Einstein Model vs Debye model.

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    Debye Einstein Model
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Discussion Overview

The discussion centers on the comparison between the Einstein model and the Debye model of atomic oscillations in solids, focusing on the concepts of independence and harmonicity of oscillators. It explores theoretical implications and contrasts between the two models.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • Some participants describe the Einstein model as treating atoms as independent oscillators, while the Debye model treats atoms as coupled oscillators vibrating collectively, with a focus on the meaning of independence in this context.
  • One participant suggests that the independence of oscillators in both models arises from the assumption of harmonicity, where forces are linear functions of displacements.
  • Another participant raises a question about whether the independence in the Einstein model is due to harmonicity or if it is the collective modes in the Debye model that are independent because of harmonicity.
  • It is noted that the Debye model can reduce to the Einstein model under certain conditions, specifically when energy bands are flat, allowing for the construction of localized oscillations from degenerate oscillators.
  • Some participants mention that optical phonon bands are often not very curved, allowing them to be approximated by Einstein oscillators.

Areas of Agreement / Disagreement

Participants express differing views on the implications of harmonicity and independence in both models, indicating that the discussion remains unresolved regarding the nuances of these concepts.

Contextual Notes

The discussion involves assumptions about harmonicity and the conditions under which the Debye model approximates the Einstein model, which may not be fully explored or agreed upon.

PsychonautQQ
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In the Einstein model, atoms are treated as independent oscillators. The Debye model on the other hand, treats atoms as coupled oscillators vibrating collectively. However, the collective modes are regarded here as independent. What is the meaning of this independence and how does it contrast with the Einstein model?
 
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The independence of the oscillators is a consequence of the assumed harmonicity of the oscillators, i.e. the forces being linear functions of the displacements. Once anharmonic terms are considered, these will give rise to scattering of oscillations on each other which is among others one reason for the limited thermal conductivity of solids.
 
you mean in the Einstein model the independence is a consequence of assumed harmonicity of oscillators? Or in the Debye model the collective modes are regarded as independent because of the assumed harmonicity?
 
PsychonautQQ said:
you mean in the Einstein model the independence is a consequence of assumed harmonicity of oscillators? Or in the Debye model the collective modes are regarded as independent because of the assumed harmonicity?

In both models. Also note that the Debye model reduces to the Einstein model when the energy bands are flat as then you can construct localized oscillations from the degenerate oscillators. Often, the bands corresponding to optical phonons are not very curved so that they can be approximated by Einstein oscillators.
 

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