Mathematical analysis of the high-resolution reciprocal space map

A reciprocal space map recorded by means of a high-resolution diffractometer is a function of two angular variables: ω and 2θ defined as angular position of the studied crystal and position of an analyser, respectively. For comparative investigations of different samples the inter-planar spacing distribution function and the lattice reflecting plane orientation distribution function are more useful. In this paper we present the integral equations, which allow one to obtain these functions through the integration of the reciprocal space map matrix. An example of the mathematical analysis of the reciprocal space map for GaAs single crystal recorded by means of a Philips MRD high-resolution diffractometer is described and well-defined analytical formulae for the apparatus functions are given