plastic / elastic

An elastic deformation is one in which the material returns to its original shape when the stress is removed.

A plastic deformation is one in which the material suffers permanent deformation. If you remove the stress and start all over again, the material will behave elastically at first in that it will return to this new 'starting' shape.

In plastic deformation, layers of atoms slide over one another, using dislocations as the 'trick' that enables them to do so. Once a layer has 'plopped' into a new set of hollows, releasing energy to the surrounding atoms as extra vibrational energy, that situation remains stable, and a reverse force will be needed to get them back again (hysteresis). This re-arrangement of atoms results in a shape change: the cross-sectional area diminishes.

Generally speaking (but polythene is an exception), materials need  a highly symmetrical crystalline structure, such as f.c.c. (but not h.c.p.) to be able to deform plastically, because you need all the randomly oriented crystals to have planes of symmetry in the direction of any particular force.

brittle / tough, malleable, ductile

The term brittle refers to the mode of fracture. The material snaps, without any apparent narrowing at the break point. The break always starts at a surface crack, and the crack gradually opens out across the specimen during the process of fracture. Brittle materials do not undergo plastic deformation. Brittle materials have no short range order in their structure (except ionic crystals).

A tough material is not brittle. The fracture it undergoes is known as ductile fracture, and is characterised (a) by necking and (b) by a 'cup-and-cone' appearance at the break. Plastic materials are tough, and vice versa. All materials, by the time they break, have formed a surface across which the break has occurred. To get to that point in a tough material, you have to apply a large force, but you then have to stretch the material a considerable distance with that force before you start to create the broken surface. This involves the expenditure of much energy. Whereas with a brittle material, once you reach the appropriate force, the material breaks apart without requiring much movement, and hence energy expenditure. That is why tough materials have a high value of energy expended / area of crack created, and why toughness can be measured in J m^-2.

A malleable material can be hammered out into very thin sheets. Gold is malleable. Malleable materials inevitably undergo plastic deformation.

A ductile material can be drawn out into fine wires. Copper is ductile. Ductile materials inevitably undergo plastic deformation.

strong / weak

These terms refer to the values of the breaking stresses.

stress, strain, Young modulus

Stress is defined as Force (tensile or compressive) divided by the cross-sectional area of the specimen at the time. Some authors use the concept of 'engineering stress', which is the current value of the force divided by the original value of the cross-sectional area. The difference is evident once necking has commenced in a ductile material. It is then possible to have a reduced force over a so much reduced area that the true stress has gone up, while the engineering stress has gone down. Since the material inevitably responds to the true stress (having re-arranged its atoms, it has no memory of what the area once was), the concept of engineering stress is of doubtful value: one might just as well state the force. Any stress-strain curve that curls downwards at its right-hand end is plotting engineering stress, and is totally unable to illustrate the concept of continued work hardening to the bitter end. It's always possible that you might be blessed with an intelligent marker. I'd be inclined to make a note near the right hand end of any such curve you draw making it clear that you know which stress you are talking about.

Strain is defined as the extension (i.e. the total extension: the difference between the current length and the original length) divided by the original length. No problems here.

The Young modulus is the gradient of the initial straight line portion of the stress-strain graph. It is sometimes known as the stiffness. Whilst on this portion of the graph, the material is said to be Hookean (i.e. it obeys Hooke's Law). The upper end of this portion of the graph is called the 'limit of proportionality'. The Young modulus is irrelevant once you get on to the plastic portion of the graph.

stiff, hard

A stiff material has a high Young Modulus.

A hard material is difficult to dent or scratch. The traditional scale of hardness (in mohs, after Frederick Mohs, and not to be confused with the mho, a former unit of conductance, otherwise known as the reciprocal ohm) had Diamond as 10 and talc (baby powder) as 0. The idea was that you placed a material at such a position in the rank order that it would scratch those beneath it and be scratched by those above it. Nowadays you apply pressure through a ball bearing of a specified size and see what pressure you need to make a dent of a particular diameter. Perhaps when I've finished writing these notes, I'll look up the details. Or you can.

You could think of hardness as 'the ability to resist permanent deformation', on the grounds that the harder material will be able to scratch a softer material when a force is applied that is above the soft material's yield point but below that of the hard material. It certainly seems to be true that high hardnesses go with high values of the yield stress.

yield point, ultimate tensile/compressive stress, elastic limit

The yield point is the point on the stress-strain curve at which a material starts to undergo plastic deformation. Obviously it is another name for the elastic limit. Beginners, working with springs, often confuse this point with the limit of proportionality.

The ultimate tensile (or compressive) stress is regarded by some as the true stress at which a material finally breaks. It is invariably the highest stress to which the specimen is subjected during the test, since the true stress goes on increasing until the breaking point is reached. However it is regarded by others as the highest engineering stress to which the material gets subjected during a test. In this case, the point will occur when the highest force has been applied, before necking has begun, and before breaking occurs. So far as engineering considerations are concerned it is obviously important to know what is the maximum force a structure can withstand, whereas a materials scientist studying the theory of intermolecular forces will be more concerned with the maximum true stress. So you takes your pick and makes your choice. But be clear which you've chosen, and make sure the examiner is clear that you are clear.

Imagine a specimen with a crack already present. We will bend it, and consider what happens to the pairs of atoms AA', BB' and CC'. 

If we represent the relevant intermolecular forces by springs, and imagine the lines of atoms each side of the dotted line to open out as in the lower diagram, then you will see that A and A' will end up further apart than C and C'. Since tension is proportional to separation for springs (and for atoms), there is a greater tension between A and A' than between any other pair of atoms down the line, so the stress is concentrated there. The total of all the tensions is what resists our attempt to bend the specimen, and holds it in equilibrium.

If we exert a greater bending moment, we increase the intermolecular forces on all the atoms, but most of all on A and A'. These two reach the maximum on the Force-separation curve before any of the others, by which time there is about half an atomic diameter of clear space between A and A'. At this point one of two things happens.

• If the atoms cannot adjust their positions to relieve the stress, A and A' come apart. The situation now is that the bending moment we are applying is being resisted by one fewer pairs of atoms, so they are all taking a slightly greater share. B and B' are already taking the As' place as chief load bearer, and they have an even greater cross to bear. So they come apart, too. So it goes on, and the material collapses along this line. 

• If, on the other hand, plastic deformation is possible, the atoms can all slide around, and some will so slide as to fill in the space between A and A'. This removes the stress, and the specimen will be permanently bent. But whole.

Start from the notion that the ions are held in a lattice, without worrying about how this is achieved. Permeating this is a 'sea' of electrons. The reason it is a 'sea' is that the electrons in question (generally the electrons in the outermost shell) would normally sit at a particular distance from their parent atom, but the ionic centres are closer together than this: which means that an electron between two ions is in a no-mans-land, belonging to both ions. So the electron can swim around all the ions freely (it can't go through the middle of them of course!), following the course of a coracle floating on  a river meandering its way around lots of little hillocks. 

In an insulator the atoms are just that bit further apart (insulators tend to be less dense than conductors), and the outer electrons are held more firmly to their atoms, while the atoms are held less firmly to each other. However, if you could excite an outer electron into the next energy level up, because higher energy levels usually have higher radii associated with them, the excited electron would now be able to drift into the next-door atom's territory, and so would be able to drift around the place. For most insulators the exciting energy required to do this is so high that the material would melt before you had achieved it. 

A semiconductor is a material in which the energy required to promote a valence electron into the conduction band is quite low, so at room temperatures a small number of electrons are able to drift around at this higher level. Warming such a material promotes more electrons into this level, and the conductivity increases (conductivity µ number of free electrons per unit volume (among other things))

Resistance arises when electrons drifting along (a current) arrive at a dislocation, because then the next-door atom isn't sufficiently close to be jumped to after all. So the electron comes crashing to a halt, turns round and goes off in another direction so as to avoid the dislocation. This process imparts energy to the region around the dislocation, and the ions around the collision vibrate more vigorously. Hence the electron has been slowed in its progress and its energy has been transferred to the material as thermal energy. 

If you heat a material, the extra random lattice vibrations mean that temporary 'dislocations' keep coming into being that impede electron flow: thus the rise of resistance in hot materials. In a semiconductor, the promotion of electrons into the conduction band is an even more important effect, which is why thermistors (lumps of semiconductor) have negative temperature coefficients of resistance.

Furthermore, the increased vibration of the dislocations means that any electrons making contact are bounced away with more energy than they had before (super-elastic collisions). Because the electrons form a sea (or gas, as it is often perceived in this context), they are not confined, and shoot off to quite distant parts of the material carrying their newly acquired KE with them. They then interact with dislocation in the new place, having by-passed all the intervening ions, dumping their energy, thereby effecting a transfer of thermal energy from the part being heated to a cooler part. That is why good conductors of electricity tend to be good conductors of thermal energy (The Wiedemann-Franz Law). Insulators have to transfer thermal energy by the much less efficient process of bumping into the next door atom, and passing it down the line, one atom at a time.

When you've chosen a material, and thought of something which might be made with it, have a good rummage through the 'Resources' files of chapters 4 and 5 of the CD. Identify and read those articles which appertain to your particular choice. It may well be that you will stick with the material you've already worked on, but that you haven't so far looked to see what the CD has got on it.