Debye temperature for Na

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  • #1
MMS
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Homework Statement


Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
Calculate the Debye temperature for Na

Homework Equations


I worked out this equation to calculate the Debye temperature (If needed I can show how)
XzxlsHT.png

The Attempt at a Solution


I plugged in all the numbers in the above equation with the correct units and I get that the Debye temperature is 280.3K. However, in literature I found that it is approximately 150K.
Is there something wrong with my calculations? Am I missing out on something here?

Thank you!
 

Answers and Replies

  • #2
SteamKing
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Homework Statement


Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
Calculate the Debye temperature for Na

Homework Equations


I worked out this equation to calculate the Debye temperature (If needed I can show how)
XzxlsHT.png

The Attempt at a Solution


I plugged in all the numbers in the above equation with the correct units and I get that the Debye temperature is 280.3K. However, in literature I found that it is approximately 150K.
Is there something wrong with my calculations? Am I missing out on something here?

Thank you!
Please provide your calculations.
 
  • #3
MMS
148
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Please provide your calculations.
BnOvrQ7.png
 
  • #4
SteamKing
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  • #6
MMS
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Anyone?
 
  • #7
SteamKing
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Anyone?
Your calculations are arithmetically correct, as far as I can see.

It's not clear that NA ⋅ ρ / MW is an accurate substitute for the N / V which is used in other Debye Temperature derivations I have seen. Your expression doesn't seem to account for the fact that since sodium is bcc, there are two atoms per cell, rather than one. It makes a difference in calculating the edge length of the cell.

I think for calculating a reasonable approximation to the Debye Temp., this is the issue which must be resolved. In some articles I have seen, the authors try to use the properties of the material measured close to the Debye Temp., like the speed of sound and the density, to come up with a more accurate calculation.
 

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