Do solids expand in low preasure?

[Panthera Leo]

Do solids expand in low preasure?

I was wondering about the volume of solid material under constant temperature, but variable preasure... What is the difference in the volume of an Iron crystal between 1atm & vacuum for example?

Do solids expand in low preasures? if yes, how much? Are there any equations?

Thanks in advance.

 

[Studiot]

Good morning Panthera Leo.

That is a thoughful question. Keep enquiring.

The answer is that indeed solids do respond to pressure or the release of pressure by contracting or expanding.

For elastic substances ( those that follow Hookes Law) there is a physical parameter, called the bulk modulus which controls this and is given the symbol K. K is similar to Young's modulus in one dimensional (linear) elastic theory and is related to it.
K is normally taken as positive in the compressive direction.

So we write

{\rm{K = }}\frac{{{\rm{compressive}}\,{\rm{force}}\,{\rm{per}}\,{\rm{unit}}\,{\rm{area}}}}{{{\rm{changein}}\,{\rm{volume}}\,{\rm{per}}\,{\rm{unit}}\,{\rm{volume}}}} = \frac{P}{{\frac{{\Delta V}}{V}}}

You will note this definition leaves K with the same units as pressure - Pascal

In the case of iron that you have mentioned K is 170 GigaPascal for iron and using the fact that 1 atmosphere is approx 10⁵ Pascal we can calculate the change in volume if we hung up a 1 metre cube of iron in a chamber and evacuated it. The expansion would obviously equal the compression the cube would undergo if we repressurised the chamber to 1 atm.

\frac{{\Delta V}}{V} = \frac{{\Delta V}}{1} = \frac{{{{10}^5}}}{{1.7*{{10}^{11}}}} = 6*{10^{ - 7}}cubicmetres

go well

 

[Panthera Leo]

Many thanks indeed studiot, Your reply is very informative and helpful :)

I was just wondering, how to calculate the expansion for a ceramic material which isn't elastic... Like a Quartz crystal (SiO2)

I am guessing the same method applies, but am I right?

Thanks again :)

 

[Studiot]

Pretty well all materials show some elasticity.

K for quartz is 37 GPa by comparison. (so it is [STRIKE]less[/STRIKE] edit: more compressible)

One thing to note is that depending upon the crystal (or other) structure of the material the elasticity may not be the same in all directions. In such cases we say the material is anisotropic = not isotropic
The bulk modulus assumes that the material is isotropic.

If this is not the case you have to consider each direction separately.

 

[AlephZero]

All materials are elastic. The difference between ceramics and steels is that ceramics are brittle and steel is not. If you hit a piece of ceramic hard with a hammer, it will break. If yuo hit a piece of steel hard, you will permanently change its shape (i.e. make a dent in it or bend it) but it won't break.

The bulk modulus for fused quartz is about 37 GPa compared with 165 to 170 for steel. So fused quartz is actually about 4.5 times "more elastic" than steel in this sense.
http://www.kayelaby.npl.co.uk/general_physics/2_2/2_2_2.html

"Ceramics" is rather a vague decription. Different types of ceramics have a wide range of K values, from about 10 GPa and up to close to 1000 GPa.

 

[Studiot]

Yes AZ is right, the smaller K is the larger deltaV/V is. ie the larger the volumetric strain.

(Previous post edited to suit.)

 

[Panthera Leo]

Many thanks for the clarification... I had a confussion between elasticity & ductility! My bad :) Now its very clear.

But something shocked me here... How could it be that quartz is more compressible than Iron?!

If the compression is related to the bond energies, then Quartz has a higher bond energy which is reflected in its melting point, Quartz melts at 1700C and Iron is about 1200C

My second question is regarding the temperature dependace of the Bulk modulus? Does it change as temperature rises? if yes what is the formula?

Thanks in advance :)

 

[Studiot]

The relationship between the elastic moduli and bond energies is not so accurate as some other properties, like specific heats.

Melting involves actual bond rupture not just stretching.

However I would observe that the crystal structure of silicon dioxide is tetrahedral and the coordination number of the silicon is 4.
On the other hand the structure of iron is body centered cubic and the coordination number of the iron is 8.

That means that to stretch a unit crystal cell for SiO₂ you have to stretch four silicon-oxygen bonds, whereas for iron you have to stretch 8 iron-iron bonds.

Also this means that the bond angles are different so the vector force triangles are different.

For uniform hydrostatic pressure the bond angles should not change, but this will not be the case for uniaxial tension or compression.

 

[Panthera Leo]

You are amazing Studiot... Truly interesting and accurate reply.

Thanks a lot indeed :)