Probability distribution of X-ray intensities in a noncentrosymmetric crystal with a degree of centrosymmetry

Abstract

The expression for the probability distribution of X-ray intensities is obtained for a non-centrosymmetric crystal possessing an approximate centre of symmetry and from this the acentric and centric distributions of Wilson are deduced as limiting cases. Theoretical expressions for the variance, test ratio q and moments of the normalized intensity z are also obtained in terms of the parameter 〈|Δr|〉 which is a measure of the degree of centrosymmetry. From the theoretical results it appears that the non-centrosymmetric nature of such a crystal could be detected by statistical tests, provided accurate z values are available and reflexions with high (sin θ/λ) values are used for the test.