Three-dimensional visualization of electron- and nuclear-density distributions in inorganic materials by MEM-based technology

The analysis of observed structure factors estimated after Rietveld analysis by the maximum-entropy method (MEM) gives electron or nuclear densities in the unit cell. The resultant densities are, more or less, biased toward a structural model in the Rietveld analysis. To overcome such a problem, we devised a sophisticated technique named MEM-based pattern fitting (MPF). For this purpose, a pattern-fitting system, RIETAN-FP, and a MEM analysis programs, PRIMA or its successor called Dysnomia, were virtually integrated into a structure-refinement system, whereby the pattern calculated from structure factors obtained by MEM is fit to the whole observed pattern. The resulting observed structure factors are analyzed again by MEM. In this way, whole-pattern fitting and MEM analysis are alternately repeated until R factors in the former no longer decrease. MPF virtually represents the crystal structure by electron or nuclear densities. MPF is, therefore, very effective in visualizing positional, occupational, and orientational disorder, chemical bonding, and anharmonic thermal motion. New programs, MPF_multi and VESTA 3, used in MPF are briefly introduced, and two representative applications of MPF to inorganic materials containing highly disordered chemical species are demonstrated.