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Maximum-entropy Method (maximum-entropy + method)
Selected AbstractsObservation of orientational disorder in the hexagonal stuffed tridymite Sr0.864Eu0.136Al2O4 by the maximum-entropy methodJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2004H. Yamada The crystal structure of a strontium europium aluminate, Sr0.864Eu0.136Al2O4, with a novel hexagonal form was investigated by a combination of Rietveld analysis and the maximum-entropy method (MEM) with synchrotron X-ray powder diffraction data. The electron density image calculated by the MEM/Rietveld method revealed that the apical oxygen ion in the AlO4 tetrahedron has a broad distribution corresponding to an extraordinarily large atomic displacement parameter. This structure could be expressed by a split-atom model, with which the Rietveld refinement gave Rwp = 2.99% and RB = 4.16%. Subsequently, MEM-based pattern fitting (MPF) decreased the R factors to Rwp = 2.81% and RB = 2.34% and the electron density image clearly showed that the apical oxygen ions of the AlO4 tetrahedra are split over three sites around a threefold axis involving an elongated distribution of the residual O ions along the c axis. These results suggest that AlO4 tetrahedra in Sr0.864Eu0.136Al2O4 are orientationally disordered. [source] Performance of a new furnace for high-resolution synchrotron powder diffraction up to 1900,K: application to determine electron density distribution of the cubic CaTiO3 perovskite at 1674,KJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2004Masatomo Yashima Accurate crystal structure analysis at high temperatures is an important challenge in science and technology. A new electric furnace for the measurement of high-resolution (,d/d = 0.03%) synchrotron radiation powder diffraction profiles from materials at high temperatures (up to 1900,K in air) has been designed and fabricated. This furnace consists of a ceramic refractory with MoSi2 heaters, an aluminium body cooled by flowing water, and a sample stage with a spinner and a controller for sample-height adjustment. In situ synchrotron powder diffraction measurement for a calcium titanate perovskite specimen at 1674,K has been performed using the furnace at beamline 3A of the Photon Factory. The electron density distribution of the cubic perovskite at 1674,K was successfully obtained using a combination of Rietveld refinement, the maximum-entropy method (MEM) and MEM-based pattern-fitting techniques. The Ti atoms exhibit covalent bonding with the O atoms in the cubic CaTiO3 perovskite at this temperature, while the Ca atoms are ionic. These results indicate that the new furnace yields high-quality data for accurate crystal structure analysis. [source] Particle size distributions from small-angle scattering using global scattering functionsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2004G. Beaucage Control and quantification of particle size distribution is of importance in the application of nanoscale particles. For this reason, polydispersity in particle size has been the focus of many simulations of particle growth, especially for nanoparticles synthesized from aerosols such as fumed silica, titania and alumina. Single-source aerosols typically result in close to a log-normal distribution in size and micrograph evidence generally supports close to spherical particles, making such particles ideal candidates for considerations of polydispersity. Small-angle X-ray scattering (SAXS) is often used to measure particle size in terms of the radius of gyration, Rg, using Guinier's law, as well as particle surface area, S/V, from the Porod constant B and the scattering invariant Q. In this paper, the unified function is used to obtain these parameters and various moments of the particle size distribution are calculated. The particle size obtained from BET analysis of gas adsorption data directly agrees with the moment calculated from S/V. Scattering results are also compared with TEM particle-counting results. The potential of scattering to distinguish between polydisperse single particles and polydisperse particles in aggregates is presented. A generalized index of polydispersity for symmetric particles, PDI = BRg4/(1.62G), where G is the Guinier prefactor, is introduced and compared with other approaches to describe particle size distributions in SAXS, specifically the maximum-entropy method. [source] Combining maximum-entropy and the Mexican hat wavelet to reconstruct the microwave skyMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2001P. Vielva We present a maximum-entropy method (MEM) and ,Mexican hat' wavelet (MHW) joint analysis to recover the different components of the microwave sky from simulated observations by the ESA Planck Surveyor satellite in a small patch of the sky . This combined method allows one to improve the CMB, Sunyaev,Zel'dovich and Galactic foregrounds separation achieved by the MEM technique alone. In particular, the reconstructed CMB map is free from any bright point-source contamination. The joint analysis also produces point-source catalogues at each Planck frequency that are more complete and accurate than those obtained by either method on its own. The results are especially improved at high frequencies where infrared galaxies dominate the point-source contribution. Although this joint technique has been performed on simulated Planck data, it could easily be applied to other multifrequency CMB experiments, such as the forthcoming NASA MAP satellite or the recently-performed BOOMERANG and MAXIMA experiments. [source] Discrete Fourier transform in arbitrary dimensions by a generalized Beevers,Lipson algorithmACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2000Martin Schneider The Beevers,Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in -dimensional space would lead to nested loops over the coordinates, respectively, and different computer code is required for each dimension. An algorithm is proposed based on the generalization of the Beevers,Lipson procedure towards transforms in -dimensional space that contains the dimension as a variable and that results in a single piece of computer code for arbitrary dimensions. The computational complexity is found to scale as , where N is the number of pixels in the map, and it is independent of the dimension of the transform. This procedure will find applications in the evaluation of Fourier maps of quasicrystals and other aperiodic crystals, and in the maximum-entropy method for aperiodic crystals. [source] Application of maximum-entropy maps in the accurate refinement of a putative acylphosphatase using 1.3,Å X-ray diffraction dataACTA CRYSTALLOGRAPHICA SECTION D, Issue 3 2008Eiji Nishibori Accurate structural refinement of a putative acylphosphatase using 1.3,Å X-ray diffraction data was carried out using charge densities determined by the maximum-entropy method (MEM). The MEM charge density clearly revealed detailed features of the solvent region of the putative acylphosphatase crystalline structure, some of which had never been observed in conventional Fourier maps. The structural model in the solvent region was constructed as distributions of anisotropic water atoms. The omit-difference MEM maps and the difference MEM maps were effective in revealing details of the protein structure, such as multiple conformations of the side chains of amino-acid residues, anisotropy of atoms and H atoms. By model building using the MEM charge densities, the reliability factors R1 and Rfree in the SHELX refinement were dramatically improved from 17.9% and 18.3% to 9.6% and 10.0%, respectively. The present results prove the usefulness of MEM in improving the accuracy of refinement of protein crystal structures. [source] | ||||||||||