# Debye temperature formula

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

### Astronuc

Staff Emeritus
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

### Astronuc

Staff Emeritus
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

### Astronuc

Staff Emeritus
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...