Debye Model of Solids: Questions & Answers

[nikolafmf]

Hello everyone,

I have two questions about the Debye model (one historical and the other theoretical).

1. Debye models oscilators as standing waves. Where did his idea come from? Is there any physical reason to suppose this? I guess he didn't compute 1000 models just to see that this one explains experimental data.

2. When we compute the number of waves, we suppose they are in a cubical container. How can one prove that results is the same for container of any other form?


Nikola

 

[Hyla Brook]

You can try to get experimental phonon dispersion graph in which you will find the linearity of the curve in the long wave region, these can be modeled as standing waves. As to the non-linear part (which generally have higher frequency), few phonons are activated at low temperature, thus the standing wave model accounts the experiment well in these cases. For the second question I cannot help.

 

[DrDu]

Debye did use standing spherical waves in a body of spherical geometry because this is the only configuration for which the equations of elasticity theory can be solved analytically. He explains this very well in his original paper P. Debye, 'Zur Theorie der spezifischen Waerme', Annalen der Physik (Leipzig) 344(14), p. 789 (1912).

To the second question: Debye didn't suppose a cubical container for the reason given above, but maybe the textbook of your teacher does so. However, there exists quite a general proof (I think by Wigner) that integral properties of a solid (like heat capacity, mean energy, pressure, ...) become independent of the specific boundary conditions in the thermodynamic limit (that is, for macroscopic bodies). So it doesn't really matter.