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) 2020 International Union of Crystallography2020-05-01International 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 76, Part 3, 2020textweekly62002-01-01T00:00+00:003762020-05-01Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances273urn:issn:2053-2733med@iucr.orgMay 20202020-05-01Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageIsotopy classification of three-dimensional embedded nets
http://scripts.iucr.org/cgi-bin/paper?me6077
Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Schulte, E.2020-04-29doi:10.1107/S2053273320005616International Union of CrystallographyThe article by Power et al. [Acta Cryst. (2020), A76, 275–301] on the isotopy classification of crystal nets is discussed.ENembedded netsisotopy classificationtopologytext/htmlIsotopy classification of three-dimensional embedded netstext3762020-04-29Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Ascientific commentaries273274Isotopy classes for 3-periodic net embeddings
http://scripts.iucr.org/cgi-bin/paper?ib5087
Entangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Power, S.C.Baburin, I.A.Proserpio, D.M.2020-03-05doi: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 netsembedded netscoordination polymersisotopy typescrystallographic frameworksEntangled embedded periodic nets and crystal frameworks are defined, along with their dimension type, homogeneity type, adjacency depth and periodic isotopy type. Periodic isotopy classifications are obtained for various families of embedded nets with small quotient graphs. The 25 periodic isotopy classes of depth-1 embedded nets with a single-vertex quotient graph are enumerated. Additionally, a classification is given of embeddings of n-fold copies of pcu with all connected components in a parallel orientation and n vertices in a repeat unit, as well as demonstrations of their maximal symmetry periodic isotopes. The methodology of linear graph knots on the flat 3-torus [0,1)3 is introduced. These graph knots, with linear edges, are spatial embeddings of the labelled quotient graphs of an embedded net which are associated with its periodicity bases.text/htmlIsotopy classes for 3-periodic net embeddingstext3762020-03-05Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Alead articles275301Texture corrections for total scattering functions
http://scripts.iucr.org/cgi-bin/paper?vk5041
Many functional materials are today synthesized in the form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kinds of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. Therefore modified expressions were derived for the most common total scattering functions, in particular the Debye scattering equation (DSE) which yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and {\cal{G}}(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Cervellino, A.Frison, R.2020-03-26doi: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 equationtexturepair distribution functionMany functional materials are today synthesized in the form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kinds of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. Therefore modified expressions were derived for the most common total scattering functions, in particular the Debye scattering equation (DSE) which yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and {\cal{G}}(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.text/htmlTexture corrections for total scattering functionstext3762020-03-26Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers302317Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions
http://scripts.iucr.org/cgi-bin/paper?ib5086
It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1, time-reversal, 1′, and a third that is introduced here, namely wedge reversion, 1†. It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1† would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Gopalan, V.2020-04-28doi:10.1107/S205327332000217XInternational Union of CrystallographyPhysical quantities in arbitrary dimensional space can be classified into 41 types using three antisymmetries within the framework of Clifford algebra.ENmultivectorswedge reversion antisymmetryClifford algebraIt is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1, time-reversal, 1′, and a third that is introduced here, namely wedge reversion, 1†. It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1† would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.text/htmlWedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensionstext3762020-04-28Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers318327Comparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surface
http://scripts.iucr.org/cgi-bin/paper?iv5004
Azimuthal plots for RHEPD (reflection high-energy positron diffraction) and RHEED (reflection high-energy electron diffraction) were calculated using dynamical diffraction theory and then compared. It was assumed that RHEPD and RHEED azimuthal plots can be collected practically by recording the intensity while rotating the sample around the axis perpendicular to the surface (for the case of X-ray diffraction, such forms of data are called Renninger scans). It was found that RHEPD plots were similar to RHEED plots if they were compared at Bragg reflections of the same order. RHEPD plots can also be determined in the region of total external reflection and for such conditions multiple scattering effects turned out to be very weak. The findings for azimuthal plots are also discussed in the context of the formation mechanisms of Kikuchi patterns.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Mitura, Z.2020-03-26doi: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 theoryazimuthal plotsRenninger scansKikuchi patternsAzimuthal plots for RHEPD (reflection high-energy positron diffraction) and RHEED (reflection high-energy electron diffraction) were calculated using dynamical diffraction theory and then compared. It was assumed that RHEPD and RHEED azimuthal plots can be collected practically by recording the intensity while rotating the sample around the axis perpendicular to the surface (for the case of X-ray diffraction, such forms of data are called Renninger scans). It was found that RHEPD plots were similar to RHEED plots if they were compared at Bragg reflections of the same order. RHEPD plots can also be determined in the region of total external reflection and for such conditions multiple scattering effects turned out to be very weak. The findings for azimuthal plots are also discussed in the context of the formation mechanisms of Kikuchi patterns.text/htmlComparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surfacetext3762020-03-26Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers328333Groupoid description of modular structures
http://scripts.iucr.org/cgi-bin/paper?ug5004
Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Nespolo, M.Souvignier, B.Stöger, B.2020-04-02doi:10.1107/S2053273320000650International Union of CrystallographyThe application of groupoids to modular crystal structures is presented.ENmodular crystal structuresgroupoidssubperiodic groupssuperposition structurespolytypismModular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.text/htmlGroupoid description of modular structurestext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers334344An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films
http://scripts.iucr.org/cgi-bin/paper?wo5036
Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Simbrunner, J.Schrode, B.Domke, J.Fritz, T.Salzmann, I.Resel, R.2020-04-02doi: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.ENepitaxyindexingmathematical crystallographyCrystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.text/htmlAn efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin filmstext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers345357Geometric realizations of abstract regular polyhedra with automorphism group H3
http://scripts.iucr.org/cgi-bin/paper?eo5106
A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Aranas, J.A.L.Loyola, M.L.2020-04-02doi: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 polyhedrageometric realizationsnon-crystallographic Coxeter group H3string C-groupsA geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.text/htmlGeometric realizations of abstract regular polyhedra with automorphism group H3text3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers358368SPIND-TC: an indexing method for two-color X-ray diffraction data
http://scripts.iucr.org/cgi-bin/paper?ib5084
Recent developments of two-color operation modes at X-ray free-electron laser facilities provide new research opportunities, such as X-ray pump/X-ray probe experiments and multiple-wavelength anomalous dispersion phasing methods. However, most existing indexing methods were developed for indexing diffraction data from monochromatic X-ray beams. Here, a new algorithm is presented for indexing two-color diffraction data, as an extension of the sparse-pattern indexing algorithm SPIND, which has been demonstrated to be capable of indexing diffraction patterns with as few as five peaks. The principle and implementation of the two-color indexing method, SPIND-TC, are reported in this paper. The algorithm was tested on both simulated and experimental data of protein crystals. The results show that the diffraction data can be accurately indexed in both cases. Source codes are publicly available at https://github.com/lixx11/SPIND-TC.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Li, X.Li, C.Liu, H.2020-04-02doi:10.1107/S2053273320001916International Union of CrystallographyAn auto-indexing method for two-color X-ray diffraction data is presented, which has been tested on both simulated and experimental protein diffraction data. The indexing yield is increased significantly compared with the previous approach using conventional indexers.ENserial crystallographytwo-color diffractionindexing algorithmRecent developments of two-color operation modes at X-ray free-electron laser facilities provide new research opportunities, such as X-ray pump/X-ray probe experiments and multiple-wavelength anomalous dispersion phasing methods. However, most existing indexing methods were developed for indexing diffraction data from monochromatic X-ray beams. Here, a new algorithm is presented for indexing two-color diffraction data, as an extension of the sparse-pattern indexing algorithm SPIND, which has been demonstrated to be capable of indexing diffraction patterns with as few as five peaks. The principle and implementation of the two-color indexing method, SPIND-TC, are reported in this paper. The algorithm was tested on both simulated and experimental data of protein crystals. The results show that the diffraction data can be accurately indexed in both cases. Source codes are publicly available at https://github.com/lixx11/SPIND-TC.text/htmlSPIND-TC: an indexing method for two-color X-ray diffraction datatext3762020-04-02Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers369375Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid
http://scripts.iucr.org/cgi-bin/paper?ae5082
The generalized Darwin–Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429–440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin–Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Bornemann, F.Li, Y.Y.Wuttke, J.2020-04-16doi:10.1107/S2053273320002065International Union of CrystallographyTo describe multiple Bragg reflection from a thick, ideally imperfect crystal, the transport equations are reformulated in three-dimensional phase space and solved by spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially for finite detectors.ENmosaic crystalsmultiple scatteringDarwin–Hamilton equationsspectral collocationThe generalized Darwin–Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429–440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin–Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.text/htmlMultiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a gridtext3762020-04-16Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers376389Testing of a `hard' X-ray interferometer for experimental investigations
http://scripts.iucr.org/cgi-bin/paper?iv5005
A `hard' X-ray LLL interferometer is tested for experimental investigations. The interferometer has both a base and a `ceiling', which are rigidly connected through columns. As a result, the interferometer does not have uncontrollable preliminary moiré. The intensity distribution is uniform in the interfering beams. It is shown that the interferometer is very sensitive to minor mechanical stresses. As a result, the interferometer must be freely placed on the goniometer head. Constant-thickness fringes are obtained using a wedge with a vertically placed apex. The volumes available for specimen placement are limited due to the existence of the ceiling. These difficulties can be overcome. The hard interferometer can be used for object and deformation investigations.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Eyramjyan, T.H.Mesropyan, M.H.Mnatsakanyan, T.S.Balyan, M.K.2020-04-16doi: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-raysLLL interferometer`hard' LLL interferometermoiré fringesA `hard' X-ray LLL interferometer is tested for experimental investigations. The interferometer has both a base and a `ceiling', which are rigidly connected through columns. As a result, the interferometer does not have uncontrollable preliminary moiré. The intensity distribution is uniform in the interfering beams. It is shown that the interferometer is very sensitive to minor mechanical stresses. As a result, the interferometer must be freely placed on the goniometer head. Constant-thickness fringes are obtained using a wedge with a vertically placed apex. The volumes available for specimen placement are limited due to the existence of the ceiling. These difficulties can be overcome. The hard interferometer can be used for object and deformation investigations.text/htmlTesting of a `hard' X-ray interferometer for experimental investigationstext3762020-04-16Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers390394Structure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of models
http://scripts.iucr.org/cgi-bin/paper?vk5039
A new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. It supports both X-ray and neutron PDFs. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally distorted structures, and complicated doped and magnetic materials. This approach could greatly reduce the traditional structure searching work and enable the possibility of high-throughput real-time auto-analysis PDF experiments in the future.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Yang, L.Juhás, P.Terban, M.W.Tucker, M.G.Billinge, S.J.L.2020-04-28doi:10.1107/S2053273320002028International Union of CrystallographyStructure-mining finds and returns the best-fit structures from structural databases given a measured pair distribution function data set. Using databases and heuristics for automation, it has the potential to save experimenters a large amount of time as they explore candidate structures from the literature.ENpair distribution functionPDFautomated fittingatomic structurestructure discoveryA new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. It supports both X-ray and neutron PDFs. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally distorted structures, and complicated doped and magnetic materials. This approach could greatly reduce the traditional structure searching work and enable the possibility of high-throughput real-time auto-analysis PDF experiments in the future.text/htmlStructure-mining: screening structure models by automated fitting to the atomic pair distribution function over large numbers of modelstext3762020-04-28Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers395409Domain formation and phase transitions in the wurtzite-based heterovalent ternaries: a Landau theory analysis
http://scripts.iucr.org/cgi-bin/paper?ug5001
Characterizing the crystalline disorder properties of heterovalent ternary semiconductors continues to challenge solid-state theory. Here, a Landau theory is developed for the wurtzite-based ternary semiconductor ZnSnN2. It is shown that the symmetry properties of two nearly co-stable phases, with space groups Pmc21 and Pbn21, imply that a reconstructive phase transition is the source of crystal structure disorder via a mixture of phase domains. The site exchange defect, which consists of two adjacent antisite defects, is identified as the nucleation mechanism of the transition. A Landau potential based on the space-group symmetries of the Pmc21 and Pbn21 phases is constructed from the online databases in the ISOTROPY software suite and this potential is consistent with a system that undergoes a paraelectric to antiferroelectric phase transition. It is hypothesized that the low-temperature Pbn21 phase is antiferroelectric within the c-axis basal plane. The dipole arrangements within the Pbn21 basal plane yield a nonpolar spontaneous polarization and the electrical susceptibility derived from the Landau potential exhibits a singularity at the Néel temperature characteristic of antiferroelectric behavior. These results inform the study of disorder in the broad class of heterovalent ternary semiconductors, including those based on the zincblende structure, and open the door to the application of the ternaries in new technology spaces.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Quayle, P.C.2020-04-28doi:10.1107/S2053273320003095International Union of CrystallographyA Landau theory for the wurtzite-based heterovalent ternary semiconductor ZnSnN2 is developed and a first-order reconstructive phase transition is proposed as the cause of observed crystal structure disorder. The model implies that the phase transition is paraelectric to antiferroelectric.ENLandau theoryphase transitionsantiferroelectricscrystalline disorder propertiesheterovalent ternary semiconductorsCharacterizing the crystalline disorder properties of heterovalent ternary semiconductors continues to challenge solid-state theory. Here, a Landau theory is developed for the wurtzite-based ternary semiconductor ZnSnN2. It is shown that the symmetry properties of two nearly co-stable phases, with space groups Pmc21 and Pbn21, imply that a reconstructive phase transition is the source of crystal structure disorder via a mixture of phase domains. The site exchange defect, which consists of two adjacent antisite defects, is identified as the nucleation mechanism of the transition. A Landau potential based on the space-group symmetries of the Pmc21 and Pbn21 phases is constructed from the online databases in the ISOTROPY software suite and this potential is consistent with a system that undergoes a paraelectric to antiferroelectric phase transition. It is hypothesized that the low-temperature Pbn21 phase is antiferroelectric within the c-axis basal plane. The dipole arrangements within the Pbn21 basal plane yield a nonpolar spontaneous polarization and the electrical susceptibility derived from the Landau potential exhibits a singularity at the Néel temperature characteristic of antiferroelectric behavior. These results inform the study of disorder in the broad class of heterovalent ternary semiconductors, including those based on the zincblende structure, and open the door to the application of the ternaries in new technology spaces.text/htmlDomain formation and phase transitions in the wurtzite-based heterovalent ternaries: a Landau theory analysistext3762020-04-28Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers4104201988421198842219884231988424New 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
http://scripts.iucr.org/cgi-bin/paper?iv5007
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. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Kohn, V.G.Smirnova, I.A.2020-04-28doi: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 diffractiontopographyintensity increase effectuneven exit surfacesingle crystalsThe 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. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.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 solutiontext3762020-04-28Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Aresearch papers421428The Fedorov–Groth law revisited: complexity analysis using mineralogical data
http://scripts.iucr.org/cgi-bin/paper?eo5108
The Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Krivovichev, S.V.Krivovichev, V.G.2020-04-28doi:10.1107/S2053273320004209International Union of CrystallographyUsing mineralogical data, it is demonstrated 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.ENsymmetrychemical compositioncomplexityShannon informationFedorov–Groth lawThe Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.text/htmlThe Fedorov–Groth law revisited: complexity analysis using mineralogical datatext3762020-04-28Copyright (c) 2020 International Union of CrystallographyActa Crystallographica Section Ashort communications429431