Forthcoming article in Acta Crystallographica Section A Foundations and Advances
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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.en-gbCopyright (c) 2019 International Union of CrystallographyInternational Union of CrystallographyInternational Union of Crystallographyhttps://journals.iucr.orgurn:issn:0108-7673Acta 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 Advancestextdaily12002-01-01T00:00+00:00med@iucr.orgActa Crystallographica Section A Foundations and AdvancesCopyright (c) 2019 International Union of Crystallographyurn:issn:0108-7673Forthcoming article in Acta Crystallographica Section A Foundations and Advanceshttp://journals.iucr.org/logos/rss10a.gif
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Still imageSolving the disordered structure of β-Cu2−xSe using the three-dimensional difference pair distribution function
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Using three-dimensional difference pair distribution function analysis of single-crystal diffuse X-ray scattering, the disordered structure copper selenide (β-Cu2−xSe) at room temperature is solved. The structure is ordered in two dimensions but disordered in the third.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Roth and Iversendoi:10.1107/S2053273319004820International Union of CrystallographyUsing three-dimensional difference pair distribution function analysis of single-crystal diffuse X-ray scattering, the disordered structure copper selenide (β-Cu2−xSe) at room temperature is solved. The structure is ordered in two dimensions but disordered in the third.enTHREE-DIMENSIONAL DIFFERENCE PAIR DISTRIBUTION FUNCTION; 3D-[DELTA]PDF; SINGLE-CRYSTAL DIFFUSE X-RAY SCATTERING; DISORDER; COPPER SELENIDE; THERMOELECTRICSUsing three-dimensional difference pair distribution function analysis of single-crystal diffuse X-ray scattering, the disordered structure copper selenide (β-Cu2−xSe) at room temperature is solved. The structure is ordered in two dimensions but disordered in the third.text/htmlSolving the disordered structure of β-Cu2−xSe using the three-dimensional difference pair distribution functiontextTheoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré images
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Using a recently developed moiré-fringe theory of X-ray diffraction, the angularly integrated moiré images of a lightly strained silicon bicrystal having an interspacing gap were simulation-computed over a wide range of crystal thicknesses and incident-beam angular width.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Jun-ichi Yoshimuradoi:10.1107/S2053273319004601International Union of CrystallographyUsing a recently developed moiré-fringe theory of X-ray diffraction, the angularly integrated moiré images of a lightly strained silicon bicrystal having an interspacing gap were simulation-computed over a wide range of crystal thicknesses and incident-beam angular width.enDIFFRACTION MOIRE FRINGES; ROTATION MOIRE; PENDELLOSUNG OSCILLATION; GAP PHASE DIFFERENCE; INTEGRATED MOIRE IMAGES; DIFFRACTION MOIRE FRINGES; ROTATION MOIRE; PENDELLOSUNG OSCILLATION; GAP PHASE DIFFERENCE; INTEGRATED MOIRE IMAGESUsing a recently developed moiré-fringe theory of X-ray diffraction, the angularly integrated moiré images of a lightly strained silicon bicrystal having an interspacing gap were simulation-computed over a wide range of crystal thicknesses and incident-beam angular width.text/htmlTheoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré imagestextIslamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction with a chapter on the use of computer algorithms to generate Islamic geometric patterns by Craig Kaplan. By Jay Bonner. Springer, 2017. Pp. XXV+525. Price USD 139.00. ISBN 978-1-4939-7921-9 (softcover) 978-1-4419-0216-0 (hardcover). ISBN 978-1-4419-0216-0.
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Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Greg McColmdoi:International Union of CrystallographyenBOOK REVIEW; ISLAMIC GEOMETRIC PATTERNStext/htmlIslamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction with a chapter on the use of computer algorithms to generate Islamic geometric patterns by Craig Kaplan. By Jay Bonner. Springer, 2017. Pp. XXV+525. Price USD 139.00. ISBN 978-1-4939-7921-9 (softcover) 978-1-4419-0216-0 (hardcover). ISBN 978-1-4419-0216-0.textExperimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystal
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Experimentally obtained non-coplanar 18-beam pinhole topographs were compared with computer simulations based on the Ewald–Laue theory.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Kouhei Okitsu et al.doi:10.1107/S2053273319002936International Union of CrystallographyExperimentally obtained non-coplanar 18-beam pinhole topographs were compared with computer simulations based on the Ewald–Laue theory.enX-RAY DIFFRACTION; DYNAMICAL THEORY; MULTIPLE REFLECTION; N-BEAM REFLECTION; PHASE PROBLEM; PROTEIN CRYSTALLOGRAPHYExperimentally obtained non-coplanar 18-beam pinhole topographs were compared with computer simulations based on the Ewald–Laue theory.text/htmlExperimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystaltextQuantum Field Theory Approach to Condensed Matter Physics. By Eduardo C. Marino. Cambridge University Press, 2017. Hardback, Pp. 532. Price GBP 64.99. ISBN 9781107074118.
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Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Malte Henkeldoi:10.1107/S2053273319002882International Union of CrystallographyenBOOK REVIEW; QUANTUM FIELD THEORY; CONDENSED MATTER PHYSICStext/htmlQuantum Field Theory Approach to Condensed Matter Physics. By Eduardo C. Marino. Cambridge University Press, 2017. Hardback, Pp. 532. Price GBP 64.99. ISBN 9781107074118.textA space for lattice representation and clustering
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Algorithms for defining the difference between two lattices are described. They are based on the work of Selling and Delone (Delaunay).Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Lawrence C. Andrews et al.doi:10.1107/S2053273319002729International Union of CrystallographyAlgorithms for defining the difference between two lattices are described. They are based on the work of Selling and Delone (Delaunay).enUNIT-CELL REDUCTION; DELAUNAY; DELONE; NIGGLI; SELLING; CLUSTERINGAlgorithms for defining the difference between two lattices are described. They are based on the work of Selling and Delone (Delaunay).text/htmlA space for lattice representation and clusteringtextFast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method
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Numerical implementations of the presented Fourier transform method and the previously reported Löwdin α-function approach for analytical determination of the two-center Coulomb integrals that appear in calculations of the electrostatic interaction energies between pseudoatom-based charge distributions are carefully examined in terms of precision and speed. The refined Fortran-based computer code allows a fast evaluation of electrostatic interaction energies with a precision of 5 × 10−5 kJ mol−1 or better using either of the two techniques.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Nguyen and Volkovdoi:10.1107/S2053273319002535International Union of CrystallographyNumerical implementations of the presented Fourier transform method and the previously reported Löwdin α-function approach for analytical determination of the two-center Coulomb integrals that appear in calculations of the electrostatic interaction energies between pseudoatom-based charge distributions are carefully examined in terms of precision and speed. The refined Fortran-based computer code allows a fast evaluation of electrostatic interaction energies with a precision of 5 × 10−5 kJ mol−1 or better using either of the two techniques.enELECTROSTATIC INTERACTION ENERGY; CHARGE DENSITY; PSEUDOATOM MODEL; FOURIER TRANSFORM; LOWDIN [ALPHA]-FUNCTIONNumerical implementations of the presented Fourier transform method and the previously reported Löwdin α-function approach for analytical determination of the two-center Coulomb integrals that appear in calculations of the electrostatic interaction energies between pseudoatom-based charge distributions are carefully examined in terms of precision and speed. The refined Fortran-based computer code allows a fast evaluation of electrostatic interaction energies with a precision of 5 × 10−5 kJ mol−1 or better using either of the two techniques.text/htmlFast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform methodtextGröbner–Shirshov bases for non-crystallographic Coxeter groups
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A Gröbner–Shirshov basis and the corresponding standard monomials for the non-crystallographic Coxeter group H4 are constructed.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Lee and Leedoi:10.1107/S2053273319002092International Union of CrystallographyA Gröbner–Shirshov basis and the corresponding standard monomials for the non-crystallographic Coxeter group H4 are constructed.enCOXETER GROUPS; GROBNER-SHIRSHOV BASIS; STANDARD MONOMIALSA Gröbner–Shirshov basis and the corresponding standard monomials for the non-crystallographic Coxeter group H4 are constructed.text/htmlGröbner–Shirshov bases for non-crystallographic Coxeter groupstextAutomatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server
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Two new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Samuel V. Gallego et al.doi:10.1107/S2053273319001748International Union of CrystallographyTwo new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately.enEQUILIBRIUM TENSORS; TRANSPORT TENSORS; OPTICAL TENSORS; NONLINEAR OPTICAL SUSCEPTIBILITY TENSORS; MAGNETIC GROUPS; TIME-REVERSAL SYMMETRY; ONSAGER RELATIONSHIPSTwo new tools hosted on the Bilbao Crystallographic Server are presented. The programs permit the automatic calculation of symmetry-adapted forms of tensor properties for magnetic and non-magnetic groups. The cases of equilibrium, transport, optical and nonlinear optical susceptibility tensors are studied separately.text/htmlAutomatic calculation of symmetry-adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic ServertextDependence of X-ray asymmetrical Bragg case plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane
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The rocking-curve dependence on the deviation of an incident X-ray plane wave from the exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Bragg case is investigated.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Minas K. Balyandoi:10.1107/S205327331900161XInternational Union of CrystallographyThe rocking-curve dependence on the deviation of an incident X-ray plane wave from the exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Bragg case is investigated.enDYNAMICAL DIFFRACTION; BRAGG CASE DIFFRACTION; DEVIATION ANGLE; X-RAY ROCKING CURVESThe rocking-curve dependence on the deviation of an incident X-ray plane wave from the exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Bragg case is investigated.text/htmlDependence of X-ray asymmetrical Bragg case plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction planetextExperimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs for a silicon crystal
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Experimentally obtained eight-beam pinhole topographs for a silicon crystal were compared with computer simulations based on the n-beam Takagi–Taupin equation and Ewald–Laue theory.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Kouhei Okitsu et al.doi:10.1107/S2053273319001499International Union of CrystallographyExperimentally obtained eight-beam pinhole topographs for a silicon crystal were compared with computer simulations based on the n-beam Takagi–Taupin equation and Ewald–Laue theory.enX-RAY DIFFRACTION; DYNAMICAL THEORY; MULTIPLE REFLECTION; COMPUTER SIMULATION; N-BEAM REFLECTION; PHASE PROBLEM; SILICON; PROTEIN CRYSTALLOGRAPHYExperimentally obtained eight-beam pinhole topographs for a silicon crystal were compared with computer simulations based on the n-beam Takagi–Taupin equation and Ewald–Laue theory.text/htmlExperimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs for a silicon crystaltextOn two special classes of parallelohedra in E6
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The structures of quasicrystals can be considered as sections of lattices of translations in higher dimensions, which has greatly stimulated the investigation of lattices in arbitrary dimensions. The structure of the cone of positive definite quadratic forms in Ed×d is investigated for d = 6. A partition of the cone in Φ and Σ domains is performed and its local symmetries are determined.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733P. Engeldoi:10.1107/S2053273319001359International Union of CrystallographyThe structures of quasicrystals can be considered as sections of lattices of translations in higher dimensions, which has greatly stimulated the investigation of lattices in arbitrary dimensions. The structure of the cone of positive definite quadratic forms in Ed×d is investigated for d = 6. A partition of the cone in Φ and Σ domains is performed and its local symmetries are determined.enTRANSLATION LATTICES; PARALLELOHEDRA; CONE OF POSITIVE QUADRATIC FORMS; [SIGMA]-SUBCONESThe structures of quasicrystals can be considered as sections of lattices of translations in higher dimensions, which has greatly stimulated the investigation of lattices in arbitrary dimensions. The structure of the cone of positive definite quadratic forms in Ed×d is investigated for d = 6. A partition of the cone in Φ and Σ domains is performed and its local symmetries are determined.text/htmlOn two special classes of parallelohedra in E6textThe characteristic radiation of copper Kα1,2,3,4
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The characterization of Cu Kα1,2,3,4 radiation is presented, including the 2p satellite. The details are robust enough to be transferable to other experiments for calibration and reference.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Hamish A. Melia et al.doi:10.1107/S205327331900130XInternational Union of CrystallographyThe characterization of Cu Kα1,2,3,4 radiation is presented, including the 2p satellite. The details are robust enough to be transferable to other experiments for calibration and reference.enX-RAY CHARACTERISTIC RADIATION; CU K[ALPHA]; PROFILE ANALYSIS; X-RAY SPECTROSCOPY; SHAKE PROBABILITYThe characterization of Cu Kα1,2,3,4 radiation is presented, including the 2p satellite. The details are robust enough to be transferable to other experiments for calibration and reference.text/htmlThe characteristic radiation of copper Kα1,2,3,4textThe chromatic symmetry of twins and allotwins
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The chromatic symmetry of twins is extended to the case of allotwins through a groupoid analysis.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Massimo Nespolodoi:10.1107/S2053273319000664International Union of CrystallographyThe chromatic symmetry of twins is extended to the case of allotwins through a groupoid analysis.enALLOTWINNING; GROUPOIDS; CHROMATIC SYMMETRY; TWIN POINT GROUPS; TWINNINGThe chromatic symmetry of twins is extended to the case of allotwins through a groupoid analysis.text/htmlThe chromatic symmetry of twins and allotwinstextThe polytopes of the H3 group with 60 vertices and their orbit decompositions
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A description is provided of polytopes with 60 vertices generated by the finite reflection group H3. Moreover, a decomposition of their vertices into orbits of lower-symmetry groups is provided.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Bourret and Grabowieckadoi:10.1107/S2053273319000640International Union of CrystallographyA description is provided of polytopes with 60 vertices generated by the finite reflection group H3. Moreover, a decomposition of their vertices into orbits of lower-symmetry groups is provided.enCOXETER GROUPS; POLYTOPES; ORBIT DECOMPOSITIONA description is provided of polytopes with 60 vertices generated by the finite reflection group H3. Moreover, a decomposition of their vertices into orbits of lower-symmetry groups is provided.text/htmlThe polytopes of the H3 group with 60 vertices and their orbit decompositionstextA hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene
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A mathematical framework for analysing aperiodic crystals encompassing a wide range of turbostratic disorders, including disorder of the first and second type, is presented. The framework uses the theory of hidden Markov models and is applied to carbon blacks and graphene.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Allen G. Hart et al.doi:10.1107/S2053273319000615International Union of CrystallographyA mathematical framework for analysing aperiodic crystals encompassing a wide range of turbostratic disorders, including disorder of the first and second type, is presented. The framework uses the theory of hidden Markov models and is applied to carbon blacks and graphene.enTURBOSTRATIC DISORDER; CARBON BLACKS; HIDDEN MARKOV MODEL; SCATTERING CROSS SECTIONSA mathematical framework for analysing aperiodic crystals encompassing a wide range of turbostratic disorders, including disorder of the first and second type, is presented. The framework uses the theory of hidden Markov models and is applied to carbon blacks and graphene.text/htmlA hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphenetextThe transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants
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Three transformation matrices (distortion, orientation and correspondence) define the crystallography of displacive phase transformations. This article explains how to calculate them and their variants, and why they should be distinguished.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Cyril Cayrondoi:10.1107/S205327331900038XInternational Union of CrystallographyThree transformation matrices (distortion, orientation and correspondence) define the crystallography of displacive phase transformations. This article explains how to calculate them and their variants, and why they should be distinguished.enPHASE TRANSFORMATIONS; MARTENSITIC TRANSFORMATION; TRANSFORMATION MATRICES; VARIANTS; DISTORTION; ORIENTATION; CORRESPONDENCEThree transformation matrices (distortion, orientation and correspondence) define the crystallography of displacive phase transformations. This article explains how to calculate them and their variants, and why they should be distinguished.text/htmlThe transformation matrices (distortion, orientation, correspondence), their continuous forms and their variantstextIdentification of the impurity phase in high-purity CeB6 by convergent-beam electron diffraction
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The impurity phase in high-purity CeB6 is unequivocally identified by first determining its space group, using an iterative convergent-beam electron diffraction approach, and following this with an atomic structure confirmation by quantitative convergent-beam electron diffraction and high-angle annular dark-field scanning transmission electron microscopy.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Peng and Nakashimadoi:10.1107/S2053273319000354International Union of CrystallographyThe impurity phase in high-purity CeB6 is unequivocally identified by first determining its space group, using an iterative convergent-beam electron diffraction approach, and following this with an atomic structure confirmation by quantitative convergent-beam electron diffraction and high-angle annular dark-field scanning transmission electron microscopy.enSPACE GROUPS; CONVERGENT-BEAM ELECTRON DIFFRACTION; IMPURITY PHASES; QUANTITATIVE CONVERGENT-BEAM ELECTRON DIFFRACTION; GJONNES-MOODIE LINES; CERIUM HEXABORIDE (CEB6); CERIUM TETRABORIDE (CEB4)The impurity phase in high-purity CeB6 is unequivocally identified by first determining its space group, using an iterative convergent-beam electron diffraction approach, and following this with an atomic structure confirmation by quantitative convergent-beam electron diffraction and high-angle annular dark-field scanning transmission electron microscopy.text/htmlIdentification of the impurity phase in high-purity CeB6 by convergent-beam electron diffractiontext