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) 2021 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) 2021 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 imagePiecewise-linear embeddings of knots and links with rotoinversion symmetry
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Rotoinversion knots and links are described using the minimum number of sticks. Such structures are attractive targets for molecular synthesis.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733O'Keeffe and Treacydoi:10.1107/S2053273321006136International Union of CrystallographyRotoinversion knots and links are described using the minimum number of sticks. Such structures are attractive targets for molecular synthesis.enKNOTS; LINKS; DECUSSATE STRUCTURES; PIECEWISE-LINEAR EMBEDDINGRotoinversion knots and links are described using the minimum number of sticks. Such structures are attractive targets for molecular synthesis.text/htmlPiecewise-linear embeddings of knots and links with rotoinversion symmetrytextOn Borromean links and related structures
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Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733O'Keeffe and Treacydoi:10.1107/S2053273321005568International Union of CrystallographyenBORROMEAN RINGS; N-BORROMEAN; ISONEMAL; PIECEWISE-LINEAR EMBEDDINGtext/htmlOn Borromean links and related structurestextOn the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal
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The presented hybrid approach for a fast and precise determination of the electrostatic potential, electric field and electric field gradient in an infinite crystal, in which the electron-density distribution is represented using a pseudoatom model, combines an efficient Ewald summation technique of the multipoles up to the hexadecapolar level with corrections that account for the nature of the boundary of an infinite periodic lattice at infinity and the short-range electron-density penetration effects.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Weatherly et al.doi:10.1107/S2053273321005532International Union of CrystallographyThe presented hybrid approach for a fast and precise determination of the electrostatic potential, electric field and electric field gradient in an infinite crystal, in which the electron-density distribution is represented using a pseudoatom model, combines an efficient Ewald summation technique of the multipoles up to the hexadecapolar level with corrections that account for the nature of the boundary of an infinite periodic lattice at infinity and the short-range electron-density penetration effects.enELECTROSTATIC POTENTIAL; ELECTRIC FIELD; ELECTRIC FIELD GRADIENT; CHARGE DENSITY; PSEUDOATOM MODEL; MULTIPOLE EXPANSION; EWALD SUMMATION; LATTICE SUMSThe presented hybrid approach for a fast and precise determination of the electrostatic potential, electric field and electric field gradient in an infinite crystal, in which the electron-density distribution is represented using a pseudoatom model, combines an efficient Ewald summation technique of the multipoles up to the hexadecapolar level with corrections that account for the nature of the boundary of an infinite periodic lattice at infinity and the short-range electron-density penetration effects.text/htmlOn the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystaltextThermodynamics of lattice vibrations in non-cubic crystals: the zinc lattice revisited
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An effective theory of lattice vibrations in anisotropic elemental crystals is outlined, based on temperature-dependent spectral cutoffs and varying Debye temperatures. The thermodynamic variables and Debye–Waller B factors of the hexagonal zinc lattice are derived.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Roman Tomaschitzdoi:10.1107/S2053273321005507International Union of CrystallographyAn effective theory of lattice vibrations in anisotropic elemental crystals is outlined, based on temperature-dependent spectral cutoffs and varying Debye temperatures. The thermodynamic variables and Debye–Waller B factors of the hexagonal zinc lattice are derived.enANISOTROPIC LATTICE VIBRATIONS; THERMODYNAMIC FUNCTIONS; DEBYE-WALLER FACTORS; NON-CUBIC CRYSTALS; TEMPERATURE-DEPENDENT SPECTRAL CUTOFF; DIRECTIONAL DEBYE TEMPERATURES; EFFECTIVE PHONON SPEED; OSCILLATOR MASS; HEAT CAPACITYAn effective theory of lattice vibrations in anisotropic elemental crystals is outlined, based on temperature-dependent spectral cutoffs and varying Debye temperatures. The thermodynamic variables and Debye–Waller B factors of the hexagonal zinc lattice are derived.text/htmlThermodynamics of lattice vibrations in non-cubic crystals: the zinc lattice revisitedtextMultiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain
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A new method is presented combining multiwavelength anomalous diffraction and Bragg coherent diffractive imaging. Combining the advantages of both approaches, it opens the possibility of simultaneously probing the strain and the unit-cell configuration.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Shabalin and Shpyrkodoi:10.1107/S2053273321004976International Union of CrystallographyA new method is presented combining multiwavelength anomalous diffraction and Bragg coherent diffractive imaging. Combining the advantages of both approaches, it opens the possibility of simultaneously probing the strain and the unit-cell configuration.enCOHERENT X-RAY DIFFRACTIVE IMAGING; MULTIWAVELENGTH ANOMALOUS DIFFRACTION; IMAGING POLARIZATION DOMAINS; ATOMIC DISPLACEMENT; LATTICE DEFORMATIONA new method is presented combining multiwavelength anomalous diffraction and Bragg coherent diffractive imaging. Combining the advantages of both approaches, it opens the possibility of simultaneously probing the strain and the unit-cell configuration.text/htmlMultiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and straintextMagnetic modes compatible with the symmetry of crystals
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The magnetic point groups are classified into 32 categories which lead to a total of 64 unique magnetic modes with the same set of directions of M. This classification gives hints on the neutron powder diffraction analysis of collinear magnetic ordering.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Piotr Fabrykiewicz et al.doi:10.1107/S2053273321004551International Union of CrystallographyThe magnetic point groups are classified into 32 categories which lead to a total of 64 unique magnetic modes with the same set of directions of M. This classification gives hints on the neutron powder diffraction analysis of collinear magnetic ordering.enMAGNETIC ORDERING; MAGNETIC SPACE GROUPS; SYMMETRY; SITE SYMMETRY; POINT GROUP; SPIN REORIENTATIONThe magnetic point groups are classified into 32 categories which lead to a total of 64 unique magnetic modes with the same set of directions of M. This classification gives hints on the neutron powder diffraction analysis of collinear magnetic ordering.text/htmlMagnetic modes compatible with the symmetry of crystalstextA topological proof of the modified Euler characteristic based on the orbifold concept
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The vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler characteristic is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Bartosz Naskręcki et al.doi:10.1107/S2053273321004320International Union of CrystallographyThe vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler characteristic is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.enEULER CHARACTERISTIC; ORBIFOLDS; SPACE-FILLING POLYHEDRA; SPACE GROUPS; ASYMMETRIC UNITSThe vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler characteristic is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.text/htmlA topological proof of the modified Euler characteristic based on the orbifold concepttextSpace Group Visualizer. By Eckhard Hitzer and Christian Perwass. Independently published, 2021. Paperback, pp. 162. Price EUR 22.25, USD 24.99. ISBN 979-8719838618.
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Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Müllerdoi:10.1107/S2053273321004174International Union of CrystallographyenSPACE-GROUP THEORY; CRYSTALLOGRAPHIC SOFTWAREtext/htmlSpace Group Visualizer. By Eckhard Hitzer and Christian Perwass. Independently published, 2021. Paperback, pp. 162. Price EUR 22.25, USD 24.99. ISBN 979-8719838618.textImprovement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions
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A new strategy for improving precision and sensitivity in the refinement of crystal structure factors is proposed. This technique will help to precisely determine the chemical bonding states of crystalline materials, which are closely related to their physical properties.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733B. Aryal et al.doi:10.1107/S2053273321004137International Union of CrystallographyA new strategy for improving precision and sensitivity in the refinement of crystal structure factors is proposed. This technique will help to precisely determine the chemical bonding states of crystalline materials, which are closely related to their physical properties.enCBED; STRUCTURE FACTORS; ELECTRON DENSITY; ELECTROSTATIC POTENTIAL; PRECISIONA new strategy for improving precision and sensitivity in the refinement of crystal structure factors is proposed. This technique will help to precisely determine the chemical bonding states of crystalline materials, which are closely related to their physical properties.text/htmlImprovement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditionstextPolarization effects of X-ray monochromators modeled using dynamical scattering theory
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Treatment of the effects of a single-crystal incident-beam monochromator in a powder diffraction experiment must be carried out using dynamical diffraction to obtain the correct intensities for reflections, due to the modification of the beam polarization by the monochromator. Theory and data are presented to verify the effect.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Marcus H. Mendenhall et al.doi:10.1107/S2053273321003879International Union of CrystallographyTreatment of the effects of a single-crystal incident-beam monochromator in a powder diffraction experiment must be carried out using dynamical diffraction to obtain the correct intensities for reflections, due to the modification of the beam polarization by the monochromator. Theory and data are presented to verify the effect.enDYNAMICAL DIFFRACTION; POWDER DIFFRACTION; INCIDENT-BEAM MONOCHROMATORS; POLARIZATIONTreatment of the effects of a single-crystal incident-beam monochromator in a powder diffraction experiment must be carried out using dynamical diffraction to obtain the correct intensities for reflections, due to the modification of the beam polarization by the monochromator. Theory and data are presented to verify the effect.text/htmlPolarization effects of X-ray monochromators modeled using dynamical scattering theorytextAn Invitation to Applied Category Theory. Seven Sketches in Compositionality. By Brendan Fong and David I. Spivak. Cambridge University Press, 2019. Paperback, pp. 348. Price GBP 37.99. ISBN 9781108711821.
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Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Berthold Stögerdoi:10.1107/S2053273321003685International Union of CrystallographyenBOOK REVIEW; CATEGORY THEORYtext/htmlAn Invitation to Applied Category Theory. Seven Sketches in Compositionality. By Brendan Fong and David I. Spivak. Cambridge University Press, 2019. Paperback, pp. 348. Price GBP 37.99. ISBN 9781108711821.textResolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon
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The resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Vladimir M. Kaganer et al.doi:10.1107/S2053273321003697International Union of CrystallographyThe resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.enX-RAY FREE-ELECTRON LASERS; X-RAY SPECTROSCOPY; BENT CRYSTALS; DIAMOND CRYSTAL OPTICS; FEMTOSECOND X-RAY DIFFRACTIONThe resolution function of a bent-crystal spectrometer for pulses of an X-ray free-electron laser is evaluated. Under appropriate conditions, the energy resolution reaches the ratio of the lattice spacing to the crystal thickness.text/htmlResolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicontextA reference-based multi-lattice indexing method integrating prior information correction and iterative refinement in protein crystallography
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A new multi-lattice indexing method based on the principle of whole-pattern matching given cell dimensions and space-group symmetry is presented for macromolecular crystallography. The proposed method features a local correction for prior information accompanied by iterative refinement of experimental parameters, both of which are numerically and experimentally demonstrated to be critical for accurately identifying multiple crystal lattices.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Qiang Zhou et al.doi:10.1107/S2053273321003521International Union of CrystallographyA new multi-lattice indexing method based on the principle of whole-pattern matching given cell dimensions and space-group symmetry is presented for macromolecular crystallography. The proposed method features a local correction for prior information accompanied by iterative refinement of experimental parameters, both of which are numerically and experimentally demonstrated to be critical for accurately identifying multiple crystal lattices.enMULTI-CRYSTAL DIFFRACTION; INDEXING ALGORITHM; MULTI-CRYSTAL DATA PROCESSING SUITE; MCDPS; PROTEIN CRYSTALLOGRAPHY; DATA REDUCTIONA new multi-lattice indexing method based on the principle of whole-pattern matching given cell dimensions and space-group symmetry is presented for macromolecular crystallography. The proposed method features a local correction for prior information accompanied by iterative refinement of experimental parameters, both of which are numerically and experimentally demonstrated to be critical for accurately identifying multiple crystal lattices.text/htmlA reference-based multi-lattice indexing method integrating prior information correction and iterative refinement in protein crystallographytextRelativistic spacetime crystals
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By appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown. Using this mapping, hidden symmetries in relativistic spacetime crystals are uncovered.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Venkatraman Gopalandoi:10.1107/S2053273321003259International Union of CrystallographyBy appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown. Using this mapping, hidden symmetries in relativistic spacetime crystals are uncovered.enSPACETIME; SPECIAL RELATIVITY; RENORMALIZED BLENDED SPACETIME; RELATIVISTIC SPACETIME CRYSTALSBy appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown. Using this mapping, hidden symmetries in relativistic spacetime crystals are uncovered.text/htmlRelativistic spacetime crystalstextOn symmetry breaking of dual polyhedra of non-crystallographic group H3
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The ubiquity of the icosahedral symmetry among various spherical molecules, fullerenes and viruses motivates the current study. The structures of dual polytopes with the H3 symmetry obtained for seven types of dominant points are described in detail. The existence of the corresponding nanotubes is explained using a symmetry-breaking mechanism. The structure of the fullerene C20 is expanded into the nanotubes C20+6N and C20+10N, using the reduction of the icosahedral symmetry to the subgroups A2 and H2, respectively.Copyright (c) 2021 International Union of Crystallographyurn:issn:2053-2733Mariia Myronovadoi:10.1107/S2053273321002254International Union of CrystallographyThe ubiquity of the icosahedral symmetry among various spherical molecules, fullerenes and viruses motivates the current study. The structures of dual polytopes with the H3 symmetry obtained for seven types of dominant points are described in detail. The existence of the corresponding nanotubes is explained using a symmetry-breaking mechanism. The structure of the fullerene C20 is expanded into the nanotubes C20+6N and C20+10N, using the reduction of the icosahedral symmetry to the subgroups A2 and H2, respectively.enCOXETER GROUPS; DUAL POLYTOPES; ORBIT DECOMPOSITIONS; FULLERENES; NANOTUBES; STELLATED POLYHEDRAThe ubiquity of the icosahedral symmetry among various spherical molecules, fullerenes and viruses motivates the current study. The structures of dual polytopes with the H3 symmetry obtained for seven types of dominant points are described in detail. The existence of the corresponding nanotubes is explained using a symmetry-breaking mechanism. The structure of the fullerene C20 is expanded into the nanotubes C20+6N and C20+10N, using the reduction of the icosahedral symmetry to the subgroups A2 and H2, respectively.text/htmlOn symmetry breaking of dual polyhedra of non-crystallographic group H3text