Physics
HSC Course
Stage 6
Ideas to implementation
Part 5: Crystals
Contents
Introduction ............................................................................... 2
Transistors take over................................................................. 4
Triode versus transistor ......................................................................4
So what is a microchip? ......................................................................7
Crystals .................................................................................. 10
What is a crystal? ..............................................................................10
The Braggs: Australian Nobel laureates ................................. 15
Electron flow in metals ........................................................... 17
The heating effects of a current .............................................. 24
Summary................................................................................. 29
Suggested answers................................................................. 31
Exercises – Part 5 ................................................................... 33
Part 5: Crystals
1
Introduction
The crystalline nature of materials once understood enabled the scientists
to make great forward leaps in the development of their understanding of
the electrical behaviour of solids. That basic understanding led to the
theoretical development of semiconductor technology and an
understanding of superconductivity.
In Part 5 you will be given opportunities to learn to:
•
discuss differences between solid state and thermionic devices and
discuss why solid state devices replaced thermionic devices
•
outline the methods used by the Braggs to determine crystal structure
and assess the impact of their contribution to an understanding of crystal
structure
•
explain that metals possess a crystal lattice structure
•
identify that the conducting properties of metals are related to the
large number of electrons able to drift through their crystal lattice
structure
•
discuss why drift velocity is related to:
•
–
the density of electrons
–
the cross sectional area of wire
–
the electronic charge
discuss how the lattice impedes the paths of electrons causing heat to
be generated.
In Part 5 you will be given opportunities to:
•
2
gather, process and present secondary information to discuss how
shortcomings in available technology lead to an increased
knowledge of the properties of materials with particular reference to
the invention of the transistor
From ideas to implementation
•
identify data sources, gather, process, analyse information and use
available evidence to assess the impact of the invention of transistors
on society with particular reference to their use in microchips and
microprocessors.
•
plan, chose equipment or resources for, and perform a first-hand
investigation to observe the heating effects of current in a range of
conductors.
Extracts from Physics Stage 6 Syllabus © Board of Studies NSW, originally
issued 1999. The most up-to-date version can be found on the Board's website
at http://www.boardofstudies.nsw.edu.au/syllabus99/syllabus2000_list.html
Part 5: Crystals
3
Transistors take over
Triode versus transistor
A triode is a modified cathode ray tube. The triode has a wire grid
inserted between the cathode and the anode. The idea is that a small
potential difference set up between the grid and the cathode can make a
large difference to the amount of current flowing through the evacuated
environment of the tube between the cathode and the anode.
The triode is useful for amplification of current in a situation such as a
radio where the signal generates a small current in the aerial that needs to
be amplified to power speakers and produce sound. The use of a triode
(or an alternative thermionic device that behaved similarly) was essential
in this application prior to 1954.
anode
grid
heating filament
cathode
A triode.
The idea was that the current set up in the radio aerial would be
introduced into the grid of the triode and the result would be a
proportionally amplified current flow between the cathode and anode and
hence in the external circuit to power the speakers.
In 1954 the transistor began to be used in radio. After that initial use the
transistor continuously replaced the triode.
4
From ideas to implementation
So what is a transistor? In the previous part of this module you learned
about p-type and n-type semiconductors and their use in photovoltaic
cells. If you don’t recall this information you should return to Part 4 and
revise that learning.
n
p
n
em
itt
er
co
lle
ct
ba
or
se
The same p and n-type semiconductor materials in contact are used to
make transistors. In a transistor the action of the device is analogous to
that of a triode. The transistor can be made in two ways. Firstly by
sandwiching a thin layer of n-type semiconductor material between two
layers of p-type semiconductor material to make a p-n-p transistor or by
sandwiching a thin layer of p-type material between two layers of n-type
material to make a p-n-p transistor. A schematic figure of a n-p-n
transistor is shown in the figure below.
A schematic of a transistor.
The thin layer of material in the centre can be made to act in the same
way as the grid in a thermionic valve. That is, the current flowing from
emitter to collector is proportional to the current introduced into the base
material. The size of the current flowing between the emitter and the
collector is therefore determined by the size of the current available to
the base. The maximum size of the current flowing between the collector
and emitter is determined by the potential supplied by an external circuit
feeding in to the collector and returning to the circuit by the emitter.
In a n-p-n transistor as shown in the figure above, electron flow from the
n-type material known as the emitter to the p-type material occurs under
the influence of a forward potential difference. This is known as a bias
voltage.
The p-type (or base) material has only a few holes so the current to plug
those holes is small. Because the p-type layer is so thin, most electrons
are attracted across the thin base by the reverse potential set up on the
other side at the p-n connection. This n-type material is acting as an
electron collector.
Part 5: Crystals
5
The large flow of electrons from the emitter to the collector n-type
semiconductor layers is proportional to the small current introduced into
the p-type layer. The result is a small current introduced in the p-type
(base) material from an external circuit such as from a radio aerial results
in a situation where a larger current is able to flow across the n-type
materials. This larger current is in proportion to the size of the current
introduced into the p-type material and therefore represents an
amplification of that introduced current.
If no current is introduced into the p-type material then there will be no
current flow across the transistor at all.
In this way a small current, such as one produced by a radio wave in an
aerial that is fed into the transistor base, can be greatly magnified by a
signal fed into the transistor collector from an external circuit.
This transistor device produces a much stronger signal in the radio circuit
than is produced in the antenna. The current in the circuit is, however,
proportionally larger. That is, the current is amplified.
The setup for a simple crystal, (one transistor) radio is shown below. If
the external circuit is connected to a small speaker an audio signal would
be heard.
itt
em
n
p
n
a small current flow into the
p-type semiconductor
results in a large but
proportional current flow
from collector to emitter
er
ba
se
co
lle
ct
or
external circuit
A transistor in a circuit acting as an amplifier. The relative thickness of the base
is magnified in this figure. The potential of the external circuit will determine the
maximum size of the current flowing between the emitter and the collector.
To see sites that outline the history of the development of the transistor see
sites on the physics websites page at:
http://www.lmpc.edu.au/science
6
From ideas to implementation
The transistor as a switch
Transistors can also be used as variable current switches in electrical
circuits. Computerised processors rely on logic circuits that work on a
binary or on/off system to operate. On/off switching devices are
important in this respect. Miniaturised switches are therefore essential.
The transistor provides the basis for such a switch.
The transistor can operate as a switch because it will not allow current to
flow at all until a threshold potential is applied to the base. In a silicon
based transistor that potential is around 0.6 V. The miniaturisation of the
transistor onto the microchip has meant that circuits using millions of
transistors or switches can be placed onto a single microchip device.
The transistor can act as a switch because the size of the electric current
introduced into the base material of the transistor can vary from zero up
to some maximum value. This controls the flow of current through the
transistor via the collector and emitter as none or at various levels.
So what is a microchip?
An electrical circuit on a square of silicon semiconductor crystal. Often
the chips are around the size of a finger nail but they may be larger in
specialised cases where the circuit is extremely complex.
Microprocessors are made on large circular silicon wafers. Each
microprocessor or chip is only a small square or rectangle on the large
wafer. At the end of the production process individual microprocessor
chips are covered in a resin to protect the circuit and are cut from the
wafer. After cutting, individual chips are covered in a protective coat of
resin and stamped so the processor can be identified. These are the
microprocessor chips you see in electronic devices. The process of
making an individual microchip is described below.
The chip is really a three dimensional complex electrical circuit with
each vertical layer built separately. Even individual components such as
transistors are built as three separate layers in the circuit. A
microprocessor circuit may be made up of millions of transistors and
connecting wires.
The microprocessor is built up in layers. It starts with a layer of p-type
silicon. Layers of conducting material or insulating silicon dioxide are
then added. These extra layers are built up using chemicals that are
affected by light. The layering process is repeated up to 20 or more
times to produce separate layers of the microchip circuit and components
onto the chip.
Part 5: Crystals
7
The circuits are built by layering insulators and conductors into a twenty
or so stack sandwich. The sandwiches are connected by thin layers of
metal. These act as wires, joining one layer with another.
Building a chip
The first step in building circuits is to apply a silicon dioxide insulator to
the surface of the silicon wafer. Once the silicon dioxide is in place, it is
covered with another layer made of a substance called photoresist. The
general process of making the microchip involves shining light through a
mask or stencil of the circuit, reducing that light image through the use of
optics, and then ‘printing’ the circuit design on a layer of soft lightsensitive material (photoresist).
The printing of the circuit and components using light is a process called
photolithography. A template is placed over photoresist and exposed to
UV light. The template shadows part of the photoresist. The rest is hit
with the UV light. The UV exposed photoresist chemical becomes
soluble. It is washed off therefore leaving a pattern of photoresist on top
of a layer of insulating silicon dioxide.
In the next step, a new layer of silicon dioxide is grown on the disc,
covering the existing silicon wafer and silicon dioxide pattern. A
conducting layer of polysilicon is then applied to the disc along with a
new layer of photoresist. The photolithography process is used make a
new pattern on the layer of polysilicon. The wafer is etched to cut away
any exposed polysilicon and silicon dioxide. The remaining photoresist is
cleaned off. This leaves a pattern of silicon dioxide interlaced with a
layer of conducting polysilicon.
Before more layers are added, completely covering the wafer, a process
called doping is used to add ions to the exposed areas of silicon on the
wafer. The doping ions alter the conductivity of the semiconducting
silicon, creating conducting points within the wafer.
After the doping, a thin layer of pure metal is added to the wafer by a
plasma spray. This is followed by another round of photolithography and
etching that leaves a pattern of metal that wires the various sandwiches
together and creates the contact points for the circuits on the next layer.
After the initial round of layering an insulator, conductor, and wiring, the
whole process repeats, over and over around 20 times. The layers slowly
build up, creating a three-dimensional circuit of thousands if not millions
of transistors.
To see pages that describe the manufacture of microchips see pages on the
physics website page at: http://www.lmpc.edu.au/science
8
From ideas to implementation
Do Exercises 5.1 to 5.4 now.
Early transistors
Early transistors were based on germanium crystals. The very first
transistor supposedly worked because it was doped with tin. However,
there is some debate about this as tin should not have made it work.
Instead it may have been an impurity in the tin that caused the first
transistor to work.
To see a page that has link that describe the chemistry and history of
germanium see a page on the physics websites page at:
http://www.lmpc.edu.au/science
To see a page that has video clips and text that describes how someone tried
to replicate the construction of the first transistor, see a site on the physics
websites page at:
http://www.lmpc.edu.au/science
Part 5: Crystals
9
Crystals
What is a crystal?
You are familiar with crystals. Make a close examination of a grain of
sugar or salt with a magnifying glass or hand lens. It will reveal that
those substances are crystals.
You have probably seen mineral samples that are crystals. The figure
below shows a sample of the mineral, quartz. The crystalline nature of
the material is obvious.
A mineral sample showing quartz crystals. (Photo: Tim Reid)
10
From ideas to implementation
Of course these crystals are very large. Many rocks are made of smaller
crystals that interlock to hold the rock together.
It may surprise you to know that metals are thought of as crystalline.
Can you think of an example of a metal or two that is obviously
crystalline in nature? If you can, write them down in the space below.
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_________________________________________________________
Looking for metal crystals
Take a walk around the neighbourhood. See if you can find a sheet of
corrugated iron that hasn’t been painted. Look closely at the surface of the
metal. Describe what you see.
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_________________________________________________________
_________________________________________________________
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Did you see the crystals? You should have. Those crystals are made up
of the metal zinc that is plated on to the surface of the corrugated iron to
protect the surface from corrosion. Because the crystals are grown
slowly the crystals reach a large size. The longer the time the crystals are
allowed to grow over the larger they tend to become. Rapid formation
of crystals results in small crystals.
Look closely at the crystals of zinc on the surface again. Can you
comment on the shape of the crystals. If so, write down what you can
see in the space below.
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_________________________________________________________
_________________________________________________________
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Did you notice that the crystals are all of a similar shape and have similar
pointed angles although some of the crystals appear to have grown into
each other? If all of the crystals were free to grow without bumping into
each other they would have very similar shapes.
Part 5: Crystals
11
Now take a look at the quartz crystals shown in the photograph on the
previous page. What can you say about the shape of the quartz crystals
shown in the figure?
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Did you say that they were of different sizes but had a similar shape?
You should have.
In general all substances that form crystals tend to form crystals of a
particular shape. In other words the chemical composition of the
material determines the shape of the crystals of that material.
Iron meteorites are chunks of iron rich material that have grown slowly
in outer space. These chunks of rock if cut with a diamond saw often
show a distinctive crystalline pattern. An example of such a crystalline
pattern is shown in the figure below.
The etched surface of an iron meteorite showing a crystalline pattern.
You may recall from the preliminary module The world communicates
that mineralogists study thin sections of rocks that are made up of
minerals with a petrological microscope.
Rocks that form from molten lava that have cooled quickly have very
small crystals. When they are examined closely they tend to have similar
shapes to examples of the same minerals that have grown slowly. The
difference is the size of the crystal. Scientists using electron microscopes
that can magnify many thousand of times tend to find a similar situation
with rocks that have cooled very fast. The crystals are really small but
are of the same shape.
The obvious conclusion from all these observations is that the crystalline
nature of a substance appears to be determined by its chemical
composition. That is, the crystalline nature of the substance is controlled
and determined at the atomic level. In other words, it is the way that the
atoms are bonded together in substance that determines the crystalline
nature of the substance.
12
From ideas to implementation
You learned in Part 2 of this module that the electron microscope can
magnify smaller objects with high resolution to see the finer detail
because the electrons used have a shorter wavelength than light. It is the
wavelength of the incident ‘radiation’ that determines the resolving
power of the instrument.
Imagine now that you are a scientist just after the turn of the 19th century.
You want to look at atoms and how they are arranged at the finest possible
level. That is the finest structure that can be seen. What sort of radiation
would you try to use? (Hint: Think about the different wavelengths of the
electromagnetic spectrum. You might also consider the size of the atom is
of the order of 10-10 m. You also need that radiation to be of a type that is
easily recorded on film.)
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_________________________________________________________
_________________________________________________________
Check your answer.
If you said in your answer to the question above, a very short wavelength
radiation would be best used to study the material, you were absolutely
correct.
The short wavelength radiation that was available at the time and could
leave a record on film was X-ray radiation. This was fortuitous because
the recently discovered X-ray radiation was easily produced by common
sources and had a wavelength that coincided with the typical distances
between atoms in crystalline materials (on the order of 10-10 m).
What’s the advantage of that you might ask? The answer is simple. The
crystals in materials are characterized by a regular arrangement of atoms.
To ‘see’ that arrangement the wavelength of the radiation must be able to
resolve the positions of individual atoms.
Soon after the discovery of X-rays by Roentgen in 1895, Max von Laue
discovered that X-rays were diffracted when passing through crystalline
solids. This diffraction pattern was similar to the effect of passing light
through an optical grating (a transparent material with hundreds or
thousands of parallel lines scratched into it per cm) to produce a
diffraction pattern.
You may have seen diffraction gratings or the effect of such gratings
today. The finely spaced lines on a CD are in effect a diffraction grating.
The reflection of light you see coming off the CD is the result of light
reflected back from the silvering beneath the diffraction grating.
Part 5: Crystals
13
If you take a cheap diode laser pointer and reflect its beam from a CD
onto a wall a reflection pattern will form on the wall. That pattern is
characteristic of the reflection of light from the irregular surface of the
CD.
Diffraction patterns
Be careful of reflections when you do this activity. Laser light may cause
permanent damage to eyes. This activity is optional.
You may have access to a small cheap laser pointer. These laser pointers
produce red light in the range 630 to 680 nm. They often come with four or
five interchangeable heads that can produce different patterns by producing
a series of dots when shone on the wall. Those dots are the result of the
small lens that the laser light shines through being cut or etched at different
angles to produce a diffraction pattern.
If you have access to a laser pointer with different pattern heads look at
the dots that are produced. Can you see how the central dot is the
brightest and most focussed?
Also notice that as you move further away from the wall where you are
shining the beam, the pattern gets bigger. That is the space between the
dots gets bigger. This effect is a type of angular magnification. The size
of the diffraction grating lens doesn’t get bigger, just the dot separations
do as the laser is moved a larger distance from the wall. If you were to
trace each of the beams back to the grating their angle with respect to one
another would not have changed over their path of travel. Notice that
even a small movement of your hand causes a relatively large movement
of the laser pattern on the wall.
You may also have access to a piece of diffraction grating. This type of
paper is often sold as wrapping paper and gives a hologram or threedimensional effect when you look through it. If the paper is clear it
produces a rainbow reflection at its surface when looked at in sunlight.
This paper has very fine lines etched into its surface. You can shine a
laser beam through the diffraction grating paper and produce the
diffraction pattern characteristic of that paper on a wall.
14
From ideas to implementation
The Braggs: Australian Nobel laureates
The diffraction of light by a crystalline substance produces a
characteristic set of dots as radiation is scattered from the different
orientations of the solid surface. This idea was used by William Henry
Bragg and his son, William Lawrence Bragg to determine the pattern of
atoms in the crystal lattice of many substances. They used this technique
with particular success in studying the structure of metals.
The technique the Braggs applied was relatively simple. The pattern of
diffraction of X-rays from the minute crystal lattice surfaces formed as a
result of the arrangement of the metal atoms was characteristic. Since
these were extremely tiny crystals (at the atomic level) the diffraction
patterns could be reinterpreted to give the angles of atoms with respect to
one another in the atomic crystal lattice.
The technique was using some new technology. The method required the
development of efficient X-ray generators, X-ray sensitive film and a
stable platform where the sample being studied could be placed so that
the reflections could be faithfully recorded.
The idea behind the Bragg's technique was that if you couldn’t see how
the atoms were arranged directly you could shine a beam of X-rays at the
crystal lattice then look at the much magnified diffraction patterns
represented as dots and recorded on film. The patterns of dots were
drawn back to a point to give the shape of the atomic crystal lattice. That
shape could then give clues on the arrangement of the atoms in the
atomic crystal.
This technique of recording crystalline structures using X-rays was used
systematically by Sir William Henry Bragg and William Lawrence Bragg
to measure interatomic distances in the crystalline lattice and to analyse
the geometrical arrangement of atoms in simple crystals.
For that pioneering work on X-ray crystallography they received the
Nobel Prize in Physics in 1915.
Part 5: Crystals
15
To learn more about the Braggs and their work see the physics websites
page at:
http://www.lmpc.edu.au/science
Do Exercise 5.5 now.
16
From ideas to implementation
Electron flow in metals
You learned in the module, Electrical energy in the home that the ability
of a solid to conduct electricity depends on the type of bonding between
the individual atoms. The model of bonding in metals can be described
as a sea of valence electrons being common property of all of the positive
atomic ions in the metal.
These electrons form a so-called sea of electrons that are relatively free
to move from positive metal ion to positive metal ion. The 'free'
electrons are said to be delocalised. They have random motion at normal
temperatures often bouncing about among positive ions but having no
uniform direction of motion.
Because of this random movement of electrons with equal numbers
moving in each direction, a steady state is established. There is no net
movement of electric charge in any direction.
The situation changes rapidly though when an electric field is applied to
the metal. The electric field produces a net velocity of the electrons in
the direction opposite to the electric field. The result is a net movement
of electric charge in one direction. There is a drift of electrons. In other
words a current flows.
Even when an electric field is applied across the conductor the passage of
the electrons through the conductor is not direct. The speed of the
electron movement within the conductor is of the order of 1.6 ¥ 106 ms-1.
-5
The electron drift speed is of the order of 1 ¥ 10 ms-1. The reason for
this discrepancy is the electrons move in largely random directions
within the conducting material, still colliding with positive ions in their
path. They simply have a net drift forward induced by the electric field.
You may recall that metal conductivity reduces with increasing
temperature. If the temperature of the conductor is increased the energy
of the electrons is increased, but the net effect is the electrons have more
collisions. The figure following shows the passage of the electrons
through a conductor under the influence of an electric field.
Part 5: Crystals
17
Dv
–
+
The path of an electron passing along a conductor. The passage of the
electron even under the influence of an electric field is still largely a random
motion. This is because of the numerous collisions with positive ions in its
passage toward the positive side of the field.
Note that in the figure above all the changes in direction of the electron
in its passage along the conductor are the result of collisions between the
electron and the positive ionic nuclei of the conductor material atoms.
Each of these collisions involves the loss of some energy. That energy is
converted to heat energy.
In general, the more collisions the electron has, the greater the resistance
to its passage. In metals this implies that as the metal heats up, the
electrons gain more energy. Their increased movement results in
increased numbers of collisions. That increases resistance to current
flow.
atoms of lattice
Electrons bouncing off the vibrating ions.
Energy is converted to heat in these collisions
Vibrations of the lattice are large and
rapid above the superconducting state.
Electrons moving through the crystal lattice. The bouncing off from positive
ions results in resistance.
18
From ideas to implementation
If the energy level of a conductor is lowered to approach absolute zero (0K)
the vibration of the ions in the crystal lattice is much reduced. How would
that affect the conductivity?
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_________________________________________________________
Check your answer.
When you switch on an electric appliance the appliance receives the flow
of electrons called the electric current almost instantly. In fact for
practical purposes the appliance receives the electric current instantly.
The signal that represents the electrical current could be thought of as
travelling at the speed of light. The flow of individual electrons along
the conductor is, however, a different matter. That velocity is often
much slower. More of the order of mms-1 not 3¥108 ms-1.
Predict how the velocity of individual electrons could be so low yet the
speed of the electric signal along the conductor could be so high. Write your
prediction in the space below then read on to see if you were correct.
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At normal temperatures the ease with which the electrons can flow in a
specific direction is controlled by two factors:
y
The purity of the metal conductor. Impurities affect the metal
structure and disrupt the electron sea. This inhibits the forward
passage of the electrons.
y
The temperature of the metal. Higher temperatures tend to cause
disruption to the passage of the electrons as the positive ions are
vibrating more as they have more energy. The electrons also have
more kinetic energy, so collisions between electrons and positive
ions are more common. These collisions are inelastic and so transfer
energy to the crystal lattice. This slows the direct passage of the
electrons.
Part 5: Crystals
19
The actual number of electrons that can flow along a particular conductor
of depends on two factors.
y
The type of material from which the conducting wire is made.
Different metals conduct with different efficiencies. The resistance
of a metal is a specific property of that metal. The relationship is
basically governed by the number of free electrons each atom in the
conductor can provide to move under the influence of an electric
field.
y
The thickness of the conductor. Like a flow of water along a pipe,
the amount of electrons that can flow along a thick (high crosssectional area) conducting wire is greater than the amount of
electrons that can flow along a thin (small cross-sectional area) wire.
The result of all these factors combined is that even for a pure metal there
is a maximum velocity for the passage of individual electrons for a
particular conductor of set cross-sectional area at a particular
temperature. That velocity is called the drift velocity of electrons.
Drift velocity of electrons
The drift velocity, v, of an electron in a conducting wire is an average
velocity rather than a real velocity. It can be calculated if the following
is known:
y
e, the charge on the electron
y
the number density of electrons or number of free electrons m-3, n
y
the cross-sectional area of the wire, A
y
the length of the conductor, l
y
the current flowing through the conductor, I
These quantities are related through the relationship
I = nAev
therefore
v=
I
nAe
Example
Determine the drift speed in a copper wire of cross- sectional area
1 ¥ 10-7 m2 if a current of 1 A is flowing through it. The n for copper
metal is 8 ¥ 1028 m-3.
20
From ideas to implementation
Solution
v=
I
nAe
1
8 ¥ 10 ¥ 1 ¥ 10 -7 ¥ 1.6 ¥ 10 -19
= 0.00078 ms -1
=
28
As you can see this drift velocity is very slow indeed!
1
If the current in the wire above is raised to 10 A, what is the new drift
velocity of the electrons in the wire from the example above?
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2
Look at the equation for determining the drift velocity of electrons
along a conductor.
v=
I
nAe
Discuss why the drift velocity is related to each of the variables
represented in the equation above.
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Check your answers.
Part 5: Crystals
21
The crystal lattice and electron passage
The passage of a free electron in a metal crystal lattice occurs from atom to
atom. That passage is impeded because of the following factors.
•
Collisions take place between conductive free electrons and the ionic
cores of the metal atoms as they vibrate about their median positions in
the lattice randomly.
•
Impurities exist in the lattice. These could include the substitution of a
smaller ion or a larger ion.
•
Lattice imperfections such as the missing atoms or caused by the
inclusion of an additional small atom of a different type into the lattice.
These all tend to disrupt the passage of the free electrons through the
lattice. That increases the resistance of the metal. The diagrams
following show situations where impurities in the metal cause an increase
in the resistance in the conductor. Note how each situation tends to
deform the lattice in some way.
22
missing atom
small atom substituting for metal ion
small additional atom
large atom substituting for metal ion
From ideas to implementation
If a free electron travelling from atom to atom in the crystal lattice
encounters an irregularity in the lattice its path must deviate in order to
navigate past the irregularity. That deviation can be considered as
resistance and is usually caused by collisions of the free electrons with
other core metal ions in the lattice.
Do Exercise 5.6 now.
Part 5: Crystals
23
The heating effects of a current
One of the activities you are required to perform in this module is to:
‘Plan, chose equipment or resources for, and perform a first-hand
investigation to observe the heating effects of current in a range of
conductors.’
Extracts from Physics Stage 6 Syllabus © Board of Studies NSW, originally
issued 1999. The most up-to-date version is to be found at
http://www.boardofstudies.nsw.edu.au/syllabus99/syllabus2000_list.html
Read the information following. You will then be asked to design an
exercise to do this activity.
For a current to produce heating effects, the conductor must resist the
flow of current. Heat is produced as power is dissipated in the
conductor. Really the power is just a way of saying the rate at which
energy is converted from electrical energy to some other form of energy.
In the case of a conducting wire electrical energy is simply converted
directly into heat energy. This is a real problem in power lines where the
electricity must be conducted along wires from a power station to the
user of the electricity many kilometres away.
The equations that describe power are:
P = I 2 R and P = VI
Where I is the current in the conductor, R is the resistance of the
conductor and V is the voltage across the conductor
Consider the resistance of copper wire of typically used in wires is
around 8 W km-1.
This means if the electricity is transported at a current of 100 A over a
distance of only 1 km from the power station, the power used in
conduction can be staggering.
24
From ideas to implementation
P = I2R
= 100 2 ¥ 8
= 80 000 W
This power is converted into heat energy. Using efficient conductors is
therefore critical. In the next part of this module you will be introduced
to the concept of using superconductors with no resistance to transport
electrical currents. The energy savings could be well worth the effort.
Consider the equations describing power. What factor should be kept
constant in order to be able to systematically study the heating effect of an
electric current in a variety of conductors as a result of power dissipation?
_________________________________________________________
_________________________________________________________
Check your answer.
The electric current supplied by a new 6 V DC battery is usually fairly
constant. This is because of the large size of the battery. Smaller
batteries have difficulty in maintaining current output for extended
periods.
In the module Electrical energy in the home you learned that the
resistance of a conductor is determined from the relationship:
R =
r¥L
where
A
r is the resistivity of the conductor used
R is the resistance
A is the cross sectional area of the conductor
L is the length of the conductor.
The units of resistivity are ohm metres ( Wm ).
An examination of this equation leads to the relationship that the
resistance is dependent upon the following factors.
•
The type of material from which the conductor is made.
•
The diameter of the conductor (assuming it is cylindrical).
This information allows the calculation of the cross-sectional area.
•
The length of the conductor.
If you were to seek to determine the heating effect of a current in a range
of conductors you would need to limit the experiment to consider only
the type of material tested as the variable. That is, the type of material
the current passes through should be the only difference in separate trials
of the experiment to determine the difference between any conductors
examined to determine the heating effects of a current.
Part 5: Crystals
25
What factors would you need to keep constant between different conductors
used in your investigation to determine the heating effects of a current?
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Check your answer.
Consider how the heat energy produced by the electrical energy can be
converted to heat energy and measured in your investigation. Measuring
the temperature of a wire directly is difficult. An easier alternative is to
indirectly the measure the rise in temperature of the wire by measuring
the energy dissipated from the wire to a known mass of water in a set
period of time.
You may recall from the module Electrical energy in the home the
experiment that you performed to measure the energy dissipated by
passing an electrical current at a known voltage across a resistive wire.
To refresh your memory the experiment is repeated below.
Do not repeat this experiment exactly again. This experiment is simply
repeated here to give you a hint as to how you might plan an experiment
to enable you to observe the heating effects of current in a range of
conductors.
You may do this activity yourself, or at your practical session with your
teacher.
You will need the following equipment to perform this experiment:
26
•
a 6 V DC power source either a battery or a transformer rectifier unit
•
a 10 cm length of nichrome wire
•
a multimeter
•
connecting wires
•
a styrofoam coffee cup that will act as a calorimeter (a device useful
to measure energy gain by a liquid)
•
a thermometer like the ones used in tropical fish tanks
•
a watch with a second hand.
From ideas to implementation
Procedure:
1
Coil the length of nichrome wire around a pencil to produce a coil.
This will act as your heating element.
2
Add 50 mL of water to the styrofoam cup using a measuring cup or a
medicine measuring cup.
3
Connect the circuit up as shown in the figure following. Make sure
you have your heating coil submerged under the water in the
styrofoam cup when you connect up the circuit to prevent
overheating the nichrome heating element.
6V
nichrome wire coil
50 mL of water
styrofoam cup
4
Connect your multimeter into the circuit in series as shown in the
circuit below with the setting dial on the A settings. Record the
current flowing in the circuit.
5
Record the temperature and time when you start heating the water.
6
Connect your multimeter into the circuit in parallel across the
nichrome wire heating element with the multimeter on the V setting.
Record the actual voltage across the nichrome heating element.
7
After three minutes measure the temperature of the water again.
Record the temperature rise. Complete the table below to calculate
the temperature rise of the water. Disconnect the battery to avoid it
going flat.
8
Calculate the energy gain of the water using the formula:
Egained = mcDT
Part 5: Crystals
where
m is the mass of water in kg (1000 mL = 1 kg)
c is the specific heat of the water (4.18 kJkg-1K-1)
DT is the temperature rise in degrees
27
temperature of water after 3 min heating = ___________________
temperature of water at start of heating = ____________________
therefore the temperature difference (DT) = __________________
mass of water, m = 0.05 kg
Egained = mcDT = _______________________________________
9
Calculate the energy input by the heating coil from the formula:
E = VIt
Current in circuit, I = ____________________________________
voltage across heating coil, V = ____________________________
time, t = 180 s
E = VIt = _____________________________________________
10 How does the energy supplied to the water by the electric heating
coil compare to the energy actually gained by the water? Propose an
explanation for any differences
______________________________________________________
______________________________________________________
You should now design an experiment based on the information above
incorporating any variations necessary to observe the heating effects of
current in a range of conductors.
Do not perform the experiment until you ensured that the procedure you
intend to use is safe. You must discuss what you intend to do with your
supervisor before you do the experiment.
After receiving approval to perform your planned experiment from your
supervisor you should perform the experiment and report your results and
observations to your teacher.
Write up your experiment as a practical report and submit it to your teacher
with your exercises for Part 6 of this module.
Remember to describe what you did and found accurately. Discuss any
improvements you might make to your experiment to improve its accuracy
in your report. It may be you could not do these modifications because of
equipment limitations. You should, however, include any proposed
improvements with your report.
28
From ideas to implementation
Summary
The differences between thermionic and solid state devices
especially with respect to triodes and transistors are:
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
The major impact of the invention of the transistor on society has
been to:
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
The Braggs developed a method of determining the crystal structure
of materials. What was that method?
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Conduction of electric currents in a metal can be explained as due to:
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part 5: Crystals
29
Drift velocity of electrons in a conductor is related to:
______________________________________________________
______________________________________________________
______________________________________________________
______________________________________________________
30
From ideas to implementation
Suggested answers
Looking for metal crystals
The shortest possible wavelength radiation that could be produced
reliably and safely would have been required to observe atomic structure.
X-ray radiation may have come to mind because it was discovered, easily
produced and relatively well understood by early in the 20th century.
X-ray radiation was also of a wavelength approaching atomic distances
and diameters.
Electron flow in metals
Resistance to conductivity should be reduced almost to zero, if not to
zero. This is because of the reduced number of collisions between the
electrons and the lack of vibrating atoms.
Drift velocity of electrons
1
v =
I
nAe
10
8 ¥ 10 ¥ 1 ¥ 10 -7 ¥ 1.6 ¥ 10 -19
= 0.0078 ms-1
=
2
28
Increasing the current flow along the wire means an increase in the
number of charges per second passing along the wire.
This is shown from I =
q
where q is the charge and t is the time.
t
The increased cross sectional area of the wire means a greater
number of atoms to facilitate movement and increase in the electrons
available to be conducted. The type of material is important because
that determines the number of electrons available in the conduction
band. The charge on the electron determines the type of interactions
the charge carrier will have with other atoms in the material along
which conduction is occurring.
Part 5: Crystals
31
The heating effects of a current
The current flowing through the conductor should be kept constant.
This can be accomplished by using a DC source such as a fresh dry cell
battery.
The length of the conductor should be kept constant. The cross-sectional
area of the conductor s tested should be the same. If using wires, then
the wires should be the same gauge wire. These factors, if kept constant,
ensures that you are looking for variation in the resistance due only to a
difference in the material from which the conductor is made.
32
From ideas to implementation
Exercises – Part 5
Exercises 5.1 to 5.6
Name: _________________________________
Exercise 5.1
Microchips and microprocessors are a part of your daily life. They have
invaded almost all aspects of the way you live. In this exercise you will
assess the impact of the invention of the transistor on society. Refer
particularly to the use of transistors in microchips and microprocessors.
To do this you must first locate relevant information eg. Internet search,
library search, survey a cross-section of your community. Then you
must collect and organise this information so you can make a judgement
about the impact of the invention of the transistor on society.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Part 5: Crystals
33
Exercise 5.2
The invention of solid state (or transistor) devices was desirable because
the use of thermionic devices was often too difficult, too costly and
required a large power input. Portability was essential to the
development of modern communication devices.
Gather, summarise and present information from secondary sources that
describe how increased knowledge of semiconductor behaviour lead to
the development of the solid state equivalent of the triode, the transistor.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Exercise 5.3
The structure of the transistor is particularly suited to being constructed
in layered manufacturing procedures such as those used in the
manufacture of microchips. Explain why.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
34
From ideas to implementation
Exercise 5.4
Describe, with the aid of diagrams how doping affects a p and n type
semiconductors and their ability to conduct electricity.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Exercise 5.5
The contribution of the Braggs to an understanding of the crystal
structure is undisputed. Assess the impact of their contribution to the
understanding of the crystalline structure of materials.
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Part 5: Crystals
35
Exercise 5.6
What are the factors in the crystal lattice of a metal that can impede the
flow of electrons causing heat to be generated?
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
36
From ideas to implementation