow, the “carbon” is
causing this discoloring.
 In making glass Aluminum oxide is added to prevent the burning. In the candy
lab we use corn syrup
 If time permits do one sample with corn starch and one without corn syrup.
Another option is have different groups use different recipes one with and
one without corn syrup.
Refraction Process
d
n1 sin c = n2 sin 90°
sin c = n2 /n1 (n2 air = 1)
sin c = 1/n1 = 1/n
sin c = (r/2)/(hypotenuse)
Hypotenuse =√(r/2)2 + h2
sin c = (r/2)/( =√(r/2)2 + h2)
r = d/2
sin c = ([d/2]/2)/( √( [d/2]/2)2 + h2)
sin c = (d/4)/( √( d/4)2 + h2)
1/n = d / 4[√ (d2 + 16 h2)]
16
1/n = d/ √(d2 + 16h2)
n = [√(d2 + 16h2)]/d
A PHYSICAL MODEL TO HELP STUDENTS
UNDERSTAND THE MELTING RANGE OF
GLASSES
L. Roy Bunnell
Southridge High School
Kennewick, WA 99338
Key Words: Glass, molecular models, amorphous, glass structure, viscosity
Prerequisite Knowledge: Little/none; this demonstration is designed for use with high school
students as they begin their study of ceramic materials, including glasses.
Objective: After seeing this demonstration, the student should have a good concept of why
glasses melt continuously, instead of having a well-defined melting point as do crystalline
materials. Additionally, the student should understand how amorphous materials differ from
crystalline ones.
Equipment and Supplies: 1-1/2 inch Styrofoam balls, available at craft stores, and
common round wooden toothpicks.
Background: When introducing students to main concepts about glass, there are several points
of difference as glass is compared to crystalline materials. There are:
1. Glass has an amorphous, disorganized network structure.
2. The primary unit of glass structure is the SiO4 tetrahedron, in which each Si atom is
surrounded by four oxygen atoms in a tetrahedral configuration.
3. Most oxygen atoms are shared between neighboring tetrahedra, so that the overall
chemical formula of fused silica is SiO2.
4. Because of the amorphous structure, the structural units are bonded with various
amounts of energy; as a result of this, glass has no definite melting point. Instead, its viscosity,
or resistance to flow, changes continuously as temperature increases.
This behavior is the reason that glass can be formed over a relatively long
temperature range. Textbooks typically use drawings such as shown in Figure 1, from Reference
1, to communicate these ideas, but many students do not understand the concepts when
communicated in this two-dimensional way. The student-involving demonstration below is an
effective way to communicate all of these ideas to students in an introductory Materials
Science course for high school students.
Procedure: Each student is given three Styrofoam balls and three standard round
wooden toothpicks. I start by showing students the primary structural unit of glass, the SiO4
tetrahedron, made from four Styrofoam balls representing oxygen ions, attached to each other
using toothpicks. The space between the spheres in the center of the tetrahedron is large
enough to accommodate a silicon ion. One of these tetrahedral is shown in Figure 2. Each
student uses his three Styrofoam balls and two toothpicks to make an equilateral triangle, as
shown in Figure 3. In the amorphous glass structure tetrahedral share corner oxygen ions, so I
give the tetrahedron to students to pass around and attach their triangles to. Each student
attaches his triangle to one of the balls of the tetrahedron, using his remaining toothpick.
Figure 4 shows the first triangle added to the tetrahedron. The attachment continues, and I
remind students that there is no wrong way
to attach the triangles, as long as the protruding ball from a tetrahedron is placed into the
center of their equilateral triangle, forming another tetrahedron. Figure 5 shows two triangles
attached to the original tetrahedron, Figure 6 shows three, and Figure 7 shows four randomlyattached triangles. Note that by the Figure 7 stage, the structure shows a lot of randomness
and some tetrahedra are attached at one point, some at two points, and so on. Also, the
unoccupied spaces between tetrahedra are of variable size. These ideas are pointed out as the
structure is built, because they are analogous to glass structure.
The construction process continues until each student has joined his triangle to the network,
and I collect the rather large model, which by now is composed of about 75 Styrofoam balls.
After pointing out various features of the model, it is time to simulate melting, at
room temperature. Since melting of a solid occurs when enough heat energy is added so that
the interatomic bonding force is overcome by lattice vibrations, a crystalline material will have
a single, well-defined melting point because its atoms are all bonded with the same amount of
energy. When an amorphous material is heated, its weakest-bonded structural units are freed
first. As more heat is added, stronger and stronger-bonded units are shaken loose into smaller
pieces until finally each structural unit is independent of the others. To “melt” the glass model
structure built by the students, I simply begin shaking it, very gently at first and then gradually
increasing the force level. Weaker-bonded pieces of the glass model begin to detach, and
students can see that detachment of these
units is breaking the network into successively smaller pieces, making the glass flow better and
thus be easier to form. I continue to shake pieces of the network until individual tetrahedral
units are becoming detached; at this point the glass would be completely melted and it would
flow relatively easily. I have used this model approach to understanding glass structure and
melting behavior now for several years with high school students, and it appears to work well.
References:
1. Jacobs, James A., and Thomas Kilduff, Engineering Materials Technology: Structures,
Processing, Properties, and Selection, Fourth Edition, Prentice-Hall, 2001.
Week 11: Ceramics: Applications
Fiber Optics
An optical fiber (or optical fibre) is a flexible, transparent fiber made of a pure glass (silica) not
much thicker than a human hair. It functions as a waveguide, or “light pipe”, to transmit light
between the two ends of the fiber. The field of applied science and engineering concerned with
the design and application of optical fibers is known as fiber optics. Optical fibers are widely
used in fiber-optic communications, which permits transmission over longer distances and at
higher bandwidths (data rates) than other forms of communication. Fibers are used instead
of metal wires because signals travel along them with less loss and are also immune
to electromagnetic interference. Fibers are also used for illumination, and are wrapped
in bundles so that they may be used to carry images, thus allowing viewing in confined spaces.
Specially-designed fibers are used for a variety of other applications, including sensors and fiber
lasers.
An optical fiber junction box.
The yellow cables are single mode fibers; the orange and blue cables are multi-mode fibers:
50/125 µm OM2 and 50/125 µm OM3 fibers respectively.
Optical fibers typically include a transparent core surrounded by a
transparent cladding material with a lower index of refraction. Light is kept in the core by total
internal reflection. This causes the fiber to act as a waveguide. Fibers that support many
propagation paths or transverse modes are called multi-mode fibers (MMF), while those that
only support a single mode are called single-mode fibers (SMF). Multi-mode fibers generally
have a wider core diameter, and are used for short-distance communication links and for
applications where high power must be transmitted. Single-mode fibers are used for most
communication links longer than 1,050 meters (3,440 ft).
Joining lengths of optical fiber is more complex than joining electrical wire or cable. The ends of
the fibers must be carefully cleaved, and thenspliced together, either mechanically or
by fusing them with heat. Special optical fiber connectors for removable connections are also
available.
History
Fiber optics, though used extensively in the modern world, is a fairly simple, and relatively old,
technology. Guiding of light by refraction, the principle that makes fiber optics possible, was
first demonstrated by Daniel Colladon and Jacques Babinet in Paris in the early 1840s. John
Tyndall included a demonstration of it in his public lectures in London, 12 years later. Tyndall
also wrote about the property of total internal reflection in an introductory book about the
nature of light in 1870: "When the light passes from air into water, the refracted ray is
bent toward the perpendicular... When the ray passes from water to air it is bent from the
perpendicular... If the angle which the ray in water encloses with the perpendicular to the
surface be greater than 48 degrees, the ray will not quit the water at all: it will be totally
reflected at the surface.... The angle which marks the limit where total reflection begins is called
the limiting angle of the medium. For water this angle is 48°27', for flint glass it is 38°41', while
for diamond it is 23°42'." Unpigmented human hairs have also been shown to act as an optical
fiber.
Practical applications, such as close internal illumination during dentistry, appeared early in the
twentieth century. Image transmission through tubes was demonstrated independently by the
radio experimenter Clarence Hansell and the television pioneer John Logie Baird in the 1920s.
The principle was first used for internal medical examinations by Heinrich Lamm in the
following decade. Modern optical fibers, where the glass fiber is coated with a transparent
cladding to offer a more suitable refractive index, appeared later in the decade.[3] Development
then focused on fiber bundles for image transmission. Harold Hopkins and Narinder Singh
Kapany at Imperial College in London achieved low-loss light transmission through a 75 cm long
bundle which combined several thousand fibers. Their article titled "A flexible fibrescope, using
static scanning" was published in the journal Nature in 1954. The first fiber optic semiflexible gastroscope was patented by Basil Hirschowitz, C. Wilbur Peters, and Lawrence E.
Curtiss, researchers at the University of Michigan, in 1956. In the process of developing the
gastroscope, Curtiss produced the first glass-clad fibers; previous optical fibers had relied on air
or impractical oils and waxes as the low-index cladding material.
A variety of other image transmission applications soon followed.
In 1880 Alexander Graham Bell and Sumner Tainter invented the 'Photophone' at the Volta
Laboratory in Washington, D.C., to transmit voice signals over an optical beam. It was an
advanced form of telecommunications, but subject to atmospheric interferences and
impractical until the secure transport of light that would be offered by fiber-optical systems. In
the late 19th and early 20th centuries, light was guided through bent glass rods to illuminate
body cavities. Jun-ichi Nishizawa, a Japanese scientist at Tohoku University, also proposed the
use of optical fibers for communications in 1963, as stated in his book published in 2004
in India. Nishizawa invented other technologies that contributed to the development of optical
fiber communications, such as the graded-index optical fiber as a channel for transmitting light
from semiconductor lasers. The first working fiber-optical data transmission system was
demonstrated by German physicist Manfred Börner at Telefunken Research Labs in Ulm in
1965, which was followed by the first patent application for this technology in 1966 . Charles K.
Kao and George A. Hockham of the British company Standard Telephones and Cables (STC)
were the first to promote the idea that the attenuation in optical fibers could be reduced below
20 decibels per kilometer (dB/km), making fibers a practical communication medium. They
proposed that the attenuation in fibers available at the time was caused by impurities that
could be removed, rather than by fundamental physical effects such as scattering. They
correctly and systematically theorized the light-loss properties for optical fiber, and pointed out
the right material to use for such fibers — silica glass with high purity. This discovery earned
Kao the Nobel Prize in Physics in 2009.
NASA used fiber optics in the television cameras sent to the moon. At the time, the use in the
cameras was classified confidential, and only those with the right security clearance or those
accompanied by someone with the right security clearance were permitted to handle the
cameras.
The crucial attenuation limit of 20 dB/km was first achieved in 1970, by researchers Robert D.
Maurer, Donald Keck, Peter C. Schultz, and Frank Zimar working for American glass maker
Corning Glass Works, now Corning Incorporated. They demonstrated a fiber with 17 dB/km
attenuation by doping silica glass with titanium. A few years later they produced a fiber with
only 4 dB/km attenuation using germanium dioxide as the core dopant. Such low attenuation
ushered in optical fiber telecommunication. In 1981, General Electric produced fused quartz
ingots that could be drawn into fiber optic strands 25 miles (40 km) long.
Attenuation in modern optical cables is far less than in electrical copper cables, leading to longhaul fiber connections with repeater distances of 70–150 kilometers (43–93 mi). The erbiumdoped fiber amplifier, which reduced the cost of long-distance fiber systems by reducing or
eliminating optical-electrical-optical repeaters, was co-developed by teams led by David N.
Payne of the University of Southampton and Emmanuel Desurvire at Bell Labs in 1986. Robust
modern optical fiber uses glass for both core and sheath, and is therefore less prone to aging. It
was invented by Gerhard Bernsee of Schott Glass in Germany in 1973.
The emerging field of photonic crystals led to the development in 1991 of photonic-crystal
fiber, which guides light by diffraction from a periodic structure, rather than by total internal
reflection. The first photonic crystal fibers became commercially available in 2000. Photonic
crystal fibers can carry higher power than conventional fibers and their wavelength-dependent
properties can be manipulated to improve performance.
Application
Optical fiber can be used as a medium for telecommunication and computer
networking because it is flexible and can be bundled as cables. It is especially advantageous for
long-distance communications, because light propagates through the fiber with little
attenuation compared to electrical cables. This allows long distances to be spanned with
few repeaters. Additionally, the per-channel light signals propagating in the fiber have been
modulated at rates as high as 111 gigabits per second by NTT, although 10 or 40 Gbit/s is typical
in deployed systems. Each fiber can carry many independent channels, each using a different
wavelength of light (wavelength-division multiplexing (WDM)). The net data rate (data rate
without overhead bytes) per fiber is the per-channel data rate reduced by the FEC overhead,
multiplied by the number of channels (usually up to eighty in commercial dense WDM systems
as of 2008). The current laboratory fiber optic data rate record, held by Bell Labs in Villarceaux,
France, is multiplexing 155 channels, each carrying 100 Gbit/s over a 7000 km fiber. Nippon
Telegraph and Telephone Corporation has also managed 69.1 Tbit/s over a single 240 km fiber
(multiplexing 432 channels, equating to 171 Gbit/s per channel). Bell Labs also broke a 100
Petabit per second kilometer barrier (15.5 Tbit/s over a single 7000 km fiber).
For short distance applications, such as a network in an office building, fiber-optic cabling can
save space in cable ducts. This is because a single fiber can carry much more data than electrical
cables such as standard category 5 Ethernet cabling, which typically runs at 1 Gbit/s. Fiber is
also immune to electrical interference; there is no cross-talk between signals in different cables,
and no pickup of environmental noise. Non-armored fiber cables do not conduct electricity,
which makes fiber a good solution for protecting communications equipment in high
voltage environments, such as power generation facilities, or metal communication structures
prone to lightning strikes. They can also be used in environments where explosive fumes are
present, without danger of ignition. Wiretapping (in this case, fiber tapping) is more difficult
compared to electrical connections, and there are concentric dual core fibers that are said to be
tap-proof.
Fibers have many uses in remote sensing. In some applications, the sensor is itself an optical
fiber. In other cases, fiber is used to connect a non-fiberoptic sensor to a measurement system.
Depending on the application, fiber may be used because of its small size, or the fact that
no electrical power is needed at the remote location, or because many sensors can
be multiplexed along the length of a fiber by using different wavelengths of light for each
sensor, or by sensing the time delay as light passes along the fiber through each sensor. Time
delay can be determined using a device such as an optical time-domain reflectometer.
Optical fibers can be used as sensors to easure strain, temperature, pressure and other
quantities by modifying a fiber so that the property to measure modulates the intensity, phase,
polarization, wavelength, or transit time of light in the fiber. Sensors that vary the intensity of
light are the simplest, since only a simple source and detector are required. A particularly useful
feature of such fiber optic sensors is that they can, if required, provide distributed sensing over
distances of up to one meter.
Extrinsic fiber optic sensors use an optical fiber cable, normally a multi-mode one, to
transmit modulated light from either a non-fiber optical sensor—or an electronic sensor
connected to an optical transmitter. A major benefit of extrinsic sensors is their ability to reach
otherwise inaccessible places. An example is the measurement of temperature
inside aircraft jet engines by using a fiber to transmit radiation into a
radiation pyrometer outside the engine. Extrinsic sensors can be used in the same way to
measure the internal temperature of electrical transformers, where the
extreme electromagnetic fields present make other measurement techniques impossible.
Extrinsic sensors measure vibration, rotation, displacement, velocity, acceleration, torque, and
twisting. A solid state version of the gyroscope, using the interference of light, has been
developed. The fiber optic gyroscope (FOG) has no moving parts, and exploits the Sagnac
effect to detect mechanical rotation.
Common uses for fiber optic sensors includes advanced intrusion detection security systems.
The light is transmitted along a fiber optic sensor cable placed on a fence, pipeline, or
communication cabling, and the returned signal is monitored and analyzed for disturbances.
This return signal is digitally processed to detect disturbances and trip an alarm if an intrusion
has occurred.
A frisbee illuminated by fiber optics
Light reflected from optical fiber illuminates exhibited model
Fibers are widely used in illumination applications. They are used as light guides in medical and
other applications where bright light needs to be shone on a target without a clear line-of-sight
path. In some buildings, optical fibers route sunlight from the roof to other parts of the building
(see non imaging optics). Optical fiber illumination is also used for decorative applications,
including signs, art, toys and artificial Christmas trees. Swarovski boutiques use optical fibers to
illuminate their crystal showcases from many different angles while only employing one light
source. Optical fiber is an intrinsic part of the light-transmitting concrete building
product, LiTraCon.
Optical fiber is also used in imaging optics. A coherent bundle of fibers is used, sometimes along
with lenses, for a long, thin imaging device called an endoscope, which is used to view objects
through a small hole. Medical endoscopes are used for minimally invasive exploratory or
surgical procedures. Industrial endoscopes (see fiberscope or borescope) are used for
inspecting anything hard to reach, such as jet engine interiors. Many microscopes use fiberoptic light sources to provide intense illumination of samples being studied.
In spectroscopy, optical fiber bundles transmit light from a spectrometer to a substance that
cannot be placed inside the spectrometer itself, in order to analyze its composition. A
spectrometer analyzes substances by bouncing light off of and through them. By using fibers, a
spectrometer can be used to study objects remotely.
An optical fiber doped with certain rare earth elements such as erbium can be used as the gain
medium of a laser or optical amplifier. Rare-earth doped optical fibers can be used to provide
signal amplification by splicing a short section of doped fiber into a regular (undoped) optical
fiber line. The doped fiber is optically pumped with a second laser wavelength that is coupled
into the line in addition to the signal wave. Both wavelengths of light are transmitted through
the doped fiber, which transfers energy from the second pump wavelength to the signal wave.
The process that causes the amplification is stimulated emission.
Optical fibers doped with a wavelength shifter collect scintillation light in physics experiments.
Optical fiber can be used to supply a low level of power (around one watt to electronics
situated in a difficult electrical environment. Examples of this are electronics in high-powered
antenna elements and measurement devices used in high voltage transmission equipment.
The iron sights for handguns, rifles, and shotguns may use short pieces of optical fiber for
contrast enhancement.
Biomedical applications of Ceramics
Bones are rigid organs that serve various functions in the human body (or generally
in vertebrates), including mechanical support, protection of soft organs, blood production
(from bone marrow), etc. Bone is a very complex tissue: strong, elastic, and self-repairing.
Damaged bone can be replaced with bone from other parts of the body (autografts), from
cadavers (allograft), or with various ceramics or metallic alloys. The use of autografts limits how
much bone is available, while the other options can result in rejection by the human body.
There has been much research towards creating artificial bone. Richard J. Lagow, at
the University of Texas at Austin, developed a way of creating a strong bone-like porous
structure from bone powder, which, when introduced in the body, can allow the growth of
blood vessels, and which can be gradually replaced by natural bone. Research at the Lawrence
Berkeley National Laboratory has resulted in a metal-ceramic composite that has, like bone, a
fine microstructure, and which may help create artificial bone. A team of British scientists have
developed "injectable bone", a soft substance which hardens in the body. They won the
Medical Futures Innovation Award for their discovery, and it is planned to test this material in
clinical trials.
Researchers at Columbia University have grown an anatomically correct human
jawbone from stem cells, though it was solid bone without the normal accessory tissues such
as bone marrow, cartilage, or a connectable blood supply. Other researchers, at
the Istec bioceramics laboratory in Italy, have produced a nearly identical substitute for human
bone out of rattan wood. The substitute bone has a porous structure permitting blood vessels
and other accessory tissues to penetrate it, allowing seamless integration into the host bone.
The process has been tested on sheep, who showed no signs of rejection after several months.
Biodegradation or biotic degradation or biotic decomposition is the chemical dissolution of
materials by bacteria or other biological means. The term is often used in relation to ecology,
waste management, biomedicine, and the natural environment (bioremediation) and is now
commonly associated with environmentally friendly products that are capable of decomposing
back into natural elements. Organic material can be degraded aerobically with oxygen,
or anaerobically, without oxygen. A term related to biodegradation is biomineralisation, in
which organic matter is converted into minerals. Biosurfactant, an extracellular surfactant
secreted by microorganisms, enhances the biodegradation process.
Biodegradable matter is generally organic material such as plant and animal matter and other
substances originating from living organisms, or artificial materials that are similar enough to
plant and animal matter to be put to use by microorganisms. Some microorganisms have a
naturally occurring, microbial catabolic diversity to degrade, transform or accumulate a huge
range of compounds including hydrocarbons (e.g. oil), polychlorinated
biphenyls (PCBs), polyaromatic hydrocarbons (PAHs), pharmaceutical substances,
radionuclides and metals. Major methodological breakthroughs in microbial
biodegradation have enabled detailed genomic, metagenomic, proteomic, bioinformatic and
other high-throughput analyses of environmentally relevant microorganisms providing
unprecedented insights into key biodegradative pathways and the ability of microorganisms to
adapt to changing environmental conditions. Products that contain biodegradable matter and
non-biodegradable matter are often marketed as biodegradable.
Week 12: Polymers
Introduction to Polymers
Polymers are molecules which consist of a long, repeating chain of smaller units called
monomers. Polymers have the highest molecular weight among any molecules, and may consist
of billions of atoms. Human DNA is a polymer with over 20 billion constituent atoms. Proteins,
or the polymers of amino acids, and many other molecules that make up life are polymers.
Polymers are the largest and most diverse class of known molecules. They even include plastics.
Monomers are molecules typically about 4-10 atoms in size, reactive in that they bond readily
to other monomers in a process called polymerization. Polymers and their polymerization
processes are so diverse that a variety of different systems exist to classify them. One major
type of polymerization is condensation polymerization, where reacting molecules release water
as a byproduct. This is the means by which all proteins are formed.
Polymers are not always straight chains of regular repeating monomers; sometimes they
consist of chains of varying length, or even chains that branch in multiple directions. Residual
monomers are often found together with the polymers they create, giving the polymers
additional properties. To coax monomers to link together in certain configurations requires a
variety of catalysts--secondary molecules which speed up reaction times. Catalysts are the basis
of most synthetic polymer production.
The repeating structural unit of most simple polymers not only reflects the monomer(s) from
which the polymers are constructed, but also provides a concise means for drawing structures
to represent these macromolecules. For polyethylene, arguably the simplest polymer, this is
demonstrated by the following equation. Here ethylene (ethene) is the monomer, and the
corresponding linear polymer is called high-density polyethylene (HDPE). HDPE is composed of
macromolecules in which n ranges from 10,000 to 100,000 (molecular weight 2*105 to 3 *106 ).
If Y and Z represent moles of monomer and polymer respectively, Z is approximately 10-5 Y. This
polymer is called polyethylene rather than polymethylene, (-CH2-)n, because ethylene is a stable
compound (methylene is not), and it also serves as the synthetic precursor of the polymer. The
two open bonds remaining at the ends of the long chain of carbons (colored magenta) are
normally not specified, because the atoms or groups found there depend on the chemical
process used for polymerization. The synthetic methods used to prepare this and other
polymers will be described later in this chapter.
Unlike simpler pure compounds, most polymers are not composed of identical molecules. The
HDPE molecules, for example, are all long carbon chains, but the lengths may vary by thousands
of monomer units. Because of this, polymer molecular weights are usually given as averages.
Two experimentally determined values are common: Mn , the number average molecular
weight, is calculated from the mole fraction distribution of different sized molecules in a
sample, and Mw , the weight average molecular weight, is calculated from the weight fraction
distribution of different sized molecules. These are defined below. Since larger molecules in a
sample weigh more than smaller molecules, the weight average Mw is necessarily skewed to
higher values, and is always greater than Mn. As the weight dispersion of molecules in a sample
narrows, Mw approaches Mn, and in the unlikely case that all the polymer molecules have
identical weights (a pure mono-disperse sample), the ratio Mw / Mn becomes unity.
A comparison of the properties of polyethylene (both LDPE & HDPE) with the natural polymers
rubber and cellulose is instructive. As noted above, synthetic HDPE macromolecules have
masses ranging from 105 to 106 amu (LDPE molecules are more than a hundred times smaller).
Rubber and cellulose molecules have similar mass ranges, but fewer monomer units because of
the monomer's larger size. The physical properties of these three polymeric substances differ
from each other, and of course from their monomers.
• HDPE is a rigid translucent solid which softens on heating above 100º C, and can be
fashioned into various forms including films. It is not as easily stretched and deformed
as is LDPE. HDPE is insoluble in water and most organic solvents, although some swelling
may occur on immersion in the latter. HDPE is an excellent electrical insulator.
• LDPE is a soft translucent solid which deforms badly above 75º C. Films made from
LDPE stretch easily and are commonly used for wrapping. LDPE is insoluble in water, but
softens and swells on exposure to hydrocarbon solvents. Both LDPE and HDPE become
brittle at very low temperatures (below -80º C). Ethylene, the common monomer for
these polymers, is a low boiling (-104º C) gas.
• Natural (latex) rubber is an opaque, soft, easily deformable solid that becomes sticky
when heated (above. 60º C), and brittle when cooled below -50º C. It swells to more
than double its size in nonpolar organic solvents like toluene, eventually dissolving, but
is impermeable to water. The C5H8 monomer isoprene is a volatile liquid (b.p. 34º C).
• Pure cellulose, in the form of cotton, is a soft flexible fiber, essentially unchanged by
variations in temperature ranging from -70 to 80º C. Cotton absorbs water readily, but is
unaffected by immersion in toluene or most other organic solvents. Cellulose fibers may
be bent and twisted, but do not stretch much before breaking. The monomer of
cellulose is the C6H12O6aldohexose D-glucose. Glucose is a water soluble solid melting
below 150º C.
To account for the differences noted here we need to consider
the nature of the aggregate macromolecular structure,
or morphology, of each substance. Because polymer
molecules are so large, they generally pack together in a nonuniform fashion, with ordered or crystalline-like regions mixed
together with disordered or amorphous domains. In some
cases the entire solid may be amorphous, composed entirely
of coiled and tangled macromolecular chains. Crystallinity
occurs when linear polymer chains are structurally oriented in a uniform three-dimensional
matrix. In the diagram on the right, crystalline domains are colored blue.
Increased crystallinity is associated with an increase in rigidity, tensile strength and opacity (due
to light scattering). Amorphous polymers are usually less rigid, weaker and more easily
deformed. They are often transparent.
Three factors that influence the degree of crystallinity are:
i) Chain length
ii) Chain branching
iii) Interchain bonding
The importance of the first two factors is nicely illustrated by the differences between LDPE and
HDPE. As noted earlier, HDPE is composed of very long unbranched hydrocarbon chains. These
pack together easily in crystalline domains that alternate with amorphous segments, and the
resulting material, while relatively strong and stiff, retains a degree of flexibility. In contrast,
LDPE is composed of smaller and more highly branched chains which do not easily adopt
crystalline structures. This material is therefore softer, weaker, less dense and more easily
deformed than HDPE. As a rule, mechanical properties such as ductility, tensile strength, and
hardness rise and eventually level off with increasing chain length.
The nature of cellulose supports the above analysis and demonstrates the importance of the
third factor (iii). To begin with, cellulose chains easily adopt a stable rod-like conformation.
These molecules align themselves side by side into fibers that are stabilized by inter-chain
hydrogen bonding between the three hydroxyl groups on each monomer unit. Consequently,
crystallinity is high and the cellulose molecules do not move or slip relative to each other. The
high concentration of hydroxyl groups also accounts for the facile absorption of water that is
characteristic of cotton.
Natural rubber is a completely amorphous polymer. Unfortunately, the potentially useful
properties of raw latex rubber are limited by temperature dependence; however, these
properties can be modified by chemical change. The cis-double bonds in the hydrocarbon chain
provide planar segments that stiffen, but do not straighten the chain. If these rigid segments
are completely removed by hydrogenation (H2 & Pt catalyst), the chains lose all constrainment,
and the product is a low melting paraffin-like semisolid of little value. If instead, the chains of
rubber molecules are slightly cross-linked by sulfur atoms, a process called vulcanization which
was discovered by Charles Goodyear in 1839, the desirable elastomeric properties of rubber are
substantially improved. At 2 to 3% cross linking a useful soft rubber, that no longer suffers
stickiness and brittleness problems on heating and cooling, is obtained. At 25 to 35%
crosslinking a rigid hard rubber product is formed. The following illustration shows a crosslinked section of amorphous rubber. By clicking on the diagram it will change to a display of the
corresponding stretched section. The more highly-ordered chains in the stretched conformation
are entropically unstable and return to their original coiled state when allowed to relax (click a
second time).
On heating or cooling most polymers undergo thermal transitions that provide insight into their
morphology. These are defined as the melt transition, Tm , and the glass transition, Tg .
Tm is the temperature at which crystalline domains lose their structure, or melt. As crystallinity
increases, so does Tm.
Tg is the temperature below which amorphous domains lose the structural mobility of the
polymer chains and become rigid glasses.
Tg often depends on the history of the sample, particularly previous heat treatment, mechanical
manipulation and annealing. It is sometimes interpreted as the temperature above which
significant portions of polymer chains are able to slide past each other in response to an applied
force. The introduction of relatively large and stiff substituents (such as benzene rings) will
interfere with this chain movement, thus increasing Tg (note polystyrene below). The
introduction of small molecular compounds called plasticizers into the polymer matrix increases
the interchain spacing, allowing chain movement at lower temperatures. with a resulting
decrease in Tg. The outgassing of plasticizers used to modify interior plastic components of
automobiles produces the "new-car smell" to which we are accustomed.
Tm and Tg values for some common addition polymers are listed below. Note that cellulose has
neither a Tm nor a Tg.
Polymer
LDPE
HDPE
PP
Tm (ºC)
110
130
175 180
175
>200 330
_110
_100
_10
90
95
Tg (ºC)
PVC PS
80
PAN
PTFE PMMA
_110
Rubber
180
30
105
_70
Rubber is a member of an important group of polymers called elastomers. Elastomers are
amorphous polymers that have the ability to stretch and then return to their original shape at
temperatures above Tg. This property is important in applications such as gaskets and O-rings,
so the development of synthetic elastomers that can function under harsh or demanding
conditions remains a practical goal. At temperatures below Tg elastomers become rigid glassy
solids and lose all elasticity. A tragic example of this caused the space shuttle Challenger
disaster. The heat and chemical resistant O-rings used to seal sections of the solid booster
rockets had an unfortunately high Tg near 0 ºC. The unexpectedly low temperatures on the
morning of the launch were below this Tg, allowing hot rocket gases to escape the seals.
Polymer chemistry or macromolecular chemistry is a multidisciplinary science that deals with
the chemical synthesis and chemical
properties of polymers or macromolecules.Accordingto IUPAC recommendations, macromolecu
les refer to the individual molecular chains and are the domain of chemistry. Polymers describe
the bulk properties of polymer materials and belong to the field of polymer physics as a subfield
of physics.
Polymer chemistry is that branch of one, which deals with the study of synthesis and properties
of macromolecules.
Biopolymers produced by living organisms:


structural proteins: collagen, keratin, elastin…

chemically functional proteins: enzymes, hormones, transport proteins…

structural polysaccharides: cellulose, chitin…

storage polysaccharides: starch, glycogen…
nucleic acids: DNA, RNA
Synthetic polymers used for plastics—fibers, paints, building
materials, furniture, mechanical parts, adhesives:




thermoplastics: polyethylene, Teflon, polystyrene, polypropylene, polyester, poly
urethane, polymethyl methacrylate, polyvinyl chloride, nylon, rayon, celluloid, silicone…
thermosetting plastics: vulcanized rubber, Bakelite, Kevlar, epoxy…
Polymers are formed by polymerization of monomers. A polymer is chemically described by
its degree of polymerisation, molar mass distribution, tacticity, copolymer distribution, the
degree of branching, by its end-groups, crosslinks, crystallinity and thermal properties such as
its glass transition temperature and melting temperature. Polymers in solution have special
characteristics with respect to solubility, viscosity and gelation.
SLIME
Slime has a wide range of behaviors. It can of course be slimey and runny like mucus. But it can
also be fairly stiff like a rubber ball and bounce.
Slime is made of two components. One is a polymer that
dissolves in water. The other is a salt that crosslinks the
polymer chains together. The two strands of polymers
here are made of a chain of carbon atoms. This slime has every other carbon with an oxygen
atom which is connected to a hydrogen. The polymer name is polyvinyl alcohol. The OH's are
why it's called "alcohol." Vinyl is the building block. It consists of 2 carbons and 3
hydrogens and readily connects to itself to form chains. Here the right carbon connects to OH.
In other polymers the OH is replaced by something else
The polymer name is polyvinyl alcohol. The OH's
are why it's called "alcohol." Vinyl is the building
block. It consists of 2 carbons and 3 hydrogens
and readily connects to itself to form chains.
Here the right carbon connects to OH. In other
polymers the OH is replaced by something else.
The salt used for crosslinking these polymer
chains together is borax (sodium borate). Borate
has one boron atom surrounded by four oxygen atoms, each with a
hydrogen. Borate's hydrogen atoms are attracted to the oxygen atoms in the polymers (dotted
lines). Likewise, borate's oxygen atoms are attracted to the hydrogen atoms in the polymers.
This holds the chains of polymers together, which gives it more stiffness. The more borate
molecules the more stiff the slime will be.
Equipment needed to do experiment
You will use the 250 mL beaker, the 100mL graduated cylinder, and the small plastic cup The
equipment is standard stock items in a chemistry class.
You will use the Borax powder. You will also use Polyvinyl alcohol. The Polyvinyl alcohol should
be prepared earlier as describe in the ASM teacher notebook. This will let you do the
experiment twice. The polyvinyl alcohol powder you have will need to be dissolved in water and
that takes some heating and a lot of stirring.
The instructions were to make up a 4% solution of polyvinyl alcohol and a 4% solution of borax.
In medicine and chemistry a 4% solution is normally interpreted to mean 4 grams of the solid
dissolved in every 100 milliliters of water.
So mass out 4.0 grams of polyvinyl alcohol and placed it in 100 mL of water. Do the same thing
with the borax.
For this experiment, determine weighed the tube filled with polyvinyl alcohol. It measured 10.8
grams.
Determine the weight of the empty polyvinyl test tube. It was 6.0 grams (see below). Therefore,
by subtracting the weight of the empty tube from the full tube of 10.8 grams, conclusion is that
you have 4.8 grams of polyvinyl alcohol.
You cannot put this in 100 mL of water, because it would not be a 4% solution. You need more
water because we have more than 4.0 grams; we had 4.8 grams. So here's the math. The
fraction 4 grams over 100 mL is 4% solution. If we divide 4 by 100, we get 0.04. We need 4.8 to
be divided by some volume that is also equal to 0.04. So we make an equation.
4 grams = 4.8 grams
100 mL ? volume
To solve for ? volume, we can do some cross multiplying.
4 grams x ? volume = 4.8 grams x 100 mL
Then divide both sides by 4 grams.
4 grams x ? volume = 4.8 grams x 100 mL
4 grams
4 grams
The 4 grams cancel on the left and we end up with:
? volume = 120 mL
So we need to dissolve the 4.8 grams of polyvinyl alcohol in 120 mL of water in order to have
the same concentration as 4 grams in 100 mL of water (4% solution).
The Borax tube with borax weighed 12.4 grams. The empty tube was the same as the empty
polyvinyl alcohol tube (6.0 grams). So that means the borax tube must be holding 6.4 grams of
borax. To make a 4% solution we need to dissolve the 6.4 grams in enough water to be equal to
4%. We use the same formula as before.
4 grams = 6.4 grams
100 mL ? volume.
4 grams x ? volume = 6.4 grams x 100 mL
Then divide both sides by 4 grams.
4 grams x ? volume = 6.4 grams x 100 mL
4 grams
4 grams
The 4 grams cancel on the left and we end up with:
? volume = 160 mL
So we need to dissolve the whole tube of borax into 160 mL of water in order to get 4%. Our
graduated cylinder only goes to 100mL, so we will first measure out 100mL followed by 60mL.
INSTRUCTIONS FOR DISSOLVING THE POLYVINYL ALCOHOL
Fill your 100mL graduated cylinder to close to the 100mL mark with tap water.
Pour the 100mL of the water into the 250mL beaker.
Get some more water and make it close to 20 mL. Add this to the 100mL of water already in the
beaker.
Pour the whole contents of the polyvinyl alcohol tube into the 120 mL of water slowly. Keep
stirring.
If the polyvinyl alcohol doesn't dissolve very easily, the different purity levels of polyvinyl
alcohol is the cause.
Apparently, polyvinyl alcohol is made from another polymer, polyvinyl acetate. See the two red
oxygens, the two gray carbons, and three white hydrogens? That's acetate. When polyvinyl
alcohol is made, these acetates are supposed to come off and be replaced by alcohol groups
(one oxygen and one hydrogen). Often not all of these acetates come off. This can make the
polyvinyl alcohol polymer not as water soluble as it would be if all acetates had come off.
If the container of the polyvinyl alcohol does not indicate the purity, it's possible that it
contained some residual polyvinyl acetate, which made it less water soluble. So that means we
have to heat it.
To begin I turned the electric stove temperature to the second lowest temperature. If using a
gas stove, turn it as low as you can. A microwave oven is another option (see below).
Here it is sitting on the smooth stove top of the electric stove. Place a thermometer in it to
check the temperature.
An alternative is the microwave oven. But you only want to heat it for about 15 seconds at a
time. You can leave the stirrer in it, but don't leave the thermometer in the beaker, it has
metal on it!
From either using the microwave or the stove top, get the temperature to between 160
degrees Fahrenheit and 180 degrees Fahrenheit. Keep stirring with the stirring rod.
If using a electric stove top, turn down the temperature to low once the liquid is above 160
degrees. Turn off the heat. Once it cools enough to pick up, set it on a plate or saucer to further
cool down. It should get below 120 degrees before using. While it's cooling we can make up the
borax solution.
Let your tap water get hot and fill up the 100mL graduated cylinder with 100mL of hot tap
water. Pour that into the plastic cup.
Remember, we need a total of 160mL of water to make the borax we have a 4% solution. So
measure 60 more milliliters of hot water and pour it into the plastic cup.
Now you can add the borax (hydrated sodium borate) to the 160mL of hot tap water. The 6.4
grams of borax and 160mL of water should be 4% solution because dividing 6.4 grams by 160mL
equals 0.04
You can use the microspatula to stir the borax to help it dissolve. The stirring rod is still in the
dissolved polyvinyl alcohol.
So here's our 4% polyvinyl alcohol solution on the left and the 4% borax solution on the right in
the picture below.
Take a picture of at this point before you mix
the two ingredients.
Notice that we have about 100mL left, even though we started with 120mL. Some of the water
must have evaporated in all the heating.
Here's a moment of decision. According to the literature, slime can be made by adding borax
solution that is from 1/20 to 1/2 the volume of the polyvinyl solution. Since we have 100mL of
polyvinyl solution, 1/20 of that is 5mL and 1/2 of that is 50mL. 5mL of the borax solution would
make it slimey and runny; 50mL should make it stiff like a rubber ball. For me, I tried about half
way in between, which is 25mL of borax solution. You can try a different amount of borax
solution. Just record how much you used.
So I measured out 25mL of the borax solution in the graduated cylinder and poured it in as I
stirred vigorously. This is where a helper is handy. Someone can do the pouring as the other
stirs vigorously and holds on to the beaker. The liquid will start getting thicker in a couple of
seconds. Stir until it won't let you stir.
In a few seconds, the polyvinyl polymers are crosslinked by the borate molecules (remember
the illustration at the beginning?) This turns the liquid into a strange gel.
At first it seemed like a clump of Jello. I was a little disappointed. But then...
It started flowing, behaving much different than Jello
Drooling and stretching while feeling cold and slimey.
It slowly engulfs whatever it encounters.
What if it also had the power to take control over the brain...?
Elmer's Glue-All contains two polymers, polyvinyl alcohol and polyvinyl acetate. The borax
cross-links these together to make something like Silly Putty. The beauty of this approach is that
it's fast. No time needed to dissolve the polyvinyl alcohol powder; however, this isn't the one I
want you to make for this lab. I just mention it for something you may do in the future.
The school children that come to our college on Science day make "Silly Putty." This "slime" is
not translucent like the type we made here with polyvinyl alcohol and borax.
Classification of Polymers
Thermoplastic Polymers
These are linear, one-dimensional polymers which have strong intramolecular covalent bonds
and weak intermolecular van Der Waals bonds. At elevated temperature, it is easy to "melt" these
bonds and have molecular chains readily slide past one another. These polymers are capable of
flow at elevated temperatures, can be remolded into different forms, and in general, are
dissolvable., under the applicatione heat, can be melted into a "liquid" state.
Thermosetting Polymers
These are three-dimensional amorphous polymers which are highly crosslinked (strong,
covalent intermolecular bonds) networks with no long-range order. Thermosetting polymers
are those resins which are "set" or "polymerized" through a chemical reaction resulting in
crosslinking of the structure into one large 3-dimensional molecular network. Once the
chemical reaction or polymerization is complete, the polymer becomes a hard, infusible,
insoluble material which cannot be softened, melted or molded non-destructively. A good
example of a thermosetting plastic is a two-part epoxy systems in which a resin and hardener
(both in a viscous state) are mixed and within several minutes, the polymerization is complete
resulting in a hard epoxy plastic.
Rubbers and Elastomers
In general, a rubber material is one which can be stretched to at least twice its original length
and rapidly contract to its original length. Rubber must be a high polymer (polymers with very
long chains) as rubber elasticity, from a molecular standpoint, is due to the coiling and uncoiling
of very long chains. To have "rubber-elastic properties" a rubber materials' use temperature
must be above its glass transition temperature and it must be amorphous in its unstretched
state since crystallinity hinders coiling and uncoiling. Rubbers are lightly crosslinked in order to
prevent chains from slipping past one another under stress without complete recovery.
"Natural rubber" is a thermoplastic, and in its natural form it becomes "soft" and sticky" on hot
days (not a good property for an automobile tire). In fact, until Mr. Goodyear discovered a
curing reaction with sulfur in 1839, rubbers were not crosslinked and did not have unique
mechanical, rubber-elastic properties.
Fibers
Many of the polymers used for synthetic fibers are identical to those used in plastics but the
two industries developed separately and employ different testing methods and terminology. A
fiber is often defined as having an aspect ratio (length/diameter) of at least 100. Synthetic fibers
are spun into continuous filaments, or chopped in shorter staple which are then twisted into
thread before weaving. The thickness of the fiber is expressed in terms of denier which is the
weight in grams of a 9000-m length of fiber. Stresses and strength of fibers are reported in terms
of tenacity in units of grams/denier. In melt spinning, polymer pellets are gravity fed into an
extruder and subjected to shear loading at elevated temperatures. The softened polymer is
delivered to the spinneret which has up to 1000 shaped holes for fiber formation. A molten
stream of polymer is forced by pressure through shaped holes and stretched into a solid state.
Then the polymer is stretched to have molecular alignment along the axial direction and
crystallized in a preferred direction so that no spherulites form. Synthetic fibers include Kevlar,
carbon, PE, PTFE, and nylon while natural fibers include silk, cotton, wool and wood pulp.
Liquid Crystals
The structure of liquid crystals such as Spectra 1000 is unique. It is a near-ideal in structure with
most of its molecules virtually stretched out. While this is not useful for textiles, it is excellent
for composite reinforcement. Continuous crystals are readily attained in liquid crystalline
polymers, as the molecules are already aligned in parallel positions in the melt whereas the
continuous morphology of PE would require elaborate processing to avoid chain entanglement
and chain folding.
Week 13: Polymers Final Week
Composites
Composite materials for construction, engineering, and other similar applications are formed by
combining two or more materials in such a way that the constituents of the composite
materials are still distinguishable, and not fully blended. One example of a composite material
is concrete, which uses cement as a binding material in combination with gravel as a
reinforcement. In many cases, concrete uses rebar as a second reinforcement, making it a
three-phase composite, because of the three elements involved.
Composite materials take advantage of the different strengths and abilities of different
materials. In the case of mud and straw bricks, for example, mud is an excellent binding
material, but it cannot stand up to compression and force well. Straw, on the other hand, is well
able to withstand compression without crumbling or breaking, and so it serves to reinforce the
binding action of the mud. Humans have been creating composite materials to build stronger
and lighter objects for thousands of years.
The majority of composite materials use two constituents: a binder or matrix and a
reinforcement. The reinforcement is stronger and stiffer, forming a sort of backbone, while the
matrix keeps the reinforcement in a set place. The binder also protects the reinforcement,
which may be brittle or breakable, as in the case of the long glass fibers used in conjunction
with plastics to make fiberglass. Generally, composite materials have excellent compressibility
combined with good tensile strength, making them versatile in a wide range of situations.
Tyvek
Tyvek (/taɪˈvɛk/) is a brand of flashspun high-density polyethylene fibers, a synthetic material;
the name is a registered trademark ofDuPont. The material is very strong; it is difficult to tear
but can easily be cut with scissors or a knife. Water vapor can pass through Tyvek (highly
breathable), but not liquid water, so the material lends itself to a variety of applications:
envelopes, car covers, air and water intrusion barriers (housewrap) under house
siding, labels, wristbands, mycology, and graphics. Tyvek is sometimes erroneously referred to
as "Tyvex."
Tyvek is a nonwoven product consisting of spunbond olefin fiber. It was first discovered in 1955
by DuPont researcher Jim White who saw polyethylene fluff coming out of a pipe in a DuPont
experimental lab. It was trademarked in 1965 and was first introduced for commercial purposes
in April 1967.
According to DuPont's website, the fibers are 0.5–10 µm (compared to 75 µm for a human
hair). The nondirectional fibers (plexifilaments) are first spun and then bonded together by heat
and pressure, without binders.
Among Tyvek's properties are:
Light weight
Class A flammability rating.
Chemical resistance
Dimensional stability
Opacity
Neutral pH
Tear resistant
Kevlar
Kevlar is the registered trademark for a para-aramid synthetic fiber, related to
other aramids such as Nomex and Technora. Developed atDuPont in 1965, this high strength
material was first commercially used in the early 1970’s as a replacement for steel in racing
tires. Typically it is spun into ropes or fabric sheets that can be used as such or as an ingredient
in composite material components.
Currently, Kevlar has many applications, ranging from bicycle tires and racing sails to body
armor because of its high tensile strength-to-weight ratio; by this measure it is 5 times stronger
than steel on an equal weight basis. It is also used to make modern drumheads that hold up
withstanding high impact. When used as a woven material, it is suitable for mooring lines and
other underwater applications.
Teflon
Teflon® is a brand of polytetrafluoroethylene (PTFE), a solid polymer that is considered to be
one of the world's most slippery substances. Accidentally invented in 1938 a laboratory in
Deepwater, New Jersey, in the United States, Teflon® has applications in a wide range of areas,
including household goods, the aerospace industry, electronics and industrial processes.
Teflon® is produced by E.I. du Pont de Nemours and Company, also known as DuPont.
http://www.nsf.gov/news/special_reports/olympics/suitup.jsp
http://www.nsf.gov/news/special_reports/olympics/skis.jsp
http://www.nsf.gov/news/special_reports/olympics/
History
PTFE is a fluorocarbon, a compound made up of carbon and fluorine, and it has the molecular
formula (C2F4)n. A chemist named Roy Plunkett accidentally invented PTFE while trying to
create a new chlorofluorocarbon in a New Jersey laboratory operated by Kinetic Chemicals Inc.,
a company that was co-founded by DuPont and General Motors. Plunkett discovered that the
white, wax-like substance that was created during one of his experiments was extremely
slippery and water-resistant. The substance was patented in 1941, and the Teflon® trademark
was registered in 1945.
Conductive and Insulating polymers
Conductive polymers and plastics are increasingly desired for a growing number of
sophisticated end-uses. Most plastics are naturally non-conductive, hence their wide use as
electrical insulators. Because of their ease of fabrication, however, polymers are highly
desirable materials of construction. Where some transfer of electrical charge is desired
modifications to the polymer must be made to increase conductivity. This has resulted in
plastics being formulated for use in four distinct application categories of increasing
conductivity:
1.
Insulating (e.g. wire coating)
2.
Dissipative ("anti-static" polymers)
3.
Conductive (materials capable of conducting modest amounts of electrical current)
4.
Highly Conductive or Shielding (materials capable of conducting significant amounts of
electrical current)
"Recent developments in conductive elastomers have provided the possibility for controlled
heating of these materials, which can be used as liners, surface coatings, food packages, arctic
wear and boots, ski accessories and a portable heating pad. The materials are for sale and the
technology could be licensed."
Week 14 Composites
COMPOSITES
Composite materials for construction, engineering, and other similar applications are formed by
combining two or more materials in such a way that the constituents of the composite
materials are still distinguishable, and not fully blended. One example of a composite material
is concrete, which uses cement as a binding material in combination with gravel as a
reinforcement. In many cases, concrete uses rebar as a second reinforcement, making it a
three-phase composite, because of the three elements involved.
Composite materials take advantage of the different strengths and abilities of different
materials. In the case of mud and straw bricks, for example, mud is an excellent binding
material, but it cannot stand up to compression and force well. Straw, on the other hand, is well
able to withstand compression without crumbling or breaking, and so it serves to reinforce the
binding action of the mud. Humans have been creating composite materials to build stronger
and lighter objects for thousands of years.
The majority of composite materials use two constituents: a binder or matrix and a
reinforcement. The reinforcement is stronger and stiffer, forming a sort of backbone, while the
matrix keeps the reinforcement in a set place. The binder also protects the reinforcement,
which may be brittle or breakable, as in the case of the long glass fibers used in conjunction
with plastics to make fiberglass. Generally, composite materials have excellent compressibility
combined with good tensile strength, making them versatile in a wide range of situations.
Engineers building anything, from a patio to an airplane, look at the unique stresses that their
construction will undergo. Extreme changes in temperature, external forces, and water or
chemical erosion are all accounted for in an assessment of needs. When building an aircraft, for
example, engineers need lightweight, strong material that can insulate and protect passengers
while surfacing the aircraft. An aircraft made of pure metal could fail catastrophically if a small
crack appeared in the skin of the airplane. On the other hand, aircraft integrating reinforced
composite materials such as fiberglass, graphite, and other hybrids will be stronger and less
likely to break up at stress points in situations involving turbulence.
Many composites are made in layers or plies, with a woven fiber reinforcement sandwiched
between layers of plastic or another similar binder. These composite materials have the
advantage of being very moldable, as in the hull of a fiberglass boat. Composites have
revolutionized a number of industries, especially the aviation industry, in which the
development of higher quality composites allows companies to build bigger and better aircraft.
Laminates
A laminate is a material that can be constructed by uniting two or more layers of material
together. The process of creating a laminate is lamination, which in common parlance refers to
the placing of something between layers of plastic and gluing them with heat, pressure, and an
adhesive.
There are different lamination processes, depending on the type of materials to be laminated.
The materials used in laminates can be the same or different, depending on the processes and
the object to be laminated. An example of the type of laminate using different materials would
be the application of a layer of plastic film — the "laminate" — on either side of a sheet
of glass — the laminated subject.
Vehicle windshields are commonly made by laminating a tough plastic film between two layers
of glass. Plywood is a common example of a laminate using the same material in each layer.
Glued and laminated dimensioned timber is used in the construction industry to make wooden
beams, Glulam, with sizes larger and stronger than can be obtained from single pieces of wood.
Another reason to laminate wooden strips into beams is quality control, as with this method
each and every strip can be inspected before it becomes part of a highly stressed component
such as an aircraft undercarriage.
Examples of laminate materials include Formica and plywood. Formica, which refers to a
specific brand name of materials by its manufacturer with the same name, and similar plastic
laminates are used in the production of decorative laminates, using either a high or low
pressure thermo-processing system. Decorative laminates (such as Maica Laminates, Wilsonart
or Laminart) are produced with kraft papers and decorative papers with a layer of overlay on
top of the decorative paper, set before pressing them with thermoprocessing into highpressure decorative laminates. A new type of HPDL is produced using real wood
veneer or multilaminar veneer as top surface. Alpikord produced by Alpi spa and Veneer-Art,
produced by Lamin-Art are examples of these types of laminate. High-pressure laminates
consists of laminates "molded and cured at pressures not lower than 1,000 lb per sq in. (70 kg
per sq cm) and more commonly in the range of 1,200 to 2,000 lb per sq in. (84 to 140 kg per sq
cm). Meanwhile, low Pressure laminate is defined as "a plastic laminate molded and cured at
pressures in general of 400 pounds per square inch (approximately 27 atmospheres or 2.8 x 106
pascals).
Laminating paper, such as photographs, can prevent it from becoming creased, sun damaged,
wrinkled, stained, smudged, abraded or marked by grease, fingerprints and environmental
concerns. Photo identification cards and credit cards are almost always laminated with plastic
film. Boxes and other containers are also laminated using a UV coating. Lamination is also used
in sculpture using wood or resin. An example of an artist who used lamination in his work is the
American, Floyd Shaman.
Further, laminates can be used to add properties to a surface, usually printed paper, that
would not have them otherwise. Sheets of vinyl impregnated with ferro-magnetic material can
allow portable printed images to bond to magnets, such as for a custom bulletin board or a
visual presentation. Specially surfaced plastic sheets can be laminated over a printed image to
allow them to be safely written upon, such as with dry erase markers or chalk. Multiple
translucent printed images may be laminated in layers to achieve certain visual effects or to
hold holographic images. Many printing businesses that do commercial lamination keep a
variety of laminates on hand, as the process for bonding many types is generally similar when
working with arbitrarily thin material.
Week 15: Composites: Failure
Analysis/Strongest Beam
Damage and Failure Analysis of Composite Materials
Progressive Damage Modeling of Composites Modeling Damage and Failure of Polymer Matrix
Composites The objective of this study was to incorporate a new composite damage
constitutive model into the DYNA3D finite element code developed at Lawrence Livermore
National Laboratory. The composite damage model used was for progressive damage of
polymer matrix composites as developed at the Stanford University composites and structures
group. The DYNA3D code used is an explicit three-dimensional finite element code for the
nonlinear dynamic analysis of materials and structures. The composite damage model used is
based on the work of Professor Fu-Kuo Chang and the thesis project of Dr. Iqbal Shahid [1993].
The implementation of the model into DYNA3D was performed by Dr. Steven Kirkpatrick as an
independent research project with the assistance of Prof. Chang and Dr. Shahid.
The technical difficulties of this research program arise from the incompatibilities of the current
form of the Chang-Shahid damage model with the DYNA3D code architecture. The damage
model was developed for design analysis of flat plate structures subjected to in-plane loadings
(2-dimensional static problems). DYNA3D is a three dimensional general purpose code for the
dynamic analysis of materials and structures. Thus, the damage model needed to be
reformulated to be implemented into DYNA3D in a computationally efficient manner.
The Chang-Shahid damage model used in this program was initially obtained from the PDCOMP
computer code developed by Dr. Shahid as part of his PhD. thesis research. As implemented in
the PDCOMP code the damage model combines design failure criteria based on polynomial
functions of stress components with progressive damage and degradation modeling for
analyses of static in-plane loadings of symmetric laminate composite plates of various
geometries both with and without cutouts and stress concentrations. The model makes an
assumption of a continuous anisotropic elastic body with degraded moduli in the damaged
regions. As incorporated in PDCOMP, the Chang-Shahid damage model is a laminate
constitutive model where the entire laminate is evaluated at any point in the plate.
The input parameters for PDCOMP are the geometry, material, layup, and loading. PDCOMP is
designed to statically increment the load up to the point where the ultimate failure load is
reached. The PDCOMP code performs both stress analysis and damage development in parallel
in each time step. Failure mechanisms of matrix cracking, fiber-matrix shear-out, and fiber
breakage are considered. If the calculated stresses are below failure levels the load is
incremented. However, if the calculated stresses are above the failure levels the progressive
damage analyses is performed.
In the progressive damage analyses, damage is incremented, properties are degraded and
updated, and stresses and deformations updated. This loop is performed iteratively until an
updated state is determined with damage and stresses that are on or below the failure surfaces
and in equilibrium with the applied load. If this updated damage state is below the ultimate
failure load the loads are again incremented and the process continues. The analyses
performed to determine updated stiffnesses is based on elastic analyses of cracked plies within
a laminate and the resulting effective reduction in stiffness. Thus the resulting stiffness update
calculations require evaluation of complex mathematical expressions and require significant
computational effort if evaluated for a significant number of elements and time steps. The
failure criteria used in PDCOMP are separated to account for different damage mechanisms of
fiber breakage, fiber-matrix shear-out, and matrix cracking.
The technical difficulties of this research program arise from the incompatibilities of the current
form of the Chang-Shahid damage model with the DYNA3D code architecture. The damage
model was developed for design analysis of flat plate structures subjected to in-plane loadings
(2-dimensional static problems). DYNA3D is a three dimensional general purpose code for the
dynamic analysis of materials and structures. Thus, the damage model needed to be
reformulated to be implemented into DYNA3D in a computationally efficient manner.
The Chang-Shahid damage model used in this program was initially obtained from the PDCOMP
computer code developed by Dr. Shahid as part of his PhD. thesis research. As implemented in
the PDCOMP code the damage model combines design failure criteria based on polynomial
functions of stress components with progressive damage and degradation modeling for
analyses of static in-plane loadings of symmetric laminate composite plates of various
geometries both with and without cutouts and stress concentrations. The model makes an
assumption of a continuous anisotropic elastic body with degraded moduli in the damaged
regions. As incorporated in PDCOMP, the Chang-Shahid damage model is a laminate
constitutive model where the entire laminate is evaluated at any point in the plate.
It was not feasible to directly tie the damage model code PDCOMP to the DYNA3D finite
element constitutive model subroutine due to the computationally intensive analyses and
algorithms performed in PDCOMP. In addition, the single integration point solid elements in
DYNA3D require a laminae constitutive model as apposed to the laminate constitutive model in
PDCOMP. Thus the approach for implementing the composite damage model into DYNA3D was
to modify the code PDCOMP to output moduli and strength curves as a function of crack
density for each ply in the layup. These material behavior curves are then used as the input
conditions for the composite constitutive model in DYNA3D. Each ply in the layup is then
analyzed in DYNA3D using a different material number with properties specified by the
associated strength and moduli curves which are input in the load curve cards.
An advantage of this approach is that the information from the progressive damage model can
be implemented into DYNA3D as material input properties and thus the calculations required in
the constitutive model can be greatly reduced. PDCOMP is run only once through with crack
densities incremented and strengths and moduli for each ply is calculated. Thus this approach is
much more computationally efficient than tying subroutines of PDCOMP directly into DYNA3D.
The disadvantage of this approach is that much of the additional analyses performed by
PDCOMP was lost and thus further development of the DYNA3D constitutive model was
needed. For example, PDCOMP would iteratively calculate the change in crack densities that
would occur for a given load increment. For DYNA3D a similar damage evolution equation or
algorithm needed to be developed. Other modifications were needed to obtain three
dimensional failure criteria since other than in-plane loading conditions were possible.
A series of quasistatic tensile tests on various laminates were simulated with the DYNA3D
version of the progressive damage model. The predictions compared well with those of
PDCOMP and the experimental data. A second type of demonstration calculation was
performed to demonstrate the performance of the progressive damage model for a dynamic
problem with out-of-plane loadings. The problem analyzed was the response of a composite
panel loaded by a low velocity ball nose impactor. Results of tests and previous analyses for this
example are given by Choi and Chang. This problem was chosen because it demonstrates the
capabilities of the model for a dynamic problem with out-of-plane loadings. The damage
mechanisms observed in the tests were primarily matrix cracking and delamination.
A sketch of the test setup for the ball impact tests is shown in Figure 1. The mass of the
impactor (with base mass) totaled 0.16 kg. The spherical nosed impactor was made of steel and
had a radius of 0.635 cm. The impacted panel was 10 cm long and 7.6 cm wide and firmly
clamped at either end as shown in Figure 13. The other two edges of the specimen were free.
The extent of damage produced in the impacted panels was determined by x-radiographs. The
damage observed in a cross-ply T300/976 carbon/epoxy panels at 6.7 m/s is shown in Figure
2a. The corresponding calculation of damage in the DYNA3D impact simulation is shown
in Figure 2b. The overall agreement between experiments and calculations for the low velocity
impact is good.
The progressive damage model appears to be a useful tool for analysis of laminate composite
structures. The class of problems for which the model was originally developed was static inplane tensile loading of structures. The development to include the model into DYNA3D
extends the model to general three-dimensional dynamic analyses of composite structures. The
initial comparisons of the model in DYNA3D indicate that the updated model can be used to
calculate low velocity impact damage that may occur in problems such as a tool dropped on a
composite aircraft panel as shown in Figure 3. Application of the model for problems with
significantly different loading conditions or higher loading rates may require further validation
or development.
It is assumed that the student is familiar with simple concepts of mechanical behavior, such as
the broad meanings of stress and strain. It would be an advantage for the student to understand
that these are really tensor quantities, although this is by no means essential. All of the terms
associated with the assumed pre-knowledge are defined in the glossary, which can be consulted
by the student at any time.
Most of the material in this package is based on a recently published book. This is:
"An Introduction to Composite Materials", D.Hull and T.W.Clyne, Cambridge University Press
(1996) Order!
This source should be consulted for background to the treatments in this module, particularly
mathematical details.
What is a Composite Material?
Most composites have strong, stiff fibers in a matrix which is weaker and less stiff. The
objective is usually to make a component which is strong and stiff, often with a low density.
Commercial material commonly has glass or carbon fibres in matrices based on thermosetting
polymers, such as epoxy or polyester resins. Sometimes, thermoplastic polymers may be
preferred, since they are mouldable after initial production. There are further classes of
composite in which the matrix is a metal or a ceramic. For the most part, these are still in a
developmental stage, with problems of high manufacturing costs yet to be overcome.
Furthermore, in these composites the reasons for adding the fibres (or, in some cases, particles)
are often rather complex; for example, improvements may be sought in creep, wear, fracture
toughness, thermal stability, etc. This software package covers simple mechanics concepts of
stiffness and strength, which, while applicable to all composites, are often more relevant to fiberreinforced polymers.
Module Structure
The module comprises three sections:



Load Transfer
Composite Laminates
Fracture Behaviour
Brief descriptions are given below of the contents of these sections, covering both the main
concepts involved and the structure of the software.
Load Transfer
Summary
This section covers basic ideas concerning the manner in an applied mechanical load is shared
between the matrix and the fibres. The treatment starts with the simple case of a composite
containing aligned, continuous fibres. This can be represented by the slab model. For loading
parallel to the fibre axis, the equal strain condition is imposed, leading to the Rule of Mixtures
expression for the Young's modulus. This is followed b y the cases of transverse loading of a
continuous fibre composite and axial loading with discontinuous fibres.
What is meant by Load Transfer?
The concept of load sharing between the matrix and the reinforcing constituent (fibre) is central
to an understanding of the mechanical behaviour of a composite. An external load (force) applied
to a composite is partly borne by the matrix and partly by the reinforcement. The load carried by
the matrix across a section of the composite is given by the product of the average stress in the
matrix and its sectional area. The load carried by the reinforcement is determined similarly.
Equating the externally imposed load to the sum of these two contributions, and dividing through
by the total sectional area, gives a basic and important equation of composite theory, sometimes
termed the "Rule of Averages".
(1)
which relates the volume-averaged matrix and fibre stresses (
), in a composite containing
a volume (or sectional area) fraction f of reinforcement, to the applied stress sA. Thus, a certain
proportion of an imposed load will be carried by the fibre and the remainder by the matrix.
Provided the response of the composite remains elastic, this proportion will be independent of
the applied load and it represents an important characteristic of the material. It depends on the
volume fraction, shape and orientation of the reinforcement and on the elastic properties of both
constituents. The reinforcement may be regarded as acting efficiently if it carries a relatively
high proportion of the externally applied load. This can result in higher strength, as well as
greater stiffness, because the reinforcement is usually stronger, as well as stiffer, than the matrix.
What happens when a Composite is Stressed?
Figure 1
Consider loading a composite parallel to the fibres. Since they are bonded together, both fibre
and matrix will stretch by the same amount in this direction, i.e. they will have equal strains,
e (Fig. 1). This means that, since the fibres are stiffer (have a higher Young modulus, E), they
will be carrying a larger stress. This illustrates the concept of load transfer, or load
partitioning between matrix and fibre, which is desirable since the fibres are better suited to
bear high stresses. By putting the sum of the contributions from each phase equal to the overall
load, the Young modulus of the composite is found (diagram). It can be seen that a "Rule of
Mixtures" applies. This is sometimes termed the "equal strain" or "Voigt" case. Page 2 in the
section covers derivation of the equation for the axial stiffness of a composite and page 3 allows
the effects on composite stiffness of the fibre/matrix stiffness ratio and the fibre volume fraction
to be explored by inputting selected values.
What about the Transverse Stiffness?
Also of importance is the response of the composite to a load applied transverse to the fibre
direction. The stiffness and strength of the composite are expected to be much lower in this case,
since the (weak) matrix is not shielded from carrying stress to the same degree as for axial
loading. Prediction of the transverse stiffness of a composite from the elastic properties of the
constituents is far more difficult than the axial value. The conventional approach is to assume
that the system can again be represented by the "slab model". A lower bound on the stiffness is
obtained from the "equal stress" (or "Reuss") assumption shown in Fig. 2. The value is an
underestimate, since in practice there are parts of the matrix effectively "in parallel" with the
fibres (as in the equal strain model), rather than "in series" as is assumed. Empirical expressions
are available which give much better approximations, such as that of Halpin-Tsai. There are
again two pages in the section covering this topic, the first (page 4) outlining derivation of the
equal stress equation for stiffness and the second (page 5) allowing this to be evaluated for
different cases. For purposes of comparison, a graph is plotted of equal strain, equal stress and
Halpin-Tsai predictions. The Halpin-Tsai expression for transverse stiffness (which is not given
in the module, although it is available in the glossary) is:
(2)
in which
Figure 2
The value of x may be taken as an adjustable parameter, but its magnitude is generally of the
order of unity. The expression gives the correct values in the limits of f=0 and f=1 and in general
gives good agreement with experiment over the complete range of fibre content. A general
conclusion is that the transverse stiffness (and strength) of an aligned composite are poor; this
problem is usually countered by making a laminate (see section on "composite laminates").
How is Strength Determined?
There are several possible approaches to prediction of the strength of a composite. If the stresses
in the two constituents are known, as for the long fibre case under axial loading, then these
values can be compared with the corresponding strengths to determine whether either will fail.
Page 6 in the section briefly covers this concept. (More details about strength are given in the
section on "Fracture Behaviour".) The treatment is a logical development from the analysis of
axial stiffness, with the additional input variable of the ratio between the strengths of fibre and
matrix.
Such predictions are in practice complicated by uncertainties about in situ strengths, interfacial
properties, residual stresses etc. Instead of relying on predictions such as those outlined above,
it is often necessary to measure the strength of the composite, usually by loading parallel,
transverse and in shear with respect to the fibers. This provides a basis for prediction of whether
a component will fail when a given set of stresses is generated (see section on "Fracture
Behavior"), although in reality other factors such as environmental degradation or the effect of
failure mode on toughness, may require attention.
What happens with Short Fibers?
Short fiber can offer advantages of economy and ease of processing. When the fibers are not
long, the equal strain condition no longer holds under axial loading, since the stress in the fibers
tends to fall off towards their ends (see Fig. 3). This means that the average stress in the matrix
must be higher than for the long fiber case. The effect is illustrated pictorially in pages 7 and 8 of
the section.
Figure 3
This lower stress in the fiber, and correspondingly higher average stress in the matrix (compared
with the long fiber case) will depress both the stiffness and strength of the composite, since the
matrix is both weaker and less stiff than the fibers. There is therefore interest in quantifying the
change in stress distribution as the fibers are shortened. Several models are in common use,
ranging from fairly simple analytical methods to complex numerical packages. The simplest is
the so-called "shear lag" model. This is based on the assumption that all of the load transfer
from matrix to fiber occurs via shear stresses acting on the cylindrical interface between the two
constituents. The build-up of tensile stress in the fiber is related to these shear stresses by
applying a force balance to an incremental section of the fiber. This is depicted in page 9 of the
section. It leads to an expression relating the rate of change of the stress in the fiber to the
interfacial shear stress at that point and the fiber radius, r.
(3)
which may be regarded as the basic shear lag relationship. The stress distribution in the fiber is
determined by relating shear strains in the matrix around the fiber to the macroscopic strain of
the composite. Some mathematical manipulation leads to a solution for the distribution of stress
at a distance x from the mid-point of the fiber which involves hyperbolic trig functions:
(4)
where e1 is the composite strain, s is the fibre aspect ratio (length/diameter) and n is a
dimensionless constant given by:
(5)
in which nm is the Poisson ratio of the matrix. The variation of interfacial shear stress along the
fiber length is derived, according to Eq.(3), by differentiating this equation, to give:
(6)
The equation for the stress in the fiber, together with the assumption of a average tensile strain in
the matrix equal to that imposed on the composite, can be used to evaluate the composite
stiffness. This leads to:
(7)
The expression in square brackets is the composite stiffness. In page 10 of the section, there is an
opportunity to examine the predicted stiffness as a function of fiber aspect ratio, fiber/matrix
stiffness ratio and fiber volume fraction. The other point to note about the shear lag model is that
it can be used to examine inelastic behavior. For example, interfacial sliding (when the
interfacial shear stress reaches a critical value) or fiber fracture (when the tensile stress in the
fiber becomes high enough) can be predicted. As the strain imposed on the composite is
increased, sliding spreads along the length of the fiber, with the interfacial shear stress unable to
rise above some critical value, ti*. If the interfacial shear stress becomes uniform at ti* along the
length of the fiber, then a critical aspect ratio, s*, can be identified, below which the fiber
cannot undergo fracture. This corresponds to the peak (central) fiber stress just attaining its
ultimate strength sf*, so that, by integrating Eq.(3) along the fiber half-length:
(8)
It follows from this that a distribution of aspect ratios between s* and s*/2 is expected, if the
composite is subjected to a large strain. The value of s* ranges from over 100, for a polymer
composite with poor interfacial bonding, to about 2-3 for a strong metallic matrix. In page 10,
the effects of changing various parameters on the distributions of interfacial shear stress and fiber
tensile stress can be explored and predictions made about whether fibers of the specified aspect
ratio can be loaded up enough to cause them to fracture.
Conclusion
After completing this section, the student should:






Appreciate that the key issue, controlling both stiffness and strength, is the way in which
an applied load is shared between fibers and matrix.
Understand how the slab model is used to obtain axial and transverse stiffness for long
fiber composites.
Realize why the slab model (equal stress) expression for transverse stiffness is an
underestimate and be able to obtain a more accurate estimate by using the Halpin-Tsai
equation.
Understand broadly why the axial stiffness is lower when the fibers are discontinuous
and appreciate the general nature of the stress field under load in this case.
Be able to use the shear lag model to predict axial stiffness and to establish whether
fibers of a given aspect ratio can be fractured by an applied load.
Note that the treatments employed neglect thermal residual stresses, which can in
practice be significant in some cases.
Composite Laminates
Summary
This section covers the advantages of lamination, the factors affecting choice of laminate
structure and the approach to prediction of laminate properties. It is first confirmed that, while
unidirectional plies can have high axial stiffness and strength, these properties are markedly
anisotropic. With a laminate, there is scope for tailoring the properties in different directions
within a plane to the requirements of the component. Both elastic and strength properties can be
predicted once the stresses on the individual plies have been established. This is done by first
studying how the stiffness of a ply depends on the angle between the loading direction and then
imposing the condition that all the individual plies in a laminate must exhibit the same strain.
The methodology for prediction of the properties of any laminate is thus outlined, although most
of the mathematical details are kept in the background.
What is a Laminate?
High stiffness and strength usually require a high proportion of fibers in the composite. This is
achieved by aligning a set of long fibers in a thin sheet (a lamina or ply). However, such
material is highly anisotropic, generally being weak and compliant (having a low stiffness) in
the transverse direction. Commonly, high strength and stiffness are required in various directions
within a plane. The solution is to stack and weld together a number of sheets, each having the
fibres oriented in different directions. Such a stack is termed a laminate. An example is shown in
the diagram. The concept of a laminate, and a pictorial illustration of the way that the stiffness
becomes more isotropic as a single ply is made into a cross-ply laminate, are presented in page 1
of this section.
What are the Stresses within a Crossply Laminate?
The stiffness of a single ply, in either axial or transverse directions, can easily be calculated. (See
the section on Load Transfer). From these values, the stresses in a crossply laminate, when
loaded parallel to the fiber direction in one of the plies, can readily be calculated. For example,
the slab model can be applied to the two plies in exactly the same way as it was applied in the
last section to fibers and matrix. This allows the stiffness of the laminate to be calculated. This
gives the strain (experienced by both plies) in the loading direction, and hence the average stress
in each ply, for a given applied stress. The stresses in fiber and matrix within each ply can also
be found from these average stresses and a knowledge of how the load is shared. In page 2 of this
section, by inputting values for the fiber/matrix stiffness ratio and fiber content, the stresses in
both plies, and in their constituents, can be found. Note that, particularly with high stiffness
ratios, most of the applied load is borne by the fibers in the "parallel" ply (the one with the fiber
axis parallel to the loading axis).
What is the Off-Axis Stiffness of a Ply?
For a general laminate, however, or a crossply loaded in some arbitrary direction, a more
systematic approach is needed in order to predict the stiffness and the stress distribution. Firstly,
it is necessary to establish the stiffness of a ply oriented so the fibers lie at some arbitrary angle
to the stress axis. Secondly, further calculation is needed to find the stiffness of a given stack.
Consider first a single ply. The stiffness for any loading angle is evaluated as follows,
considering only stresses in the plane of the ply The applied stress is first transformed to give the
components parallel and perpendicular to the fibers. The strains generated in these directions can
be calculated from the (known) stiffness of the ply when referred to these axes. Finally, these
strains are transformed to values relative to the loading direction, giving the stiffness.
Figure 4
These three operations can be expressed mathematically in tensor equations. Since we are only
concerned with stresses and strains within the plane of the ply, only 3 of each (two normal and
one shear) are involved. The first step of resolving the applied stresses, sx, sy and txy, into
components parallel and normal to the fiber axis, s1, s2 and t12 (see Fig. 4), depends on the angle,
f between the loading direction (x) and the fibre axis (1)
How to Make the strongest paper bridge?
How to Make a Strong Paper Bridge
By Jordan Whitehouse, eHow Contributor
Construct a paper bridge to learn
about how a real bridge works.
Making a strong paper bridge requires concentration, attention to detail and a desire to
learn and have fun. Many teachers ask their students to build paper bridges to teach them
about the purpose and construction techniques of real bridges. Bridges are under two
types of force: compression and tension. Both are in action when any weight is placed on a
bridge. Compression pushes weight down on the structure and tightens it. Tension
stretches the structure of the bridge. In bridge construction, the triangle is used because it
supports both compression and tension.
Other People Are Reading


How to Make Paper Bridges

How to Make a Bridge Out of Paper



Print this article
Things You'll Need



Two wooden blocks of the same size
Several pieces of paper
Glue
Instructions
1.
o
1
Find a solid surface, like a table or the floor, that is even. Place the wooden blocks on the surface
about six inches away from each other.
o
2
Use a truss bridge as the model for your construction. Roll the paper into dense tubes and tape
the tubes closed. Rolling the paper will ensure that the bridge will not buckle and that it will be
able to sustain compression.
o

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o
3
Construct the truss bridge by mirroring the design of a real truss bridge. This means that you will
have to design two railroad-looking formations with the paper that you have rolled. The railroad
formations will provide the horizontal structure of the bridge.
o
4
Attach the railroad formations on top of each other by gluing paper rolls to evenly spaced
sections of the formations. These paper rolls will be perpendicular to the railroad formations. To
add even more strength to the paper bridge, glue paper rolls diagonally across the squares that
were formed between the two railroad formations. Each square in the bridge will look like it has
four triangles within it. You can also glue extra pieces of paper to the areas on the bridge where
the perpendicular sections meet the horizontal sections. Doing this secures the attachments
even more.
o
5
Place the paper bridge so that it spans the length of the wooden blocks. Add an increasing
number of coins to different sections of the bridge to test how strong the bridge is.
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Instructions
1.
Penny Bridge For Younger Students
o
1
Stack three books on a table or desk edge and the other three on an opposite table or desk
edge. Set the tables the same distance apart as a sheet of standard white paper, less an inch on
either side for the paper to rest on top.
o
2
Fold the white paper in whatever way the students choose, they should discuss different
methods and try different ideas for this part of the exercise.
o

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o
2.
3
Lay the paper across the top of the book supports. Add pennies one at a time, laying them
across the span of the folded paper the students have created. Do no place pennies on the book
ends of the paper. Let the students continue putting pennies on the bridge until they see how
many it supports until it fails. Have them try different designs to see which is the strongest.
Constructed Paper Bridge
o
4
Draw out a bridge design using different span techniques and determine which is the one you
will use to construct your bridge. Various types of bridges such as the Warren Span conform well
to using paper to construct the bridge, others such as cable suspension bridges do not.
o
5
Roll tubes of paper to create some of the elements of the bridge. Create as many tubes as you
think you may need. You can seal them by running a thin line of glue on the outside end of the
paper just before you reach the end of rolling it. Let the tubes dry.
o
6
Cut tubes down to create shorter elements. You can flatten tubes by pressing them down to
create a strong level element as well. Flattening ends of some tubes and gluing them together is
a good way to create strong joints. Begin putting your bridge together. As you go use the
clothespins to hold joints or areas you have glued, but these must be removed later.
o
7
Insert toothpicks into certain areas of the bridge for support if it is allowed. You can overlap
tubes by placing a smaller tube inside a larger one, insert the toothpicks through the joint then
clip off the ends at the outside edge of the tube. Toothpicks should not be used for building any
portion of the bridge, only as added joint support if that technique is allowed.
o
8
Create the span of the bridge by putting together trusses and a platform along the bottom of
the bridge. Use standard flat paper, cut to fit, to cover the road surface of the bridge. Glue all
the elements in place. Set the bridge across the wood blocks. Use the pennies to continue adding
weight to test the strength of the bridge, or bridges if this is a group activity.
Read more: How to Make Paper Bridges |
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Week 17: Properties of Wood:
Properties of Wood
Society of Wood Science and Technology
Introduction
Wood is our most important raw material. It is important not only because it is used for
literally hundreds of products, but also because it is a renewable natural resource. Through
careful planning and use, forests will provide a perpetual supply of wood.
Wood is a cellular material of biological origin. Even though it is all around us, it isn’t as simple
as we often think. As you learned in Unit 1 Slide Set 2, it is a very complex material with many
properties. One definition of wood is that it is a hygroscopic, anisotropic material of biological
origin.
Hygroscopic means it has the ability to attract moisture from the air.
Anisotropic means that its structure and properties vary in different directions.
The biological origin of wood implies diversity and variation, between and within different
species of trees. These things are among the many factors, which affect wood properties. The
fundamental structure of wood, from the molecular to cellular or anatomical level, determines
the properties and behavior of wood. In the slides that follow, we will discover some important
wood properties that are linked to its structure.
Wood and Moisture Relationships: The Hygroscopic Nature of Wood
All wood in growing trees contains a considerable amount of water due to the need for water
as part of the photosynthesis and growth processes. This water is commonly called sap.
Although sap contains some materials in solution, it is mainly made of water.
Forms of water in wood
Water is contained in wood as either bound water or free water. Bound water is held within
cell walls by bonding forces between water and cellulose molecules. Free water is contained in
the cell cavities and is not held by these forces – it is comparable to water in a pipe.
The amount of water in wood expressed as a percent of the dry weight is called the “Moisture
Content”
Moisture content is calculated with the following formula:
Moisture content (%) = Weight of water in wood X 100
Weight of totally dry wood
Water movement in wood
There are two things we are interested in concerning water movement in wood: 1)drying that
occurs before manufacture and use as finished wood products;
2)and the gain and loss of water in response to changes in environmental conditions
surrounding the wood.
In both drying and end use, water normally moves from higher to lower zones of moisture
concentration, although extreme temperature differences on opposite sides of a board can
reverse this normal direction.
Water moves through wood as liquid or vapor
through several kinds of passageways.
These are:
--cell cavities of fibers and vessels,
--ray cells, pit chambers (microscopic openings on the sides of cell walls) and their pit
membrane openings,
--and the cell walls themselves.
Water movement along the grain is many times faster than across the grain.
Free water moves through cell cavities and pit openings (microscopic openings on the sides of
cell walls). During drying it is moved by capillary forces that exert a pull on the free water
deeper in the wood. This is similar to the movement of water in a wick.
Bound water moves as vapor through empty cell cavities and pit openings as well as directly
through cell walls. The basic cause of bound water movement is differences in water vapor
pressure caused by relative humidity, moisture content, and temperature differences.
Equilibrium Moisture Content (EMC) Relationship
Once wood has been dried below the fiber saturation point (the point when the cell walls are
still fully saturated but there is NO free water remaining), it seldom regains any free water that
would increase the moisture content above that point. Only prolonged soaking in water will do
so.
Once wood has been dried below the fiber saturation point (the point when the cell walls are
still fully saturated but there is NO free water remaining), it seldom regains any free water that
would increase the moisture content above that point. Only prolonged soaking in water will do
so.
The EMC a piece of wood achieves depends on the relative humidity and temperature of the
surrounding air. The relationship between EMC, relative humidity, and temperature is shown in
the next slide. As seen from the plot in the next slide, if wood is kept in air at 70 o F and 65
percent relative humidity, it will either gain or lose water until it reaches approximately 12.5
percent moisture content. EMC increases as relative humidity increases and decreases as
temperature increases.
Shrinkage and Swelling
Shrinkage and swelling are the cause of many of the problems that occur in wood during drying
and in use, therefore, an understanding of them will help minimize such problems.
Splitting, warping, and open joints are examples of problems that occur due to uneven
shrinkage.
When water begins to leave the cell walls at the fiber saturation point, the walls begin to shrink.
Even after drying is complete, wood will shrink and swell as relative humidity varies and water
either leaves or enters the cell walls.
Stresses that can cause splitting and warp develop because wood shrinks or swells by different
amounts in the radial, tangential, and longitudinal directions due to its anisotropic nature, and
because during any moisture content change, different parts of a piece of wood are at different
moisture contents. These differences cause internal stresses in parts of the wood that are
attempting to shrink or swell without success due to restraint from the surrounding wood.
Shrinkage and swelling are defined as:
Shrinkage(percent) = wet dimension –dry dimensionX 100
wet dimension
Swelling(percent) = wet dimension –dry dimensionX 100
dry dimension
Typical shrinkage values for wood are shown in this slide. Tangential shrinkage is generally
about twice as large as radial shrinkage, and longitudinal shrinkage ranges from approximately
one-tenth to one-hundredth of either radial or tangential shrinkage. The result is uneven
dimensional changes.
Density and Specific Gravity
Density (ρ) of a material is defined to be the mass per unit volume and is calculated using the
following equation:
= mass/volume
Density of the substance that makes up a wood cell wall has been found to be about 1.5 g/cm3.
However, an actual sample of wood also contains air in the cell lumens, so most woods have a
density less than 1 g/cm3.
Density of a sample of wood is usually calculated as the weight density instead of mass:
Wt density = weight of wood with moisture
volume of wood with moisture
Specific gravity
Specific gravity is a measure of the amount of solid cell wall substance and is also known as
“relative density”. It is a ratio of the density of a substance to the density of water. In our case,
the oven dry (OD) weight of a wood sample is used as the basis and comparison is made with
the weight of the displaced volume of water. In equation form this is:
SG = OD weight of wood
Weight of an equal volume of water
Be sure to note: OD oven dry weight is always used as the numerator in this equation. Oven dry
weight is the weight with no water in the sample, MC = 0%
Factors that influence wood specific gravity include:

moisture content: higher MC = lower SG, up to the fiber saturation point; above the FSP
no change in SG with changes in MC, SG is highest at MC = 0

proportion of wood volume made of various kinds of cell types and cell wall thicknesses:
numerous, thick cell walls = high SG

size of cells and cell lumens: large cells with large lumens = low SG
The range of SG for a few commercial woods is shown on the specific gravity ruler in the next
slide. Most of them fall between 0.35 and 0.65. Woods from other parts of the world exhibit a
much greater range, with SGs reported as low as 0.04 and as high as 1.40.
Mechanical Properties (for example: strength, stress, strain, toughness, stiffness,
elasticity)
An understanding of wood and moisture relationships is of great importance to the
manufacture and use of wood products, as is an understanding of the mechanical properties of
wood.
And, just as shrinking and swelling of wood vary in the radial, tangential, and longitudinal
directions, so do various mechanical properties of wood.
So, wood is anisotropic in both its hygroscopic behavior as well as its mechanical behavior.
Wood is one of the most useful raw materials for human beings. Wood can be used for building
houses, bridges, chairs, tables and other things.
One thing we have to know before building a house is “how strong is the wood?”
Wood is an elastic material, which is bent, but not broken, when the load is small
but if the load is too big, then the wood will break.
The elastic natureof wood is illustrated in the next slide. The degree of deformation a piece of
wood will undergo is proportional to the amount of load applied.
Wood is elastic up to a point, called the elastic or proportional limit. If loads are applied
belowthe elastic limit and then removed, the wood will go back or spring back to its original
shape. If a load is applied that exceeds the elastic limit and is then removed, the wood will go
back only partially to its original shape. This is because the load applied was too much for the
wood to stand and damage to the wood occurred.
If the applied load is very, very high, the wood is no longer able to support this high load and
the wood breaks.
Wood behaves in an elastic manner up to a point called the elastic or proportional limit. This
means that for values of load below the elastic limit, the load and deflection are proportional to
each other. Once the load level passes the elastic limit, the load and deflection are no longer
proportional. For 1 unit increase in load, there is greater than a 1 unit increase in deflection,
until the ultimate breaking point.
In general, wood is stronger when loads are applied parallel to the grain than perpendicular to
the grain. This is because wood is an anisotropic material.
The 3-D structure of a wood cube is shown in the next slide. An arrow indicates the direction of
wood grain. R indicates the radial surface. T indicates the tangential surface. The X stands for
the cross-sectional surface. As shown by the cube, the structure of the three surfaces is
different.
As a result, the strength of wood varies with grain direction.
Three important mechanical properties of wood are used as a measure of its strength. These
properties are compression, tension, and bending.
Compression is defined as two forces or loads acting along the same axis, trying to shorten a
dimension or reduce the volume of the wood. As shown in this slide, compressive forces can act
on the wood parallel to the grain or perpendicular to the grain. Compressive forces can also act
at an angle to the grain. As a general rule, compressive strength parallel to the grain is greater
than compressive strength perpendicular to the grain.
Wood is a very strong material in compression parallel to the grain. A piece of air-dry Douglasfir wood an inch square on the cross section and 3 inches in length can support 4900 psi
(pounds per square inch) which is strong enough to support a police car. One tiny piece of
wood can support a heavy car without breaking.
Tension is defined as two forces or loads acting along the same axis trying to lengthen a
dimension or increase the volume of the wood. Wood is the strongest in tension parallel to the
grain due to the orientation of wood fibers. Wood is not strong in tension perpendicular to the
grain.
Pound for pound, wood is stronger than steel in tension parallel to the grain.
Bending strength is expressed as a degree of deflection with a given force or load on a wood
beam. A test of bending strength is set up as shown on this slide. The load is applied at the
center of the wood beam with two support ends. Both compression and tension stresses are
present. Bending strength is a measure of the resistance to failing. Stiffness is a measure of the
ability to bend freely and regain normal shape.
The ability of a tiny piece of wood to support a heavy police car shows just how strong a
building material wood is. As mentioned earlier, the anisotropic nature of wood affects its
strength.
However, on top of this anisotropic nature, a great number of other factors can affect the
strength of wood. For example, the density, moisture content, temperature of the surrounding
service area, duration of wood service, and the defects of wood play important roles in
determining the mechanical properties of wood. Many of the characteristics of wood which
may be considered as defects arise from the biological origin of wood.
Week 17: Measuring Tools
MICROSCOPY
Microscopy is the technical field of using microscopes to view samples and objects that cannot
be seen with the unaided eye (objects that are not within the resolution range of the normal
eye). There are three well-known branches of microscopy, optical, electron, and scanning probe
microscopy.
Optical and electron microscopy involve the diffraction, reflection,
or refraction of electromagnetic radiation/electron beams interacting with the specimen, and
the subsequent collection of this scattered radiation or another signal in order to create an
image. This process may be carried out by wide-field irradiation of the sample (for example
standard light microscopy and transmission electron microscopy) or by scanning of a fine beam
over the sample (for example confocal laser scanning microscopy and scanning electron
microscopy). Scanning probe microscopy involves the interaction of a scanning probe with the
surface of the object of interest. The development of microscopy revolutionized biology and
remains an essential technique in the life and physical sciences.
OPTICAL
Optical or light microscopy involves passing visible light transmitted through or reflected from
the sample through a single or multiple lenses to allow a magnified view of the sample.[1] The
resulting image can be detected directly by the eye, imaged on a photographic
plate or captured digitally. The single lens with its attachments, or the system of lenses and
imaging equipment, along with the appropriate lighting equipment, sample stage and support,
makes up the basic light microscope. The most recent development is the digital microscope,
which uses a CCD camera to focus on the exhibit of interest. The
image is shown on a computer screen, so eye-pieces
are unnecessary.
Limitations
Limitations of standard optical microscopy (bright
field microscopy) lie in three areas;
The technique can only image dark or strongly
refracting objects effectively.
.

Diffraction limits resolution to approximately
(see: microscope).
Live 0.2
cellsmicrometres
in particular generally
lack sufficient contrast to be studied successfully, internal
structures
thefocus
cell are
colorless
transparent.

Outofof
light
from and
points
outside The
the most common way to increase contrast
focal plane reduces image clarity.

is to stain the different structures with selective dyes, but this involves killing and fixing the
sample. Staining may also introduce artifacts, apparent structural details that are caused by the
processing of the specimen and are thus not a legitimate feature of the specimen.
These limitations have all been overcome to some extent by specific microscopy techniques
that can non-invasively increase the contrast of the image. In general, these techniques make
use of differences in the refractive index of cell structures. It is comparable to looking through a
glass window: you (bright field microscopy) don't see the glass but merely the dirt on the glass.
There is however a difference as glass is a denser material, and this creates a difference in
phase of the light passing through. The human eye is not sensitive to this difference in phase
but clever optical solutions have been thought out to change this difference in phase into a
difference in amplitude (light intensity).
A scanning electron microscope (SEM) is a type of electron microscope that images a sample
by scanning it with a beam of electrons in a raster scan pattern. The electrons interact with the
atoms that make up the sample producing signals that contain information about the sample's
surface topography, composition, and other properties such as electrical conductivity.
History
The first SEM image was obtained by Max Knoll, who in 1935 obtained an image of silicon
steel showing electron channeling contrast.[1]Further pioneering work on the physical principles
of the SEM and beam specimen interactions was performed by Manfred von Ardenne in
1937,[2][3] who produced a British patent[4] but never made a practical instrument. The SEM was
further developed by Professor Sir Charles Oatley and his postgraduate student Gary Stewart
and was first marketed in 1965 by the Cambridge Scientific Instrument Company as the
"Stereoscan". The first instrument was delivered to DuPont.
Scanning process and image formation
Schematic diagram of an SEM.
In a typical SEM, an electron beam is thermionically emitted from an electron gun fitted with
a tungsten filament cathode. Tungsten is normally used in thermionic electron guns because it
has the highest melting point and lowest vapour pressure of all metals, thereby allowing it to be
heated for electron emission, and because of its low cost. Other types of electron emitters
include lanthanum hexaboride (LaB6) cathodes, which can be used in a standard tungsten
filament SEM if the vacuum system is upgraded and field emission guns (FEG), which may be of
the cold-cathode type using tungsten single crystal emitters or the thermally
assisted Schottky type, using emitters of zirconium oxide.
The electron beam, which typically has an energy ranging from 0.2 keV to 40 keV, is focused by
one or two condenser lenses to a spot about 0.4 nm to 5 nm in diameter. The beam passes
through pairs of scanning coils or pairs of deflector plates in the electron column, typically in
the final lens, which deflect the beam in the x and y axes so that it scans in a raster fashion over
a rectangular area of the sample surface.
When the primary electron beam interacts with the sample, the electrons lose energy by
repeated random scattering and absorption within a teardrop-shaped volume of the specimen
known as the interaction volume, which extends from less than 100 nm to around 5 µm into the
surface. The size of the interaction volume depends on the electron's landing energy, the
atomic number of the specimen and the specimen's density. The energy exchange between the
electron beam and the sample results in the reflection of high-energy electrons by elastic
scattering, emission of secondary electrons by inelastic scattering and the emission
of electromagnetic radiation, each of which can be detected by specialized detectors. The beam
current absorbed by the specimen can also be detected and used to create images of the
distribution of specimen current. Electronic amplifiers of various types are used to amplify the
signals, which are displayed as variations in brightness on a computer monitor (or, for vintage
models, on a cathode ray tube). Each pixel of computer video memory is synchronized with the
position of the beam on the specimen in the microscope, and the resulting image is therefore a
distribution map of the intensity of the signal being emitted from the scanned area of the
specimen. In older microscopes image may be captured by photography from a high-resolution
cathode ray tube, but in modern machines image is saved to a computer data storage.
Low-temperature SEM magnification series for a snow crystal. The crystals are captured, stored,
and sputter-coated with platinum at cryo-temperatures for imaging.
Magnification
An SEM micrograph of a house fly compound eye surface at 450× magnification.
Magnification in a SEM can be controlled over a range of up to 6 orders of magnitude from
about 10 to 500,000 times. Unlike optical and transmission electron microscopes, image
magnification in the SEM is not a function of the power of the objective lens. SEMs may
have condenser and objective lenses, but their function is to focus the beam to a spot, and not
to image the specimen. Provided the electron gun can generate a beam with sufficiently small
diameter, a SEM could in principle work entirely without condenser or objective lenses,
although it might not be very versatile or achieve very high resolution. In a SEM, as in scanning
probe microscopy, magnification results from the ratio of the dimensions of the raster on the
specimen and the raster on the display device. Assuming that the display screen has a fixed size,
higher magnification results from reducing the size of the raster on the specimen, and vice
versa. Magnification is therefore controlled by the current supplied to the x, y scanning coils, or
the voltage supplied to the x, y deflector plates, and not by objective lens power.
Materials
Back scattered electron imaging, quantitative X-ray analysis, and X-ray mapping of specimens
often requires that the surfaces be ground and polished to an ultra smooth surface. Specimens
that undergo WDS or EDS analysis are often carbon coated. In general, metals are not coated
prior to imaging in the SEM because they are conductive and provide their own pathway to
ground.
Fractography is the study of fractured surfaces that can be done on a light microscope or
commonly, on an SEM. The fractured surface is cut to a suitable size, cleaned of any organic
residues, and mounted on a specimen holder for viewing in the SEM.
Integrated circuits may be cut with a focused ion beam (FIB) or other ion beam milling
instrument for viewing in the SEM. The SEM in the first case may be incorporated into the FIB.
Metals, geological specimens, and integrated circuits all may also be chemically polished for
viewing in the SEM.
Special high-resolution coating techniques are required for high-magnification imaging of
inorganic thin films.