Variance method for the evaluation of particle size and dislocation density from x-ray Bragg peaks

Abstract

A method is presented to determine the particle size and internal strain from broadened x-ray peaks obtained on small coherent domains containing dislocations. In contrast with the evaluation techniques applied earlier, the proposed procedure requires only the measurement of a single line profile. It is based on the asymptotic behavior of the second-and fourth-order restricted moments. At the asymptotic part of the second-order restricted moment, the finite grain size causes a linear diffraction vector dependence, while that of the dislocation-induced strain is logarithmic. On the fourth-order moment, the two sources of broadening result in cubic and parabolic behavior. The method is illustrated by analyzing x-ray peaks measured on a cold-and hot-deformed AlMg alloy and on a nanocrystalline iron powder.