Crystalline Solids
Revised: 4/28/15
CRYSTALLINE SOLIDS
Adapted from Experiments by A.B. Ellis et al, ICE
LABORATORY NOTEBOOK
All work for this experiment must be recorded, attached, or answered in the ELN. Create a
Pre/InLab page in this week’s Experiment folder. An objectives and observations (data) sections
are required, chemical/equipment tables and procedures are NOT required. No Post Lab page is
required for this experiment.
INTRODUCTION
Many exciting discoveries are found at the interfaces between traditional scientific disciplines
such as the interaction between researchers in chemistry, physics, and engineering that has led to
the emerging field of material science: the study of the synthesis, composition, and properties of
solids. In this experiment we will investigate the composition and properties of one class of
material – crystalline solids containing cube-like building blocks called cubic unit cells.
Primitive and body centered cubic unit cells are created from two different arrangements of
square array layers. Layering of close packed arrays creates face centered cubic unit cells. (You
should read “Crystal Structures with Cubic Unit Cells” before proceeding further.) Students
will investigate models to determine composition and observe the properties of actual samples of
a metal alloy called nitinol and a superconductor with the formula YBa2Cu3O7.
Nitinol (NiTi)
“Smart” materials have the ability to respond to physical stimulus in a predictable,
preprogrammed way. One such material, the metal alloy NiTi, is called a “memory metal”
because it can be twisted or bent without causing crystal defects and returns to its original shape
when heated. This alloy is referred to as "nitinol", a name derived from the lab where it was
discovered in 1965: Nickel Titanium - Naval Ordinance Laboratory. At high temperatures, the
atoms of the nitinol are arranged in the orderly crystalline austenite form that resists distortion.
At low temperatures, the atoms of nitinol are arranged in the more disordered martensite form
that can easily be twisted and bent. The difference between the two forms can be understood by
looking at the unit cell of each: austenite has a regular body centered cubic structure while
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martensite has a related, but distorted structure. During the process of cooling, the high
temperature austenite exists until the transition temperature (the point where the solid-solid
transition occurs between austenite and martensite) is reached. At this temperature the distortion
to the martensite form can be seen by rotating the body center cubic unit cell of the austenite
form on a diagonal and then pulling the middle layer of atoms (outlined in blue) to the right
while pushing the top and bottom layers to the left (Figure 1).
45o
rotation
high temperature
austenite form
beginning of distortion
at transition temperature
Figure 1. The distortion of the austenite form of NiTi.
If the alloy is bent while in the lower temperature martensite phase, gentle heating of the metal
above the transition temperature (into the austenite phase) restores the original shape. If a new
permanent shape is desired, the metal can be annealed (programmed) at very high temperatures
(in a flame) to retain the "memory" of a new shape. Slightly altering the one to one ratio of Ni to
Ti (i.e., Ni0.99Ti1.01) changes the transition temperature. Therefore, at room temperature one
sample of nitinol can be in the martensite form, while another can be in the austenite form.
The “1-2-3” Superconductor (YBa2Cu3O7)
This superconductor is commonly called "1-2-3" because of the yttrium, barium, copper atom
ratio. The three dimensional structure of the superconductor is very similar to that of perovskite,
CaTiO3 (Figure 2). The perovskite structure can be found by starting at a face centered cubic
unit cell then moving down ½ the cell’s edge length and over ½ the face diagonal’s length. The
smaller cations (Ti4+) in the octahedral holes of the fcc body center become the corner spheres
and the larger cations (Ca2+) that were on the fcc corner are now the body center. The anions
(O2-) that were in the fcc face center are now on the edges.
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shift vertically 1/2 edge length
& over 1/2 a face diagonal
Ti4+
Ca2+
face centered
cubic unit cell
perovskite
structure
O2Figure 2. The unit cell of CaTiO3.
The unit cell of YBa2Cu3O7 is created by stacking three pervoskite unit cells. The calcium ions
(Ca2+) are replaced by Ba2+ in the 1st and 3rd unit cells and Y3+ in the 2nd unit cell while the
titanium ions (Ti4+) are replaced by Cu2+ and/or Cu3+. Two oxide ions (O2-) are omitted from the
1st and 3rd unit cells and four oxides are omitted from the 2nd unit cell. (Figure 3).
Cu2+/Cu3+
Ba2+
O2Y3+
Figure 3. The unit cell of YBa2Cu3O7.
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In this experiment the interaction between a cooled superconductor and a magnet will be
observed. Understanding this and other properties of superconductors requires knowledge of
band theory. "Band theory" is a bonding model for solids that explains conductivity by assuming
that a higher energy level exists above valence electrons called a "conduction band". The
electrons in this band are not attached to (localized on) individual atoms, but are free to move
(delocalized) throughout the entire solid. The "band gap" is the energy needed to promote an
electron from the lower energy valence band to the higher energy conduction band (Figure 4).
Electrons cannot cross the large band gap of insulators (nonmetals), thus no electrical current can
be produced. Depending on conditions, electrons can cross the moderately sized band gap in
semiconductors (semimetals) to create a current. Electrons can always cross the small band gap
of conductors (metals) with the input of ordinary thermal energy (at room temp) to create a
current. Raising the temperature of a metal results in thermally excited atoms that cause electron
scattering in the conduction band and thus, lower conductivity (higher resistance). In ordinary
metals resistance decreases as the temperature decreases but still remains greater than zero
because of scattering of electrons caused by defects in crystals. However, at very low
temperatures, some
Figure 4. Band Theory for solids.
metals (or metal oxides) undergo a solid-solid transition and the resistance drops to zero,
allowing electrical current to flow without hindrance. This remarkable phenomenon is called
"superconductivity". In superconductors, current flows indefinitely and is caused by pairs of
electrons called "Cooper pairs". The combined momentum of Cooper pairs is not affected by
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electron scattering and resistance drops to zero below some critical phase transition temperature
(Tc). Above Tc, the Cooper pairs dissociate, superconductivity ceases, and the solid becomes
normal conducting material. The Tc for YBa2Cu3O7 is 95 K.
In this experiment, a Samarium containing magnet will be brought near the YBa2Cu3O7
superconductor cooled in N2(l) (77 K). When the magnet’s magnetic field lines penetrate the
superconductor a current is induced. This current creates an opposing magnetic field in the
superconductor which repels the magnet and leads to its levitation. (Figure 5)
magnet
perpendicular current
induced in
superconductor
super
conductor
magnetic field induced
in superconductor
(perpendicular to current
& antiparallel to magnet's field
Figure 5. Induced current and magnetic field of the superconductor.
The height at which the magnet is levitated reflects the tendency to minimize the total energy of
the system: The internal energy of the superconductor increases as the magnet moves closer to
the surface and the gravitational potential energy increases as the magnet moves further away
from the surface. The levitation height reflects the minimum total energy based on the sum of
these two opposing forces.
In this experiment students will inspect models of monoatomic and polyatomic solids containing
cubic unit cells to gain a clear understanding of their three dimensional structure. The memory
and acoustic properties of nitinol will be observed and compared with the cubic unit cell models
of the austenite and martensite forms. The YBa2Cu3O7 superconductor will be cooled so the
levitation of a rare earth magnet can be observed and its model will be investigated.
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SAFETY PRECAUTIONS
Safety goggles and lab aprons must be worn in lab at all times. Liquid nitrogen is extremely cold
(–321°F!). Contact with skin may result in severe frostbite. If any liquid nitrogen spills on
clothing, remove the clothing immediately, as the trapped liquid will cause severe frostbite to the
skin beneath the clothing. Do not touch any metal dipped into liquid nitrogen until it has
warmed to room temperature. Do not place liquid nitrogen in a closed container; it can rapidly
expand and explosively shatter a container that is not properly vented. Use plastic tweezers to
handle superconductors and rare earth magnets; the solids may be toxic. The solid state models
contain small spheres and rods - if any are dropped on the floor, pick them up to prevent slips or
falls. Wash your hands before leaving lab. Report any spills, accidents, or injuries to your TA.
Before starting the experiment, the TA will asks you to do a quick demonstration or talk-through
one of the following:
1) How to remove a rod that has been in liquid nitrogen?
2) Assemble the superconductor setup for this experiment (without the liquid nitrogen)
Make sure you watch the videos on the course website and read the documents to prepare. These
demonstrations will be done every week. Everyone will have presented at least one topic by the
end of the quarter. The demonstrations should be short (>1 min) and will be graded.
PROCEDURES
Because of limitations with the number of models, you will probably need to perform the parts of
this experiment out of the order indicated. All ELN entries should be in complete sentences that
fully convey the information obtained in lab.
Part A: Solids with Square Array Layers
1. The following questions pertain to the primitive, body centered cubic (bcc), CsCl, and NaTl
models. Using the Sketch editor on the ELN, sketch the cubes and spheres to create the unit
cells for primitive, body centered cubic, CsCl, and NaTl.
a. Use colorless and darkened spheres to indicate the different atoms or ions for CsCl and
NaTl.
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b. Provide the arrangement of metal atoms for the two cubes that when repeated create the
unit cell of NaTl.
Choose the correct response for each of the following.
2. The tiny pink sphere is in a
cubic / tetrahedral / octahedral hole in the primitive cubic model.
cubic / tetrahedral / octahedral hole in the body centered cubic model.
3. The unit cell of CsCl is primitive / body centered cubic. The holes in this unit cell are
cubic / tetrahedral / octahedral.
4. The unit cell of NaTl is based on the repetition of a primitive / body centered cubic
structure. The holes in this unit cell are cubic / tetrahedral / octahedral.
5. How many of each of the two cubes drawn for NaTl are required to create its unit cell?
(Hint: The face of one unit cell is also the face of another unit cell. Therefore, faces on
opposite sides of a unit cell should be superimposable.)
6. Calculate the empirical formula for CsCl and NaTl using their unit cells or coordination
numbers. All work must be shown to receive credit.
Nitinol
Record all observations, no prompts are given below.
1. Warm some water to 70-80°C using a hot plate. Obtain a piece of NiTi wire and bend it into
a new shape. Drop the wire into the warm water. Try it again when the wire is cool.
2. Grasp the ends of the wire and place the center of the wire in a candle flame. Bend the wire
into a V shape with the point of the V in the flame. (The wire will resist bending initially,
but will deform when hot.) Once the V shape forms, remove the wire from the flame and
wave it in the air to cool. Bend the wire into a new shape and then dip it into warm water.
3. Obtain two different NiTi rods. Drop each one on the floor.
4. Put the martensite rod into warm water (70-80°C) for a few minutes. Remove the rod with
tongs (do not touch, it may be too hot to handle) and drop it on the floor.
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5. Put austenite rod in a styrofoam cup containing N2(l) for a few minutes, remove the rod with
tongs and drop it on the lab bench. (Caution: N2(l) is extremely cold (–321°F!) and can
cause severe frostbite!)
6. Slowly warm the martensite rod in a water bath, taking it out occasionally (every 5-10°C)
and dropping it on the floor. Record the sound as a "ring", "intermediate", or "thud" for each
temperature measurement (in °C).
7. Inspect the models for the two forms of nitinol labeled Model #1 & Model #2. Which is
austenite and which is martensite? What is the unit cell of the austenite form?
DISCUSSION
Choose the correct response for each of the following.
1. At room temperature the wire is in the (martensite / austenite) phase. At 50-60°C the wire
is in the (martensite / austenite) phase.
2. The wire is in the (martensite / austenite) phase in the flame. Why can the wire be bent at
room temperature, but returns to the V shape when warmed?
3. The “room temperature” austenite rod makes a (thud / intermediate / ring) sound at room
temperature. Why?
4. What sound does the “room temperature” martensite rod make when it warms? Why?
What sound does the “room temperature” austenite rod make when it cools? Why?
5. What is the temperature range where the solid-solid transition occurs?
PROCEDURES
Part B: Solids with Close Packed Layers
The following questions pertain to the cubic close packed (ccp), face centered cubic (fcc), NaCl,
and CaTiO3 models.
Choose the correct response for each of the following.
(1) The packing order of the cubic close packed model is: A-A / A-B-A / A-B-C.
The tiny pink sphere is in a: cubic / tetrahedral / octahedral hole.
The tiny black sphere is in a: cubic / tetrahedral / octahedral hole.
(2) For the face centered cubic model…
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the tiny pink sphere is in a: cubic / tetrahedral / octahedral hole.
the tiny black sphere is in a: cubic / tetrahedral / octahedral hole.
(3) Sketch the cubes and spheres to create the unit cells for primitive, body centered cubic,
CsCl, and NaTl. Use labeled colorless and darkened spheres to indicate the different atoms
or ions for NaCl and CaTiO3.
(4) Fill in the coordination number for each of the following:
a. Any sphere in the face centered cubic model.
b. Ions of the NaCl model: Na+
Cl
−
(5) Calculate the empirical formula for NaCl and CaTiO3 using their unit cells or coordination
numbers. All work must be shown to receive credit.
(6) What type of holes are filled in
a. in NaCl? cubic / tetrahedral / octahedral.
b. in CaTiO3 (fcc)? cubic / tetrahedral / octahedral.
Superconductor
1. Check out a magnet from your TA. (Loss of magnet will result in a 5 point deduction from
lab report score.)
2. Using plastic tweezers, place the larger superconductor pellet on a stack of pennies in the
center of a cutoff Styrofoam cup. The pellet should be level with the top edge of the cup.
(Scrape off loose material from the pellet with a spatula. If the pellet is broken, use the
largest piece, flat side up.) Use plastic tweezers to place the smaller magnet on the
superconductor.
3. Carefully pour N2(l) into the cup, covering the pennies and the bottom of the pellet. Touch
the magnet gently with tweezers - it should spin. Allow the N2(l) to evaporate so the pellet
and magnet warm back to room temperature. (To avoid frostbite, do not touch pellet or
magnet until warmed.)
4. Inspect the models for the superconductor. Which model is face centered cubic? Which is
perovskite? How many units cells are present in model #2? Calculate the empirical formula
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from the perovskite model. (The atoms are represented by the following spheres: Y: red;
Ba: black; Cu: blue; O: colorless.)
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