Lattice Vibrational Spectrum of Imperfect Crystals

Abstract

The influence of lattice defects on the normal modes of vibration of crystals is investigated by means of perturbation theory. The calculations have been carried to the second order, and the effect of holes on the vibrational partition function has been determined. It is found that through their influence on the lattice vibrational free energy, a pair of holes in a crystal attract each other with an average force whose potential diminishes asymptotically as 1/R6.