Acta Crystallographica Section A
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.enCopyright (c) 2015 International Union of Crystallography2015-02-27International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A: Foundations and Advances, Volume 71, Part 2, 2015textyearly62002-01-01T00:00+00:002712015-02-27Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances141urn:issn:2053-2733med@iucr.orgFebruary 20152015-02-27Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2015/02/00/isscontsbdy.html
Still imageThe revival of the Bravais lattice
http://scripts.iucr.org/cgi-bin/paper?me0569
The implications of the paper by Grimmer [Acta Cryst. (2015), A71, 143–149] are discussed.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Flack, H.D.2015-02-11doi:10.1107/S2053273315002557International Union of CrystallographyCrystallographers need to understand better the Bravais lattice.ENBravais latticesphase transformationscell reductioncrystallographic nomenclatureThe implications of the paper by Grimmer [Acta Cryst. (2015), A71, 143–149] are discussed.text/htmlThe revival of the Bravais latticetext2712015-02-11Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Ascientific commentaries141142Partial order among the 14 Bravais types of lattices: basics and applications
http://scripts.iucr.org/cgi-bin/paper?eo5044
Neither International Tables for Crystallography (ITC) nor available crystallography textbooks state explicitly which of the 14 Bravais types of lattices are special cases of others, although ITC contains the information necessary to derive the result in two ways, considering either the symmetry or metric properties of the lattices. The first approach is presented here for the first time, the second has been given by Michael Klemm in 1982. Metric relations between conventional bases of special and general lattice types are tabulated and applied to continuous equi-translation phase transitions.Copyright (c) 2015 Hans Grimmerurn:issn:2053-2733Grimmer, H.2015-01-29doi:10.1107/S2053273314027351International Union of CrystallographyThe partial order among Bravais types of lattices obtained by considering special cases is derived from their space-group symmetry and applied to continuous equi-translation phase transitions.ENBravais latticestranslationengleiche subgroupsphase transitionsNeither International Tables for Crystallography (ITC) nor available crystallography textbooks state explicitly which of the 14 Bravais types of lattices are special cases of others, although ITC contains the information necessary to derive the result in two ways, considering either the symmetry or metric properties of the lattices. The first approach is presented here for the first time, the second has been given by Michael Klemm in 1982. Metric relations between conventional bases of special and general lattice types are tabulated and applied to continuous equi-translation phase transitions.text/htmlPartial order among the 14 Bravais types of lattices: basics and applicationstext2712015-01-29Copyright (c) 2015 Hans GrimmerActa Crystallographica Section Aresearch papers143149The affine and Euclidean normalizers of the subperiodic groups
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The affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane-group Euclidean normalizers have been considered.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733VanLeeuwen, B.K.Valentín De Jesús, P.Litvin, D.B.Gopalan, V.2015-01-23doi:10.1107/S2053273314024395International Union of CrystallographyThe affine and Euclidean normalizers of the subperiodic groups are derived and listed.ENsubperiodic groupsnormalizersaffine normalizersEuclidean normalizersThe affine and Euclidean normalizers of the subperiodic groups, the frieze groups, the rod groups and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane-group Euclidean normalizers have been considered.text/htmlThe affine and Euclidean normalizers of the subperiodic groupstext2712015-01-23Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers150160Generalized Penrose tiling as a quasilattice for decagonal quasicrystal structure analysis
http://scripts.iucr.org/cgi-bin/paper?dm5059
The generalized Penrose tiling is, in fact, an infinite set of decagonal tilings. It is constructed with the same rhombs (thick and thin) as the conventional Penrose tiling, but its long-range order depends on the so-called shift parameter (s ∈ 〈0; 1)). The structure factor is derived for the arbitrarily decorated generalized Penrose tiling within the average unit cell approach. The final formula works in physical space only and is directly dependent on the s parameter. It allows one to straightforwardly change the long-range order of the refined structure just by changing the s parameter and keeping the tile decoration unchanged. This gives a great advantage over the higher-dimensional method, where every change of the tiling (change in the s parameter) requires the structure model to be built from scratch, i.e. the fine division of the atomic surfaces has to be redone.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Chodyn, M.Kuczera, P.Wolny, J.2015-01-23doi:10.1107/S2053273314024917International Union of CrystallographyDecorated generalized Penrose tiling is described as a potential quasilattice for models of decagonal quasicrystals. Its advantage over the conventional Penrose tiling is that its long-range order can be continuously changed if the tile decoration is fixed.ENdecagonal quasicrystalsgeneralized Penrose tilingaverage unit cellThe generalized Penrose tiling is, in fact, an infinite set of decagonal tilings. It is constructed with the same rhombs (thick and thin) as the conventional Penrose tiling, but its long-range order depends on the so-called shift parameter (s ∈ 〈0; 1)). The structure factor is derived for the arbitrarily decorated generalized Penrose tiling within the average unit cell approach. The final formula works in physical space only and is directly dependent on the s parameter. It allows one to straightforwardly change the long-range order of the refined structure just by changing the s parameter and keeping the tile decoration unchanged. This gives a great advantage over the higher-dimensional method, where every change of the tiling (change in the s parameter) requires the structure model to be built from scratch, i.e. the fine division of the atomic surfaces has to be redone.text/htmlGeneralized Penrose tiling as a quasilattice for decagonal quasicrystal structure analysistext2712015-01-23Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers161168A simple approach to estimate isotropic displacement parameters for hydrogen atoms
http://scripts.iucr.org/cgi-bin/paper?kx5038
A simple combination of riding motion and an additive term is sufficient to estimate the temperature-dependent isotropic displacement parameters of hydrogen atoms, for use in X-ray structure refinements. The approach is validated against neutron diffraction data, and gives reasonable estimates in a very large temperature range (10–300 K). The model can be readily implemented in common structure refinement programs without auxiliary software.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Madsen, A.Ø.Hoser, A.A.2015-01-23doi:10.1107/S2053273314025133International Union of CrystallographyA simple approach to estimate temperature-dependent isotropic motion of hydrogen atoms is proposed. The model is validated against experimental data.ENhydrogen atomsisotropic thermal motiondisplacement parametersA simple combination of riding motion and an additive term is sufficient to estimate the temperature-dependent isotropic displacement parameters of hydrogen atoms, for use in X-ray structure refinements. The approach is validated against neutron diffraction data, and gives reasonable estimates in a very large temperature range (10–300 K). The model can be readily implemented in common structure refinement programs without auxiliary software.text/htmlA simple approach to estimate isotropic displacement parameters for hydrogen atomstext2712015-01-23Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers169174Group-theoretical analysis of aperiodic tilings from projections of higher-dimensional lattices Bn
http://scripts.iucr.org/cgi-bin/paper?pc5046
A group-theoretical discussion on the hypercubic lattice described by the affine Coxeter–Weyl group Wa(Bn) is presented. When the lattice is projected onto the Coxeter plane it is noted that the maximal dihedral subgroup Dh of W(Bn) with h = 2n representing the Coxeter number describes the h-fold symmetric aperiodic tilings. Higher-dimensional cubic lattices are explicitly constructed for n = 4, 5, 6. Their rank-3 Coxeter subgroups and maximal dihedral subgroups are identified. It is explicitly shown that when their Voronoi cells are decomposed under the respective rank-3 subgroups W(A3), W(H2) × W(A1) and W(H3) one obtains the rhombic dodecahedron, rhombic icosahedron and rhombic triacontahedron, respectively. Projection of the lattice B4 onto the Coxeter plane represents a model for quasicrystal structure with eightfold symmetry. The B5 lattice is used to describe both fivefold and tenfold symmetries. The lattice B6 can describe aperiodic tilings with 12-fold symmetry as well as a three-dimensional icosahedral symmetry depending on the choice of subspace of projections. The novel structures from the projected sets of lattice points are compatible with the available experimental data.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Koca, M.Ozdes Koca, N.Koc, R.2015-01-23doi:10.1107/S2053273314025492International Union of CrystallographyA general technique has been introduced for the projection of the hypercubic lattices into two- and three-dimensional subspaces with dihedral and icosahedral residual symmetries, respectively. Eigenvalues and corresponding eigenvectors of the Cartan matrix (Gram matrix) determine the projected subspace and symmetry of the aperiodic tilings.ENlatticesCoxeter–Weyl groupsstrip projectioncut-and-project techniquequasicrystallographyaperiodic tilingsA group-theoretical discussion on the hypercubic lattice described by the affine Coxeter–Weyl group Wa(Bn) is presented. When the lattice is projected onto the Coxeter plane it is noted that the maximal dihedral subgroup Dh of W(Bn) with h = 2n representing the Coxeter number describes the h-fold symmetric aperiodic tilings. Higher-dimensional cubic lattices are explicitly constructed for n = 4, 5, 6. Their rank-3 Coxeter subgroups and maximal dihedral subgroups are identified. It is explicitly shown that when their Voronoi cells are decomposed under the respective rank-3 subgroups W(A3), W(H2) × W(A1) and W(H3) one obtains the rhombic dodecahedron, rhombic icosahedron and rhombic triacontahedron, respectively. Projection of the lattice B4 onto the Coxeter plane represents a model for quasicrystal structure with eightfold symmetry. The B5 lattice is used to describe both fivefold and tenfold symmetries. The lattice B6 can describe aperiodic tilings with 12-fold symmetry as well as a three-dimensional icosahedral symmetry depending on the choice of subspace of projections. The novel structures from the projected sets of lattice points are compatible with the available experimental data.text/htmlGroup-theoretical analysis of aperiodic tilings from projections of higher-dimensional lattices Bntext2712015-01-23Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers175185Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank
http://scripts.iucr.org/cgi-bin/paper?sc5081
The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\G where Γ is the Sohncke group of the macromolecular crystal and G is the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Chirikjian, G.Sajjadi, S.Toptygin, D.Yan, Y.2015-01-29doi:10.1107/S2053273314024358International Union of CrystallographyIn order to characterize molecular-replacement search spaces, the structure of Sohncke groups is examined. It is observed that proteins most often crystallize in Sohncke groups with small torsion subgroups.ENBieberbach groupsSohncke groupsprotein crystalsnormal subgroupsThe main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\G where Γ is the Sohncke group of the macromolecular crystal and G is the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.text/htmlMathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Banktext2712015-01-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers186194Twinning of aragonite – the crystallographic orbit and sectional layer group approach
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The occurrence frequency of the {110} twin in aragonite is explained by the existence of an important substructure (60% of the atoms) which crosses the composition surface with only minor perturbation (about 0.2 Å) and constitutes a common atomic network facilitating the formation of the twin. The existence of such a common substructure is shown by the C2/c pseudo-eigensymmetry of the crystallographic orbits, which contains restoration operations whose linear part coincides with the twin operation. Furthermore, the local analysis of the composition surface in the aragonite structure shows that the structure is built from slices which are fixed by the twin operation, confirming and reinforcing the crystallographic orbit analysis of the structural continuity across the composition surface.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Marzouki, M.-A.Souvignier, B.Nespolo, M.2015-01-29doi:10.1107/S2053273314027156International Union of CrystallographyThe mimetic twinning of aragonite is explained by the high degree of pseudo-symmetry of the crystallographic orbits and the action of the twin operation on the structure slices which form the composition surface.ENaragonitecrystallographic orbitseigensymmetrysectional layer grouptwinningThe occurrence frequency of the {110} twin in aragonite is explained by the existence of an important substructure (60% of the atoms) which crosses the composition surface with only minor perturbation (about 0.2 Å) and constitutes a common atomic network facilitating the formation of the twin. The existence of such a common substructure is shown by the C2/c pseudo-eigensymmetry of the crystallographic orbits, which contains restoration operations whose linear part coincides with the twin operation. Furthermore, the local analysis of the composition surface in the aragonite structure shows that the structure is built from slices which are fixed by the twin operation, confirming and reinforcing the crystallographic orbit analysis of the structural continuity across the composition surface.text/htmlTwinning of aragonite – the crystallographic orbit and sectional layer group approachtext2712015-01-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers195202Statistical tests against systematic errors in data sets based on the equality of residual means and variances from control samples: theory and applications
http://scripts.iucr.org/cgi-bin/paper?pc5048
Statistical tests are applied for the detection of systematic errors in data sets from least-squares refinements or other residual-based reconstruction processes. Samples of the residuals of the data are tested against the hypothesis that they belong to the same distribution. For this it is necessary that they show the same mean values and variances within the limits given by statistical fluctuations. When the samples differ significantly from each other, they are not from the same distribution within the limits set by the significance level. Therefore they cannot originate from a single Gaussian function in this case. It is shown that a significance cutoff results in exactly this case. Significance cutoffs are still frequently used in charge-density studies. The tests are applied to artificial data with and without systematic errors and to experimental data from the literature.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Henn, J.Meindl, K.2015-01-29doi:10.1107/S2053273314027363International Union of CrystallographyResiduals from artificial and from published data are tested against the hypothesis of being identically distributed. An anharmonic motion model reduces the number of rare events in the lowest resolution range.ENfit-quality indicatorsstatistical testsresidualsleast-squares refinementStatistical tests are applied for the detection of systematic errors in data sets from least-squares refinements or other residual-based reconstruction processes. Samples of the residuals of the data are tested against the hypothesis that they belong to the same distribution. For this it is necessary that they show the same mean values and variances within the limits given by statistical fluctuations. When the samples differ significantly from each other, they are not from the same distribution within the limits set by the significance level. Therefore they cannot originate from a single Gaussian function in this case. It is shown that a significance cutoff results in exactly this case. Significance cutoffs are still frequently used in charge-density studies. The tests are applied to artificial data with and without systematic errors and to experimental data from the literature.text/htmlStatistical tests against systematic errors in data sets based on the equality of residual means and variances from control samples: theory and applicationstext2712015-01-29Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers203211On the number of k-faces of primitive parallelohedra
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Dehn–Sommerville relations for simple (simplicial) polytopes are applied to primitive parallelohedra. New restrictions on numbers of k-faces of non-principal primitive parallelohedra are explicitly formulated for five-, six- and seven-dimensional parallelohedra.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Zhilinskii, B.2015-02-04doi:10.1107/S205327331402806XInternational Union of CrystallographyLinear relations between numbers of k-faces of non-principal primitive parallelohedra are obtained from Dehn–Sommerville relations for simple polytopes.ENprimitive parallelohedrasimple polytopesDehn–Sommerville relationsDehn–Sommerville relations for simple (simplicial) polytopes are applied to primitive parallelohedra. New restrictions on numbers of k-faces of non-principal primitive parallelohedra are explicitly formulated for five-, six- and seven-dimensional parallelohedra.text/htmlOn the number of k-faces of primitive parallelohedratext2712015-02-04Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers212215Color groups arising from index-n subgroups of symmetry groups
http://scripts.iucr.org/cgi-bin/paper?eo5042
One of the main goals in the study of color symmetry is to classify colorings of symmetrical objects through their color groups. The term color group is taken to mean the subgroup of the symmetry group of the uncolored symmetrical object which induces a permutation of colors in the coloring. This work looks for methods of determining the color group of a colored symmetric object. It begins with an index n subgroup H of the symmetry group G of the uncolored object. It then considers H-invariant colorings of the object, so that the color group H* will be a subgroup of G containing H. In other words, H ≤ H* ≤ G. It proceeds to give necessary and sufficient conditions for the equality of H* and G. If H* ≠ G and n is prime, then H* = H. On the other hand, if H* ≠ G and n is not prime, methods are discussed to determine whether H* is G, H or some intermediate subgroup between H and G.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Felix, R.P.Junio, A.O.2015-02-04doi:10.1107/S2053273314028071International Union of CrystallographyGiven a subgroup H of the symmetry group G of an object, an H-invariant coloring of the object has a color group which is a subgroup of G containing H. A method is described for determining whether this subgroup is G, H or some intermediate subgroup.ENperfect coloringcolor symmetrycolor groupsorbitsOne of the main goals in the study of color symmetry is to classify colorings of symmetrical objects through their color groups. The term color group is taken to mean the subgroup of the symmetry group of the uncolored symmetrical object which induces a permutation of colors in the coloring. This work looks for methods of determining the color group of a colored symmetric object. It begins with an index n subgroup H of the symmetry group G of the uncolored object. It then considers H-invariant colorings of the object, so that the color group H* will be a subgroup of G containing H. In other words, H ≤ H* ≤ G. It proceeds to give necessary and sufficient conditions for the equality of H* and G. If H* ≠ G and n is prime, then H* = H. On the other hand, if H* ≠ G and n is not prime, methods are discussed to determine whether H* is G, H or some intermediate subgroup between H and G.text/htmlColor groups arising from index-n subgroups of symmetry groupstext2712015-02-04Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers216224Computational analysis of thermal-motion effects on the topological properties of the electron density
http://scripts.iucr.org/cgi-bin/paper?pc5050
The distributions of bond topological properties (BTPs) of the electron density upon thermal vibrations of the nuclei are computationally examined to estimate different statistical figures, especially uncertainties, of these properties. The statistical analysis is based on a large ensemble of BTPs of the electron densities for thermally perturbed nuclear geometries of the formamide molecule. Each bond critical point (BCP) is found to follow a normal distribution whose covariance correlates with the displacement amplitudes of the nuclei involved in the bond. The BTPs are found to be markedly affected not only by normal modes of the significant bond-stretching component but also by modes that involve mainly hydrogen-atom displacements. Their probability distribution function can be decently described by Gumbel-type functions of positive (negative) skewness for the bonds formed by non-hydrogen (hydrogen) atoms.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Michael, J.R.Koritsanszky, T.2015-02-11doi:10.1107/S2053273315001199International Union of CrystallographyCorrelations between different local topological properties of the electron density due to nuclear vibrations are analysed via computational statistics.ENelectron densitybond topological propertiesmean-square displacement amplitudesprobability distribution functionstandard uncertaintyequilibrium geometryThe distributions of bond topological properties (BTPs) of the electron density upon thermal vibrations of the nuclei are computationally examined to estimate different statistical figures, especially uncertainties, of these properties. The statistical analysis is based on a large ensemble of BTPs of the electron densities for thermally perturbed nuclear geometries of the formamide molecule. Each bond critical point (BCP) is found to follow a normal distribution whose covariance correlates with the displacement amplitudes of the nuclei involved in the bond. The BTPs are found to be markedly affected not only by normal modes of the significant bond-stretching component but also by modes that involve mainly hydrogen-atom displacements. Their probability distribution function can be decently described by Gumbel-type functions of positive (negative) skewness for the bonds formed by non-hydrogen (hydrogen) atoms.text/htmlComputational analysis of thermal-motion effects on the topological properties of the electron densitytext2712015-02-11Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers225234Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation
http://scripts.iucr.org/cgi-bin/paper?td5023
Accurate structure refinement from electron-diffraction data is not possible without taking the dynamical-diffraction effects into account. A complete three-dimensional model of the structure can be obtained only from a sufficiently complete three-dimensional data set. In this work a method is presented for crystal structure refinement from the data obtained by electron diffraction tomography, possibly combined with precession electron diffraction. The principle of the method is identical to that used in X-ray crystallography: data are collected in a series of small tilt steps around a rotation axis, then intensities are integrated and the structure is optimized by least-squares refinement against the integrated intensities. In the dynamical theory of diffraction, the reflection intensities exhibit a complicated relationship to the orientation and thickness of the crystal as well as to structure factors of other reflections. This complication requires the introduction of several special parameters in the procedure. The method was implemented in the freely available crystallographic computing system Jana2006.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Palatinus, L.Petříček, V.Corrêa, C.A.2015-02-11doi:10.1107/S2053273315001266International Union of CrystallographyA method for structure refinement from electron diffraction tomography data is introduced.ENdynamical diffractionelectron diffraction tomographyelectron crystallographyAccurate structure refinement from electron-diffraction data is not possible without taking the dynamical-diffraction effects into account. A complete three-dimensional model of the structure can be obtained only from a sufficiently complete three-dimensional data set. In this work a method is presented for crystal structure refinement from the data obtained by electron diffraction tomography, possibly combined with precession electron diffraction. The principle of the method is identical to that used in X-ray crystallography: data are collected in a series of small tilt steps around a rotation axis, then intensities are integrated and the structure is optimized by least-squares refinement against the integrated intensities. In the dynamical theory of diffraction, the reflection intensities exhibit a complicated relationship to the orientation and thickness of the crystal as well as to structure factors of other reflections. This complication requires the introduction of several special parameters in the procedure. The method was implemented in the freely available crystallographic computing system Jana2006.text/htmlStructure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementationtext2712015-02-11Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers235244Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20
http://scripts.iucr.org/cgi-bin/paper?ae5002
The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565–574; Hansen & Coppens (1978). Acta Cryst. A34, 909–921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6–7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Michael, J.R.Volkov, A.2015-01-23doi:10.1107/S2053273314024838International Union of CrystallographyCartesian real spherical harmonics for l ≤ 20 and the corresponding normalization factors for the deformation density functions with an accuracy to 35 significant figures have been generated using the Wolfram Mathematica software and converted to a Fortran90 code.ENspherical harmonicspseudoatom modelcharge densityThe widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565–574; Hansen & Coppens (1978). Acta Cryst. A34, 909–921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6–7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.text/htmlDensity- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20text2712015-01-23Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Ashort communications245249Symmetry of Crystals and Molecules. By Mark Ladd. Oxford University Press, 2014. Pp. xxi + 433. Price GBP 55.00 (hardback). ISBN 978-0-19-967088-8.
http://scripts.iucr.org/cgi-bin/paper?xo0004
Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Nespolo, M.2015-02-28doi:10.1107/S2053273315001916International Union of CrystallographyENbook reviewcrystal symmetrymolecular symmetrytext/htmlSymmetry of Crystals and Molecules. By Mark Ladd. Oxford University Press, 2014. Pp. xxi + 433. Price GBP 55.00 (hardback). ISBN 978-0-19-967088-8.text2712015-02-28Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Abook reviews250252Hans Wondratschek (1925–2014)
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Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Hahn, Th.2015-02-28doi:10.1107/S2053273315001990International Union of CrystallographyObituary for Hans Wondratschek.ENObituaryInternational Tables for Crystallographysymmetrymathematical crystallographyapatitespyromorphitestext/htmlHans Wondratschek (1925–2014)text2712015-02-28Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aobituaries253254