A Bayesian approach to phase extension

D. S. Sivia, W. I. F. David and S. Hull

Rutherford Appleton Laboratory

The lack of phase information in diffraction data has always made the solution of crystal structures a challenging problem. While the difficulty can often be reduced by having several sets of measurements related by known changes, as in isomorphous replacement or anomalous dispersion, most experiments consist of a single data-set. The successful solution of a crystal structure then hinges on the use of additional information, in one way or another: this can range from a good initial estimate of the answer, or a general knowledge of the atomic connectivity, to just the physical positivity of the electron density distribution. In this talk, we consider the case when part of the structure is known, such as the location of the heavier atoms or a ring-fragment, and wish to use this knowledge to help solve the remainder; in particular, we focus on the situation when the diffraction data are from a powdered sample.

We will begin with an elementary outline of the phase problem and a brief review of the conventional heavy-atom method. A Bayesian view of the situation will then be presented, with an emphasis on the case of powder diffraction data, and the theory illustrated with

several examples.

Sivia, DS, and David, WIF, J Phys Chem Solids 62 (2001) 2119-2127.

Hull, S, Keen, DA, Sivia, DS, Berastegui, P, J Solid State Chem 165 (2002) 363-371.