“…16,17 Charge density distribution of Sb x CoSb 3Àx was determined by the maximum-entropy method (MEM) using the MEM-based pattern fitting (MPF) method, with the programs Rietan-FP and PRIMA. [18][19][20] Split pseudo-Voigt functions were used to fit Bragg peaks and the peak profile was calculated within 15 6 FWHM (full width at half maximum) of peak position. A Legendre polynomial was fitted to background intensities with 10 adjustable parameters.…”
Modeling the hydration of mono-atomic anions from the gas phase to the bulk phase: The case of the halide ions F−, Cl−, and Br− J. Chem. Phys. 136, 044509 (2012) Structure, energetics, and reactions of alkali tetramers J. Chem. Phys. 136, 014306 (2012) Influence of solute-solvent coordination on the orientational relaxation of ion assemblies in polar solvents J. Chem. Phys. 136, 014501 (2012) Theoretical study of the aqueous solvation of HgCl2: Monte Carlo simulations using second-order Moller-Plessetderived flexible polarizable interaction potentials J. Chem. Phys. 136, 014502 (2012) A two-dimensional-reference interaction site model theory for solvation structure near solid-liquid interface
“…16,17 Charge density distribution of Sb x CoSb 3Àx was determined by the maximum-entropy method (MEM) using the MEM-based pattern fitting (MPF) method, with the programs Rietan-FP and PRIMA. [18][19][20] Split pseudo-Voigt functions were used to fit Bragg peaks and the peak profile was calculated within 15 6 FWHM (full width at half maximum) of peak position. A Legendre polynomial was fitted to background intensities with 10 adjustable parameters.…”
Modeling the hydration of mono-atomic anions from the gas phase to the bulk phase: The case of the halide ions F−, Cl−, and Br− J. Chem. Phys. 136, 044509 (2012) Structure, energetics, and reactions of alkali tetramers J. Chem. Phys. 136, 014306 (2012) Influence of solute-solvent coordination on the orientational relaxation of ion assemblies in polar solvents J. Chem. Phys. 136, 014501 (2012) Theoretical study of the aqueous solvation of HgCl2: Monte Carlo simulations using second-order Moller-Plessetderived flexible polarizable interaction potentials J. Chem. Phys. 136, 014502 (2012) A two-dimensional-reference interaction site model theory for solvation structure near solid-liquid interface
“…MEM-based pattern fitting (MPF) was proposed to address such a problem and determine more reliable electronor nuclear-density distributions (Izumi et al, 2001;Izumi and Dilanian, 2002;Izumi 2004). In MPF, MEM analyses and whole-pattern fitting (w.p.f.)…”
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, Cu 2 CO 3 (OH) 2 (malachite), and Sr 9 In(PO 4 ) 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.
“…Thus, the MEM and MPF analyses are alternately repeated (REMEDY cycle) until the reliability indices reach minima. 12) Crystal structures can be seen clearly from EDDs determined by MPF.…”
The 27R-SiAlON crystal with the general formula Si 3¹x Al 6+x O x N 10¹x (Z = 3) was characterized using laboratory X-ray powder diffraction (Cu K¡ 1 ) and energy dispersive X-ray spectroscopy. The [Si:Al] molar ratios were determined to be [0.12(1):0.88(1)], corresponding to x = 1.9(1). The Si 1.1(1) Al 7.9(1) O 1.9(1) N 8.1(1) compound is trigonal with space group R3m (centrosymmetric). The hexagonal unit-cell dimensions are a = 0.305991(4) nm, c = 7.1454(1) nm and V = 0.57940(1) nm 3 . The structural parameters of the initial model were taken from those of 27R-AlON (Al 9 O 3 N 7 ), which were subsequently refined by the Rietveld method. The final structural model showed the positional disordering of two of the five types of (Si,Al) sites. The maximum-entropy methodbased pattern fitting 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 disordered crystal structure was successfully described by overlapping five types of domains with ordered atom arrangements. The distribution of atomic positions in one of the five types of domains can be achieved in the space group R3m. The atom arrangements in the four other domains are noncentrosymmetric with the space group R3m. Two of the four types of domains are related by a pseudo-symmetry inversion, and the two remaining domains also have each other the inversion pseudo-symmetry. The very similar domain structure was also reported for 27R-AlON.
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