Open-access and free articles 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) 2022 International Union of CrystallographyInternational Union of CrystallographyInternational Union of Crystallographyurn:issn:0108-7673texthttps://journals.iucr.orgOpen-access and free articles in Acta Crystallographica Section A Foundations and AdvancesActa 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/htmlyearly2002-01-01T00:00+00:006urn:issn:0108-7673Acta Crystallographica Section A Foundations and Advancesmed@iucr.orgCopyright (c) 2022 International Union of CrystallographyOpen-access and free articles in Acta Crystallographica Section A: Foundations and Advanceshttp://journals.iucr.org/logos/rss10a.gif
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Still imageSimulating dark-field X-ray microscopy images with wavefront propagation techniques
http://scripts.iucr.org/cgi-bin/paper?iv5021
Dark-field X-ray microscopy is a diffraction-based synchrotron imaging technique capable of imaging defects in the bulk of extended crystalline samples. Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi–Taupin equations and wavefront propagation. The approach is validated by comparing simulated images with experimental data from a near-perfect single crystal of diamond containing a single stacking-fault defect in the illuminated volume.doi:10.1107/S205327332200866XInternational Union of Crystallographytexturn:issn:2053-2733DIFFRACTION IMAGING; DYNAMICAL DIFFRACTION; SIMULATIONhttps://creativecommons.org/licenses/by/4.0/Simulating dark-field X-ray microscopy images with wavefront propagation techniquesDark-field X-ray microscopy is a diffraction-based synchrotron imaging technique capable of imaging defects in the bulk of extended crystalline samples. Numerical simulations are presented of image formation in such a microscope using numerical integration of the dynamical Takagi–Taupin equations and wavefront propagation. The approach is validated by comparing simulated images with experimental data from a near-perfect single crystal of diamond containing a single stacking-fault defect in the illuminated volume.The simulation of a dark-field X-ray microscopy experiment using wavefront propagation techniques and numerical integration of the Takagi–Taupin equations is shown. The approach is validated by comparing with measurements of a near-perfect diamond crystal containing a single stacking-fault defect.en2022-10-10Carlsen, M.Detlefs, C.Yildirim, C.Ræder, T.Simons, H.text/html2053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org6research papers2022-10-10490https://creativecommons.org/licenses/by/4.0/78482November 20222053-2733Extending the novel |ρ|-based phasing algorithm to the solution of anomalous scattering substructures from SAD data of protein crystals
http://scripts.iucr.org/cgi-bin/paper?ae5119
Owing to the importance of the single-wavelength anomalous diffraction (SAD) technique, the recently developed |ρ|-based phasing algorithm (SM,|ρ|) incorporating the inner-pixel preservation (ipp) procedure [Rius & Torrelles (2021). Acta Cryst A77, 339–347] has been adapted to the determination of anomalous scattering substructures and its applicability tested on a series of 12 representative experimental data sets, mostly retrieved from the Protein Data Bank. To give an idea of the suitability of the data sets, the main indicators measuring their quality are also given. The dominant anomalous scatterers are either SeMet or S atoms, or metals/clusters incorporated by soaking. The resulting SAD-adapted algorithm solves the substructures of the test protein crystals quite efficiently.doi:10.1107/S2053273322008622International Union of Crystallographytexturn:issn:2053-2733SM,|[RHO]| PHASING ALGORITHM; SMAR PHASING; IPP DENSITY MODIFICATION; SAD-SMAR; |[RHO]|-BASED DIRECT METHODS; STRUCTURE SOLUTIONhttps://creativecommons.org/licenses/by/4.0/Extending the novel |ρ|-based phasing algorithm to the solution of anomalous scattering substructures from SAD data of protein crystalsOwing to the importance of the single-wavelength anomalous diffraction (SAD) technique, the recently developed |ρ|-based phasing algorithm (SM,|ρ|) incorporating the inner-pixel preservation (ipp) procedure [Rius & Torrelles (2021). Acta Cryst A77, 339–347] has been adapted to the determination of anomalous scattering substructures and its applicability tested on a series of 12 representative experimental data sets, mostly retrieved from the Protein Data Bank. To give an idea of the suitability of the data sets, the main indicators measuring their quality are also given. The dominant anomalous scatterers are either SeMet or S atoms, or metals/clusters incorporated by soaking. The resulting SAD-adapted algorithm solves the substructures of the test protein crystals quite efficiently.The novel SM,|ρ| phasing algorithm has been adapted to the determination of anomalous scattering substructures from single-wavelength anomalous diffraction (SAD) data of protein crystals and successfully tested on data sets mostly retrieved from the Protein Data Bank.en2022-10-10Rius, J.Torrelles, X.text/html2022-10-10research papers6Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org2053-27332053-2733November 202247378https://creativecommons.org/licenses/by/4.0/481On single-crystal total scattering data reduction and correction protocols for analysis in direct space. Corrigendum
http://scripts.iucr.org/cgi-bin/paper?me6196
The name of the third author of the article by Koch et al. [Acta Cryst. (2021). A77, 611–636] is corrected.doi:10.1107/S2053273322009081International Union of Crystallographytexturn:issn:2053-2733PAIR DISTRIBUTION FUNCTION ANALYSIS; PDF ANALYSIS; SINGLE-CRYSTAL 3D DIFFERENTIAL PDF; TOTAL SCATTERING; DATA REDUCTION; CUIR2S4On single-crystal total scattering data reduction and correction protocols for analysis in direct space. CorrigendumThe name of the third author of the article by Koch et al. [Acta Cryst. (2021). A77, 611–636] is corrected.Corrigendum to the article by Koch et al. [Acta Cryst. (2021). A77, 611–636].en2022-11-01Koch, R.J.Roth, N.Liu, Y.Ivashko, O.Dippel, A.-C.Petrovic, C.Iversen, B.B.Zimmermann, M. v.Bozin, E.S.text/html51578515November 20222053-27332053-2733med@iucr.orgActa Crystallographica Section A: Foundations and Advances6addenda and errata2022-11-01Towards a machine-readable literature: finding relevant papers based on an uploaded powder diffraction pattern
http://scripts.iucr.org/cgi-bin/paper?ae5116
A prototype application for machine-readable literature is investigated. The program is called pyDataRecognition and serves as an example of a data-driven literature search, where the literature search query is an experimental data set provided by the user. The user uploads a powder pattern together with the radiation wavelength. The program compares the user data to a database of existing powder patterns associated with published papers and produces a rank ordered according to their similarity score. The program returns the digital object identifier and full reference of top-ranked papers together with a stack plot of the user data alongside the top-five database entries. The paper describes the approach and explores successes and challenges.doi:10.1107/S2053273322007483International Union of Crystallographytexturn:issn:2053-2733MACHINE-READABLE SCIENTIFIC LITERATURE; DATA-DRIVEN LITERATURE SEARCH; POWDER DIFFRACTION; DATA SIMILARITY; CIFhttps://creativecommons.org/licenses/by/4.0/Towards a machine-readable literature: finding relevant papers based on an uploaded powder diffraction patternA prototype application for machine-readable literature is investigated. The program is called pyDataRecognition and serves as an example of a data-driven literature search, where the literature search query is an experimental data set provided by the user. The user uploads a powder pattern together with the radiation wavelength. The program compares the user data to a database of existing powder patterns associated with published papers and produces a rank ordered according to their similarity score. The program returns the digital object identifier and full reference of top-ranked papers together with a stack plot of the user data alongside the top-five database entries. The paper describes the approach and explores successes and challenges.A prototype application, pyDataRecognition, is described and tested. It has the goal that, given a measured powder diffraction pattern, it will return a list of publications from the IUCr Journals database that might be related based on the similarity to powder diffraction data deposited for those publications. This explores the possibility of a machine-readable literature where, for example, relevant studies may be found automatically through data similarity matches of online databases.en2022-08-19Özer, B.Karlsen, M.A.Thatcher, Z.Lan, L.McMahon, B.Strickland, P.R.Westrip, S.P.Sang, K.S.Billing, D.G.Ravnsbaek, D.B.Billinge, S.J.L.text/html2053-2733September 202278https://creativecommons.org/licenses/by/4.0/394386research papers2022-08-192053-27335med@iucr.orgActa Crystallographica Section A: Foundations and AdvancesCrystallographic phase retrieval method for liquid crystal bicontinuous phases: indicator-based method
http://scripts.iucr.org/cgi-bin/paper?ik5003
An indicator-based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. Such liquid crystals have large structural disorder; the number of independent Bragg reflections that can be observed is limited. This paper proposes two indicators to identify plausible combination(s) of crystallographic phases, i.e. electron-density distribution. The indicators are based on the characteristics of the liquid crystals: amphiphilic molecules diffuse mainly in the direction parallel to polar–nonpolar interfaces and the electron density in the direction parallel to the interfaces is averaged. One indicator is the difference between the maximum and minimum electron density, and the other is calculated from the Hessian matrix of the electron density. Using test data, the electron densities were calculated for all possible phase combinations and indicators were obtained. The results indicated that the electron densities with the minimum indicators were close to the true electron density. Therefore, this method is effective for phase retrieval. The accuracy of the phase retrieval decreased when the volume fraction of the region including the triply periodic minimal surface increased.doi:10.1107/S2053273322006970International Union of Crystallographytexturn:issn:2053-2733LYOTROPIC LIQUID CRYSTALS; TRIPLY PERIODIC MINIMAL SURFACES; CRYSTALLOGRAPHIC PHASE RETRIEVALhttps://creativecommons.org/licenses/by/4.0/Crystallographic phase retrieval method for liquid crystal bicontinuous phases: indicator-based methodAn indicator-based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. Such liquid crystals have large structural disorder; the number of independent Bragg reflections that can be observed is limited. This paper proposes two indicators to identify plausible combination(s) of crystallographic phases, i.e. electron-density distribution. The indicators are based on the characteristics of the liquid crystals: amphiphilic molecules diffuse mainly in the direction parallel to polar–nonpolar interfaces and the electron density in the direction parallel to the interfaces is averaged. One indicator is the difference between the maximum and minimum electron density, and the other is calculated from the Hessian matrix of the electron density. Using test data, the electron densities were calculated for all possible phase combinations and indicators were obtained. The results indicated that the electron densities with the minimum indicators were close to the true electron density. Therefore, this method is effective for phase retrieval. The accuracy of the phase retrieval decreased when the volume fraction of the region including the triply periodic minimal surface increased.An indicator-based crystallographic phase retrieval method has been developed for diffraction data of bicontinuous cubic phases of lyotropic liquid crystals. The electron densities with the minimum indicators are close to the true electron density.en2022-07-28Oka, T.text/html2053-2733September 202243078https://creativecommons.org/licenses/by/4.0/4362022-07-28research papers5Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org2053-2733Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
http://scripts.iucr.org/cgi-bin/paper?uv5005
Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600–610] is that unimodularity is no longer assumed in this paper.doi:10.1107/S2053273322006714International Union of Crystallographytexturn:issn:2053-2733PURE DISCRETE SPECTRUM; REGULAR MODEL SETS; NON-UNIMODULAR SUBSTITUTION; PISOT FAMILY SUBSTITUTION; MEYER SETShttps://creativecommons.org/licenses/by/4.0/Pure discrete spectrum and regular model sets on some non-unimodular substitution tilingsSubstitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600–610] is that unimodularity is no longer assumed in this paper.The equivalence between pure discrete spectrum and regular model sets on some non-unimodular substitution tilings is established. This will help to provide useful information about the cut-and-project scheme used in the description of quasiperiodic structures.en2022-08-12Lee, J.-Y.text/html78https://creativecommons.org/licenses/by/4.0/4514372053-2733September 20222053-27335med@iucr.orgActa Crystallographica Section A: Foundations and Advancesresearch papers2022-08-12Origin of irregular X-ray mirage fringes from a bent, thin crystal
http://scripts.iucr.org/cgi-bin/paper?iv5025
The dynamical theory of diffraction is used to analyse irregular X-ray mirage interference fringes observed in Si220 X-ray reflection topography from a weakly bent, thin crystal due to gravity. The origin of the irregular fringes is attributed to the interference between mirage diffracted beams and a reflected beam from the back surface, which is a new type of interference fringe. The irregular fringes are reproduced by calculating the reflected intensities numerically. The effects of absorption and thermal vibration are quite important for the reproduction. The result shows that the interference fringes depend on the strain as well as the thickness of the crystal, which indicates that the fringes should be useful for analysing weak strain in a crystal as an application.doi:10.1107/S2053273322006143International Union of Crystallographytexturn:issn:2053-2733INTERFERENCE FRINGES; MIRAGE FRINGES; BENT CRYSTAL; DYNAMICAL THEORY OF X-RAY DIFFRACTIONhttps://creativecommons.org/licenses/by/4.0/Origin of irregular X-ray mirage fringes from a bent, thin crystalThe dynamical theory of diffraction is used to analyse irregular X-ray mirage interference fringes observed in Si220 X-ray reflection topography from a weakly bent, thin crystal due to gravity. The origin of the irregular fringes is attributed to the interference between mirage diffracted beams and a reflected beam from the back surface, which is a new type of interference fringe. The irregular fringes are reproduced by calculating the reflected intensities numerically. The effects of absorption and thermal vibration are quite important for the reproduction. The result shows that the interference fringes depend on the strain as well as the thickness of the crystal, which indicates that the fringes should be useful for analysing weak strain in a crystal as an application.Irregular X-ray mirage interference fringes observed in Si220 X-ray reflection topography from a weakly bent, thin crystal are analysed using the dynamical theory of diffraction. The origin is the interference between two or more mirage diffracted beams and one reflected beam from the back surface.en2022-07-28Fukamachi, T.Kawamura, T.text/html2053-2733September 202278https://creativecommons.org/licenses/by/4.0/429422research papers2022-07-282053-27335Acta Crystallographica Section A: Foundations and Advancesmed@iucr.orgA finite difference scheme for integrating the Takagi–Taupin equations on an arbitrary orthogonal grid
http://scripts.iucr.org/cgi-bin/paper?iv5022
Calculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi–Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. This dictates, especially at low scattering angles, an oblique grid of uneven step sizes. Here a finite difference scheme is presented that carries out this integration in slab-shaped samples on an arbitrary orthogonal grid by implicitly utilizing Fourier interpolation. The scheme achieves the expected second-order convergence and a similar error to the traditional approach for similarly dense grids.doi:10.1107/S2053273322004934International Union of Crystallographytexturn:issn:2053-2733DYNAMICAL DIFFRACTION; X-RAY TOPOGRAPHYhttps://creativecommons.org/licenses/by/4.0/A finite difference scheme for integrating the Takagi–Taupin equations on an arbitrary orthogonal gridCalculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi–Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. This dictates, especially at low scattering angles, an oblique grid of uneven step sizes. Here a finite difference scheme is presented that carries out this integration in slab-shaped samples on an arbitrary orthogonal grid by implicitly utilizing Fourier interpolation. The scheme achieves the expected second-order convergence and a similar error to the traditional approach for similarly dense grids.A finite difference scheme for integrating the Takagi–Taupin equations inside a slab-shaped crystal is demonstrated and tested.en2022-07-08Carlsen, M.Simons, H.text/html5med@iucr.orgActa Crystallographica Section A: Foundations and Advances2053-27332022-07-08research papers39578https://creativecommons.org/licenses/by/4.0/4012053-2733September 2022Multidimensional color codes for chair tilings
http://scripts.iucr.org/cgi-bin/paper?ae5109
Ordered aperiodic structures have been of interest to the crystallographic community for several decades, and study of them has in turn led to the study of lattice substitution systems, model sets and chair tilings. In this work a color code for chair tilings in arbitrary dimensions is presented. In two and three dimensions, it is expedient to translate the digital codes into colors. An explicit example of a three-dimensional color coding covering one octant is constructed. The tiling is then extended to the whole three-dimensional space and an indication is given of how to do this in arbitrary dimensions. Illustrations of some four-dimensional objects are also shown. The principle of color coding can be applied to other complex tilings such as brick tiling.doi:10.1107/S2053273322004065International Union of Crystallographytexturn:issn:2053-2733CHAIR TILINGS; LETTER CODES; DIGITAL CODES; COLOR CODES; APERIODIC STRUCTURES; QUASICRYSTALShttps://creativecommons.org/licenses/by/4.0/Multidimensional color codes for chair tilingsOrdered aperiodic structures have been of interest to the crystallographic community for several decades, and study of them has in turn led to the study of lattice substitution systems, model sets and chair tilings. In this work a color code for chair tilings in arbitrary dimensions is presented. In two and three dimensions, it is expedient to translate the digital codes into colors. An explicit example of a three-dimensional color coding covering one octant is constructed. The tiling is then extended to the whole three-dimensional space and an indication is given of how to do this in arbitrary dimensions. Illustrations of some four-dimensional objects are also shown. The principle of color coding can be applied to other complex tilings such as brick tiling.A color code for chair tilings in arbitrary dimensions is presented. The code can be applied also to other lattice substitution tilings.en2022-06-17Ben-Abraham, S.I.Flom, D.text/html2053-2733July 202235978https://creativecommons.org/licenses/by/4.0/3632022-06-17research papers4Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org2053-2733Identification of a coherent twin relationship from high-resolution reciprocal-space maps
http://scripts.iucr.org/cgi-bin/paper?lu5017
Twinning is a common crystallographic phenomenon which is related to the formation and coexistence of several orientation variants of the same crystal structure. It may occur during symmetry-lowering phase transitions or during the crystal growth itself. Once formed, twin domains play an important role in defining physical properties: for example, they underpin the giant piezoelectric effect in ferroelectrics, superelasticity in ferroelastics and the shape-memory effect in martensitic alloys. Regrettably, there is still a lack of experimental methods for the characterization of twin domain patterns. Here, a theoretical framework and algorithm are presented for the recognition of ferroelastic domains, as well as the identification of the coherent twin relationship using high-resolution reciprocal-space mapping of X-ray diffraction intensity around split Bragg peaks. Specifically, the geometrical theory of twinned ferroelastic crystals [Fousek & Janovec (1969). J. Appl. Phys. 40, 135–142] is adapted for the analysis of the X-ray diffraction patterns. The necessary equations are derived and an algorithm is outlined for the calculation of the separation between the Bragg peaks, diffracted from possible coherent twin domains, connected to one another via a mismatch-free interface. It is demonstrated that such separation is always perpendicular to the planar interface between mechanically matched domains. For illustration purposes, the analysis is presented of the separation between the peaks diffracted from tetragonal and rhombohedral domains in the high-resolution reciprocal-space maps of BaTiO3 and PbZr1−xTixO3 crystals. The demonstrated method can be used to analyse the response of multi-domain patterns to external perturbations such as electric field, change of temperature or pressure.doi:10.1107/S2053273322002534International Union of Crystallographytexturn:issn:2053-2733FERROELASTIC DOMAINS; DOMAIN WALLS; HIGH-RESOLUTION X-RAY DIFFRACTIONhttps://creativecommons.org/licenses/by/4.0/Identification of a coherent twin relationship from high-resolution reciprocal-space mapsTwinning is a common crystallographic phenomenon which is related to the formation and coexistence of several orientation variants of the same crystal structure. It may occur during symmetry-lowering phase transitions or during the crystal growth itself. Once formed, twin domains play an important role in defining physical properties: for example, they underpin the giant piezoelectric effect in ferroelectrics, superelasticity in ferroelastics and the shape-memory effect in martensitic alloys. Regrettably, there is still a lack of experimental methods for the characterization of twin domain patterns. Here, a theoretical framework and algorithm are presented for the recognition of ferroelastic domains, as well as the identification of the coherent twin relationship using high-resolution reciprocal-space mapping of X-ray diffraction intensity around split Bragg peaks. Specifically, the geometrical theory of twinned ferroelastic crystals [Fousek & Janovec (1969). J. Appl. Phys. 40, 135–142] is adapted for the analysis of the X-ray diffraction patterns. The necessary equations are derived and an algorithm is outlined for the calculation of the separation between the Bragg peaks, diffracted from possible coherent twin domains, connected to one another via a mismatch-free interface. It is demonstrated that such separation is always perpendicular to the planar interface between mechanically matched domains. For illustration purposes, the analysis is presented of the separation between the peaks diffracted from tetragonal and rhombohedral domains in the high-resolution reciprocal-space maps of BaTiO3 and PbZr1−xTixO3 crystals. The demonstrated method can be used to analyse the response of multi-domain patterns to external perturbations such as electric field, change of temperature or pressure.The theory and algorithm are presented for the assignment of ferroelastic domains to the individual components of split Bragg peaks in high-resolution reciprocal-space maps. The formalism of mechanical compatibility of ferroelastic domains is further developed for the analysis of the geometry of the reciprocal space. The application of the algorithm to the reciprocal-space maps of tetragonal BaTiO3 and rhombohedral PbZr1−xTixO3 crystals is demonstrated.en2022-04-28Gorfman, S.Spirito, D.Zhang, G.Detlefs, C.Zhang, N.text/htmlMay 20222053-2733https://creativecommons.org/licenses/by/4.0/17178158research papers2022-04-282053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org3Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. I. Theory
http://scripts.iucr.org/cgi-bin/paper?wo5039
The epitaxial growth of molecular crystals at single-crystalline surfaces is often strongly related to the first monolayer at the substrate surface. The present work presents a theoretical approach to compare three-dimensional lattices of epitaxially grown crystals with two-dimensional lattices of the molecules formed within the first monolayer. Real-space and reciprocal-space representations are considered. Depending on the crystallographic orientation relative to the substrate surface, proper linear combinations of the lattice vectors of the three-dimensional unit cell result in a rhomboid in the xy plane, representing a two-dimensional projection. Mathematical expressions are derived which provide a relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell. It is found that rotational symmetries of the monolayers are reflected by the epitaxial order. Positive and negative orientations of the crystallographic contact planes are correlated with the mirror symmetry of the surface unit cells, and the corresponding mathematical expressions are derived. The method is exemplarily applied to data obtained in previous grazing-incidence X-ray diffraction (GIXD) measurements with sample rotation on thin films of the conjugated molecules 3,4;9,10-perylenetetracarboxylic dianhydride (PTCDA), 6,13-pentacenequinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and dicyanovinyl-quaterthiophene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. This work introduces the possibility to study three-dimensional crystal growth nucleated by an ordered monolayer by combining two different experimental techniques, GIXD and low-energy electron diffraction, which has been implemented in the second part of this work.doi:10.1107/S2053273322002182International Union of Crystallographytexturn:issn:2053-2733CRYSTALLOGRAPHIC LATTICES; SURFACE UNIT CELL; GIXD; MATHEMATICAL CRYSTALLOGRAPHY; THIN FILMShttps://creativecommons.org/licenses/by/4.0/Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. I. TheoryThe epitaxial growth of molecular crystals at single-crystalline surfaces is often strongly related to the first monolayer at the substrate surface. The present work presents a theoretical approach to compare three-dimensional lattices of epitaxially grown crystals with two-dimensional lattices of the molecules formed within the first monolayer. Real-space and reciprocal-space representations are considered. Depending on the crystallographic orientation relative to the substrate surface, proper linear combinations of the lattice vectors of the three-dimensional unit cell result in a rhomboid in the xy plane, representing a two-dimensional projection. Mathematical expressions are derived which provide a relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell. It is found that rotational symmetries of the monolayers are reflected by the epitaxial order. Positive and negative orientations of the crystallographic contact planes are correlated with the mirror symmetry of the surface unit cells, and the corresponding mathematical expressions are derived. The method is exemplarily applied to data obtained in previous grazing-incidence X-ray diffraction (GIXD) measurements with sample rotation on thin films of the conjugated molecules 3,4;9,10-perylenetetracarboxylic dianhydride (PTCDA), 6,13-pentacenequinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and dicyanovinyl-quaterthiophene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. This work introduces the possibility to study three-dimensional crystal growth nucleated by an ordered monolayer by combining two different experimental techniques, GIXD and low-energy electron diffraction, which has been implemented in the second part of this work.A general formalism to determine the surface unit cell of a three-dimensional crystallographic lattice is presented.en2022-04-11Simbrunner, J.Domke, J.Forker, R.Resel, R.Fritz, T.text/html26278https://creativecommons.org/licenses/by/4.0/2712053-2733May 20223med@iucr.orgActa Crystallographica Section A: Foundations and Advances2053-27332022-04-11research papersCorrelation between two- and three-dimensional crystallographic lattices for epitaxial analysis. II. Experimental results
http://scripts.iucr.org/cgi-bin/paper?wo5040
While the crystal structure of the polymorph phase can be studied in three dimensions conveniently by X-ray methods like grazing-incidence X-ray diffraction (GIXD), the first monolayer is only accessible by surface-sensitive methods that allow the determination of a two-dimensional lattice. Here, GIXD measurements with sample rotation are compared with distortion-corrected low-energy electron diffraction (LEED) experiments on conjugated molecules: 3,4;9,10-perylenetetracarboxylic dianhydride (PTCDA), 6,13-pentacenequinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and dicyanovinyl-quaterthiophene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. For these molecular crystals, which exhibit different crystallographic lattices and crystal orientations as well as epitaxial properties, the geometric parameters of the three-dimensional lattice are compared with the corresponding geometry of the first monolayer. A comparison of the monolayer lattice from LEED investigations with the multilayer lattices determined by rotated GIXD experiments reveals a correlation between the first monolayer and the epitaxial growth of three-dimensional crystals together with lattice distortions and re-alignment of molecules. The selected examples show three possible scenarios of crystal growth on top of an ordered monolayer: (i) growth of a single polymorph, (ii) growth of three different polymorphs; in both cases the first monolayer serves as template. In the third case (iii) strong lattice distortion and distinct molecular re-alignments from the monolayer to epitaxially grown crystals are observed. This is the second part of our work concerning the correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. In the first part, the theoretical basis has been derived which provides a mathematical relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell, together with their orientation to the single-crystalline substrate. In this work, a combined experimental approach of GIXD and LEED is introduced which can be used to investigate the effect of the epitaxial monolayer on the structural properties of molecular crystals grown on top.doi:10.1107/S2053273322002170International Union of Crystallographytexturn:issn:2053-2733ORGANIC EPITAXY; GIXD; LEED; THIN FILMS; INDEXING; POLYMORPHISMhttps://creativecommons.org/licenses/by/4.0/Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. II. Experimental resultsWhile the crystal structure of the polymorph phase can be studied in three dimensions conveniently by X-ray methods like grazing-incidence X-ray diffraction (GIXD), the first monolayer is only accessible by surface-sensitive methods that allow the determination of a two-dimensional lattice. Here, GIXD measurements with sample rotation are compared with distortion-corrected low-energy electron diffraction (LEED) experiments on conjugated molecules: 3,4;9,10-perylenetetracarboxylic dianhydride (PTCDA), 6,13-pentacenequinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and dicyanovinyl-quaterthiophene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. For these molecular crystals, which exhibit different crystallographic lattices and crystal orientations as well as epitaxial properties, the geometric parameters of the three-dimensional lattice are compared with the corresponding geometry of the first monolayer. A comparison of the monolayer lattice from LEED investigations with the multilayer lattices determined by rotated GIXD experiments reveals a correlation between the first monolayer and the epitaxial growth of three-dimensional crystals together with lattice distortions and re-alignment of molecules. The selected examples show three possible scenarios of crystal growth on top of an ordered monolayer: (i) growth of a single polymorph, (ii) growth of three different polymorphs; in both cases the first monolayer serves as template. In the third case (iii) strong lattice distortion and distinct molecular re-alignments from the monolayer to epitaxially grown crystals are observed. This is the second part of our work concerning the correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. In the first part, the theoretical basis has been derived which provides a mathematical relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell, together with their orientation to the single-crystalline substrate. In this work, a combined experimental approach of GIXD and LEED is introduced which can be used to investigate the effect of the epitaxial monolayer on the structural properties of molecular crystals grown on top.Organic epitaxy is studied experimentally in terms of the correlation of the involved two- and three-dimensional crystallographic lattices.en2022-04-11Simbrunner, J.Domke, J.Sojka, F.Jeindl, A.Otto, F.Gruenewald, M.Hofmann, O.T.Fritz, T.Resel, R.Forker, R.text/htmlhttps://creativecommons.org/licenses/by/4.0/28278272May 20222053-27332053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org3research papers2022-04-11Ab initio reconstruction from one-dimensional crystal diffraction data
http://scripts.iucr.org/cgi-bin/paper?iv5020
Filamentary and rod-like assemblies are ubiquitous in biological systems, and single such assemblies can form one-dimensional (1D) crystals. New, intense X-ray sources, such as X-ray free-electron lasers, make it feasible to measure diffraction data from single 1D crystals. Such experiments would present some advantages, since cylindrical averaging of the diffraction data in conventional fiber diffraction analysis is avoided, there is coherent signal amplification relative to single-particle imaging, and the diffraction data are oversampled compared with those from a 3D crystal so that the phase problem is better determined than for a 3D crystal [Millane (2017). Acta Cryst. A73, 140–150]. Phasing of 1D crystal diffraction data is examined, by simulation, using an iterative projection algorithm. Ab initio phasing is feasible with realistic noise levels and little envelope information is required if a shrink-wrap algorithm is also incorporated. Some practical aspects of the proposed experiments are explored.doi:10.1107/S2053273322001942International Union of Crystallographytexturn:issn:2053-27331D CRYSTALS; PHASE PROBLEM; ITERATIVE PROJECTION ALGORITHMS; SHRINK-WRAP ALGORITHM; FILAMENTShttps://creativecommons.org/licenses/by/4.0/Ab initio reconstruction from one-dimensional crystal diffraction dataFilamentary and rod-like assemblies are ubiquitous in biological systems, and single such assemblies can form one-dimensional (1D) crystals. New, intense X-ray sources, such as X-ray free-electron lasers, make it feasible to measure diffraction data from single 1D crystals. Such experiments would present some advantages, since cylindrical averaging of the diffraction data in conventional fiber diffraction analysis is avoided, there is coherent signal amplification relative to single-particle imaging, and the diffraction data are oversampled compared with those from a 3D crystal so that the phase problem is better determined than for a 3D crystal [Millane (2017). Acta Cryst. A73, 140–150]. Phasing of 1D crystal diffraction data is examined, by simulation, using an iterative projection algorithm. Ab initio phasing is feasible with realistic noise levels and little envelope information is required if a shrink-wrap algorithm is also incorporated. Some practical aspects of the proposed experiments are explored.Methods for reconstructing electron densities from diffraction amplitudes alone, measured from single 1D crystals, are described and illustrated by simulation. Ab initio phasing is demonstrated using an iterative projection algorithm.en2022-04-05Arnal, R.D.Millane, R.P.text/html2053-2733May 202224978https://creativecommons.org/licenses/by/4.0/2612022-04-05research papers3Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org2053-2733Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO4)n− tetrahedra
http://scripts.iucr.org/cgi-bin/paper?uv5008
Chain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO4)n− tetrahedra, where T = Si4+ plus P5+, V5+, As5+, Al3+, Fe3+ and B3+. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). The unit cell (or repeat unit) of the chain graph generates the chain graph through action of translational symmetry operators. The (infinite) chain graph is converted into a finite graph by wrapping edges that exit the unit cell such that they link to vertices within the unit cell that are translationally equivalent to the vertices to which they link in the chain graph, and the wrapped graph preserves all topological information of the chain graph. A symbolic algebra is developed that represents the degree of each vertex in the wrapped graph. The wrapped graph is represented by its adjacency matrix which is modified to indicate the direction of wrapped edges, up (+c) or down (−c) along the direction of polymerization. The symbolic algebra is used to generate all possible vertex connectivities for graphs with ≤8 vertices. This method of representing chain graphs by finite matrices may now be inverted to generate all non-isomorphic chain graphs with ≤8 vertices for all possible vertex connectivities. MatLabR2019b code is provided for computationally intensive steps of this method and ∼3000 finite graphs (and associated adjacency matrices) and ∼1500 chain graphs are generated.doi:10.1107/S2053273322001747International Union of Crystallographytexturn:issn:2053-2733BOND TOPOLOGY; TETRAHEDRA; CHAIN GRAPH; ADJACENCY MATRIX; VERTEX SET; EDGE SET; SILICATES; GRAPH GENERATION; ISOMORPHISM; TRANSLATIONAL SYMMETRYhttps://creativecommons.org/licenses/by/4.0/Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO4)n− tetrahedraChain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO4)n− tetrahedra, where T = Si4+ plus P5+, V5+, As5+, Al3+, Fe3+ and B3+. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). The unit cell (or repeat unit) of the chain graph generates the chain graph through action of translational symmetry operators. The (infinite) chain graph is converted into a finite graph by wrapping edges that exit the unit cell such that they link to vertices within the unit cell that are translationally equivalent to the vertices to which they link in the chain graph, and the wrapped graph preserves all topological information of the chain graph. A symbolic algebra is developed that represents the degree of each vertex in the wrapped graph. The wrapped graph is represented by its adjacency matrix which is modified to indicate the direction of wrapped edges, up (+c) or down (−c) along the direction of polymerization. The symbolic algebra is used to generate all possible vertex connectivities for graphs with ≤8 vertices. This method of representing chain graphs by finite matrices may now be inverted to generate all non-isomorphic chain graphs with ≤8 vertices for all possible vertex connectivities. MatLabR2019b code is provided for computationally intensive steps of this method and ∼3000 finite graphs (and associated adjacency matrices) and ∼1500 chain graphs are generated.Chains of TO4n− tetrahedra are represented as chain graphs in which tetrahedra are represented as vertices and the linkage between tetrahedra is represented as edges. Topologically distinct chain graphs are generated for all possible chain stoichiometries (up to a boundary number of tetrahedra) using the formalisms of graph theory, making possible the comparison of observed chain arrangements with all topologically possible chain arrangements.en2022-04-04Day, M.C.Hawthorne, F.C.text/html212https://creativecommons.org/licenses/by/4.0/23378May 20222053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org32053-27332022-04-04research papersObjective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancement
http://scripts.iucr.org/cgi-bin/paper?ou5022
Statistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudosymmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), also known as crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists of the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal-to-noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.doi:10.1107/S2053273322000845International Union of Crystallographytexturn:issn:2053-2733PLANE SYMMETRY GROUPS; PROJECTED LAUE CLASSES; FEDOROV-TYPE PSEUDOSYMMETRIES; INFORMATION THEORY; CRYSTALLOGRAPHIC IMAGE PROCESSINGhttps://creativecommons.org/licenses/by/4.0/Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov-type pseudosymmetries and its optimal image-quality enhancementStatistically sound crystallographic symmetry classifications are obtained with information-theory-based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov-type pseudosymmetries and varying amounts of noise serve as examples. Contrary to traditional crystallographic symmetry classifications with an image processing program such as CRISP, the classification process does not need to be supervised by a human being and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), also known as crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists of the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal-to-noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.Information-theoretic crystallographic symmetry classifications distinguish between genuine symmetries and strong Fedorov-type pseudosymmetries in noisy crystal patterns in two dimensions. Because these classifications require neither visual comparisons of image pairs nor subjective interpretations of `symmetry deviation quantifiers' by human beings, they enable the optimal crystallographic processing of an experimental image that results in a significantly enhanced signal-to-noise ratio of a microscopic study of a crystal.en2022-04-28Moeck, P.text/html17278199https://creativecommons.org/licenses/by/4.0/2053-2733May 20223med@iucr.orgActa Crystallographica Section A: Foundations and Advances2053-27332022-04-28research papersA simplified relationship between the modified O-lattice and the rotation matrix for generating the coincidence site lattice of an arbitrary Bravais lattice system
http://scripts.iucr.org/cgi-bin/paper?lu5012
The coincidence site lattice (CSL) is important for characterizing the structure and energy state of grain boundaries in polycrystalline materials. A simplified relationship between the modified O-lattice and the corresponding rotation matrix is proposed to establish a general formula for the CSL and the near coincidence site lattice (NCSL) in Bravais lattice systems. The general formula paves the way to computer simulation and crystallographic analysis of grain boundaries.doi:10.1107/S2053273322000171International Union of Crystallographytexturn:issn:2053-2733GRAIN BOUNDARIES; PHASE TRANSITIONS; COINCIDENCE SITE LATTICE; CSL; NEAR COINCIDENCE SITE LATTICE; NCSL; ROTATION MATRIX; O-LATTICEhttps://creativecommons.org/licenses/by/4.0/A simplified relationship between the modified O-lattice and the rotation matrix for generating the coincidence site lattice of an arbitrary Bravais lattice systemThe coincidence site lattice (CSL) is important for characterizing the structure and energy state of grain boundaries in polycrystalline materials. A simplified relationship between the modified O-lattice and the corresponding rotation matrix is proposed to establish a general formula for the CSL and the near coincidence site lattice (NCSL) in Bravais lattice systems. The general formula paves the way to computer simulation and crystallographic analysis of grain boundaries.A simplified relationship between the modified O-lattice and the rotation matrix of any Bravais lattice was established for the generation of a coincidence site lattice wherever it exists.en2022-02-18Liu, H.text/htmlresearch papers2022-02-182053-2733Acta Crystallographica Section A: Foundations and Advancesmed@iucr.org2March 20222053-2733148https://creativecommons.org/licenses/by/4.0/78139