Volume of a solid at absolute zero

• B
Gold Member
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

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Staff Emeritus
How accurate do you need to be?

Gold Member
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.

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PeroK
Staff Emeritus
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.

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em3ry
Gold Member
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

Gold Member
The spacing should be zero absolute zero
What ?

Delta2
Gold Member
The distance between atoms. Not the distance between atom centers.

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".

Delta2
Gold Member
I have already calculated the radii for all elements for multiple allotropes.