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Atomic Displacement Parameters (atomic + displacement_parameter)
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] Multipole electron-density modelling of synchrotron powder diffraction data: the case of diamondACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2010H. Svendsen Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with limited sample preparation. Thus, potential systematic errors such as extinction and twinning commonly encountered in single-crystal studies of small-unit-cell inorganic structures can be overcome with synchrotron powder diffraction. It is shown that the standard Hansen,Coppens multipole model is not flexible enough to fit the static theoretical structure factors, whereas fitting of thermally smeared structure factors has much lower residuals. If thermally smeared structure factors (experimental or theoretical) are fitted with a slightly wrong radial model (s2p2 instead of sp3) the radial scaling parameters (`,' parameters) are found to be inadequate and the `error' is absorbed into the atomic displacement parameter. This directly exposes a correlation between electron density and thermal parameters even for a light atom such as carbon, and it also underlines that in organic systems proper deconvolution of thermal motion is important for obtaining correct static electron densities. [source] Thermal expansion and atomic displacement parameters of cubic KMgF3 perovskite determined by high-resolution neutron powder diffractionJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2002I. G. Wood The structure of KMgF3 has been determined by high-resolution neutron powder diffraction at 4.2,K, room temperature and at 10,K intervals from 373,K to 1223,K. The material remains cubic at all temperatures. The average volumetric coefficient of thermal expansion in the range 373,1223,K was found to be 7.11,(3) × 10,5,K,1. For temperatures between 4.2 and 1223,K, a second-order Grüneisen approximation to the zero-pressure equation of state, with the internal energy calculated via a Debye model, was found to fit well, with the following parameters: ,D = 536,(9),K, Vo = 62.876,(6),Å3, = 6.5,(1) and (VoKo/,,) = 3.40,(2) × 10,18,J, where ,D is the Debye temperature, Vo is the volume at T = 0, is the first derivative with respect to pressure of the incompressibility (Ko) and ,, is a Grüneisen parameter. The atomic displacement parameters were found to increase smoothly with T and could be fitted using Debye models with ,D in the range 305,581,K. At 1223,K, the displacement of the F ions was found to be much less anisotropic than that in NaMgF3 at this temperature. [source] A new approach to calculating powder diffraction patterns based on the Debye scattering equationACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010Noel William Thomas A new method is defined for the calculation of X-ray and neutron powder diffraction patterns from the Debye scattering equation (DSE). Pairwise atomic interactions are split into two contributions, the first from lattice-pair vectors and the second from cell-pair vectors. Since the frequencies of lattice-pair vectors can be directly related to crystallite size, application of the DSE is thereby extended to crystallites of lengths up to ~200,nm. The input data correspond to unit-cell parameters, atomic coordinates and displacement factors. The calculated diffraction patterns are characterized by full backgrounds as well as complete reflection profiles. Four illustrative systems are considered: sodium chloride (NaCl), ,-quartz, monoclinic lead zirconate titanate (PZT) and kaolinite. The effects of varying crystallite size on diffraction patterns are calculated for NaCl, quartz and kaolinite, and a method of modelling static structural disorder is defined for kaolinite. The idea of partial diffraction patterns is introduced and a treatment of atomic displacement parameters is included. Although the method uses pair distribution functions as an intermediate stage, it is anticipated that further progress in reducing computational times will be made by proceeding directly from crystal structure to diffraction pattern. [source] Towards the best model for H atoms in experimental charge-density refinementACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2009Anna A. Hoser The consequences of different treatments of H atoms in experimental charge-density studies are discussed. Geometric and topological parameters obtained after applying four different H-atom models in multipolar refinement on high-resolution X-ray data only were compared with the results obtained for a reference joint high-resolution X-ray/neutron refinement. The geometry and the topological critical point and integrated parameters closest to the reference values were obtained after a mixed refinement (high-order refinement of heavy atoms, low-angle refinement of H atoms and elongation of the X,H distance to the average neutron bond lengths) supplemented by an estimation of the anisotropic thermal motions of H atoms using the SHADE program. Such a procedure works very well even for strong hydrogen bonds. The worst fit to the reference results for both critical point and integrated parameters was obtained when only the standardization to the average neutron X,H distances was applied. The non-H-atom parameters are also systematically influenced by the H-atom modeling. In order to compare topological and integrated properties calculated for H and non-H atoms in multipolar refinement when there are no neutron data, the same treatment of H atoms (ideally the mixed refinement + estimated anisotropic atomic displacement parameters for H atoms) should be applied. [source] Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolutionACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2007Andreas Hofmann The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100,K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20,K. It is thus shown that the increased thermal smearing at 100,K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20,K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than dmin = 0.63,Å. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters. [source] Atomic resolution studies of carbonic anhydrase IIACTA CRYSTALLOGRAPHICA SECTION D, Issue 5 2010Craig A. Behnke Carbonic anhydrase has been well studied structurally and functionally owing to its importance in respiration. A large number of X-ray crystallographic structures of carbonic anhydrase and its inhibitor complexes have been determined, some at atomic resolution. Structure determination of a sulfonamide-containing inhibitor complex has been carried out and the structure was refined at 0.9,Å resolution with anisotropic atomic displacement parameters to an R value of 0.141. The structure is similar to those of other carbonic anhydrase complexes, with the inhibitor providing a fourth nonprotein ligand to the active-site zinc. Comparison of this structure with 13 other atomic resolution (higher than 1.25,Å) isomorphous carbonic anhydrase structures provides a view of the structural similarity and variability in a series of crystal structures. At the center of the protein the structures superpose very well. The metal complexes superpose (with only two exceptions) with standard deviations of 0.01,Å in some zinc,protein and zinc,ligand bond lengths. In contrast, regions of structural variability are found on the protein surface, possibly owing to flexibility and disorder in the individual structures, differences in the chemical and crystalline environments or the different approaches used by different investigators to model weak or complicated electron-density maps. These findings suggest that care must be taken in interpreting structural details on protein surfaces on the basis of individual X-ray structures, even if atomic resolution data are available. [source] Extraction of functional motion in trypsin crystal structuresACTA CRYSTALLOGRAPHICA SECTION D, Issue 8 2005Andrea Schmidt The analysis of anisotropic atomic displacement parameters for the direct extraction of functionally relevant motion from X-ray crystal structures of Fusarium oxysporum trypsin is presented. Several atomic resolution structures complexed with inhibitors or substrates and determined at different pH values and temperatures were investigated. The analysis revealed a breathing-like molecular motion conserved across trypsin structures from two organisms and three different crystal forms. Directional motion was observed suggesting a change of the width of the substrate-binding cleft and a change in the length of the specificity pocket. The differences in direction of motion across the structures are dependent on the mode of substrate or inhibitor binding and the chemical environment around the active-site residues. Together with the occurrence of multiple-residue conformers, they reflect spatial rearrangement throughout the deacylation pathway. [source] Use of TLS parameters to model anisotropic displacements in macromolecular refinementACTA CRYSTALLOGRAPHICA SECTION D, Issue 1 2001M. D. Winn An essential step in macromolecular refinement is the selection of model parameters which give as good a description of the experimental data as possible while retaining a realistic data-to-parameter ratio. This is particularly true of the choice of atomic displacement parameters, where the move from individual isotropic to individual anisotropic refinement involves a sixfold increase in the number of required displacement parameters. The number of refinement parameters can be reduced by using collective variables rather than independent atomic variables and one of the simplest examples of this is the TLS parameterization for describing the translation, libration and screw-rotation displacements of a pseudo-rigid body. This article describes the implementation of the TLS parameterization in the macromolecular refinement program REFMAC. Derivatives of the residual with respect to the TLS parameters are expanded in terms of the derivatives with respect to individual anisotropic U values, which in turn are calculated using a fast Fourier transform technique. TLS refinement is therefore fast and can be used routinely. Examples of TLS refinement are given for glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and a transcription activator GerE, for both of which there is data to only 2.0,Å, so that individual anisotropic refinement is not feasible. GAPDH has been refined with between one and four TLS groups in the asymmetric unit and GerE with six TLS groups. In both cases, inclusion of TLS parameters gives improved refinement statistics and in particular an improvement in R and free R values of several percent. Furthermore, GAPDH and GerE have two and six molecules in the asymmetric unit, respectively, and in each case the displacement parameters differ significantly between molecules. These differences are well accounted for by the TLS parameterization, leaving residual local displacements which are very similar between molecules and to which NCS restraints can be applied. [source] | ||||||||||