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1-Determine the density of states for a two-dimensional continuous medium using periodic boundary conditions. 2- In...

1-Determine the density of states for a two-dimensional continuous medium using periodic boundary conditions.

2- 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. Explain the meaning of this independence, and contrast it with that in the Einstein model.

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Expert Solution

1)

2)   In Einstein and Debye model ,if we comapre the two .In Einstein model a solid that treat each constituent atom asa an independent harmonic oscillator .In case of heat capacity we know per particle is dimensionless units.

   

In Einsteain model ,the independence of the oscillator is a consequence of the assumed harmonicity of the oscillators .that is ,the force being linear functions of the displacements.In case of unharmonic oscillator they will give rise to scattering of oscillations on each other which is the reason for limited thermal conductivity of the solids.

genius_generous answered 2 years ago
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