Question

Assume there is a 2-dimensional crystalline sample, in which the ions can vibrate within the crystal plane (but not out of plane). It is a square lattice with lattice constant a. The sample itself is a square with side length L. There are N=L²/a² atoms in the sample.

(a) Derive the form of the density of states D(w). (The answer can be expressed in terms of dw/dk.)

(b) Assume the phonon dispersion relation is w= vk, calculate the density of states explicitly based on the result of (a).

Answer 1

We of stels Da-)-上-上 0A0 2.