# Debye temperature for Na

1. Dec 17, 2015

### MMS

1. The problem statement, all variables and given/known data
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

2. Relevant equations
I worked out this equation to calculate the Debye temperature (If needed I can show how)

3. 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!

2. Dec 18, 2015

### SteamKing

Staff Emeritus

3. Dec 18, 2015

### MMS

4. Dec 18, 2015

### SteamKing

Staff Emeritus

5. Dec 18, 2015

### MMS

6. Dec 19, 2015

### MMS

Anyone?

7. Dec 19, 2015

### SteamKing

Staff Emeritus
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.