Blundell Thermal Physics · Problem 24.5

Phonons

Physics — Statistical Mechanics · phonon-dispersion-2d-square-lattice

Problem

Generalize the treatment of a monatomic linear chain to the transverse vibrations of atoms on a (two-dimensional) square lattice of atoms and show that ω=(2Km)1/2[2−cos⁡qxa−cos⁡qya]1/2,(24.36)\omega = \left(\frac{2K}{m}\right)^{1/2}[2 - \cos q_x a - \cos q_y a]^{1/2}, \tag{24.36} and derive an expression for the speed of sound.

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