MEM-based pattern fitting

PRIMA) entropy method from powder diffraction data, F. Izumi and R. A. Dilanian, in Recent Research Developments in Physics, Transworld Research Network, Trivandrum, 2002, Vol. 3, Part II, pp. 699 726 and Beyond the ability of Rietveld analysis MEM based pattern fitting, F. Izumi, Solid State Ionics, 2004, 172, 1 6 ... 

Data Processing for Elucidation of the Diffusion Paths of Mobile Oxide Ions in Ionic Conductors Rietveld Analysis, Maximum Entropy Method (MEM), and MEM-Based Pattern Fitting (MPF)... 

The experimental diffraction data were analyzed by a combined technique involving Rietveld analysis, the maximum entropy method (MEM), and MEM-based pattern fitting (MPF) [10-15]. Rietveld analysis, which is used to refine the crystal structure from the powder diffraction data by a least squares method, was carried out using the RIETAN-2000 program [27], which yields structure factors and their errors after structural refinement. It is known that MEM can be used to obtain a nuclear density distribution map based on neutron structure factors and their errors [5, 6, 8, 10-15, 26-29] any type of complicated nuclear density distribution is allowed so long as it satisfies the symmetry requirements. MEM calculations were carried out using the PRIMA program [29]. To reduce the bias imposed by the simple structural model in the Rietveld refinement, an iterative procedure known as the REMEDY cycle [29] was applied after MEM analysis (Fig. 6.3). In this procedure, structure factors... 

Table 6.6 Refined crystal parameters and reliability factors in Rietveld and MEM-based-pattern-fitting analyses for (Pro.9Lao.i)2(Nio.74Cuo.2iGao,o5)04+a 1288.8 K (5 = 0.0154(3)) [15]...

In 1995, an elaborated method was developed for accurate structure analysis using X-ray powder diffraction data, that is, the MEM/Rietveld method [1,9]. The method enables us to construct the fine structural model up to charge density level, and is a self-consistent analysis with MEM charge density reconstruction of powder diffraction data. It also includes the Rietveld powder pattern fitting based on the model derived from the MEM charge density. To start the methods, it is necessary to have a primitive (or preliminary) structural model. The Rietveld method using this primitive structural model is called the pre-Rietveld analysis. It is well known that the MEM can provide useful information purely from observed structure factor data beyond a presumed crystal structure model used in the pre-Rietveld analysis. The flow chart of the method is shown in Fig. 2. 

In BLH-NhaCo()2, the guest species in the galleries are highly disordered. MEM is quite effective for detailed structure analysis of such an intercalation compound. In MEM-based whole-pattern fitting (MPF), crystal structures are expressed not by structure parameters such as fractional coordinates and atomic displacement parameters but by electron densities in the unit cell. Therefore, MPF allows us to represent the disordered atomic configuration in a more appropriate way than conventional Rietveld analysis adopting a split-atom model. The... 

FIGURE 7 Powder X-ray (synchrotron) diffraction patterns and the corresponding fitting results of Y< C82 based on the calculated intensities from the MEM electron density. 

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