Atomic Vibration in Einstein & Debye Models

[sirwan]

according to Einstein all atoms in solid vibrating with the same frequency , while in the Debye's mode there are a band of frequency i.e not all the atoms would have the same frequency, my question is that , that is the idea behind the Debye's model? or why the frequency of vibrating of atoms differ from one other in the same type of crystal.

 

[Electric Red]

according to Einstein all atoms in solid vibrating with the same frequency , while in the Debye's mode there are a band of frequency i.e not all the atoms would have the same frequency, my question is that , that is the idea behind the Debye's model? or why the frequency of vibrating of atoms differ from one other in the same type of crystal.

Sorry, I do not completely understand what your question is. Could you say that again?

 

[sirwan]

In solid crystal, according to Debye Model .why the frequency of vibration of one atom Different from one another? or why all atoms not vibrating with the same frequency. thanks

 

[Electric Red]

Well, the Debye model differs a little from the model of Einstein.
At low temperatures, the Debye model is more accurate than that of Einstein.

But to fully answer your question, just take a look at this:
Debye model - Wikipedia, the free encyclopedia

Hope this helps you, otherwise just tell me.

 

[gadong]

In the Debye model, vibrations can have any wavelength that is consistent with the periodicity of the crystal.

The smallest wavelength (highest frequency) corresponds to the interatomic spacing. The longest wavelength (lowest frequency) corresponds to the size of the crystal itself. The allowed wavelengths in between these limits are multiples of the interatomic spacing.

The above conditions need to be applied in 3-dimensional space, but that does not change much. The actual relationship between frequency and wavelength is material dependent, and is only linear at low frequencies.