Random field of internal stresses from point defects in a crystal

Abstract

The variance and correlation function are calculated for the internal stress field created by point defects situated independently at random lattice points in a crystal. For equal concentration dilatations, the amplitude of the internal stresses in a fcc lattice is several times the amplitude in an fcc lattice. It is shown that the stress field is practically uncorrelated and its probability density function is represented by an Edgeworth asymptotic series. An asymptotic representation of the stress distribution is proposed in the form of a superposition of a discrete stress spectrum and a normally distributed “background.”