The probability distribution of structure factors with non-integral indices. II. The P1 case

The probability distribution of the structure factors with non-integral indices is derived in P1. For integral values of at least one of the indices, the intensity distribution coincides with that provided by Wilson's statistics, but may strongly differ when the indices are (or are close to) half-integers. The deviations are stronger when the integral part of the indices is small, and increase with the size of the structure. In favourable circumstances, moduli and phases of the reflections may be accurately estimated.