Is there a formula for the temperature dependence of Debye temperature?

[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?

 

[Astronuc]

I believe the Debye temperature is dependent on the material/element.

http://hyperphysics.phy-astr.gsu.edu/Hbase/Tables/thrcn2.html

http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/Debye.html

Of course, thermal conductivity is temperature dependent.

 

[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

 

[Astronuc]

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

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 $\rho$N_A/A, where $\rho$ is the density, N_A is Avogadro's number, A is the atomic mass.

 

[Gokul43201]

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

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.

 

[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?

 

[Astronuc]

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?

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.

 

[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.

 

[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...