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

The probability distribution of structure factors with non-integral indices is derived. The distributions are first studied in the one-dimensional cas e, to understand their main features, then the three-dimensional case is tr eated. Only the P1 group is taken into consideration. For integral values o f the indices, the distributions coincide with those provided by Wilson sta tistics but may strongly differ from them when the indices are (or are clos e to) half-integrals and are sufficiently small. In these cases, the moduli and phases of the reflections may be accurately estimated in the absence o f any structural information. Conditional distributions are also derived wh ich are able to estimate moduli or phases by exploiting the prior informati on on the specific crystal structure.