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) 2022 International Union of Crystallography2021-12-23International 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 78, Part 1, 2022textweekly62002-01-01T00:00+00:001782021-12-23Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances1urn:issn:2053-2733med@iucr.orgDecember 20212021-12-23Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageA new method for lattice reduction using directional and hyperplanar shearing
http://scripts.iucr.org/cgi-bin/paper?lu5009
A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called `basis rhombicity' which is the sum of the absolute values of the elements of the metric tensor associated with the basis. The levels of reduction are quite similar to those obtained with the Lenstra–Lenstra–Lovász (LLL) algorithm, at least up to the moderate dimensions that have been tested (lower than 20). The method can be used to reduce unit cells attached to given hyperplanes.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Cayron, C.2022-01-01doi:10.1107/S2053273321011037International Union of CrystallographyA new algorithm for lattice reduction based on a series of directional and hyperplanar shears and driven by the decrease of the basis rhombicity is proposed. It can be used to reduce unit cells in dimension 3 and higher.ENlattice reductionhyperplaneleft inversealgorithmA geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called `basis rhombicity' which is the sum of the absolute values of the elements of the metric tensor associated with the basis. The levels of reduction are quite similar to those obtained with the Lenstra–Lenstra–Lovász (LLL) algorithm, at least up to the moderate dimensions that have been tested (lower than 20). The method can be used to reduce unit cells attached to given hyperplanes.text/htmlA new method for lattice reduction using directional and hyperplanar shearingtext1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Aresearch papers19Effects of Voigt diffraction peak profiles on the pair distribution function
http://scripts.iucr.org/cgi-bin/paper?vk5047
Powder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Beyer, J.Roth, N.Brummerstedt Iversen, B.2022-01-01doi:10.1107/S2053273321011840International Union of CrystallographyGeneral expressions for peak broadening in reciprocal and direct space are derived based on the Voigt function.ENpair distribution functionpeak profileVoigt functionstrain effectssize effectsPowder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.text/htmlEffects of Voigt diffraction peak profiles on the pair distribution functiontext1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Aresearch papers1020Chiral spiral cyclic twins
http://scripts.iucr.org/cgi-bin/paper?uv5004
A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Hornfeck, W.2022-01-01doi:10.1107/S2053273321012237International Union of CrystallographyTwo-dimensional point patterns for cyclic twins of six-, eight-, ten- and 12-fold symmetry are generated based on a general parametrization in combination with specific integer sequences following from a common construction scheme.ENchiralspiralcyclic twinsA formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.text/htmlChiral spiral cyclic twinstext1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Aresearch papers2135On the frequency module of the hull of a primitive substitution tiling
http://scripts.iucr.org/cgi-bin/paper?uv5002
Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal {\bb Z}-module, where {\bb Z} is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Say-awen, A.L.D.Frettlöh, D.De Las Peñas, M.L.A.N.2022-01-01doi:10.1107/S2053273321012572International Union of CrystallographyAs part of the study of aperiodic tilings and tiling spaces, the frequency module of the hull of a primitive substitution tiling is computed.ENfrequency moduleprimitive substitution tilingsaperiodic tilingsquasicrystalsUnderstanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal {\bb Z}-module, where {\bb Z} is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles.text/htmlOn the frequency module of the hull of a primitive substitution tilingtext1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Aresearch papers3655The intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells
http://scripts.iucr.org/cgi-bin/paper?ae5110
The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Pedersen, M.C.Robins, V.Hyde, S.T.2022-01-01doi:10.1107/S2053273321012936International Union of CrystallographyThe group–subgroup structure of the symmetry groups describing the Diamond and Gyroid minimal surfaces in their conventional unit cells is presented.ENminimal surfaceshyperbolic geometrysymmetry groupssubgroup latticesconventional unit cellsThe intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.text/htmlThe intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cellstext1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Ashort communications5658Numerical Problems in Crystallography. By M. A. Wahab. Springer, 2021. Hardcover, pp. xv + 387. ISBN 9789811597534. Price EUR 83.19.
http://scripts.iucr.org/cgi-bin/paper?xo0183
Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Nespolo, M.2022-01-01doi:10.1107/S2053273321012468International Union of CrystallographyENbook reviewcrystallographic computingtext/htmlNumerical Problems in Crystallography. By M. A. Wahab. Springer, 2021. Hardcover, pp. xv + 387. ISBN 9789811597534. Price EUR 83.19.text1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Abook reviews5962Uwe Grimm (1963–2021)
http://scripts.iucr.org/cgi-bin/paper?es5037
Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Baake, M.McGrath, R.Römer, R.A.2022-01-01doi:10.1107/S2053273321012791International Union of CrystallographyObituary for Uwe Grimm.ENobituaryquasicrystalsquasi-periodic systemsaperiodic ordergroup theorytext/htmlUwe Grimm (1963–2021)text1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Aobituaries6364Report of the Executive Committee for 2020
http://scripts.iucr.org/cgi-bin/paper?es5035
The report of the Executive Committee for 2020 is presented.Copyright (c) 2022 International Union of Crystallographyurn:issn:2053-2733Ashcroft, A.T.2022-01-01doi:10.1107/S2053273321012067International Union of CrystallographyThe report of the Executive Committee for 2020 is presented.ENInternational Union of CrystallographyIUCrExecutive CommitteeThe report of the Executive Committee for 2020 is presented.text/htmlReport of the Executive Committee for 2020text1782022-01-01Copyright (c) 2022 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography6598