The application of the convolution relations in the X-ray line breadth analysis. I

Abstract

An X-ray diffraction profile resulting from microstructural changes in materials is a convolution of the instrumental and the true diffraction profile. The simultaneous convolutions of the functional forms representing the respective profiles are dealt with. The convolution of schoening's true diffraction profile, originating from the cauchy particle-size profile and the guassian strain profile with the instrumental profile having several functional forms (namely, gaussian, cauchy and an intermediate exponential one), has been examined and applied to profiles of several cold-worked alloys and vapour-deposited silver films. A fairly good agreement for the calculated and experimental integral breadths of the profiles has been observed for a gaussian instrumental function. The analysis gives a confirmation of the functional forms assumed and also of the schoening's particle size and strain parameters.