Phonon model of vacancy-interstitial pair formation in solids

Bonds between neighboring atoms in a solid are imperfect harmonic oscillators. Through consideration of the nonlinearities, it is shown that vacancy-interstitial defect pairs can be described in terms of phonon dynamical variables. The effective spring constants are determined by self-consistency requirements. An inhomogeneous solution is found to the equations of the self-consistent spring constants; it describes an atom breaking its bonds to its neighbors, resulting in a defect pair.