Debye temperature

1. Aug 16, 2008

hugonot

I guess is Debye temperature dependent on temperature? I.e TD(T)?
Does anybody know a theoretical formula for temperature dependence of Debye temperature?

Last edited: Aug 16, 2008
2. Aug 16, 2008

Staff: Mentor

3. Aug 16, 2008

hugonot

Thanks, However, I know this references.
My problem is:
I have got specific temperature dependence C(T) for the solid compound.
I can estimate Debye temperature from the fit, but it will be only one value for the whole range of temperatures.
How can I estimate Debye temperature at specific temperature?
How can t be estimated from material dependent variables? I know the formula for TD http://en.wikipedia.org/wiki/Debye_model but what should I use as N and V?
If V stands for volume, what means N or rather how to calculate it?
Could you give me an example? I mixed up

4. Aug 16, 2008

Staff: Mentor

In the Wikipedia article cited - http://en.wikipedia.org/wiki/Debye_model#Debye.27s_derivation - N is the number of atoms.

If the atomic density is given by $\rho$NA/A, where $\rho$ is the density, NA is Avogadro's number, A is the atomic mass.

Last edited: Aug 16, 2008
5. Aug 16, 2008

Gokul43201

Staff Emeritus
Any temperature dependence in the Debye Temperature comes from temperature dependences in elastic constants (and due to thermal expansion). These changes are small: about 1 part in 1000 to 1000,000 per Kelvin.

6. Aug 19, 2008

hugonot

Thanks for both responses.
I have still a problem with N/V (number per atoms in unit volume).
I have got elementary cell volume V and mass weight of the molecule M.
The cryst. group is P1-. I don't have density,
How can I calculate N/V?

7. Aug 19, 2008

Staff: Mentor

What type of molecule, i.e. is this a mineral or alloy?

For some basic lattices, there is usually a given number of atoms/cell and a unit cell volume based on the geometry and lattice parameters. It's a close estimate to get N/V, if one doesn't have mass density.

8. Aug 19, 2008

hugonot

My molecule is organic compound - benzene derivative, I visualised elementary cell but
it seems complicated to calculate the number of atoms...
I have got cell parameters.

9. Aug 20, 2008

hugonot

Where can I find a procedure for Debye model evaluation or tables of this integral value?
I have found a reference to the tables by HARRISON but not available for me...