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Assumptions:

- 1.
- Each atom has a certain equilibrium position in the lattice
- 2.
- Vibrations are harmonic with frequency

So we have 3*N* harmonic oscillators, and heat capacity
is

**Problem With Einstein Model:**- At low
*T*heat capacity is . This is too fast! The experimental result is . **Reason:**- Atoms move
*cooperatively:*if atom A goes to the left, its neighbor might accommodate by going the same way! Einstein model does*not*account for this.We must introduce

*collective motion.*

© 1997

Wed Oct 1 00:45:35 EDT 1997