Changes in Macroscopic Shape, Lattice Parameter, and Density in Crystals Due to Point Defects

Abstract

It is demonstrated that a crystal of arbitrary shape filled with a fine random distribution of centers of dilatation will dilate homogeneously. No elastic approximations are made, and the results should hold for strains of any magnitude. By use of an average and perfect reference lattice embedded in the strained crystal, it is then shown that the lattice dilatation as measured by x-ray lattice parameter measurements and by macroscopic dimensional measurements should be the same along any direction when the number of substitutional atomic sites remains constant. Perturbing effects due to x-ray diffuse scattering should cause negligible error in determining the positions of the Laue-Bragg maxima under usual conditions. All results should apply also to the case of thermal dilatation at temperatures up to the melting point. The use of density measurements in the determination of point defect concentrations is discussed. Experimental data are reviewed.