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) 2020 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) 2020 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 imageThe Fedorov-Groth law revisited: complexity analysis using mineralogical data
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Using mineralogical data, we demonstrate that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov-Groth law.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Sergey V. Krivovichev et al.doi:10.1107/S2053273320004209International Union of CrystallographyUsing mineralogical data, we demonstrate that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov-Groth law.enSYMMETRY; CHEMICAL COMPOSITION; COMPLEXITY; SHANNON INFORMATION; FEDOROV-GROTH LAW.; SYMMETRY, CHEMICAL COMPOSITION, COMPLEXITY, SHANNON INFORMATION, FEDOROV-GROTH LAW.Using mineralogical data, we demonstrate that chemical simplicity measured as an amount of Shannon information per atom on average corresponds to higher symmetry measured as an order of the point group of a mineral, which provides a modern formulation of the Fedorov-Groth law.text/htmlThe Fedorov-Groth law revisited: complexity analysis using mineralogical datatextNew kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution
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The analytical solution of the problem of X-ray spherical wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Kohn and Smirnovadoi:10.1107/S2053273320003794International Union of CrystallographyThe analytical solution of the problem of X-ray spherical wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect.enX-RAY DIFFRACTION; TOPOGRAPHY; INTENSITY INCREASE EFFECT; UNEVEN EXIT SURFACE; SINGLE CRYSTALThe analytical solution of the problem of X-ray spherical wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect.text/htmlNew kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solutiontextDomain Formation and Phase Transitions in the Wurtzite-based Heterovalent Ternaries: a Landau Theory Analysis
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A Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN2is developed, and a first order, reconstructive phase transition is proposed to be the cause of observed crystal structure disorder. The model infers that the phase transition is paraelectric to antiferroelectric.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Paul C. Quayledoi:10.1107/S2053273320003095International Union of CrystallographyA Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN2is developed, and a first order, reconstructive phase transition is proposed to be the cause of observed crystal structure disorder. The model infers that the phase transition is paraelectric to antiferroelectric.enLANDAU THEORY; PHASE TRANSITION; ANTIFERROELECTRICSA Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN2is developed, and a first order, reconstructive phase transition is proposed to be the cause of observed crystal structure disorder. The model infers that the phase transition is paraelectric to antiferroelectric.text/htmlDomain Formation and Phase Transitions in the Wurtzite-based Heterovalent Ternaries: a Landau Theory AnalysistextDirect Recovery of Interfacial Topography from Coherent X-ray Reflectivity: Model Calculations for a One-Dimensional Interface
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The inversion of X-ray reflectivity to reveal the topography of a one-dimensional interface is evaluated through model calculations.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Paul Fenterdoi:10.1107/S2053273320003046International Union of CrystallographyThe inversion of X-ray reflectivity to reveal the topography of a one-dimensional interface is evaluated through model calculations.enCOHERENT REFLECTIVITY; SURFACE TOPOGRAPHY; PHASE PROBLEMThe inversion of X-ray reflectivity to reveal the topography of a one-dimensional interface is evaluated through model calculations.text/htmlDirect Recovery of Interfacial Topography from Coherent X-ray Reflectivity: Model Calculations for a One-Dimensional InterfacetextThe quaternion-based spatial coordinate and orientation frame alignment problems
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Quaternion methods for obtaining solutions to the problem of finding global rotations that optimally align pairs of corresponding lists of 3D spatial and/or orientation data are critically studied. The existence of multiple literatures and historical contexts are pointed out, and the algebraic solutions of the quaternion approach to the classic 3D spatial problem are emphasized. The treatment is extended to novel quaternion-based solutions to the alignment problems for 4D translation and orientation data.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Andrew J. Hansondoi:10.1107/S2053273320002648International Union of CrystallographyQuaternion methods for obtaining solutions to the problem of finding global rotations that optimally align pairs of corresponding lists of 3D spatial and/or orientation data are critically studied. The existence of multiple literatures and historical contexts are pointed out, and the algebraic solutions of the quaternion approach to the classic 3D spatial problem are emphasized. The treatment is extended to novel quaternion-based solutions to the alignment problems for 4D translation and orientation data.enPLEASE PROVIDE FOUR OR FIVE KEYWORDSQuaternion methods for obtaining solutions to the problem of finding global rotations that optimally align pairs of corresponding lists of 3D spatial and/or orientation data are critically studied. The existence of multiple literatures and historical contexts are pointed out, and the algebraic solutions of the quaternion approach to the classic 3D spatial problem are emphasized. The treatment is extended to novel quaternion-based solutions to the alignment problems for 4D translation and orientation data.text/htmlThe quaternion-based spatial coordinate and orientation frame alignment problemstextTexture corrections for total scattering functions
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The Debye scattering equation (DSE) is generalized and augmented in order to account for moderate texture effects, yielding the differential cross section as a function of atomic coordinates and texture coefficients subject to symmetry constraints. Implications for the evaluation of the pair distribution function (PDF) as a direct transform of powder diffraction data from textured samples are also discussed.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Cervellino and Frisondoi:10.1107/S2053273320002521International Union of CrystallographyThe Debye scattering equation (DSE) is generalized and augmented in order to account for moderate texture effects, yielding the differential cross section as a function of atomic coordinates and texture coefficients subject to symmetry constraints. Implications for the evaluation of the pair distribution function (PDF) as a direct transform of powder diffraction data from textured samples are also discussed.enDEBYE SCATTERING EQUATION; TEXTURE; PAIR DISTRIBUTION FUNCTIONThe Debye scattering equation (DSE) is generalized and augmented in order to account for moderate texture effects, yielding the differential cross section as a function of atomic coordinates and texture coefficients subject to symmetry constraints. Implications for the evaluation of the pair distribution function (PDF) as a direct transform of powder diffraction data from textured samples are also discussed.text/htmlTexture corrections for total scattering functionstextTesting of a `hard' X-ray interferometer for experimental investigations
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A new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Tigran H. Eyramjyan et al.doi:10.1107/S2053273320002314International Union of CrystallographyA new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.enX-RAYS; LLL INTERFEROMETER; `HARD' LLL INTERFEROMETER; MOIREA new type of X-ray LLL interferometer, a `hard' interferometer, which has both a base and a `ceiling', is tested for experimental investigations. The tested interferometer has no preliminary uncontrollable moiré and can be used for object and deformation investigations.text/htmlTesting of a `hard' X-ray interferometer for experimental investigationstextWedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions
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All physical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Venkatraman Gopalandoi:10.1107/S205327332000217XInternational Union of CrystallographyAll physical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.enMULTIVECTORS; WEDGE REVERSION ANTISYMMETRY; CLIFFORD ALGEBRAAll physical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.text/htmlWedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensionstextStructure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models
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Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Long Yang et al.doi:10.1107/S2053273320002028International Union of CrystallographyenPLEASE PROVIDE KEYWORDStext/htmlStructure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of modelstextGeometric realizations of abstract regular polyhedra with automorphism group H3
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A method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H3.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Aranas and Loyoladoi:10.1107/S2053273320001564International Union of CrystallographyA method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H3.enABSTRACT REGULAR POLYHEDRA; GEOMETRIC REALIZATIONS; NON-CRYSTALLOGRAPHIC COXETER GROUP H3; STRING C-GROUPSA method is adapted to generate a full rank realization of an abstract regular polyhedron with automorphism group H3.text/htmlGeometric realizations of abstract regular polyhedra with automorphism group H3textAn efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films
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A method is described for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films comprising various crystal orientations and/or polymorphs by measuring reciprocal-lattice vectors.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Josef Simbrunner et al.doi:10.1107/S2053273320001266International Union of CrystallographyA method is described for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films comprising various crystal orientations and/or polymorphs by measuring reciprocal-lattice vectors.enEPITAXY; INDEXING; MATHEMATICAL CRYSTALLOGRAPHYA method is described for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films comprising various crystal orientations and/or polymorphs by measuring reciprocal-lattice vectors.text/htmlAn efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin filmstextComparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surface
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Features of azimuthal plots for RHEED and its new counterpart, RHEPD, are discussed. The plots, for both electrons and positrons, are determined using dynamical diffraction theory.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Zbigniew Mituradoi:10.1107/S2053273320001205International Union of CrystallographyFeatures of azimuthal plots for RHEED and its new counterpart, RHEPD, are discussed. The plots, for both electrons and positrons, are determined using dynamical diffraction theory.enDYNAMICAL DIFFRACTION THEORY; AZIMUTHAL PLOTS; RENNINGER SCANS; KIKUCHI PATTERNSFeatures of azimuthal plots for RHEED and its new counterpart, RHEPD, are discussed. The plots, for both electrons and positrons, are determined using dynamical diffraction theory.text/htmlComparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surfacetextGroupoid description of modular structures
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The application of groupoids to modular crystal structures is presented.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Massimo Nespolo et al.doi:10.1107/S2053273320000650International Union of CrystallographyThe application of groupoids to modular crystal structures is presented.enMODULAR CRYSTAL STRUCTURES; GROUPOIDS; SUBPERIODIC GROUPS; SUPERPOSITION STRUCTURES; POLYTYPISMThe application of groupoids to modular crystal structures is presented.text/htmlGroupoid description of modular structurestextIsotopy classes for 3-periodic net embeddings
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Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Stephen Power et al.doi:10.1107/S2053273320000625International Union of CrystallographyEntangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.enPERIODIC NETS; EMBEDDED NETS; COORDINATION POLYMERS; ISOTOPY TYPES; CRYSTALLOGRAPHIC FRAMEWORKSEntangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type.text/htmlIsotopy classes for 3-periodic net embeddingstextA Journey into Reciprocal Space: A Crystallographer's Perspective. By A. M. Glazer. Morgan & Claypool, 2017. Paperback, pp. 190. Price USD 55.00. ISBN 9781681746203.
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Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Berthold Stögerdoi:10.1107/S2053273319006983International Union of CrystallographyenBOOK REVIEW; RECIPROCAL SPACEtext/htmlA Journey into Reciprocal Space: A Crystallographer's Perspective. By A. M. Glazer. Morgan & Claypool, 2017. Paperback, pp. 190. Price USD 55.00. ISBN 9781681746203.text