From last time: Why are some materials solids at room temperature, and others are liquids or gases? The temperature of a material is related to the average.

From last time:

Why are some materials solids at room temperature, and others are liquids or gases?

The temperature of a material is related to the average kinetic energy of the atoms. To become a liquid, the average kinetic energy must be about the same as the potential energy of the bonds – so that they can be broken. For a solid, KE << PE; for a liquid, KE ~ PE and for a gas KE >>PE.

Solids 3

structure and strength

from last time:

a summary…

Bond type restrictions conductivity

ionic Charge – nns are opposite charge

poor

covalent Direction – bond angles maximised

poor

metallic None! excellant

breaking bonds

The type of bonds that hold a material together also determine what sort of forces that material is strong or weak to, and whether it will deform, permanently or not, or break under stress.

This can be understood in terms of the restrictions on the bonds.

but first, a look at solid structures…

Crystals are solids that have long range order – the atoms are bound into neat, repeating units.

Solid metals are all crystalline. All ionic solids, and many covalent solids are also crystalline. You can consider a crystal as one gigantic molecule, made of repeating units (called basis cells).

but there are always imperfections, see the additional notes on the web about this!

Crystals

amorphous solids

amorphous – means no shape (morph = shape)

amorphous solids have no long range atomic order, although they may have short range order. They often form when a liquid is cooled quickly, and many little crystals form, giving a solid with many different bits or subunits

Purely ionic bonds don’t allow the formation of amorphous solids – too many restrictions – but covalent and metallic solids can be amorphous.

Glasses, which are made of SiO2 plus various impurities, are amorphous. Especially when there are lots of impurities. Crystal structures which are tetrahedral more easily become amorphous because the bonds can swing around easily.

Glasses are such a common example of an amorphous material that often the term “glass” or “glassy” is used rather than amorphous.

polymers

How come rubber, which has covalent bonds, is bendy rather than brittle, like chalk?

because it’s a polymer!

Polymers are long chains of carbon, with stuff like hydrogen hanging off the sides. The chains are loosely held to each other by being physically tangled, by van der Waals bonds and sometimes by cross-linking (strong bonds).

They are elastic because the long molecules can slide past each other, and twist and bend, because they are only bound in one dimension.

The more cross linking there is, the more rigid they become, because they get held together in 3 dimensions.

Polymers form amorphous solids because they don’t stack neatly – they get tangled so they rarely form crystals

How to break things

How to break things.

There are different ways of applying a force (stress) to produce a deformation (strain).

Compression – squashingTension – pullingShear – pushing at an angle (sliding)Torsion – twistingBending – you know what bending is!Pressure – applying force all over, e.g. via a fluid

The amount that something stretches or compresses is determined by the Young’s (elastic) modulus of the material.

Y = stress/ strain =

Big Y – less stretchy.

Note that in many books the symbol E is used for Young’s modulus.

Tension and compression

xx

AF

x

x

strain

stress

steel

aluminium

ultimate strength

The Young’s modulus, also known as elastic modulus, is the gradient of the stress-strain graph.

Many materials are strong to compression – bonds are being compressed, so the atoms are not quite at their equilibrium distances anymore.

Tension usually breaks materials more easily – the attractive part of the interatomic potential isn’t as strong as the repulsive part, so bonds come apart!

Interatomic potential

stableattractive

repulsive

pause for thought 1

For a given applied stress, a material with a large Youngs modulus will:

a. stretch lessb. stretch morec. be less likely to breakd. be more likely to breake. a and cf. b and d

than a material with a small Young’s modulus.

and the answer is…

For a given applied stress, a material with a large Young’s modulus will:

a. stretch less

than a material with a small Young’s modulus.

Young’s modulus is defined as stress over strain – a large Young’s modulus means only a small stretch. But this is not directly related to the ultimate strength!

breaking

Breaking or rupture happens when the ultimate strength of a material is exceeded. The ultimate strength is given as a force per unit area, for example the ultimate strength of steel is around 108 N.m-2 (depending on type). The maximum force you can apply is therefore the strength the cross sectional area. Any more than this and it will break. Materials also have maximum shear stresses, and hydraulic (pressure) stresses.

Shear forces

Shear forces act to distort an object, usually by changing the angle between solid faces.

The stress and strain are related by the rigidity or shear modulus,

G =

lx

AF

F

x

l

The bigger G is, the less the thing will distort.

When a shear force acts on a material it changes the alignment of the atoms – this moves nearest neighbours closer or further, changes bond lengths, and also changes bond angles!

Pressure – applying force evenly all over

The amount an object will compress depends on the bulk modulus –

B =

VV

AF

V

F

V

The bigger B is, the less the object will compress.

Bending and Twisting

Bending and twisting both involve shear forces.

Bending is also a combination of tension and compressions.

stretchedcompressed

putting it together…

So now we know what sort of distortions different forces cause, and we also know about different types of bonds, so why are metals ductile and malleable, but covalent and ionic solids brittle?

because of the restrictions!

Ionic solids have charge restrictions, Covalent materials have direction restrictions, Metals have no restrictions!

Metals are ductile and malleable:

metallic bonds have no directional constraints and no nearest neighbour constraints – moving the atoms around a bit, provided they can stay close enough together to remain bonded, doesn’t make much difference. So they bend but don’t easily come apart.

force

Covalent bonds are very directional – move one atom a bit, you change the bond angles and it is no longer bound, and the structure comes apart. Covalent materials are weak to shear forces!

SiO O

force

SiO

O

Ionic bonds are not directional, but they have nearest neighbour constraints – shift things across a bit, suddenly you’ve got positives near positives, and negatives near negatives…

Ionic bonds are also weak to shear forces!

and finally, something to think about for next time…

Why are bones much stronger to compression and tension than to twisting or bending?

And given that your tibias have a cross sectional area of about 3 cm2, and a Young’s modulus of about 1.6 1010 N.m2, how much do your tibias compress when you get up in the morning?