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PsychonautQQ

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In summary, the Einstein model treats atoms as independent oscillators due to the assumed harmonicity of their forces, while the Debye model considers atoms as coupled oscillators with collective modes that are regarded as independent, also due to the assumed harmonicity. However, when the energy bands are flat, the Debye model reduces to the Einstein model.

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PsychonautQQ

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DrDu

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PsychonautQQ

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DrDu

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PsychonautQQ said:

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.

The Einstein model assumes that all atoms in a solid vibrate with the same frequency, while the Debye model takes into account the different vibrational frequencies of atoms in a solid.

The Debye model is generally considered to be more accurate for describing the heat capacity of solids, especially at low temperatures.

The Einstein model does not account for anharmonicity, as it assumes that all vibrations are harmonic.

The Einstein and Debye models are both valid for solids with a well-defined lattice structure, but they may not accurately describe the heat capacity of amorphous or disordered solids.

At high temperatures, the Einstein model predicts a constant heat capacity, while the Debye model predicts that the heat capacity will approach a linear increase with temperature.

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