Abstract

The probability density of phase angles for structures with one or more atoms on known positions Sim (1959). Acta Cryst. 12, 813-818 is expressed in terms of normalized difference-structure factors, and used to calculate standard deviations of phases and expectation values for amplitudes (|Er|) of the normalized difference-structure factors. Numerical results are tabulated for various values of |E1| and |E2|, i.e. the minimum and maximum |Er| value a given reflection can have. Applications to the DIRDIF procedures van den Hark, Prick & Beurskens (1976). Acta Cryst. A32, 816-821 are described. New applications are the calculation of the a priori probability density function for |Er| values, and a statistical rriethod for the detection of a centre of symmetry in the remaining part of the structure. For the statistical method, a centricity parameter, Xc, which is unity for centric and zero for acentric distributions, is defined; for the difference structure, Xc is calculated by an iterative procedure, extrapolating towards zero contribution of the known part of the structure. Numerical results for 13 test structures are given.