Phonon energy and atomic vibration energy

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SUMMARY

The discussion centers on the relationship between phonon energy and atomic vibration energy in materials, specifically addressing whether the average energy of a phonon vibration mode applies to individual atoms or the material as a whole. The consensus is that represents the energy of the material as a whole, not individual atoms. Consequently, as the size of the material increases, the amplitude of atomic oscillations decreases while maintaining a constant .

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camilo
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When we say that a phonon vibration mode has an average energy <E> are we saying that all atoms (or harmonic oscillators) in a piece of matter (eg. a nanoparticle) will also has that energy, or that the piece of matter as a whole will have that energy ?
In the second case the amplitude of the oscillations of the atoms will be lower the bigger the piece of matter, for a constant <E>, I guess.

Thank you.
 
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The second option is correct and also your conclusion.
 
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