A computer program, Dysnomia, for the maximum-entropy method (MEM) has been tested for the evaluation and advancement of MEM-based pattern fitting (MPF). Dysnomia is a successor to PRIMA, which was the only program integrated with RIETAN-FP for MPF. Two types of MEM algorithms, i.e., 0th-order single-pixel approximation and a variant of the Cambridge algorithm, were implemented in Dysnomia in combination with a linear combination of the “generalized F constraints” and arbitrary weighting factors for them. Dysnomia excels PRIMA in computation speed, memory efficiency, and scalability owing to parallel processing and automatic switching of discrete Fourier transform and fast Fourier transform depending on sizes of grids and observed reflections. These features of Dysnomia were evaluated for MPF analyses from X-ray powder diffraction data of three different types of compounds: taurine, Cu2CO3(OH)2 (malachite), and Sr9In(PO4)7. Reliability indices in MPF analyses proved to have been improved by using multiple F constraints and weighting factors based on lattice-plane spacings, d, in comparison with those obtained with PRIMA.

Crystal structure and structural disorder of Ba3MgSi2O8 were reinvestigated by laboratory X-ray powder diffraction. The title compound was found to be trigonal with space group P3m1, Z=1, and unit-cell dimensions a=0.561 453(4) nm, c=0.727 629(4) nm, and V=0.198 641(2) nm3. The initial structural model used for structure refinement was taken from that of glaserite (K3NaS2O8) and modified by a split-atom model. In the split-atom model, one of the two types of Ba sites and that of SiO4 tetrahedra were, respectively, positionally and orientationally disordered. The new crystal structure and structural disorder were refined by the Rietveld method. The maximum-entropy-method-based pattern fitting (MPF) method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The final reliability indices calculated from MPF were Rwp=6.52%, S=1.36, Rp=4.84%, RB=0.97%, and RF=0.52%. Details of the disorder structure of Ba3MgSi2O8 are shown in the three-dimensional and two-dimensional electron-density distribution maps determined by MPF.