Acta Crystallographica Section A
http://journals.iucr.org/a/issues/2015/02/00/isscontsbdy.html
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 Crystallography2015-01-22International 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+00:002712015-01-22Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances141urn:issn:2053-2733med@iucr.orgJanuary 20152015-01-22Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2015/02/00/isscontsbdy.html
Still imageThe affine and Euclidean normalizers of the subperiodic groups
http://scripts.iucr.org/cgi-bin/paper?dm5060
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 papers00Generalized 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 papers00A 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 papers00Group-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 papers00Density- 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 communications00