Open-access and free articles in Acta Crystallographica Section A: Foundations of Crystallography
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.en-gbCopyright (c) 2019 International Union of CrystallographyInternational Union of CrystallographyInternational Union of Crystallographyhttps://journals.iucr.orgurn:issn:0108-7673Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlOpen-access and free articles in Acta Crystallographica Section A Foundations and Advancestextyearly62002-01-01T00:00+00:00med@iucr.orgActa Crystallographica Section A Foundations and AdvancesCopyright (c) 2019 International Union of Crystallographyurn:issn:0108-7673Open-access and free articles in Acta Crystallographica Section A: Foundations of Crystallographyhttp://journals.iucr.org/logos/rss10a.gif
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Still imageConverting three-space matrices to equivalent six-space matrices for Delone scalars in S6
http://scripts.iucr.org/cgi-bin/paper?ae5074
The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Andrews, L.C.Bernstein, H.J.Sauter, N.K.2020-01-01doi:10.1107/S2053273319014542International Union of CrystallographyGiven a matrix for transforming vectors in the three-space of unit-cell edge vectors, the corresponding matrix to transform vectors in the six-space of Delone scalars is derived.enDELAUNAY; DELONE; CENTERING TRANSFORMATIONS; CENTERED LATTICES; REDUCED CELLS; LATTICE CENTERING; NIGGLI; SELLING; MATRIX TRANSFORMATIONSThe transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)text/htmlConverting three-space matrices to equivalent six-space matrices for Delone scalars in S6text761https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2020-01-0179research papers2053-2733January 2020med@iucr.org832053-2733X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses
http://scripts.iucr.org/cgi-bin/paper?iv5002
The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Kaganer, V.M.Petrov, I.Samoylova, L.2020-01-01doi:10.1107/S2053273319014347International Union of CrystallographyA strongly bent crystal diffracts kinematically when the bending radius is small compared with the critical radius given by the ratio of the extinction length to the Darwin width of the reflection. Under these conditions, the spectral resolution of the X-ray free-electron laser pulse is limited by the crystal thickness and can be better than under dynamical diffraction conditions.enX-RAY FREE-ELECTRON LASERS; X-RAY SPECTROSCOPY; BENT CRYSTALS; DIAMOND CRYSTAL OPTICS; FEMTOSECOND X-RAY DIFFRACTION; DYNAMICAL DIFFRACTIONThe use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.text/htmlX-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulsestext761https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2020-01-0155research papers2053-2733January 2020med@iucr.org692053-2733Cluster-mining: an approach for determining core structures of metallic nanoparticles from atomic pair distribution function data
http://scripts.iucr.org/cgi-bin/paper?lk5048
A novel approach for finding and evaluating structural models of small metallic nanoparticles is presented. Rather than fitting a single model with many degrees of freedom, libraries of clusters from multiple structural motifs are built algorithmically and individually refined against experimental pair distribution functions. Each cluster fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Banerjee, S.Liu, C.-H.Jensen, K.M.ØJuhás, P.Lee, J.D.Tofanelli, M.Ackerson, C.J.Murray, C.B.Billinge, S.J.L.2020-01-01doi:10.1107/S2053273319013214International Union of CrystallographyA novel approach for finding and evaluating structural models of small metallic nanoparticles is presented.enSTRUCTURAL MODELS; NANOPARTICLES; CLUSTERS; PAIR DISTRIBUTION FUNCTIONS; DATA MINING; SCREENINGA novel approach for finding and evaluating structural models of small metallic nanoparticles is presented. Rather than fitting a single model with many degrees of freedom, libraries of clusters from multiple structural motifs are built algorithmically and individually refined against experimental pair distribution functions. Each cluster fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.text/htmlCluster-mining: an approach for determining core structures of metallic nanoparticles from atomic pair distribution function datatext761https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2020-01-0124research papers2053-2733January 2020med@iucr.org312053-2733Elastic propagation of fast electron vortices through amorphous materials
http://scripts.iucr.org/cgi-bin/paper?lk5051
This work studies the elastic scattering behavior of electron vortices when propagating through amorphous samples. A formulation of the multislice approach in cylindrical coordinates is used to theoretically investigate the redistribution of intensity between different angular momentum components due to scattering. To corroborate and elaborate on our theoretical results, extensive numerical simulations are performed on three model systems (Si3N4, Fe0.8B0.2, Pt) for a wide variety of experimental parameters to quantify the purity of the vortices, the net angular momentum transfer, and the variability of the results with respect to the random relative position between the electron beam and the scattering atoms. These results will help scientists to further improve the creation of electron vortices and enhance applications involving them.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Löffler, S.Sack, S.Schachinger, T.2019-11-04doi:10.1107/S2053273319012889International Union of CrystallographyThis article describes the scattering behavior of electron vortices inside amorphous samples. It focuses on the vortex purity, net angular momentum transfer, and statistical variations due to random beam and atom positions.enELECTRON VORTEX BEAMS; AMORPHOUS MATERIALS; ELASTIC SCATTERINGThis work studies the elastic scattering behavior of electron vortices when propagating through amorphous samples. A formulation of the multislice approach in cylindrical coordinates is used to theoretically investigate the redistribution of intensity between different angular momentum components due to scattering. To corroborate and elaborate on our theoretical results, extensive numerical simulations are performed on three model systems (Si3N4, Fe0.8B0.2, Pt) for a wide variety of experimental parameters to quantify the purity of the vortices, the net angular momentum transfer, and the variability of the results with respect to the random relative position between the electron beam and the scattering atoms. These results will help scientists to further improve the creation of electron vortices and enhance applications involving them.text/htmlElastic propagation of fast electron vortices through amorphous materialstext756https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-11-04902research papers2053-2733November 2019med@iucr.org9102053-2733Relativistic correction of atomic scattering factors for high-energy electron diffraction
http://scripts.iucr.org/cgi-bin/paper?lk5052
Relativistic electron diffraction depends on linear and quadratic terms in the electric potential, the latter being neglected in the frequently used relativistically corrected Schrödinger equation. The quadratic electric potential term modifies atomic scattering amplitudes in particular for large-angle scattering and backscattering. The respective correction increases with increasing scattering angle, increasing atomic number and increasing kinetic energy. Conventional tabulations for electron scattering and its large-angle extrapolations can be amended in closed form by a universal correction based on the screened Coulomb potential squared.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Lentzen, M.2019-10-24doi:10.1107/S2053273319012191International Union of CrystallographyRelativistic electron diffraction depends on linear and quadratic terms in the electric potential, the latter being neglected in the frequently used relativistically corrected Schrödinger equation. Conventional tabulations for electron scattering and its large-angle extrapolations can be amended in closed form by a universal correction based on the screened Coulomb potential squared.enELECTRON DIFFRACTION; ATOMIC SCATTERING FACTORS; RELATIVITY THEORY; SCHRODINGER EQUATIONRelativistic electron diffraction depends on linear and quadratic terms in the electric potential, the latter being neglected in the frequently used relativistically corrected Schrödinger equation. The quadratic electric potential term modifies atomic scattering amplitudes in particular for large-angle scattering and backscattering. The respective correction increases with increasing scattering angle, increasing atomic number and increasing kinetic energy. Conventional tabulations for electron scattering and its large-angle extrapolations can be amended in closed form by a universal correction based on the screened Coulomb potential squared.text/htmlRelativistic correction of atomic scattering factors for high-energy electron diffractiontext756https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-10-24861research papers2053-2733November 2019med@iucr.org8652053-2733X-ray interference fringes from a weakly bent plane-parallel crystal with negative strain gradient
http://scripts.iucr.org/cgi-bin/paper?lk5040
Under the anomalous transmission condition in the Bragg mode, X-ray interference fringes were observed between two beams with different hyperbolic trajectories in a very weakly bent plane-parallel perfect crystal with negative strain gradient. The origin of the fringes was analysed based on the dynamical theory of diffraction for a distorted crystal. In the reflected beam from the entrance surface, the interference fringes were observed between once- and twice-reflected beams from the back surface. In the transmitted beam from the back surface, the interference fringes were observed between the direct beam and once-reflected beam from the entrance surface. In the emitted beam from the lateral surface, the interference fringes were observed between the beams after different numbers of reflections in the crystal. The multiply reflected beams were formed by a combined result of long propagation length along the beam direction with large divergence of the refracted beams when the strain gradient was negative. The period of these interference fringes was sensitive to very weak strain, of the order of 10−7.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Fukamachi, T.Jongsukswat, S.Ju, D.Negishi, R.Hirano, K.Kawamura, T.2019-10-07doi:10.1107/S2053273319011859International Union of CrystallographyIn the waves emitted from the entrance, back and lateral surfaces of a very weakly bent plane-parallel perfect crystal with negative strain gradient, X-ray interference fringes between two refracted beams with different hyperbolic trajectories were observed when the strain was very weak, of the order of 10−7.enINTERFERENCE FRINGES; MIRAGE FRINGES; X-RAY BEAM TRAJECTORY; BENT CRYSTAL; MULTIPLE BRAGG DIFFRACTION; DYNAMICAL THEORY OF X-RAY DIFFRACTIONUnder the anomalous transmission condition in the Bragg mode, X-ray interference fringes were observed between two beams with different hyperbolic trajectories in a very weakly bent plane-parallel perfect crystal with negative strain gradient. The origin of the fringes was analysed based on the dynamical theory of diffraction for a distorted crystal. In the reflected beam from the entrance surface, the interference fringes were observed between once- and twice-reflected beams from the back surface. In the transmitted beam from the back surface, the interference fringes were observed between the direct beam and once-reflected beam from the entrance surface. In the emitted beam from the lateral surface, the interference fringes were observed between the beams after different numbers of reflections in the crystal. The multiply reflected beams were formed by a combined result of long propagation length along the beam direction with large divergence of the refracted beams when the strain gradient was negative. The period of these interference fringes was sensitive to very weak strain, of the order of 10−7.text/htmlX-ray interference fringes from a weakly bent plane-parallel crystal with negative strain gradienttext756https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-10-07842research papers2053-2733November 2019med@iucr.org8502053-2733Bayesian machine learning improves single-wavelength anomalous diffraction phasing
http://scripts.iucr.org/cgi-bin/paper?ae5069
Single-wavelength X-ray anomalous diffraction (SAD) is a frequently employed technique to solve the phase problem in X-ray crystallography. The precision and accuracy of recovered anomalous differences are crucial for determining the correct phases. Continuous rotation (CR) and inverse-beam geometry (IBG) anomalous data collection methods have been performed on tetragonal lysozyme and monoclinic survivin crystals and analysis carried out of how correlated the pairs of Friedel's reflections are after scaling. A multivariate Bayesian model for estimating anomalous differences was tested, which takes into account the correlation between pairs of intensity observations and incorporates the a priori knowledge about the positivity of intensity. The CR and IBG data collection methods resulted in positive correlation between I(+) and I(−) observations, indicating that the anomalous difference dominates between these observations, rather than different levels of radiation damage. An alternative pairing method based on near simultaneously observed Bijvoet's pairs displayed lower correlation and it was unsuccessful for recovering useful anomalous differences when using the multivariate Bayesian model. In contrast, multivariate Bayesian treatment of Friedel's pairs improved the initial phasing of the two tested crystal systems and the two data collection methods.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Garcia-Bonete, M.-J.Katona, G.2019-10-07doi:10.1107/S2053273319011446International Union of CrystallographyThe a posteriori probability densities of anomalous structure-factor amplitude differences were estimated by the Markov chain Monte Carlo machine-learning method. The model incorporated the correlation between the different Bijvoet pairs and the improved estimates were shown to be beneficial for SAD phasing.enSINGLE-WAVELENGTH X-RAY ANOMALOUS DIFFRACTION; SAD; FRIEDEL PAIRS; BIJVOET PAIRS; CONTINUOUS ROTATION DATA COLLECTION; INVERSE-BEAM GEOMETRY; BAYESIAN INFERENCE; SURVIVINSingle-wavelength X-ray anomalous diffraction (SAD) is a frequently employed technique to solve the phase problem in X-ray crystallography. The precision and accuracy of recovered anomalous differences are crucial for determining the correct phases. Continuous rotation (CR) and inverse-beam geometry (IBG) anomalous data collection methods have been performed on tetragonal lysozyme and monoclinic survivin crystals and analysis carried out of how correlated the pairs of Friedel's reflections are after scaling. A multivariate Bayesian model for estimating anomalous differences was tested, which takes into account the correlation between pairs of intensity observations and incorporates the a priori knowledge about the positivity of intensity. The CR and IBG data collection methods resulted in positive correlation between I(+) and I(−) observations, indicating that the anomalous difference dominates between these observations, rather than different levels of radiation damage. An alternative pairing method based on near simultaneously observed Bijvoet's pairs displayed lower correlation and it was unsuccessful for recovering useful anomalous differences when using the multivariate Bayesian model. In contrast, multivariate Bayesian treatment of Friedel's pairs improved the initial phasing of the two tested crystal systems and the two data collection methods.text/htmlBayesian machine learning improves single-wavelength anomalous diffraction phasingtext756https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-10-07851research papers2053-2733November 2019med@iucr.org8602053-2733XGANDALF – extended gradient descent algorithm for lattice finding
http://scripts.iucr.org/cgi-bin/paper?ae5071
Serial crystallography records still diffraction patterns from single, randomly oriented crystals, then merges data from hundreds or thousands of them to form a complete data set. To process the data, the diffraction patterns must first be indexed, equivalent to determining the orientation of each crystal. A novel automatic indexing algorithm is presented, which in tests usually gives significantly higher indexing rates than alternative programs currently available for this task. The algorithm does not require prior knowledge of the lattice parameters but can make use of that information if provided, and also allows indexing of diffraction patterns generated by several crystals in the beam. Cases with a small number of Bragg spots per pattern appear to particularly benefit from the new approach. The algorithm has been implemented and optimized for fast execution, making it suitable for real-time feedback during serial crystallography experiments. It is implemented in an open-source C++ library and distributed under the LGPLv3 licence. An interface to it has been added to the CrystFEL software suite.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Gevorkov, Y.Yefanov, O.Barty, A.White, T.A.Mariani, V.Brehm, W.Tolstikova, A.Grigat, R.-R.Chapman, H.N.2019-08-30doi:10.1107/S2053273319010593International Union of CrystallographyA description and evaluation are given of XGANDALF, extended gradient descent algorithm for lattice finding, an algorithm developed for fast and accurate indexing of snapshot diffraction patterns.enINDEXING; XGANDALF; CRYSTFEL; MULTIPLE LATTICES; SERIAL CRYSTALLOGRAPHYSerial crystallography records still diffraction patterns from single, randomly oriented crystals, then merges data from hundreds or thousands of them to form a complete data set. To process the data, the diffraction patterns must first be indexed, equivalent to determining the orientation of each crystal. A novel automatic indexing algorithm is presented, which in tests usually gives significantly higher indexing rates than alternative programs currently available for this task. The algorithm does not require prior knowledge of the lattice parameters but can make use of that information if provided, and also allows indexing of diffraction patterns generated by several crystals in the beam. Cases with a small number of Bragg spots per pattern appear to particularly benefit from the new approach. The algorithm has been implemented and optimized for fast execution, making it suitable for real-time feedback during serial crystallography experiments. It is implemented in an open-source C++ library and distributed under the LGPLv3 licence. An interface to it has been added to the CrystFEL software suite.text/htmlXGANDALF – extended gradient descent algorithm for lattice findingtext5752019-08-30Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers694med@iucr.orgSeptember 20197042053-2733The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigenda
http://scripts.iucr.org/cgi-bin/paper?ae5073
Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Cayron, C.2019-08-30doi:10.1107/S2053273319009276International Union of CrystallographyThree equations in Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] are corrected.enSYMMETRIES; METRIC TENSOR; LATTICE; POINT GROUPAppendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.text/htmlThe transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigendatext5752019-08-30Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2019 International Union of Crystallography2053-2733addenda and errata777med@iucr.orgSeptember 20197772053-2733A new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactors
http://scripts.iucr.org/cgi-bin/paper?sc5131
Structural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Hoeher, A.Mergelsberg, S.Borkiewicz, O.J.Dove, P.M.Michel, F.M.2019-08-23doi:10.1107/S2053273319008623International Union of CrystallographyA novel method is introduced for in situ X-ray total scattering experiments. Two examples of the method as applied to non-classical nucleation and crystal growth studies are discussed.enIN SITU X-RAY TOTAL SCATTERING; CRYSTALLIZATION; AMORPHOUS CALCIUM PHOSPHATE; AMORPHOUS CALCIUM CARBONATE; PAIR DISTRIBUTION FUNCTION ANALYSISStructural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis.text/htmlA new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactorstext5752019-08-23Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers758med@iucr.orgSeptember 20197652053-2733Theoretical study of the properties of X-ray diffraction moiré fringes. I. Corrigenda and addenda
http://scripts.iucr.org/cgi-bin/paper?td5062
Seven corrections are made and several supplementary equations are added to the article by Yoshimura [Acta Cryst. (2015), A71, 368–381].https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Yoshimura, J.2019-06-26doi:10.1107/S2053273319006557International Union of CrystallographySeven corrections are made and several supplementary equations are added to the article by Yoshimura [Acta Cryst. (2015), A71, 368–381].enDIFFRACTION MOIRE FRINGES; PENDELLOSUNG OSCILLATION; PHASE JUMP; GAP PHASESeven corrections are made and several supplementary equations are added to the article by Yoshimura [Acta Cryst. (2015), A71, 368–381].text/htmlTheoretical study of the properties of X-ray diffraction moiré fringes. I. Corrigenda and addendatext4752019-06-26Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733addenda and errata652med@iucr.orgJuly 20196542053-2733Theoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré images
http://scripts.iucr.org/cgi-bin/paper?td5060
Using a theory of X-ray diffraction moiré fringes developed in a previous paper, labelled Part I [Yoshimura (2015). Acta Cryst. A71, 368–381], the X-ray moiré images of a silicon bicrystal having a weak curvature strain and an interspacing gap, assumed to be integrated for an incident-wave angular width, are simulation-computed over a wide range of crystal thicknesses and incident-wave angular width, likely under practical experimental conditions. Along with the simulated moiré images, the graphs of characteristic quantities on the moiré images are presented for a full understanding of them. The treated moiré images are all of rotation moiré. Mo Kα1 radiation and the 220 reflection were assumed in the simulation. The results of this simulation show that fringe patterns, which are significantly modified from simple straight fringes of rotation moiré, appear in some ranges of crystal thicknesses and incident-wave angular width, due to a combined effect of Pendellösung oscillation and an added phase difference from the interspacing gap, under the presence of a curvature strain. The moiré fringes which slope to the perpendicular direction to the diffraction vector in spite of the assumed condition of rotation moiré, and fringe patterns where low-contrast bands are produced with a sharp bend of fringes arising along the bands are examples of the modified fringe pattern. This simulation study provides a wide theoretical survey of the type of bicrystal moiré image produced under a particular condition.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Yoshimura, J.2019-06-26doi:10.1107/S2053273319004601International Union of CrystallographyUsing a recently developed moiré-fringe theory of X-ray diffraction, the angularly integrated moiré images of a lightly strained silicon bicrystal having an interspacing gap were simulation-computed over a wide range of crystal thicknesses and incident-beam angular width.enDIFFRACTION MOIRE FRINGES; ROTATION MOIRE; PENDELLOSUNG OSCILLATION; GAP PHASE DIFFERENCE; INTEGRATED MOIRE IMAGESUsing a theory of X-ray diffraction moiré fringes developed in a previous paper, labelled Part I [Yoshimura (2015). Acta Cryst. A71, 368–381], the X-ray moiré images of a silicon bicrystal having a weak curvature strain and an interspacing gap, assumed to be integrated for an incident-wave angular width, are simulation-computed over a wide range of crystal thicknesses and incident-wave angular width, likely under practical experimental conditions. Along with the simulated moiré images, the graphs of characteristic quantities on the moiré images are presented for a full understanding of them. The treated moiré images are all of rotation moiré. Mo Kα1 radiation and the 220 reflection were assumed in the simulation. The results of this simulation show that fringe patterns, which are significantly modified from simple straight fringes of rotation moiré, appear in some ranges of crystal thicknesses and incident-wave angular width, due to a combined effect of Pendellösung oscillation and an added phase difference from the interspacing gap, under the presence of a curvature strain. The moiré fringes which slope to the perpendicular direction to the diffraction vector in spite of the assumed condition of rotation moiré, and fringe patterns where low-contrast bands are produced with a sharp bend of fringes arising along the bands are examples of the modified fringe pattern. This simulation study provides a wide theoretical survey of the type of bicrystal moiré image produced under a particular condition.text/htmlTheoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré imagestext4752019-06-26Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers610med@iucr.orgJuly 20196232053-2733Experimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystal
http://scripts.iucr.org/cgi-bin/paper?wo5032
Non-coplanar 18-beam X-ray pinhole topographs for a silicon crystal were computer simulated by fast Fourier transforming the X-ray rocking amplitudes that were obtained by solving the n-beam (n = 18) Ewald–Laue dynamical theory (E-L&FFT method). They were in good agreement with the experimentally obtained images captured using synchrotron X-rays. From this result and further consideration based on it, it has been clarified that the X-ray diffraction intensities when n X-ray waves are simultaneously strong in the crystal can be computed for any n by using the E-L&FFT method.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Okitsu, K.Imai, Y.Yoda, Y.2019-04-30doi:10.1107/S2053273319002936International Union of CrystallographyExperimentally obtained non-coplanar 18-beam pinhole topographs were compared with computer simulations based on the Ewald–Laue theory.enX-RAY DIFFRACTION; DYNAMICAL THEORY; MULTIPLE REFLECTION; N-BEAM REFLECTION; PHASE PROBLEM; PROTEIN CRYSTALLOGRAPHYNon-coplanar 18-beam X-ray pinhole topographs for a silicon crystal were computer simulated by fast Fourier transforming the X-ray rocking amplitudes that were obtained by solving the n-beam (n = 18) Ewald–Laue dynamical theory (E-L&FFT method). They were in good agreement with the experimentally obtained images captured using synchrotron X-rays. From this result and further consideration based on it, it has been clarified that the X-ray diffraction intensities when n X-ray waves are simultaneously strong in the crystal can be computed for any n by using the E-L&FFT method.text/htmlExperimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystaltext3752019-04-30Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers483med@iucr.orgMay 20194882053-2733A space for lattice representation and clustering
http://scripts.iucr.org/cgi-bin/paper?ae5061
Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Andrews, L.C.Bernstein, H.J.Sauter, N.K.2019-04-30doi:10.1107/S2053273319002729International Union of CrystallographyAlgorithms for defining the difference between two lattices are described. They are based on the work of Selling and Delone (Delaunay).enUNIT-CELL REDUCTION; DELAUNAY; DELONE; NIGGLI; SELLING; CLUSTERINGAlgorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)text/htmlA space for lattice representation and clusteringtext3752019-04-30Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers593med@iucr.orgMay 20195992053-2733Experimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs for a silicon crystal
http://scripts.iucr.org/cgi-bin/paper?wo5031
In this study, experimentally obtained eight-beam pinhole topographs for a silicon crystal using synchrotron X-rays were compared with computer-simulated images, and were found to be in good agreement. The experiment was performed with an asymmetric all-Laue geometry. However, the X-rays exited from both the bottom and side surfaces of the crystal. The simulations were performed using two different approaches: one was the integration of the n-beam Takagi–Taupin equation, and the second was the fast Fourier transformation of the X-ray amplitudes obtained by solving the eigenvalue problem of the n-beam Ewald–Laue theory as reported by Kohn & Khikhlukha [Acta Cryst. (2016), A72, 349–356] and Kohn [Acta Cryst. (2017), A73, 30–38].https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Okitsu, K.Imai, Y.Yoda, Y.Ueji, Y.2019-04-30doi:10.1107/S2053273319001499International Union of CrystallographyExperimentally obtained eight-beam pinhole topographs for a silicon crystal were compared with computer simulations based on the n-beam Takagi–Taupin equation and Ewald–Laue theory.enX-RAY DIFFRACTION; DYNAMICAL THEORY; MULTIPLE REFLECTION; COMPUTER SIMULATION; N-BEAM REFLECTION; PHASE PROBLEM; SILICON; PROTEIN CRYSTALLOGRAPHYIn this study, experimentally obtained eight-beam pinhole topographs for a silicon crystal using synchrotron X-rays were compared with computer-simulated images, and were found to be in good agreement. The experiment was performed with an asymmetric all-Laue geometry. However, the X-rays exited from both the bottom and side surfaces of the crystal. The simulations were performed using two different approaches: one was the integration of the n-beam Takagi–Taupin equation, and the second was the fast Fourier transformation of the X-ray amplitudes obtained by solving the eigenvalue problem of the n-beam Ewald–Laue theory as reported by Kohn & Khikhlukha [Acta Cryst. (2016), A72, 349–356] and Kohn [Acta Cryst. (2017), A73, 30–38].text/htmlExperimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs for a silicon crystaltext3752019-04-30Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers474med@iucr.orgMay 20194822053-2733Characterizing modulated structures with first-principles calculations: a unified superspace scheme of ordering in mullite
http://scripts.iucr.org/cgi-bin/paper?gv5003
The benefit of computational methods applying density functional theory for the description and understanding of modulated crystal structures is investigated. A method is presented which allows one to establish, improve and test superspace models including displacive and occupational modulation functions from first-principles calculations on commensurate structures. The total energies of different configurations allow one to distinguish stable and less stable structure models. The study is based on a series of geometrically optimized superstructures of mullite (Al4+2xSi2−2xO10−x) derived from the superspace group Pbam(α0½)0ss. Despite the disordered and structurally complex nature of mullite, the calculations on ordered superstructures are very useful for determining the ideal Al/Si ordering in mullite, extracting atomic modulation functions as well as understanding the SiO2–Al2O3 phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Klar, P.B.Etxebarria, I.Madariaga, G.2019-02-12doi:10.1107/S2053273319000846International Union of CrystallographyQuantitative parameters of modulated crystal structures are determined from density functional theory calculations applied to superstructures obtained using the superspace formalism. The example of mullite is used to demonstrate that with this approach versatile aspects ranging from ordering phenomena to phase diagrams can be understood on a new level.enDENSITY FUNCTIONAL THEORY (DFT); SUPERSPACE; MODULATION FUNCTIONS; AL/SI ORDERING; SILICATES; MULLITEThe benefit of computational methods applying density functional theory for the description and understanding of modulated crystal structures is investigated. A method is presented which allows one to establish, improve and test superspace models including displacive and occupational modulation functions from first-principles calculations on commensurate structures. The total energies of different configurations allow one to distinguish stable and less stable structure models. The study is based on a series of geometrically optimized superstructures of mullite (Al4+2xSi2−2xO10−x) derived from the superspace group Pbam(α0½)0ss. Despite the disordered and structurally complex nature of mullite, the calculations on ordered superstructures are very useful for determining the ideal Al/Si ordering in mullite, extracting atomic modulation functions as well as understanding the SiO2–Al2O3 phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.text/htmlCharacterizing modulated structures with first-principles calculations: a unified superspace scheme of ordering in mullitetext2752019-02-12Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers260med@iucr.orgMarch 20192722053-2733Bonding network and stability of clusters: the case study of Al13TM4 pseudo-tenfold surfaces
http://scripts.iucr.org/cgi-bin/paper?vf5005
Clusters, i.e. polyhedral geometric entities, are widely used to describe the structure of complex intermetallic compounds. However, little is generally known about their physical significance. The atomic and electronic structures of the Al13TM4 complex intermetallic compounds (TM = Fe, Co, Ru, Rh) have been investigated using a wide range of ab initio tools in order to examine the influence of the chemical composition on the pertinence of the bulk structure description based on 3D clusters. In addition, since surface studies were found to be a relevant approach to address the question of cluster stability in complex phases, the interplay of the cluster substructure with the 2D surface is addressed in the case of the Al13Co4(100) and Al13Fe4(010) surfaces.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Scheid, P.Chatelier, C.Ledieu, J.Fournée, V.Gaudry, É.2019-02-28doi:10.1107/S2053273319000202International Union of CrystallographyThe physical significance of clusters in Al13TM4 compounds is invesitgated through ab initio methods based on density functional theory.enCOMPLEX INTERMETALLIC COMPOUNDS; SURFACES; BONDING; DENSITY FUNCTIONAL THEORYClusters, i.e. polyhedral geometric entities, are widely used to describe the structure of complex intermetallic compounds. However, little is generally known about their physical significance. The atomic and electronic structures of the Al13TM4 complex intermetallic compounds (TM = Fe, Co, Ru, Rh) have been investigated using a wide range of ab initio tools in order to examine the influence of the chemical composition on the pertinence of the bulk structure description based on 3D clusters. In addition, since surface studies were found to be a relevant approach to address the question of cluster stability in complex phases, the interplay of the cluster substructure with the 2D surface is addressed in the case of the Al13Co4(100) and Al13Fe4(010) surfaces.text/htmlBonding network and stability of clusters: the case study of Al13TM4 pseudo-tenfold surfacestext2752019-02-28Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers314med@iucr.orgMarch 20193242053-2733Full real-space analysis of a dodecagonal quasicrystal
http://scripts.iucr.org/cgi-bin/paper?vf5004
The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki–Gähler tiling. Although the Niizeki–Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Schenk, S.Zollner, E.M.Krahn, O.Schreck, B.Hammer, R.Förster, S.Widdra, W.2019-02-28doi:10.1107/S2053273319000056International Union of CrystallographyAnalysis of a dodecagonal quasicrystal based on 8100 vertices from atomically resolved scanning tunnelling microscopy has been carried out. A detailed frequency and orientational analysis is presented for the triangle–square–rhomb tiling of a BaTiO3-derived quasicrystal.en2D OXIDE QUASICRYSTAL; BATIO3 ON PT(111); DODECAGONAL TILING; STATISTICAL ANALYSIS; SCANNING TUNNELLING MICROSCOPYThe atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki–Gähler tiling. Although the Niizeki–Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.text/htmlFull real-space analysis of a dodecagonal quasicrystaltext2752019-02-28Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers307med@iucr.orgMarch 20193132053-2733Group-theoretical analysis of 1:3 A-site-ordered perovskite formation
http://scripts.iucr.org/cgi-bin/paper?kx5068
The quadruple perovskites AA′3B4X12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Talanov, M.V.2019-02-28doi:10.1107/S2053273318018338International Union of CrystallographyA group-theoretical analysis of 1:3 A-site-ordered perovskite structures is reported.enQUADRUPLE 1:3 A-SITE-ORDERED PEROVSKITES; GROUP-THEORETICAL ANALYSIS; LOW-SYMMETRY PHASES; FULL SET OF ORDER PARAMETERS; TILTS OF OCTAHEDRA; ARCHETYPE STRUCTUREThe quadruple perovskites AA′3B4X12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.text/htmlGroup-theoretical analysis of 1:3 A-site-ordered perovskite formationtext2752019-02-28Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers379med@iucr.orgMarch 20193972053-2733