Solving crystal structures from powder data - III: The use of the probability distributions for estimating the |F|'s

Decomposition programs of powder patterns play a basic role for crystal structure solution from powder data. Indeed, they provide the structure-factor ampli- tudes to which direct or Patterson methods can be applied. The decomposition process is not always satisfactory: large errors in the estimates frequently frustrate any attempt to solve crystal structures. This paper describes a probabilistic method that, integrated with the Le Bail algorithm, is able to improve amplitude estimates. The method uses triplet-invariant distribution functions, from which marginal distributions estimating structure-factor moduli were derived.