Some Applications of Probability Theory in Direct Methods
It may seem somewhat surprising at first that probability theory has played such an important role in the solution of the crystal structure determination problem. Crystals, which are usually defined in terms of the long range ordering they display, might appear to be poor samples on which to apply a mathematical model devised to deal with random experiments. It is the realization that the periodically repeating motif could itself be depicted as consisting of atoms randomly distributed (Wilson, 1949) that allowed the phase problem to be phrased and solved in a probabilistic framework. Since then, there have been numerous applications of probability theory to the problem of crystal structure determination. They have essentially provided a solution for the case of small molecule crystal structures.
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