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 imageElastic 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 materialstext6752019-11-04Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers902med@iucr.orgNovember 20199102053-2733Relativistic 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 diffractiontext6752019-10-24Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers861med@iucr.orgNovember 20198652053-2733X-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 gradienttext6752019-10-07Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers842med@iucr.orgNovember 20198502053-2733Bayesian 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 phasingtext6752019-10-07Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers851med@iucr.orgNovember 20198602053-2733XGANDALF – 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 findingtext755https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-08-30694research papers2053-2733September 2019med@iucr.org7042053-2733The 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. Corrigendatext755Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances2019-08-30777addenda and errata2053-2733September 2019med@iucr.org7772053-2733A 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 reactorstext755https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-08-23758research papers2053-2733September 2019med@iucr.org7652053-2733Theoretical 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 addendatext754https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-06-26652addenda and errata2053-2733July 2019med@iucr.org6542053-2733Theoretical 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 imagestext754https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-06-26610research papers2053-2733July 2019med@iucr.org6232053-2733Experimentally 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 crystaltext753https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-04-30483research papers2053-2733May 2019med@iucr.org4882053-2733A 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 clusteringtext753https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-04-30593research papers2053-2733May 2019med@iucr.org5992053-2733Experimentally 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 crystaltext753https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-04-30474research papers2053-2733May 2019med@iucr.org4822053-2733Characterizing 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 mullitetext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-12260research papers2053-2733March 2019med@iucr.org2722053-2733Bonding 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 surfacestext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-28314research papers2053-2733March 2019med@iucr.org3242053-2733Full 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 quasicrystaltext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-28307research papers2053-2733March 2019med@iucr.org3132053-2733Group-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 formationtext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-28379research papers2053-2733March 2019med@iucr.org3972053-2733CO2 adsorption in Y zeolite: a structural and dynamic view by a novel principal-component-analysis-assisted in situ single-crystal X-ray diffraction experiment
http://scripts.iucr.org/cgi-bin/paper?sc5122
The increasing efficiency of detectors and brightness of X-rays in both laboratory and large-scale facilities allow the collection of full single-crystal X-ray data sets within minutes. The analysis of these `crystallographic big data' requires new tools and approaches. To answer these needs, the use of principal component analysis (PCA) is proposed to improve the efficiency and speed of the analysis. Potentialities and limitations of PCA were investigated using single-crystal X-ray diffraction (XRD) data collected in situ on Y zeolite, in which CO2, acting as an active species, is thermally adsorbed while cooling from 300 to 200 K. For the first time, thanks to the high sensitivity of single-crystal XRD, it was possible to determine the sites where CO2 is adsorbed, the increase in their occupancy while the temperature is decreased, and the correlated motion of active species, i.e. CO2, H2O and Na+. PCA allowed identification and elimination of problematic data sets, and better understanding of the trends of the occupancies of CO2, Na+ and water. The quality of the data allowed for the first time calculation of the enthalpy (ΔH) and entropy (ΔS) of the CO2 adsorption by applying the van 't Hoff equation to in situ single-crystal data. The calculation of thermodynamic values was carried out by both traditional and PCA-based approaches, producing comparable results. The obtained ΔH value is significant and involves systems (CO2 and Y zeolite) with no toxicity, superb stability and chemical inertness. Such features, coupled with the absence of carbonate formation and framework inertness upon adsorption, were demonstrated for the bulk crystal by the single-crystal experiment, and suggest that the phenomenon can be easily reversed for a large number of cycles, with CO2 released on demand. The main advantages of PCA-assisted analysis reside in its speed and in the possibility of it being applied directly to raw data, possibly as an `online' data-quality test during data collection, without any a priori knowledge of the crystal structure.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Conterosito, E.Palin, L.Caliandro, R.van Beek, W.Chernyshov, D.Milanesio, M.2019-02-06doi:10.1107/S2053273318017618International Union of CrystallographyIn situ single-crystal X-ray diffraction data were used to unravel the structural dynamics and enthalpy and entropy of adsorption of CO2 into Y zeolite. A principal-component-analysis- (PCA) based approach is applied in an innovative way to single-crystal X-ray diffraction data analysis, allowing one to selectively detect the information from the subset of active atoms. The potential of and limitations of PCA in single-crystal diffraction are discussed.enIN SITU STUDIES; Y ZEOLITE; PRINCIPAL COMPONENT ANALYSIS; ENTHALPY OF ADSORPTION; ENTROPY OF ADSORPTIONThe increasing efficiency of detectors and brightness of X-rays in both laboratory and large-scale facilities allow the collection of full single-crystal X-ray data sets within minutes. The analysis of these `crystallographic big data' requires new tools and approaches. To answer these needs, the use of principal component analysis (PCA) is proposed to improve the efficiency and speed of the analysis. Potentialities and limitations of PCA were investigated using single-crystal X-ray diffraction (XRD) data collected in situ on Y zeolite, in which CO2, acting as an active species, is thermally adsorbed while cooling from 300 to 200 K. For the first time, thanks to the high sensitivity of single-crystal XRD, it was possible to determine the sites where CO2 is adsorbed, the increase in their occupancy while the temperature is decreased, and the correlated motion of active species, i.e. CO2, H2O and Na+. PCA allowed identification and elimination of problematic data sets, and better understanding of the trends of the occupancies of CO2, Na+ and water. The quality of the data allowed for the first time calculation of the enthalpy (ΔH) and entropy (ΔS) of the CO2 adsorption by applying the van 't Hoff equation to in situ single-crystal data. The calculation of thermodynamic values was carried out by both traditional and PCA-based approaches, producing comparable results. The obtained ΔH value is significant and involves systems (CO2 and Y zeolite) with no toxicity, superb stability and chemical inertness. Such features, coupled with the absence of carbonate formation and framework inertness upon adsorption, were demonstrated for the bulk crystal by the single-crystal experiment, and suggest that the phenomenon can be easily reversed for a large number of cycles, with CO2 released on demand. The main advantages of PCA-assisted analysis reside in its speed and in the possibility of it being applied directly to raw data, possibly as an `online' data-quality test during data collection, without any a priori knowledge of the crystal structure.text/htmlCO2 adsorption in Y zeolite: a structural and dynamic view by a novel principal-component-analysis-assisted in situ single-crystal X-ray diffraction experimenttext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-06214research papers2053-2733March 2019med@iucr.org2222053-2733Principles of weakly ordered domains in intermetallics: the cooperative effects of atomic packing and electronics in Fe2Al5
http://scripts.iucr.org/cgi-bin/paper?gv5002
Many complex intermetallic structures feature a curious juxtaposition of domains with strict 3D periodicity and regions of much weaker order or incommensurability. This article explores the basic principles leading to such arrangements through an investigation of the weakly ordered channels of Fe2Al5. It starts by experimentally confirming the earlier crystallographic model of the high-temperature form, in which nearly continuous columns of electron density corresponding to disordered Al atoms emerge. Then electronic structure calculations on ordered models are used to determine the factors leading to the formation of these columns. These calculations reveal electronic pseudogaps near 16 electrons/Fe atom, an electron concentration close to the Al-rich side of the phase's homogeneity range. Through a reversed approximation Molecular Orbital (raMO) analysis, these pseudogaps are correlated with the filling of 18-electron configurations on the Fe atoms with the support of isolobal σ Fe–Fe bonds. The resulting preference for 16 electrons/Fe requires a fractional number of Al atoms in the Fe2Al5 unit cell. Density functional theory–chemical pressure (DFT-CP) analysis is then applied to investigate how this nonstoichiometry is accommodated. The CP schemes reveal strong quadrupolar distributions on the Al atoms of the channels, suggestive of soft atomic motions along the undulating electron density observed in the Fourier map that allow the Al positions to shift easily in response to compositional changes. Such a combination of preferred electron counts tied to stoichiometry and continuous paths of CP quadrupoles could provide predictive indicators for the emergence of channels of disordered or incommensurately spaced atoms in intermetallic structures.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Vinokur, A.I.Hilleke, K.P.Fredrickson, D.C.2019-02-21doi:10.1107/S2053273318017461International Union of CrystallographyThe Fe2Al5 structure is remarkable among intermetallic phases for its channels of weakly ordered Al atoms. This article traces the origins of these channels to the cooperative effects of soft atomic motions dictated by chemical pressure quadrupoles and preferred electron concentrations.enINTERMETALLIC PHASES; CHANNEL STRUCTURES; CHEMICAL BONDING THEORY; DISORDER; INCOMMENSURABILITYMany complex intermetallic structures feature a curious juxtaposition of domains with strict 3D periodicity and regions of much weaker order or incommensurability. This article explores the basic principles leading to such arrangements through an investigation of the weakly ordered channels of Fe2Al5. It starts by experimentally confirming the earlier crystallographic model of the high-temperature form, in which nearly continuous columns of electron density corresponding to disordered Al atoms emerge. Then electronic structure calculations on ordered models are used to determine the factors leading to the formation of these columns. These calculations reveal electronic pseudogaps near 16 electrons/Fe atom, an electron concentration close to the Al-rich side of the phase's homogeneity range. Through a reversed approximation Molecular Orbital (raMO) analysis, these pseudogaps are correlated with the filling of 18-electron configurations on the Fe atoms with the support of isolobal σ Fe–Fe bonds. The resulting preference for 16 electrons/Fe requires a fractional number of Al atoms in the Fe2Al5 unit cell. Density functional theory–chemical pressure (DFT-CP) analysis is then applied to investigate how this nonstoichiometry is accommodated. The CP schemes reveal strong quadrupolar distributions on the Al atoms of the channels, suggestive of soft atomic motions along the undulating electron density observed in the Fourier map that allow the Al positions to shift easily in response to compositional changes. Such a combination of preferred electron counts tied to stoichiometry and continuous paths of CP quadrupoles could provide predictive indicators for the emergence of channels of disordered or incommensurately spaced atoms in intermetallic structures.text/htmlPrinciples of weakly ordered domains in intermetallics: the cooperative effects of atomic packing and electronics in Fe2Al5text752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-21297research papers2053-2733March 2019med@iucr.org3062053-2733Grazing-incidence small-angle X-ray scattering study of correlated lateral density fluctuations in W/Si multilayers
http://scripts.iucr.org/cgi-bin/paper?vk5033
A structural characterization of W/Si multilayers using X-ray reflectivity (XRR), scanning transmission electron microscopy (STEM) and grazing-incidence small-angle X-ray scattering (GISAXS) is presented. STEM images revealed lateral, periodic density fluctuations in the Si layers, which were further analysed using GISAXS. Characteristic parameters of the fluctuations such as average distance between neighbouring fluctuations, average size and lateral distribution of their position were obtained by fitting numerical simulations to the measured scattering images, and these parameters are in good agreement with the STEM observations. For the numerical simulations the density fluctuations were approximated as a set of spheroids distributed inside the Si layers as a 3D paracrystal (a lattice of spheroids with short-range ordering but lacking any long-range order). From GISAXS, the density of the material inside the density fluctuations is calculated to be 2.07 g cm−3 which is 89% of the bulk value of the deposited layer (2.33 g cm−3).https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Nikolaev, K.V.Yakunin, S.N.Makhotkin, I.A.Rie, J.Medvedev, R.V.Rogachev, A.V.Trunckin, I.N.Vasiliev, A.L.Hendrikx, C.P.Gateshki, M.Kruijs, R.W.E.Bijkerk, F.2019-02-12doi:10.1107/S2053273318017382International Union of CrystallographyAn inhomogeneity of material in W/Si multilayer structures was studied with grazing-incidence small-angle X-ray scattering. The experimental study revealed lateral density fluctuations in the Si spacer layers.enDIFFUSE SCATTERING; DENSITY FLUCTUATIONS; MULTILAYER COATINGS; THIN FILMSA structural characterization of W/Si multilayers using X-ray reflectivity (XRR), scanning transmission electron microscopy (STEM) and grazing-incidence small-angle X-ray scattering (GISAXS) is presented. STEM images revealed lateral, periodic density fluctuations in the Si layers, which were further analysed using GISAXS. Characteristic parameters of the fluctuations such as average distance between neighbouring fluctuations, average size and lateral distribution of their position were obtained by fitting numerical simulations to the measured scattering images, and these parameters are in good agreement with the STEM observations. For the numerical simulations the density fluctuations were approximated as a set of spheroids distributed inside the Si layers as a 3D paracrystal (a lattice of spheroids with short-range ordering but lacking any long-range order). From GISAXS, the density of the material inside the density fluctuations is calculated to be 2.07 g cm−3 which is 89% of the bulk value of the deposited layer (2.33 g cm−3).text/htmlGrazing-incidence small-angle X-ray scattering study of correlated lateral density fluctuations in W/Si multilayerstext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-12342research papers2053-2733March 2019med@iucr.org3512053-2733High-speed tensor tomography: iterative reconstruction tensor tomography (IRTT) algorithm
http://scripts.iucr.org/cgi-bin/paper?vk5029
The recent advent of tensor tomography techniques has enabled tomographic investigations of the 3D nanostructure organization of biological and material science samples. These techniques extended the concept of conventional X-ray tomography by reconstructing not only a scalar value such as the attenuation coefficient per voxel, but also a set of parameters that capture the local anisotropy of nanostructures within every voxel of the sample. Tensor tomography data sets are intrinsically large as each pixel of a conventional X-ray projection is substituted by a scattering pattern, and projections have to be recorded at different sample angular orientations with several tilts of the rotation axis with respect to the X-ray propagation direction. Currently available reconstruction approaches for such large data sets are computationally expensive. Here, a novel, fast reconstruction algorithm, named iterative reconstruction tensor tomography (IRTT), is presented to simplify and accelerate tensor tomography reconstructions. IRTT is based on a second-rank tensor model to describe the anisotropy of the nanostructure in every voxel and on an iterative error backpropagation reconstruction algorithm to achieve high convergence speed. The feasibility and accuracy of IRTT are demonstrated by reconstructing the nanostructure anisotropy of three samples: a carbon fiber knot, a human bone trabecula specimen and a fixed mouse brain. Results and reconstruction speed were compared with those obtained by the small-angle scattering tensor tomography (SASTT) reconstruction method introduced by Liebi et al. [Nature (2015), 527, 349–352]. The principal orientation of the nanostructure within each voxel revealed a high level of agreement between the two methods. Yet, for identical data sets and computer hardware used, IRTT was shown to be more than an order of magnitude faster. IRTT was found to yield robust results, it does not require prior knowledge of the sample for initializing parameters, and can be used in cases where simple anisotropy metrics are sufficient, i.e. the tensor approximation adequately captures the level of anisotropy and the dominant orientation within a voxel. In addition, by greatly accelerating the reconstruction, IRTT is particularly suitable for handling large tomographic data sets of samples with internal structure or as a real-time analysis tool during the experiment for online feedback during data acquisition. Alternatively, the IRTT results might be used as an initial guess for models capturing a higher complexity of structural anisotropy such as spherical harmonics based SASTT in Liebi et al. (2015), improving both overall convergence speed and robustness of the reconstruction.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Gao, Z.Guizar-Sicairos, M.Lutz-Bueno, V.Schröter, A.Liebi, M.Rudin, M.Georgiadis, M.2019-02-06doi:10.1107/S2053273318017394International Union of CrystallographyA fast and robust reconstruction algorithm for small-angle scattering tensor tomography, named iterative reconstruction tensor tomography, is presented. It employs a second-rank tensor model and an iterative error backpropagation to simplify and accelerate tensor tomography reconstruction.enSMALL-ANGLE X-RAY SCATTERING; TENSOR TOMOGRAPHY; ITERATIVE RECONSTRUCTION ALGORITHMThe recent advent of tensor tomography techniques has enabled tomographic investigations of the 3D nanostructure organization of biological and material science samples. These techniques extended the concept of conventional X-ray tomography by reconstructing not only a scalar value such as the attenuation coefficient per voxel, but also a set of parameters that capture the local anisotropy of nanostructures within every voxel of the sample. Tensor tomography data sets are intrinsically large as each pixel of a conventional X-ray projection is substituted by a scattering pattern, and projections have to be recorded at different sample angular orientations with several tilts of the rotation axis with respect to the X-ray propagation direction. Currently available reconstruction approaches for such large data sets are computationally expensive. Here, a novel, fast reconstruction algorithm, named iterative reconstruction tensor tomography (IRTT), is presented to simplify and accelerate tensor tomography reconstructions. IRTT is based on a second-rank tensor model to describe the anisotropy of the nanostructure in every voxel and on an iterative error backpropagation reconstruction algorithm to achieve high convergence speed. The feasibility and accuracy of IRTT are demonstrated by reconstructing the nanostructure anisotropy of three samples: a carbon fiber knot, a human bone trabecula specimen and a fixed mouse brain. Results and reconstruction speed were compared with those obtained by the small-angle scattering tensor tomography (SASTT) reconstruction method introduced by Liebi et al. [Nature (2015), 527, 349–352]. The principal orientation of the nanostructure within each voxel revealed a high level of agreement between the two methods. Yet, for identical data sets and computer hardware used, IRTT was shown to be more than an order of magnitude faster. IRTT was found to yield robust results, it does not require prior knowledge of the sample for initializing parameters, and can be used in cases where simple anisotropy metrics are sufficient, i.e. the tensor approximation adequately captures the level of anisotropy and the dominant orientation within a voxel. In addition, by greatly accelerating the reconstruction, IRTT is particularly suitable for handling large tomographic data sets of samples with internal structure or as a real-time analysis tool during the experiment for online feedback during data acquisition. Alternatively, the IRTT results might be used as an initial guess for models capturing a higher complexity of structural anisotropy such as spherical harmonics based SASTT in Liebi et al. (2015), improving both overall convergence speed and robustness of the reconstruction.text/htmlHigh-speed tensor tomography: iterative reconstruction tensor tomography (IRTT) algorithmtext752https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2019-02-06223research papers2053-2733March 2019med@iucr.org2382053-2733Resolving 500 nm axial separation by multi-slice X-ray ptychography
http://scripts.iucr.org/cgi-bin/paper?wo5033
Multi-slice X-ray ptychography offers an approach to achieve images with a nanometre-scale resolution from samples with thicknesses larger than the depth of field of the imaging system by modeling a thick sample as a set of thin slices and accounting for the wavefront propagation effects within the specimen. Here, we present an experimental demonstration that resolves two layers of nanostructures separated by 500 nm along the axial direction, with sub-10 nm and sub-20 nm resolutions on two layers, respectively. Fluorescence maps are simultaneously measured in the multi-modality imaging scheme to assist in decoupling the mixture of low-spatial-frequency features across different slices. The enhanced axial sectioning capability using correlative signals obtained from multi-modality measurements demonstrates the great potential of the multi-slice ptychography method for investigating specimens with extended dimensions in 3D with high resolution.https://creativecommons.org/licenses/by/4.0/urn:issn:2053-2733Huang, X.Yan, H.He, Y.Ge, M.Öztürk, H.Fang, Y.-L.L.Ha, S.Lin, M.Lu, M.Nazaretski, E.Robinson, I.K.Chu, Y.S.2019-02-12doi:10.1107/S2053273318017229International Union of CrystallographyCombining multi-slice ptychography with multi-modality scanning probe microscopy reconstructs two planes of nanostructures separated by 500 nm with sub-20 nm lateral resolution, assisted by simultaneously measured fluorescence maps for decoupling low-spatial-frequency features.enX-RAY PTYCHOGRAPHY; MULTI-SLICE APPROACH; NANOSTRUCTURESMulti-slice X-ray ptychography offers an approach to achieve images with a nanometre-scale resolution from samples with thicknesses larger than the depth of field of the imaging system by modeling a thick sample as a set of thin slices and accounting for the wavefront propagation effects within the specimen. Here, we present an experimental demonstration that resolves two layers of nanostructures separated by 500 nm along the axial direction, with sub-10 nm and sub-20 nm resolutions on two layers, respectively. Fluorescence maps are simultaneously measured in the multi-modality imaging scheme to assist in decoupling the mixture of low-spatial-frequency features across different slices. The enhanced axial sectioning capability using correlative signals obtained from multi-modality measurements demonstrates the great potential of the multi-slice ptychography method for investigating specimens with extended dimensions in 3D with high resolution.text/htmlResolving 500 nm axial separation by multi-slice X-ray ptychographytext752https://creativecommons.org/licenses/by/4.0/Acta Crystallographica Section A: Foundations and Advances2019-02-12336research papers2053-2733March 2019med@iucr.org3412053-2733A side-by-side comparison of the solidification dynamics of quasicrystalline and approximant phases in the Al–Co–Ni system
http://scripts.iucr.org/cgi-bin/paper?gv5001
Quasicrystals and their approximants have triggered widespread interest due to the challenge of solving their complex crystal structures as well as their possibly exceptional properties. The structural motifs of approximants are similar to those of the corresponding quasicrystals, but to what extent are their crystallization pathways the same? Unfortunately, there have been very few in situ experimental investigations to answer this question. Here, by leveraging the high penetrating power of hard X-rays, synchrotron-based X-ray tomography was conducted in order to capture the nucleation and growth of a decagonal quasicrystal and its related approximant. The combination of data-driven computational analysis with new thermodynamic databases allowed the characterization, with high precision, of the constitutional and kinetic driving forces for crystallization. The experimental results prove that the growth of both crystals from a liquid is dominated by first-order kinetics. Nevertheless, and somewhat surprisingly, significant differences were observed in their rates of nucleation and growth. The reasons for such divergent behaviours are discussed in light of contemporary theories of intermetallic crystallization.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Han, I.Xiao, X.Sun, H.Shahani, A.J.2019-02-06doi:10.1107/S2053273318017114International Union of CrystallographyThe nucleation and growth dynamics of a decagonal quasicrystal and its approximant `X' phase are considered. Various similarities and differences are elucidated.enQUASICRYSTALS; APPROXIMANT PHASES; SYNCHROTRON RADIATION; NUCLEATION AND GROWTHQuasicrystals and their approximants have triggered widespread interest due to the challenge of solving their complex crystal structures as well as their possibly exceptional properties. The structural motifs of approximants are similar to those of the corresponding quasicrystals, but to what extent are their crystallization pathways the same? Unfortunately, there have been very few in situ experimental investigations to answer this question. Here, by leveraging the high penetrating power of hard X-rays, synchrotron-based X-ray tomography was conducted in order to capture the nucleation and growth of a decagonal quasicrystal and its related approximant. The combination of data-driven computational analysis with new thermodynamic databases allowed the characterization, with high precision, of the constitutional and kinetic driving forces for crystallization. The experimental results prove that the growth of both crystals from a liquid is dominated by first-order kinetics. Nevertheless, and somewhat surprisingly, significant differences were observed in their rates of nucleation and growth. The reasons for such divergent behaviours are discussed in light of contemporary theories of intermetallic crystallization.text/htmlA side-by-side comparison of the solidification dynamics of quasicrystalline and approximant phases in the Al–Co–Ni systemtext752https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2019-02-06281research papers2053-2733March 2019med@iucr.org2962053-2733Thermoelectric transport properties in magnetically ordered crystals. Corrigendum and addenda
http://scripts.iucr.org/cgi-bin/paper?kx5070
A correction and additions concerning the limiting point groups are made to the article by Grimmer [Acta Cryst. (2017), A73, 333–345].Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Grimmer, H.2019-02-06doi:10.1107/S2053273318016947International Union of CrystallographyA correction and additions concerning the limiting point groups are made to the article by Grimmer [Acta Cryst. (2017), A73, 333–345].enTHERMOELECTRICITY; TRANSPORT PROPERTIES; MAGNETIC ORDER; GALVANOMAGNETIC EFFECTS; THERMOMAGNETIC EFFECTSA correction and additions concerning the limiting point groups are made to the article by Grimmer [Acta Cryst. (2017), A73, 333–345].text/htmlThermoelectric transport properties in magnetically ordered crystals. Corrigendum and addendatext752Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances2019-02-06409addenda and errata2053-2733March 2019med@iucr.org4092053-2733Ted Janssen and aperiodic crystals
http://scripts.iucr.org/cgi-bin/paper?gv5004
This article reviews some of Ted Janssen's (1936–2017) major contributions to the field of aperiodic crystals. Aperiodic crystals are long-range ordered structures without 3D lattice translations and encompass incommensurately modulated phases, incommensurate composites and quasicrystals. Together with Pim de Wolff and Aloysio Janner, Ted Janssen invented the very elegant theory of superspace crystallography that, by adding a supplementary dimension to the usual 3D space, allows for a deeper understanding of the atomic structure of aperiodic crystals. He also made important contributions to the understanding of the stability and dynamics of aperiodic crystals, exploring their fascinating physical properties. He constantly interacted and collaborated with experimentalists, always ready to share and explain his detailed understanding of aperiodic crystals.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733de Boissieu, M.2019-02-06doi:10.1107/S2053273318016765International Union of CrystallographyTed Janssen's contributions to the field of aperiodic crystals are reviewed.enAPERIODIC CRYSTALS; SUPERSPACE CRYSTALLOGRAPHY; LATTICE DYNAMICS; PHASONS; TED JANSSENThis article reviews some of Ted Janssen's (1936–2017) major contributions to the field of aperiodic crystals. Aperiodic crystals are long-range ordered structures without 3D lattice translations and encompass incommensurately modulated phases, incommensurate composites and quasicrystals. Together with Pim de Wolff and Aloysio Janner, Ted Janssen invented the very elegant theory of superspace crystallography that, by adding a supplementary dimension to the usual 3D space, allows for a deeper understanding of the atomic structure of aperiodic crystals. He also made important contributions to the understanding of the stability and dynamics of aperiodic crystals, exploring their fascinating physical properties. He constantly interacted and collaborated with experimentalists, always ready to share and explain his detailed understanding of aperiodic crystals.text/htmlTed Janssen and aperiodic crystalstext752https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2019-02-06273research papers2053-2733March 2019med@iucr.org2802053-2733