Beyond the ability of Rietveld analysis: MEM-based pattern fitting

A multipurpose pattern-fitting program, RIETAN-2000, and a software package, VENUS, for three-dimensional (3D) visualization were substantially combined to grow into an integrated system for whole-pattern fitting (w.p.f.) based on the maximum entropy method (MEM). In MEM-based pattern fitting (MPF), ‘observed’ structure factors resulting from Rietveld analysis are analyzed by MEM to yield improved structure factors, Fc(MEM). Then, we carry out w.p.f. where structure factors are fixed at the Fc(MEM)s. Fo(w.p.f.) data estimated after w.p.f. are analyzed again by MEM. MEM analysis and w.p.f. are alternately repeated until R factors in the latter no longer decrease. These iterative processes enable us to minimize a bias imposed by a structural model for the Rietveld analysis on final electron/nuclear densities. MPF is flexible enough to be capable of modeling static and dynamic disorder, chemical bonds, nonlocalized electrons, and anharmonic thermal motion better than the Rietveld method. Applications of MPF to structure refinements of five compounds with disordered structures have demonstrated its excellent performance and effectiveness.