PDFFIT , a program for full pro ® le structural re ® nement of the atomic pair distribution function

The program PDFFIT is designed for the full pro®le structural re®nement of the atomic pair distribution function (PDF). In contrast to conventional structure re®nement based on Bragg intensities, the PDF probes the local structure of the studied material. The program presented here allows the re®nement of atomic positions, anisotropic thermal parameters and site occupancies as well as lattice parameters and experimental factors. By selecting individual atom types one can calculate partial and differential PDFs in addition to the total PDF. Furthermore one can re®ne multiple data sets and/or multiple structural phases. The program is controlled by a command language which includes a Fortran style interpreter supporting loops and conditional statements. This command language is also used to de®ne the relation between re®nement parameters and structural or experimental information, allowing virtually any constraint to be implemented in the model. PDFFIT is written in Fortran-77, and the source code and documentation are available via the World Wide Web. 1. Introduction The determination of crystal structures is an important part of chemistry, physics and, of course, crystallography. Conventional structure determination is based on the analysis of the intensities and positions of Bragg re¯ections which only allows the determination of the long-range average structure of the crystal. For powder diffraction data this is now routinely performed using the Rietveld (Rietveld, 1969) method. It should be kept in mind that the analysis of Bragg scattering assumes a perfect long-range periodicity of the crystal. However, many materials are quite disordered and, even more important, the key to a deeper understanding of their properties is the study of deviations from the average structure or the study of the local atomic arrangements (Billinge, 1996). Deviations from the average structure result in the occurrence of diffuse scattering which contains information about two-body interactions (Welberry & Butler, 1995; Frey, 1995). One method to reveal the local structure of crystals is the analysis of the PDF. This method is long known in the ®eld of studies of short-range order in liquids and glasses but has recently been The PDF is obtained from the powder diffraction data via a sine Fourier transform of the normalized scattering intensity S…Q†: