Volume of a solid at absolute zero

[em3ry]

TL;DR Summary

Volume of a solid at absolute zero

How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature

 

[Vanadium 50]

How accurate do you need to be?

 

[em3ry]

accurate enough that I can calculate the average distance between atoms in a solid at room temperature so I can calculate the vibrational frequency when given the velocity of the atoms. Now I know there might be better ways to calculate the vibrational frequency but I want to do it this way first.

 

[Vanadium 50]

That doesn't really answer the question. You could do the calculation with the room temperature spacing. If you say "that's not accurate enough", we're right back to "How accurate do you need to be?"

In any event, the coefficient of thermal expansion is often linear in T. In that case, the shrinkage is half of what it would be by using the room temperature coefficient.

 

[em3ry]

The room temperature spacing (minus the atomic radius) is exactly what I am trying to calculate. The easiest way to do that is to determine how much solids shrink. The spacing should be zero absolute zero

If the coefficient is linear than I should be able to figure this out

 

[dRic2]

The spacing should be zero absolute zero

What ?

 

[em3ry]

The distance between atoms. Not the distance between atom centers.

 

[phyzguy]

The distance between atoms. Not the distance between atom centers.

How do you define "the distance between atoms"? Atoms are not billiard balls. They don't have a well defined "edge".

 

[Baluncore]

Maybe consider size from the viewpoint of ionic radius.
https://en.wikipedia.org/wiki/Ionic_radius
https://en.wikipedia.org/wiki/Atomic_radius

 

[em3ry]

I have already calculated the radii for all elements for multiple allotropes.

 

[Baluncore]

The distance between atoms. Not the distance between atom centers.

So are you saying that at absolute zero, you model the atoms like billiard balls, all still, and packed together, without any gaps at the surface contacts. You hypothesise that as the material is heated, the average KE increases, the balls move about more but remain bonded, and the average gap between the balls must increase, because billiard balls are incompressible?

 

[snorkack]

Ice Ih has the property of having a density maximum at 62 K. Yes, it shrinks on cooling above absolute zero.