Volume of a solid at absolute zero

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Discussion Overview

The discussion revolves around the volume change of solids as they are cooled from room temperature to absolute zero, particularly focusing on the implications of thermal expansion coefficients and atomic spacing at low temperatures. Participants explore the calculations involved in determining the average distance between atoms and the vibrational frequencies of solids.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how much a typical solid shrinks when cooled to absolute zero, noting the variability of the coefficient of linear thermal expansion with temperature.
  • Another participant asks for the required accuracy of the calculations, suggesting that the room temperature spacing could suffice for some purposes.
  • A participant expresses the intent to calculate the average distance between atoms at room temperature to derive vibrational frequencies, acknowledging that there may be alternative methods.
  • Concerns are raised about the accuracy of using room temperature coefficients for calculations, with a suggestion that a linear approximation could yield a shrinkage value that is half of what would be calculated using the room temperature coefficient.
  • One participant asserts that the spacing between atoms should approach zero at absolute zero, while another clarifies that this refers to the distance between atoms rather than their centers.
  • There is a discussion about defining the "distance between atoms," with some participants noting the challenges in defining atomic boundaries and suggesting the use of ionic or atomic radii for clarity.
  • A participant mentions having calculated radii for various elements and allotropes, indicating a depth of prior research on the topic.
  • Another participant hypothesizes about modeling atoms as rigid spheres at absolute zero, discussing the implications of thermal motion and bonding as temperature increases.
  • A specific property of Ice Ih is introduced, noting its density maximum at 62 K and its behavior upon cooling above absolute zero.

Areas of Agreement / Disagreement

Participants express differing views on the accuracy required for calculations and the implications of atomic spacing at absolute zero. There is no consensus on the best approach to model atomic distances or the effects of temperature on solid volume.

Contextual Notes

Participants acknowledge the complexity of defining atomic distances and the limitations of using linear thermal expansion coefficients, which may vary with temperature. The discussion includes unresolved assumptions about atomic behavior at absolute zero.

em3ry
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TL;DR
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
 
Last edited:
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How accurate do you need to be?
 
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.
 
Last edited:
  • Skeptical
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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.
 
Last edited:
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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
 
em3ry said:
The spacing should be zero absolute zero
What ?
 
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The distance between atoms. Not the distance between atom centers.
 
em3ry said:
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".
 
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  • #10
I have already calculated the radii for all elements for multiple allotropes.
 
  • #11
em3ry said:
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?
 
  • #12
Ice Ih has the property of having a density maximum at 62 K. Yes, it shrinks on cooling above absolute zero.
 

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