Advancing Physics AS

Name ………………………………………………………

Chapter 4 Testing materials

Student Notes The entry below is taken from the 2008 OCR specification which combines the topics to be taught in Chapters 4 and 5.

Module PA 2: Designer materials This section is about materials and how their properties are related to their uses and their structures. Microscopic images are used to give evidence of structure at different scales. The physics may be put into perspective through contexts such as the study of medical replacement materials, biological materials and engineering materials. Human and cultural issues arise, for example, in considering the impact of materials on technology and society and through the aesthetic appeal of materials.

It is not intended that candidates acquire a detailed knowledge of a wide range of materials, and the terminology associated with each. It is intended that they have a reading comprehension of terms needed to understand accounts of the structure, uses and properties of materials. Examples should include: a metal, a semiconductor, a ceramic, a long-chain polymer and a composite material.

Properties to be studied are restricted to simple mechanical and electrical properties.

Candidates should develop skills of measurement, instrumentation and identification of uncertainty. It is expected that this will be taught in part through measurement tasks carried out in teams and reported to others.

Recommended Prior Knowledge ● Some of this work is provided with a foundation in PA Module 1 Communication, in particular through ideas of resistance and conductance in circuits. If candidates are not confident with measuring resistance with an ohmmeter or with thinking of current as a flow of charged particles, that work may need to be brought forward here if PA Module 2 Designer Materials is taught before PA Module 1 Communication.

Assessable learning outcomes

1. Knowledge and understanding of phenomena, concepts and relationships by describing and explaining cases of:

(i) simple mechanical behaviour: types of deformation and fracture;

(ii) simple electrical behaviour: the broad distinction between metals, semiconductors and insulators (only in terms of the number of mobile charge carriers, not their mobility);

(iii) direct evidence of the size of particles and their spacing;

(iv) behaviour and structure of classes of materials: metals, ceramics, polymers, composites;

(v) one method of measuring:

Young modulus and fracture stress;

electrical conductivity or resistivity.

Page | 2 2. Scientific communication and comprehension of the language and representations of physics,

by making appropriate use of the terms:

(i) for mechanical properties and behaviour: stress, strain, Young modulus, fracture stress and yield stress, stiff, elastic, plastic, ductile, hard, brittle, tough;

(ii) for electrical properties: resistivity, conductivity, charged carrier density;

ability to sketch and interpret:

(iii) stress–strain graphs up to fracture;

(iv) tables and diagrams comparing materials by properties;

(v) images showing structures of materials.

3. Quantitative and mathematical skills, knowledge and understanding by making calculations and estimates involving:

(i) R = ρl ; G = σ A A l

(ii) tensile/compressive stress, strain, Young modulus E = stress . strain

A Revision Checklist for Chapter 4 can be found on the Advancing Physics CD-ROM.

Page | 3 Section 4.1: Just the job - Getting a feel for materials

Learning outcomes ● A material chosen for a particular application must have the right combination of properties. ● Classes of materials include metals, glasses, ceramics and polymers. ● Composite materials combine the properties of more than one material. ● Compressive forces tend to squash an object; tensile forces tend to stretch it. ● Brittle materials snap easily; tough materials do not.

Some historical background (see PowerPoint presentation ‘Historical background of materials’) Materials have had such an impact in the past that historical eras have been named after the available materials: (i) The Stone Age (pre-2500 BC): hard/brittle materials used to make earthenware, tools and weapons. (ii) The Bronze Age ( 2500 BC to 500 BC): hard, tougher material and quite malleable. (iii) The Iron Age ( 500 BC to 1850 AD): hard, tough, ductile and cheap. Used to make sophisticated tools, bridges, ships etc). (iv) 19th Century: steel (an alloy of iron) became available: increased strength and lower brittleness. Allowed larger structures to be made. (v) 20th Century: composite materials (synthetic) and plastics became available, which provided greater strength and flexibility together with a low density. Proved to be particularly useful in the aircraft and civil engineering industries. (vi) Future trends: high temperature superconductors; nanotechnology, which enables new materials to be synthesised at a molecular and atomic level; advanced materials for electronic and photonic devices (e.g. optical computing) etc.

Materials to choose from We open with a discussion of the properties of various materials and how these properties are suited to particular jobs. The sheer range of materials available to us should become apparent as should the enormous volumes being processed globally.

Question 10S Short Answer 'Exploring the range of materials' This set of images portrays a range of materials in action, each with a question about its properties and uses. It emphasises non-physics aspects – including environmental and aesthetic issues convenient to create a broad context, and interest.

Getting a feel for materials Here we move in from the broad picture to concentrate on the physical properties of materials. The experiments that follow are intended to provide a gentle introduction. Some of the activities will be revision of GCSE work. The point is to emphasise that each material has its own profile of properties. The experiments will be run as a circus, or part circus / part demonstration. A more formal version of tensile testing is found in the next section where the Young modulus is calculated.

Page | 4 Activity 10E Experiment 'Tensile testing: Getting a feel for materials 1' Activity 20E Experiment 'Compressive testing: Getting a feel for materials 2' Activity 30E Experiment 'Hardness testing: Getting a feel for materials 3' Activity 40E Experiment ‘Tear testing: getting a feel for materials 4’ Activity 50E Experiment 'Measuring density: Getting a feel for materials 5'

Revision notes on density

density = mass  volume or  = m / V

If the mass in grams and the volume is in cubic centimetres, the density is in grams per cubic centimetre or g/cm3. If the mass in kilograms and the volume is in cubic metres, the density is in kilograms per cubic metre or kg/m3.

Mixing units 1 m = 100 cm 1 m3 = (100 cm)  (100 cm)  (100 cm) = 1 000 000 cm3 and 1 kg = 1 000 g

Water has a density of 1 000 kg/m3 which is 1 000 kg which is 1 000  1 000 g = 1 g/cm3 1 m3 1 000 000 cm3

To convert from g/cm3 to kg/m3, multiply by 1000. To convert from kg/m3 to g/cm3, divide by 1000.

Some values of density: Material Density in kg/m3 Density in g/cm3 air 1.3 0.0013 wood (balsa) 200 0.20 wood (oak) 720 0.72 ice 920 0.92 high density polythene 960 0.96 bone 1100 1.1 breeze block 1400 1.4 brick 1700 1.7 concrete (ordinary mix) 2200 2.0 glass-reinforced plastic 1900 1.9 glass 2500 2.5 aluminium 2700 2.7 steel (high-tensile) 7800 7.8 copper 8900 8.9 lead 11400 11.4 mercury 13600 13.6 uranium 18700 18.7 platinum 21500 21.5

Page | 5 Some key words (See A-Z) – You have now been introduced to a number of these terms. Fuller descriptions and explanations will follow.

Mechanical characteristics The mechanical characteristics of a material have to do with its behaviour when subjected to forces which try to stretch, compress, bend or twist it. The mechanical characteristics of a material determine its stiffness, its strength, its flexibility or brittleness and its toughness. Other characteristics include its density, whether or not it is elastic or plastic and whether it is ductile and malleable.

A tensile force (tension) tends to stretch an object. A compressive force (compression) tends to compress an object.

Density is the mass per unit volume of a substance. Solids and liquids vary in density mostly because elements have different atomic masses. Lead is much more dense than aluminium. mainly because lead atoms are much heavier than aluminium atoms.

Stiffness is to do with the difficulty of stretching or bending a material (e.g. a metal sheet is stiffer than a polythene sheet of the same dimensions). Ceramics are stiff because of the strong directional bonds between the atoms or ions.

Hardness is to do with how difficult it is to dent a material (e.g. a steel knife is much harder than a plastic knife).

Brittleness is to do with how easy it is to snap a material (e.g. a potato crisp is much more brittle than a lettuce leaf). The brittleness of glass is a consequence of defects such as fine surface cracks, which propagate easily through the material.

Toughness is to do with how hard it is to snap a material, that is, with the extent to which a material is resistant to the propagation of cracks. It is the opposite of brittleness. Metals are tough because cracks do not propagate easily, due to the non-directional nature of metallic bonds. There is no one simple quantitative measure of toughness, though it can be approximated by the ratio of the energy dissipated during the fracture to the area of new surface created.

Elasticity is to do with the ability of a material to regain its shape (e.g. a rubber band regains its original length when released). When a metal or ceramic stretches elastically, the bonds between neighbouring atoms extend very slightly. In a polymer the atoms rotate about their bonds.

Plasticity is to do with permanent stretching or distortion of a material (e.g. a polythene strip stretches permanently if extended too much).

Ductility is to do with how easy it is to draw a material into a wire (e.g. copper is easier to draw into a wire than tungsten). Metals are ductile because the non-directional metallic bonds allow ions to slide past one another.

Malleability is to do with how easy it is to hammer or press a sheet of material into a required shape (e.g. a lead sheet is easier to fit on a roof than a tin sheet).

Page | 6 Classifying materials This second part of section 4.1 develops the idea that materials can be classified. Through a discussion of bones, the student book distinguishes 'tension' from 'compression' and 'brittle' from 'tough' materials. Later in section 4.2, you will begin to treat material properties quantitatively.

At this point we will introduce the materials database and materials selection charts. The charts plot one property against another (e.g. Young modulus for stiffness against density): the quantitative ranges in behaviour very clearly cluster like materials into classes. More than this, the range of values within a class of materials raises the question of why – and leads to consideration of how properties relate to material structure (taken up in chapter 5).

Both database and charts may be useful for your materials research and presentation.

This reading introduces the materials selection charts: Reading 100T Text to read: 'Introduction to materials selection charts'

This key reading explains in more detail what materials selection charts are, and through specific examples demonstrates their power as an aid to materials selection in the design process and also as a route to thinking about controlling properties (through understanding materials structure – the theme taken up in chapter 5). From here you can also find all related resources, including interactive charts embedded in a web site supplied on the Advancing Physics AS CD-ROM.

Display Material 15O OHT 'Material selection charts'

Materials selection charts are a novel approach to presenting mechanical characteristics, and help us to understand:  how each class of materials (metals, ceramics, polymers etc) has a characteristic range of values for a given property  how the properties of a material reflect the underlying microstructure, and can therefore be usefully improved by scientists and engineers  the engineering context of material properties in designing and making things, since this invariably means making trade-offs between two or more properties (including the cost!)

Five materials selection charts are introduced below. To understand how to interpret and use the charts in depth, study Reading 100T 'Introduction to materials selection charts'. More interactive versions of the charts can be found in File 5L 'Interactive materials selection charts'.

Page | 7 1. Young modulus and density – classes of materials

Physical Insights  Stiffness measures how much something stretches elastically when a load is applied. Young modulus measures stiffness and is a material constant, i.e. it is the same whatever the size of the test-piece.

 Young modulus and density both depend on the atomic packing within the material, and Young modulus depends on the type of bonding between the atoms (electron bond, covalent, ionic etc.)

 Note how the materials all lie roughly on a diagonal – Young modulus is strongly correlated to density.

 The metal and polymer bubbles are small – this is because material composition and processing do not have a significant effect on density or Young modulus.

 Woods have very different stiffnesses depending on whether they are loaded 'with' or 'across' the grain. This is because of the aligned stiff cellulose micro-fibres. Both paper and MDF are made from wood pulp and so have similar densities, but have little directional variation in Young modulus.

 Foams have the lowest densities because they have pores full of air.

 Note that the scales are logarithmic, because of the large ranges of values.

Page | 8 Applications of the chart  Stiff lightweight materials are hard to find, for things like sports products and bicycles – composites appear to offer a good compromise, but they are usually quite expensive, and wood is still used for cheaper products (e.g. oars).

 Many applications require stiff materials, e.g. roof beams.

 Many applications require low density materials, e.g. packaging foams.

 Polymers don't seem like a good choice for stiff, lightweight products – but they can be reinforced by incorporating stiffening ribs into the design (for instance, look inside a mains plug).

 Ceramics are quite light and very stiff – but their poor tensile strength and toughness means they are likely to fracture.

2. Young modulus and density – metals and polymers

Page | 9  Young modulus and density both depend on the atomic packing within the material, and Young modulus depends on the type of bonding between the atoms (electron bond, covalent, ionic etc.)

 Note how the materials all lie roughly on a diagonal – Young modulus is strongly correlated to density.  The metal and polymer bubbles are small – this is because material composition and processing do not have a significant effect on density or Young modulus.

 Foams have the lowest densities because they have pores full of air.

 Note that the scales are logarithmic, because of the large ranges of values.

Applications of the chart  Stiff lightweight materials are hard to find, for things like sports products and bicycles – composites appear to offer a good compromise, but they are usually quite expensive, and wood is still used for cheaper products (e.g. oars).

 Many applications require stiff materials, e.g. roof beams.

 Many applications require low density materials, e.g. packaging foams.

 Polymers don't seem like a good choice for stiff, lightweight products – but they can be reinforced by incorporating stiffening ribs into the design (for instance, look inside a plug).

 Ceramics are quite light and very stiff – but their poor tensile strength and toughness means they are likely to fracture.

3. Strength and toughness – classes of materials

Page | 10 Physical Insights  Strength measures the resistance of a material to failure, given by the applied stress (or load per unit area).

 The chart shows yield strength in tension for all materials, except for ceramics for which compressive strength is shown (their tensile strength being much lower).

 Toughness measures the energy required to propagate a crack through a material; it is important for things which suffer impact.

 The material bubbles are large, particularly for metals – this is because material composition and processing have a significant effect on strength and toughness.

 The tensile strengths of brittle materials are very sensitive to the presence of flaws.

 Metals are tough because they deform plastically instead of propagating cracks.

 Cast iron is often brittle because it contains graphite flakes which behave like little cracks within the metal.

 Quenching carbon steel makes it very hard but brittle; tempered steel is tougher but less strong than after quenching.

 Note that the scales are logarithmic, because of the large ranges of values.

Applications of the chart  There are many cases where strength is no good without toughness. Saw blades, hammer heads and engine components are commonly made of quenched and tempered steel to get moderately high strength with good toughness .

 Steel is often used to absorb energy in car impacts because it is tough and strong.

Page | 11  Ceramics cannot be used for components which suffer impact because of their low toughness.

 Polymers are quite sensitive to cracks and defects as they do not absorb much energy when they fracture; they are often considered to be tough however because of their ductility – energy is absorbed straining the material to failure. This makes them good for children's toys, when their low strength is also not important.

4. Strength and toughness – metals

Physical Insights  Strength measures the resistance of a material to failure, given by the applied stress (or load per unit area).

 The chart shows yield strength in tension for all materials, except for ceramics for which compressive strength is shown (their tensile strength being much lower).

Page | 12  Toughness measures the energy required to propagate a crack through a material; it is important for things which suffer impact.

 The material bubbles are large, particularly for metals – this is because material composition and processing have a significant effect on strength and toughness.

 The tensile strengths of brittle materials are very sensitive to the presence of flaws.

 Metals are tough because they deform plastically instead of propagating cracks.

 Cast iron is often brittle because it contains graphite flakes which behave like little cracks within the metal.

 Quenching carbon steel makes it very hard but brittle; tempered steel is tougher but less strong than after quenching.

 Note that the scales are logarithmic, because of the large ranges of values.

 Steel is often used to absorb energy in car impacts because it is tough and strong.

 Ceramics cannot be used for components which suffer impact because of their low toughness.

5. Electrical resistivity and cost – metals and polymers

Page | 13 Physical Insights  Metals are much better conductors than other materials because their atoms are ionised, bonded by a 'sea' of free electrons which also carry current.

 Pure metals are better conductors than alloys – this is because electrons travelling through the lattice of ions are obstructed by irregularities such as alloying atoms.

 Polymers and ceramics are good insulators because their electrons are all tightly bound to individual atoms or ions.

 Semiconductors are 'doped' with elements which provide extra electrons (n-type) or provide positive holes (p-type) which can move freely.  Note that the scales are logarithmic, because of the large ranges of values – electrical resistivity spans over 24 orders of magnitude!

Applications of the chart  This chart is important for designing components at a reasonable cost which require good electrical insulation (e.g. plug casings, made of polymers) or good electrical conductivity (e.g. electric power cables, made of aluminium or copper).

 Gold and silver have the best conductivities but are too expensive to be widely used, except as connectors in electronic applications.

 Electrical conductors are also generally good thermal conductors because their free electrons contribute to thermal conduction. However some insulators such as marbles Page | 14 and diamond are very good thermal conductors, because energy is transmitted though vibrations of the atomic lattice. Thus metals may be good for saucepans, while some ceramics such as fire bricks insulate the wall of a kiln.

See also File 5L Launchable File: 'Interactive materials selection charts' This provides an interactive route through the materials selection charts, providing a wider range of charts to study, showing how thinking about choosing materials for a purpose can involve looking along many axes.

See also File 10D Spreadsheet Data Table: 'Materials database'. This is a resource to return to on more than one occasion. Data for about a dozen properties of some 50 materials is provided in spreadsheet format. You can generate a list ordered by property, search for materials with properties in certain ranges, create your own graphs and calculate composite properties. Also included is a materials database commentary. This document, in searchable html format, provides a commentary for each of the materials in the database.

Section 4.2: Better buildings - Measuring and using mechanical properties

Learning outcomes ● Ceramic materials such as brick and concrete are strong in compression but weak in tension. ● The strength of a material is represented by both its breaking stress and yield stress. ● The stiffness of a material is represented by its Young modulus. ● The Young modulus is found from the initial linear gradient of a stress-strain graph. ● Materials are elastic up to the elastic limit; then they either fracture or show plastic deformation.

Page | 15 force extension stress ● Stress  Strain  Young modulus  area original length strain

Tension and compression Loading a material in tension causes stretching (increase in length) and loading a material in compression causes squashing (decrease in length). Some materials (e.g. stone) are strong in compression but not in tension.

Display Material 30O OHT 'Tension and compression at home'

Tension and compression at home

tie beam across roof in tension, stops roof spreading out

walls compressed by weight of roof

heavy bed loads floor

floors bend- stretched underneath

weight of building pushes down

ground compressed foundations pushes up

Display Material 20O OHT 'Forces of tension and compression'

Page | 16 Bones under compression and tension

thinner thick arm bone thigh bone

Bone in compression. Bone in tension. Compressive forces squash Tensile forces stretch the the bone. bone along its length.

Bone bends. Bone breaks. On the outside of the bend, A break occurs where a bone is in tension. On the crack develops in the inside of the bend bone surface which is in tension. is in compression.

Activity 100E Experiment Plot and look: measuring breaking stress of materials. Here you will look at an example of how to deal with measuring a quantity that varies from sample to sample. The stress needed to break a material does not have one single exact value. This is because one sample will not be identically the same as another. Samples of wood from different parts of a tree may have different grain and fibre structures. A sample may have imperfections that weaken it. And samples will not have exactly the same dimensions. This means that values for the breaking force and breaking stress will spread over a range. When designing something using a material, it may be just as important to know how much the breaking stress varies, as to know its average value.

Stress, strain and the Young modulus We start with a simple demonstration experiment to obtain a force-extension graph for copper wire. The wire is stretched until it breaks.

Page | 17 The experimental arrangement is the same as that used in Activity 10E of this chapter. Copper wire of diameter 0.28 mm should be used. The original length should be recorded for later use. Original length = ………………………………………… m

Copper wire may spring back when it breaks. The sharp edges are dangerous so bridges must be placed over the wire and eye protection must be worn.

Force / N

Extension / cm

Force / N

Extension / cm

Add the values to the set of axes below.

Now use the space below to sketch the graphs you would expect to obtain if the experiment were to be repeated with a sample that is (a) twice as long as the one used and (b) twice the diameter of the one used. You should start by sketching the graph you have just obtained, but allow for the fact that extensions and forces may be quite different.

Notes:

Page | 18 Example Calculate the breaking stress of the copper sample that was stretched in the experiment above. To do this you should use the graph to determine the largest force that could be Page | 19 applied to the copper and then calculate the cross sectional area of the copper using the value of the diameter supplied. Take care with units and very awkward numbers!

…………………………………………………………………………………………………………

Now that you understand the meaning of stress you might wish to revisit Activity 10E so that you can calculate the breaking stresses of the materials used.

Logarithmic scale of stress

100,000 105 diamond

10,000 104

glass Each main division represents a factor of 10 1,000 103

Two main divisions represent a factor of 100 102 mild steel, kevlar 10  10 = 100 = 102

10 101 wood

1 100 foamed polymers

0.1 10–1 Display Material 40O OHT 'Strengths of some materials'

0.01 10–2 Page | 20

You cannot have zero on a logarithmic scale. At the lower end, it goes 0.1, 0.01, 0.001, and so on, getting smaller and smaller but never reaching zero. Page | 21 Example (a) Calculate the maximum strain of the copper sample used in the experiment above. Give your answer as a number and as a percentage.

…………………………………………………………………………………………………………

(b) Calculate the strain at which the copper wire first underwent plastic deformation. Give your answer as a number and as a percentage.

…………………………………………………………………………………………………………

………………………………………………………………………………………………………… Page | 22 Display Material 50O OHT 'The Young modulus'

The Young modulus 1

Many materials stretch in a uniform way. Increase the stretching force in equal steps, and the extension increases in equal steps too, in proportion. That is, the strain is proportional to the stress producing it. This is the same as Hooke's law – the stretching of a spring is proportional to the stretching force you apply.

3F stress  stress  2F   = F A F

strain  0 0  extension 0 x 2x 3x x strain  = L strain  stress ...... graph is straight line

ratio stress is constant strain

stress Young modulus = strain  E = 

The Young modulus 2

large strain for little stress _ little strain for large stress material is flexible, easy to _ material is stiff, hard to stretch stretch

0 0 0 0 strain  strain 

e.g. polymer e.g. diamond, steel

The Young modulus is large for a stiff material (large stress, small strain). Graph is steep.

The Young modulus is a property of the material not the specimen. Units of the Young modulus MN m–2 or MPa; for stiff materials GN m–2 or GPa. Same as units of stress, because strain is a ratio of two lengths, e.g. extension is 1% of length

Page | 23 We now make the preceding observations quantitative by investigating and measuring the stiffness of a material through tensile testing.

Activity 150E Experiment 'Measuring the stiffness of a material' You will need to think carefully about ways to measure the extension with high precision and how to measure the diameter of the wire.

Summary graphs:

The graphs of stress and strain would be the same regardless of the length or diameter of the samples. Develop an argument to justify this statement.

…………………………………………………………………………………………………………

Page | 24 elastic plastic region, plastic region, region extension uniform necking has along length begun

400

300

200

+ fracture 100

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 39.0 39.1 39.2 strain /%

Display Material 60O OHT 'Stress-strain graph for steel'

Notice that the stress shows a dip when data is collected using a tensometer as in the case shown above. The tensometer measures the stress in the sample when the length is changed. No such dip is seen when applying weights to stretch the wire as we did.

Points to note: You should add these to your graph after discussion in class. (a) elastic region (b) plastic region (c) yield point

Brittle and ductile fracture You may have had a chance to look at the fracture surfaces. A brittle material will fracture without plastic deformation whereas a ductile material undergoes plastic deformation before fracture. Images of the different fracture surfaces are given below.

Display Material 10S Computer Screen ‘Ductile and brittle fracture’

The two images are scanning electron micrographs of brittle and ductile fracture of materials under tensile test. The left-hand specimen failed through ductile fracture and there is evidence of plastic deformation around the edge of the fracture surface. The right hand image shows a more extensive fracture surface.

Page | 25 The images below were taken from Advanced Physics by Tom Duncan1. The image on the left shows the stages leading to the fracture of a ductile material and the image on the right shows the typical cup and cone that is characteristic of ductile fracture.

The images below were taken from The Mechanical and Thermal Properties of Materials by Collieu and Powney2. The left-hand image shows the formation of a neck in a 2mm-diameter piece of aluminium. The plastic deformation is very apparent after the fracture in the right hand diagram.

Section 4.3: Conducting well; conducting badly Measuring and using electrical properties

Learning outcomes ● Electrical conductivity is a property which varies over a vast range.

1 Tom Duncan, Advanced Physics (fourth edition), John Murray, 1994 2 Anthony Mc B Collieu and Derek J Powney, The Mechanical and Thermal Properties of Materials , Edward Arnold, 1973 Page | 26 ● It is important to distinguish between the properties of an object or sample (e.g. resistance) and those of a material (e.g. resistivity). ● In selecting a material for a particular application, many different properties may have to be taken into account. ● Calculations of conductivity using G = σ A / L and resistivity using R = ρ L / A.

The basic electrical ideas (current, potential difference and resistance) will be needed at this stage. You will need to be able to set up a circuit to find the resistance of a component. The very different magnitudes of resistances for conductors and insulators should be observed.

By examining how the dimensions of a body affect its resistance, you should develop the idea of a property of the material itself, its resistivity (or conductivity).

Introducing resistance We begin with some revision – how to find the resistance of a component and develop the idea of resistivity by looking at the effect of dimensions on resistance.

Activity 310E Experiment 'Measuring resistance of good conductors' Activity 330E Experiment 'Measuring the resistance of two insulators'

Activity 340E Experiment 'How the dimensions of a conductor affect resistance'

Display Material 110O OHT 'Conductivity and resistivity'

Conductivity and resistivity

length L

conductance G resistance R area A

conductance 2G resistance R 2 area 2A GA R 1 A two pieces side by side conduct twice as well as one – so have half the resistance

length L resistance R area A G length 2L conductance resistance 2R 2 1 G area A RL L two pieces end-on conduct half as well as one – so have twice the resistance

You need to know length L to find cross-sectional area A to find conductance G from conductivity  resistance R from resistivity  A L G = G = 1 R = 1 R = L R G A unit: siemens (S) unit: ohm () conductivity  from conductance G resistivity  from resistance R GL 1 1 RA  =  =  =  = A   L _1 unit: S m unit: m Conductivity  and resistivity  give the same information in complementary ways

Page | 27 Logarithmic scale of resistivity and conductivity

conductivity / S m–1

8 silver, copper, gold 10– 8 10 superconductors—zero resistance metals are the best conductors nickel, iron – 6 6 alloys generally conduct less well steel, bronze 10 10 than pure metals

10– 4 104

doped germanium 10– 2 10 2

pure germanium 1 1 semiconductors conduct, but not very well 10 2 10– 2 pure silicon

10 4 10– 4

10 6 10– 6

Pyrex glass 108 10– 8

alumina 1010 10–10

12 – 12 insulators conduct very little, Perspex, lead glass 10 10 almost not at all

1014 10–14 polystyrene 1016 10– 16

1018 10– 18

resistivity /  m

Display Material 100O OHT 'Range of values of conductivity'

The conductivity of the best conductor, silver, is 1024 times greater than the conductivity of the best insulator, polystyrene. Note that semiconductors are midway through the range of values for resistivity (or conductivity).

Activity 350E Experiment 'Good measurements of electrical resistivity' This experiment involves a discussion of uncertainty.

Page | 28 Section 4.4: Problems of measuring mechanical and electrical properties

Learning outcomes ● Watch out for natural variations between samples; plot the values and find the range. ● Start with a rough measurement or calculation, to identify the problems to be solved. ● Small quantities, close to the resolution of an instrument, are hard to measure with low uncertainty. ● If A α d 2, the percentage uncertainty in A is double that in d . ● To improve a measurement, identify the largest source of uncertainty and try to reduce that first. ● Look out for systematic errors and try to remove them.

The following experiments may have been completed already:

Activity 100E Experiment Plot and look: measuring breaking stress of materials. Activity 150E Experiment 'Measuring the stiffness of a material' Activity 350E Experiment 'Good measurements of electrical resistivity'

Further practice in the calculation of uncertainties can be gained from: Question 210D Data Handling Calculating with uncertainties: Chapters 4-5 and Case study: the ocean from space (pages 220-224 of the student text)

Page | 29 Questions and activities additional to those in the Student Notes Section Essential Optional 4.1 Qu 1-6 AS text p 79 Question 20C Comprehension: The Bronze Age Read AS text pp 75-78 Question 30C Comprehension: Portraits in plastic Activity 160S Software based 'Cycle frame Question 10S Short Answer 'Exploring design' the range of materials' Activity 60E Experiment 'Comparing thermal Reading 100T Text to read: 'Introduction conductivities: Getting a feel for materials 6' to materials selection charts' Activity 70E Experiment 'Electrical conduction: Getting a feel for materials 7'

Activity 90H Home Experiment 'Anisotropy in an apple' Activity 100H Home Experiment 'Creep in an everyday material' Activity 110H Home Experiment 'Time effects in an everyday material' Activity 120H Home Experiment 'Time effects in custard' Activity 130H Home Experiment 'Stiff jelly'

Reading 10T Text to read: Steel – the most important material? Reading 20T Text to read: Materials from nature 4.2 Qu 1-7 AS text p 87 Reading 50T Text to Read 'Fantastic fibres' Read AS text p 80-86

Question 10E Estimate ‘Making estimates about the mechanical behaviour of materials’

Question 40S Short Answer ‘Analysis of tensile testing experiments’ Question 45S Short Answer 'Calculations on stress, strain and the Young modulus' Question 50 S Short Answer ‘Measuring the Young modulus’

Question 50D Data Handling 'Stress, strain and the Young modulus'

Reading 40S Text to Study 'Hooke's Law and the Young modulus' Reading 60S Text to Study 'More about log scales' 4.3 Qu 1-6 AS text p 90 Question 60D Data handling 'Resistivity and Read AS text pp 88-89 conductivity'

Question 20E Estimate 'Making Question 90X Explanation-Exposition 'Review estimates about the electrical behaviour questions' of materials' Question 70S Short Answer 'Electrical properties' Question 80S Short Answer 'Resistivity and conductivity calculations' Question 100S Short Answer ‘Conductance and conductivity’

Page | 30 4.4 Qu 1-6 AS text p 94 Case study: the ocean from space (pages 220- Read AS text pp 91-93 224 of the student text)

Question 210D Data Handling ‘Calculating with uncertainties: Chapters 4-5’

Page | 31