Dynamics of point defects in crystals

Abstract

A partitioning technique has been used to study the detailed dynamics of the atoms associated with a point defect, treating them a pseudomolecule. The concept of the spectral density function of a normal mode has been introduced to study the time dependence of the vibrational modes of the pseudomolecule. Relaxed and persistent modes of vibration correspond to the well behaved and singular parts respectively of the spectral density function. It has been shown rigorously that simple vacancies in square and simple cubic lattices with nearest neighbour interactions do not have localized modes of vibration.