Atomic Vibration in Einstein & Debye Models

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Discussion Overview

The discussion centers on the differences between the Einstein and Debye models of atomic vibration in solids, specifically addressing the frequency of vibrations among atoms in a crystal. Participants explore the implications of these models and seek to understand why atoms in the same type of crystal vibrate at different frequencies according to the Debye model.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that the Einstein model posits all atoms in a solid vibrate at the same frequency, while the Debye model allows for a range of frequencies among atoms.
  • Questions are raised regarding the fundamental reasons for the differences in vibration frequencies of atoms within the same crystal structure.
  • One participant suggests that the Debye model is more accurate at low temperatures compared to the Einstein model.
  • Another participant explains that in the Debye model, vibrations can have various wavelengths determined by the periodicity of the crystal, with the relationship between frequency and wavelength being material-dependent.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the Debye model and its implications, indicating that the discussion remains unresolved with multiple competing views on the topic.

Contextual Notes

Some participants express confusion about the specific questions being asked, suggesting that assumptions or definitions may not be fully clarified. The relationship between frequency and wavelength is noted to be linear only at low frequencies, indicating potential limitations in the discussion.

sirwan
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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.
 
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sirwan said:
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?
 
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
 
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.
 
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.
 

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