Question

Consider a square lattice that has got one atom of mass m at one lattice point.
It interacts with 1st nearest neighbours only and phonon dispersion relation
varies sinusoidally.
(a) In the long-wavelength limit, obtain the density of phonon states D(W) =
dN/dw, i.e., the number of lattice-vibration modes per frequency.
(b) At high temperature (KT >> hw), find the mean square displacement of an
atom from its equilibrium position, and comment on the stability of two-
dimensional crystals interval dw. ​

Answer 1

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Here's your answer

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