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 imageCharacterizing 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 20193972053-2733CO2 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 experimenttext2752019-02-06Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers214med@iucr.orgMarch 20192222053-2733Principles 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 Fe2Al5text2752019-02-21Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers297med@iucr.orgMarch 20193062053-2733High-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) algorithmtext2752019-02-06Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers223med@iucr.orgMarch 20192382053-2733Grazing-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 multilayerstext2752019-02-12Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers342med@iucr.orgMarch 20193512053-2733Resolving 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 ptychographytext2752019-02-12Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/4.0/2053-2733research papers336med@iucr.orgMarch 20193412053-2733A 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 systemtext2752019-02-06Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers281med@iucr.orgMarch 20192962053-2733Thermoelectric 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 addendatext2752019-02-06Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2019 International Union of Crystallography2053-2733addenda and errata409med@iucr.orgMarch 20194092053-2733Ted 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 crystalstext2752019-02-06Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers273med@iucr.orgMarch 20192802053-2733Rotational switches in the two-dimensional fullerene quasicrystal
http://scripts.iucr.org/cgi-bin/paper?vf5003
One of the essential components of molecular electronic circuits are switching elements that are stable in two different states and can ideally be switched on and off many times. Here, distinct buckminsterfullerenes within a self-assembled monolayer, forming a two-dimensional dodecagonal quasicrystal on a Pt-terminated Pt3Ti(111) surface, are identified to form well separated molecular rotational switching elements. Employing scanning tunneling microscopy, the molecular-orbital appearance of the fullerenes in the quasicrystalline monolayer is resolved. Thus, fullerenes adsorbed on the 36 vertex configuration are identified to exhibit a distinctly increased mobility. In addition, this finding is verified by differential conductance measurements. The rotation of these mobile fullerenes can be triggered frequently by applied voltage pulses, while keeping the neighboring molecules immobile. An extensive analysis reveals that crystallographic and energetic constraints at the molecule/metal interface induce an inequality of the local potentials for the 36 and 32.4.3.4 vertex sites and this accounts for the switching ability of fullerenes on the 36 vertex sites. Consequently, a local area of the 8/3 approximant in the two-dimensional fullerene quasicrystal consists of single rotational switching fullerenes embedded in a matrix of inert molecules. Furthermore, it is deduced that optimization of the intermolecular interactions between neighboring fullerenes hinders the realization of translational periodicity in the fullerene monolayer on the Pt-terminated Pt3Ti(111) surface.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Paßens, M.Karthäuser, S.2019-01-01doi:10.1107/S2053273318015681International Union of CrystallographyLocal potential differences between the 36 and 32.4.3.4 vertex configurations are identified within a two-dimensional dodecagonal fullerene monolayer. In a local area of the 8/3 approximant, rotational switching fullerenes on 36 vertex sites are revealed by scanning tunneling microscopy.enROTATIONAL SWITCHES; FULLERENES; INTERFACIAL INTERACTIONS; GEOMETRIC FRUSTRATION; DODECAGONAL QUASICRYSTALS; SQUARE-TRIANGLE TILING; SCANNING TUNNELING MICROSCOPYOne of the essential components of molecular electronic circuits are switching elements that are stable in two different states and can ideally be switched on and off many times. Here, distinct buckminsterfullerenes within a self-assembled monolayer, forming a two-dimensional dodecagonal quasicrystal on a Pt-terminated Pt3Ti(111) surface, are identified to form well separated molecular rotational switching elements. Employing scanning tunneling microscopy, the molecular-orbital appearance of the fullerenes in the quasicrystalline monolayer is resolved. Thus, fullerenes adsorbed on the 36 vertex configuration are identified to exhibit a distinctly increased mobility. In addition, this finding is verified by differential conductance measurements. The rotation of these mobile fullerenes can be triggered frequently by applied voltage pulses, while keeping the neighboring molecules immobile. An extensive analysis reveals that crystallographic and energetic constraints at the molecule/metal interface induce an inequality of the local potentials for the 36 and 32.4.3.4 vertex sites and this accounts for the switching ability of fullerenes on the 36 vertex sites. Consequently, a local area of the 8/3 approximant in the two-dimensional fullerene quasicrystal consists of single rotational switching fullerenes embedded in a matrix of inert molecules. Furthermore, it is deduced that optimization of the intermolecular interactions between neighboring fullerenes hinders the realization of translational periodicity in the fullerene monolayer on the Pt-terminated Pt3Ti(111) surface.text/htmlRotational switches in the two-dimensional fullerene quasicrystaltext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers41med@iucr.orgJanuary 2019492053-2733Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
http://scripts.iucr.org/cgi-bin/paper?vf5001
This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Oǧuz, E.C.Socolar, J.E.S.Steinhardt, P.J.Torquato, S.2019-01-01doi:10.1107/S2053273318015528International Union of CrystallographyThis work examines the long-wavelength scaling properties of self-similar substitution tilings, placing them in their hyperuniformity classes. Quasiperiodic, non-PV (Pisot–Vijayaraghavan number) and limit-periodic examples are analyzed. Novel behavior is demonstrated for certain limit-periodic cases.enSUBSTITUTION TILING; HYPERUNIFORMITY; DIFFRACTION; LIMIT-PERIODIC TILINGS; NON-PISOT TILINGS; QUASIPERIODIC TILINGSThis work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.text/htmlHyperuniformity and anti-hyperuniformity in one-dimensional substitution tilingstext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers3med@iucr.orgJanuary 2019132053-2733Ab initio phasing of the diffraction of crystals with translational disorder
http://scripts.iucr.org/cgi-bin/paper?ae5053
To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Morgan, A.J.Ayyer, K.Barty, A.Chen, J.P.J.Ekeberg, T.Oberthuer, D.White, T.A.Yefanov, O.Chapman, H.N.2019-01-01doi:10.1107/S2053273318015395International Union of CrystallographyThis article reports on the combined use of Bragg reflections and diffuse scatter for structure determination in crystallography.enX-RAY DIFFRACTION; DIFFUSE SCATTERING; PHASE RETRIEVAL; MACROMOLECULAR CRYSTALLOGRAPHYTo date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.text/htmlAb initio phasing of the diffraction of crystals with translational disordertext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers25med@iucr.orgJanuary 2019402053-2733Selling reduction versus Niggli reduction for crystallographic lattices
http://scripts.iucr.org/cgi-bin/paper?ae5054
The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Andrews, L.C.Bernstein, H.J.Sauter, N.K.2019-01-01doi:10.1107/S2053273318015413International Union of CrystallographyThe unit-cell reduction described by Selling and used by Delone (Delaunay) is explained in a simple form.enUNIT-CELL REDUCTION; DELAUNAY; DELONE; NIGGLI; SELLINGThe unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.text/htmlSelling reduction versus Niggli reduction for crystallographic latticestext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers115med@iucr.orgJanuary 20191202053-2733Reducing dynamical electron scattering reveals hydrogen atoms
http://scripts.iucr.org/cgi-bin/paper?td5055
Compared with X-rays, electron diffraction faces a crucial challenge: dynamical electron scattering compromises structure solution and its effects can only be modelled in specific cases. Dynamical scattering can be reduced experimentally by decreasing crystal size but not without a penalty, as it also reduces the overall diffracted intensity. In this article it is shown that nanometre-sized crystals from organic pharmaceuticals allow positional refinement of the hydrogen atoms, even whilst ignoring the effects of dynamical scattering during refinement. To boost the very weak diffraction data, a highly sensitive hybrid pixel detector was employed. A general likelihood-based computational approach was also introduced for further reducing the adverse effects of dynamic scattering, which significantly improved model accuracy, even for protein crystal data at substantially lower resolution.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Clabbers, M.T.B.Gruene, T.van Genderen, E.Abrahams, J.P.2019-01-01doi:10.1107/S2053273318013918International Union of CrystallographyExperimental and computational reduction of dynamical electron scattering allows for visualizing of individual hydrogen atoms.enDYNAMICAL SCATTERING; ELECTRON DIFFRACTION; HYDROGEN ATOMS; NANOCRYSTALS; HYBRID PIXEL DETECTORCompared with X-rays, electron diffraction faces a crucial challenge: dynamical electron scattering compromises structure solution and its effects can only be modelled in specific cases. Dynamical scattering can be reduced experimentally by decreasing crystal size but not without a penalty, as it also reduces the overall diffracted intensity. In this article it is shown that nanometre-sized crystals from organic pharmaceuticals allow positional refinement of the hydrogen atoms, even whilst ignoring the effects of dynamical scattering during refinement. To boost the very weak diffraction data, a highly sensitive hybrid pixel detector was employed. A general likelihood-based computational approach was also introduced for further reducing the adverse effects of dynamic scattering, which significantly improved model accuracy, even for protein crystal data at substantially lower resolution.text/htmlReducing dynamical electron scattering reveals hydrogen atomstext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers82med@iucr.orgJanuary 2019932053-2733Aspherical scattering factors for SHELXL – model, implementation and application
http://scripts.iucr.org/cgi-bin/paper?ib5060
A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Lübben, J.Wandtke, C.M.Hübschle, C.B.Ruf, M.Sheldrick, G.M.Dittrich, B.2019-01-01doi:10.1107/S2053273318013840International Union of CrystallographyA new aspherical scattering factor formalism was implemented in SHELXL. It relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. The automated atom-type assignment was derived from the invariom formalism.enSHELXL; INVARIOMS; ASPHERICAL SCATTERING FACTORS; QUANTUM CRYSTALLOGRAPHYA new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.text/htmlAspherical scattering factors for SHELXL – model, implementation and applicationtext1752019-01-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers50med@iucr.orgJanuary 2019622053-2733Report of the Executive Committee for 2017
http://scripts.iucr.org/cgi-bin/paper?es5004
The report of the Executive Committee for 2017 is presented.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Ashcroft, A.T.2019-01-01doi:10.1107/S205327331801330XInternational Union of CrystallographyThe report of the Executive Committee for 2017 is presented.enINTERNATIONAL UNION OF CRYSTALLOGRAPHY; EXECUTIVE COMMITTEEThe report of the Executive Committee for 2017 is presented.text/htmlReport of the Executive Committee for 2017text1752019-01-01Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2019 International Union of Crystallography2053-2733international union of crystallography165med@iucr.orgJanuary 20192092053-2733Rigid units revisited
http://scripts.iucr.org/cgi-bin/paper?me6016
Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Phillips, A.E.2018-09-01doi:10.1107/S2053273318012007International Union of CrystallographyRigid-unit modes, which allow coordination polyhedra to remain undistorted and hence cost little energy, provide a way of understanding many important physical properties. Campbell et al. [Acta Cryst. (2018). A74, 408–424] have developed an elegant new algebraic approach to finding these distortion modes.enRIGID-UNIT MODES; SILICATES; PEROVSKITES; TUNGSTEN BRONZEStext/htmlRigid units revisitedtext5742018-09-01Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2018 International Union of Crystallography2053-2733scientific commentaries406med@iucr.orgSeptember 20184072053-2733Ab initio structure determination of nanocrystals of organic pharmaceutical compounds by electron diffraction at room temperature using a Timepix quantum area direct electron detector. Corrigendum
http://scripts.iucr.org/cgi-bin/paper?td9026
Corrections are made to Table 1 in the article by van Genderen et al. [Acta Cryst. (2016), A72, 236–242].https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733van Genderen, E.Clabbers, M.T.B.Das, P.P.Stewart, A.Nederlof, I.Barentsen, K.C.Portillo, Q.Pannu, N.S.Nicolopoulos, S.Gruene, T.Abrahams, J.P.2018-10-30doi:10.1107/S2053273318014079International Union of CrystallographyA correction is made to the article by van Genderen et al. [Acta Cryst. (2016), A72, 236–242].enELECTRON NANOCRYSTALLOGRAPHY; TIMEPIX QUANTUM AREA DETECTOR; CARBAMAZEPINE; NICOTINIC ACID; ELECTRON DIFFRACTION STRUCTURE DETERMINATIONCorrections are made to Table 1 in the article by van Genderen et al. [Acta Cryst. (2016), A72, 236–242].text/htmlAb initio structure determination of nanocrystals of organic pharmaceutical compounds by electron diffraction at room temperature using a Timepix quantum area direct electron detector. Corrigendumtext746https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-10-30709addenda and errata2053-2733November 2018med@iucr.org7092053-2733Atomic scale analyses of {\bb Z}-module defects in an NiZr alloy
http://scripts.iucr.org/cgi-bin/paper?td5054
Some specific structures of intermetallic alloys, like approximants of quasicrystals, have their unit cells and most of their atoms located on a periodic fraction of the nodes of a unique {\bb Z}-module [a set of the irrational projections of the nodes of a (N > 3-dimensional) lattice]. Those hidden internal symmetries generate possible new kinds of defects like coherent twins, translation defects and so-called module dislocations that have already been discussed elsewhere [Quiquandon et al. (2016). Acta Cryst. A72, 55–61; Sirindil et al. (2017). Acta Cryst. A73, 427–437]. Presented here are electron microscopy observations of the orthorhombic phase NiZr – and its low-temperature monoclinic variant – which reveal the existence of such defects based on the underlying {\bb Z}-module generated by the five vertices of the regular pentagon. New high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) observations demonstrate the agreement between the geometrical description of the structure in five dimensions and the experimental observations of fivefold twins and translation defects.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Sirindil, A.Kobold, R.Mompiou, F.Lartigue-Korinek, S.Perriere, L.Patriarche, G.Quiquandon, M.Gratias, D.2018-10-04doi:10.1107/S2053273318011439International Union of CrystallographyThis article describes the observation and determination of {\bb Z}-module defects (twins, translation faults and module dislocations) in NiZr by high-resolution electron microscopy (HREM), and scanning transmission electron microscopy bright-field (STEM-BF) and high-angle annular dark-field (STEM-HAADF).en{\BB Z}-MODULE; DEFECTS; TWINS; DISLOCATIONS; HREM-HAADFSome specific structures of intermetallic alloys, like approximants of quasicrystals, have their unit cells and most of their atoms located on a periodic fraction of the nodes of a unique {\bb Z}-module [a set of the irrational projections of the nodes of a (N > 3-dimensional) lattice]. Those hidden internal symmetries generate possible new kinds of defects like coherent twins, translation defects and so-called module dislocations that have already been discussed elsewhere [Quiquandon et al. (2016). Acta Cryst. A72, 55–61; Sirindil et al. (2017). Acta Cryst. A73, 427–437]. Presented here are electron microscopy observations of the orthorhombic phase NiZr – and its low-temperature monoclinic variant – which reveal the existence of such defects based on the underlying {\bb Z}-module generated by the five vertices of the regular pentagon. New high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) observations demonstrate the agreement between the geometrical description of the structure in five dimensions and the experimental observations of fivefold twins and translation defects.text/htmlAtomic scale analyses of {\bb Z}-module defects in an NiZr alloytext6742018-10-04Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papersmed@iucr.orgNovember 20182053-2733Calculation of absorption and secondary scattering of X-rays by spherical amorphous materials in an asymmetric transmission geometry. Corrigendum
http://scripts.iucr.org/cgi-bin/paper?ib9014
A revised version of Table 2 of Bendert et al. [Acta Cryst. (2013). A69, 131–139] is provided.Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Bendert, J.C.Blodgett, M.E.Kelton, K.F.2018-09-01doi:10.1107/S205327331801166XInternational Union of CrystallographyCorrections to Table 2 in Bendert et al. [Acta Cryst. (2013). A69, 131–139] are reported.enX-RAY SCATTERING; ATTENUATION CORRECTION FACTORS; SECONDARY SCATTERINGA revised version of Table 2 of Bendert et al. [Acta Cryst. (2013). A69, 131–139] is provided.text/htmlCalculation of absorption and secondary scattering of X-rays by spherical amorphous materials in an asymmetric transmission geometry. Corrigendumtext5742018-09-01Acta Crystallographica Section A: Foundations and AdvancesCopyright (c) 2018 International Union of Crystallography2053-2733addenda and errata613med@iucr.orgSeptember 20186132053-2733A symmetry roadmap to new perovskite multiferroics
http://scripts.iucr.org/cgi-bin/paper?me6013
Copyright (c) 2018 International Union of Crystallographyurn:issn:2053-2733Woodward, P.M.2018-07-05doi:10.1107/S2053273318009294International Union of CrystallographyThe new approach to the design of technologically important perovskites described by Senn and Bristowe [Acta Cryst. (2018), A74, 303–321] is discussed.enPEROVSKITES; MULTIFERROICS; SYMMETRYtext/htmlA symmetry roadmap to new perovskite multiferroicstext744Copyright (c) 2018 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances2018-07-05291scientific commentaries2053-2733July 2018med@iucr.org2922053-2733Specular reflection intensity modulated by grazing-incidence diffraction in a wide angular range
http://scripts.iucr.org/cgi-bin/paper?wo5025
Grazing-incidence X-ray diffraction (GID) is a well known technique for the characterization of crystal surfaces. A theoretical study has been performed of the sensitivity of GID to the structure of a crystal surface and distorted nanometre-thin surface layers. To simulate GID from crystals that have a complex subsurface structure, a matrix formalism of the dynamical diffraction theory has been applied. It has been found that the azimuthal rocking curves of a crystal that has a distorted subsurface, measured over a wide angular range, show asymmetric thickness oscillations with two distinguishable sets of frequencies: one corresponding to the diffraction in the single-crystal subsurface layer and the second corresponding to the diffraction in the single-crystal substrate. Therefore, azimuthal rocking curves allow characterization of the subsurface structure of a single crystal. Furthermore, thickness oscillations induced by evanescent diffraction modulate the specular reflection intensity, showing high-intensity modulations. This will potentially allow implementation of subsurface crystal characterization using, for instance, a laboratory-scale X-ray diffractometer.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Nikolaev, K.V.Makhotkin, I.A.Yakunin, S.N.Kruijs, R.W.E.Chuev, M.A.Bijkerk, F.2018-09-01doi:10.1107/S2053273318008963International Union of CrystallographyA theoretical description is given of the novel X-ray diffraction effect in single-crystal structures with a distorted crystal subsurface based on the dynamical theory of diffraction.enCRYSTAL SURFACE; GRAZING-INCIDENCE X-RAY DIFFRACTION; GID; SPECULAR REFLECTION; AZIMUTHAL ROCKING CURVESGrazing-incidence X-ray diffraction (GID) is a well known technique for the characterization of crystal surfaces. A theoretical study has been performed of the sensitivity of GID to the structure of a crystal surface and distorted nanometre-thin surface layers. To simulate GID from crystals that have a complex subsurface structure, a matrix formalism of the dynamical diffraction theory has been applied. It has been found that the azimuthal rocking curves of a crystal that has a distorted subsurface, measured over a wide angular range, show asymmetric thickness oscillations with two distinguishable sets of frequencies: one corresponding to the diffraction in the single-crystal subsurface layer and the second corresponding to the diffraction in the single-crystal substrate. Therefore, azimuthal rocking curves allow characterization of the subsurface structure of a single crystal. Furthermore, thickness oscillations induced by evanescent diffraction modulate the specular reflection intensity, showing high-intensity modulations. This will potentially allow implementation of subsurface crystal characterization using, for instance, a laboratory-scale X-ray diffractometer.text/htmlSpecular reflection intensity modulated by grazing-incidence diffraction in a wide angular rangetext5742018-09-01Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers545med@iucr.orgSeptember 20185522053-2733Estimating the structure factors in X-ray diffraction
http://scripts.iucr.org/cgi-bin/paper?vk5022
This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Fewster, P.F.2018-08-08doi:10.1107/S2053273318007593International Union of CrystallographyThe meaning of the structure factor and how it impacts on the determination of structures are reassessed. A route to obtaining the structure factors is presented for several data collection methods and crystal qualities.enSTRUCTURE FACTORS; IMPERFECT CRYSTALS; DIFFRACTION THEORY; SERIAL CRYSTALLOGRAPHY; POWDER DIFFRACTIONThis article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.text/htmlEstimating the structure factors in X-ray diffractiontext5742018-08-08Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers481med@iucr.orgSeptember 20184982053-2733Response to Fraser & Wark's comments on A new theory for X-ray diffraction
http://scripts.iucr.org/cgi-bin/paper?ae5046
The criticisms of my theory, as given by Fraser & Wark [(2018), Acta Cryst. A74, 447–456], are built on a misunderstanding of the concept and the methodology I have used. The assumption they have made rules out my description from which they conclude that my theory is proved to be wrong. They assume that I have misunderstood the diffraction associated with the shape of a crystal and my calculation is only relevant to a parallelepiped and even that I have got wrong. It only appears wrong to Fraser & Wark because the effect I predict has nothing to do with the crystal shape. The effect though can be measured as well as the crystal shape effects. This response describes my reasoning behind the theory, how it can be related to the Ewald sphere construction, and the build-up of the full diffraction pattern from all the scatterers in a stack of planes. It is the latter point that makes the Fraser & Wark analysis incomplete. The description given in this article describes my approach much more precisely with reference to the Ewald sphere construction. Several experiments are described that directly measure the predictions of the new theory, which are explained with reference to the Ewald sphere description. In its simplest terms the new theory can be considered as giving a thickness to the Ewald sphere surface, whereas in the conventional theory it has no thickness. Any thickness immediately informs us that the scattering from a peak at the Bragg angle does not have to be in the Bragg condition to be observed. I believe the conventional theory is a very good approximation, but as soon as it is tested with careful experiments it is shown to be incomplete. The new theory puts forward the idea that there is persistent intensity at the Bragg scattering angle outside the Bragg condition. This intensity is weak (∼10−5) but can be observed in careful laboratory experiments, despite being on the limit of observation, yet it has a profound impact on how we should interpret diffraction patterns.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Fewster, P.F.2018-07-18doi:10.1107/S2053273318007489International Union of CrystallographyIn response to the comments by Fraser & Wark [(2018), Acta Cryst. A74, 447–456], experimental evidence and an explanation of the new theory in the context of a modified Ewald sphere construction are presented.enDIFFRACTION THEORY; POWDER DIFFRACTION; SMALL CRYSTALSThe criticisms of my theory, as given by Fraser & Wark [(2018), Acta Cryst. A74, 447–456], are built on a misunderstanding of the concept and the methodology I have used. The assumption they have made rules out my description from which they conclude that my theory is proved to be wrong. They assume that I have misunderstood the diffraction associated with the shape of a crystal and my calculation is only relevant to a parallelepiped and even that I have got wrong. It only appears wrong to Fraser & Wark because the effect I predict has nothing to do with the crystal shape. The effect though can be measured as well as the crystal shape effects. This response describes my reasoning behind the theory, how it can be related to the Ewald sphere construction, and the build-up of the full diffraction pattern from all the scatterers in a stack of planes. It is the latter point that makes the Fraser & Wark analysis incomplete. The description given in this article describes my approach much more precisely with reference to the Ewald sphere construction. Several experiments are described that directly measure the predictions of the new theory, which are explained with reference to the Ewald sphere description. In its simplest terms the new theory can be considered as giving a thickness to the Ewald sphere surface, whereas in the conventional theory it has no thickness. Any thickness immediately informs us that the scattering from a peak at the Bragg angle does not have to be in the Bragg condition to be observed. I believe the conventional theory is a very good approximation, but as soon as it is tested with careful experiments it is shown to be incomplete. The new theory puts forward the idea that there is persistent intensity at the Bragg scattering angle outside the Bragg condition. This intensity is weak (∼10−5) but can be observed in careful laboratory experiments, despite being on the limit of observation, yet it has a profound impact on how we should interpret diffraction patterns.text/htmlResponse to Fraser & Wark's comments on A new theory for X-ray diffractiontext5742018-07-18Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers457med@iucr.orgSeptember 20184652053-2733A group-theoretical approach to enumerating magnetoelectric and multiferroic couplings in perovskites
http://scripts.iucr.org/cgi-bin/paper?ou5003
A group-theoretical approach is used to enumerate the possible couplings between magnetism and ferroelectric polarization in the parent Pm{\overline 3}m perovskite structure. It is shown that third-order magnetoelectric coupling terms must always involve magnetic ordering at the A and B sites which either transforms both as R-point or both as X-point time-odd irreducible representations (irreps). For fourth-order couplings it is demonstrated that this criterion may be relaxed allowing couplings involving irreps at X-, M- and R-points which collectively conserve crystal momentum, producing a magnetoelectric effect arising from only B-site magnetic order. In this case, exactly two of the three irreps entering the order parameter must be time-odd irreps and either one or all must be odd with respect to inversion symmetry. It is possible to show that the time-even irreps in this triad must transform as one of: X1+, M3,5− or R5+, corresponding to A-site cation order, A-site antipolar displacements or anion rocksalt ordering, respectively. This greatly reduces the search space for type-II multiferroic perovskites. Similar arguments are used to demonstrate how weak ferromagnetism may be engineered and a variety of schemes are proposed for coupling this to ferroelectric polarization. The approach is illustrated with density functional theory calculations on magnetoelectric couplings and, by considering the literature, suggestions are given of which avenues of research are likely to be most promising in the design of novel magnetoelectric materials.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Senn, M.S.Bristowe, N.C.2018-07-05doi:10.1107/S2053273318007441International Union of CrystallographyA symmetry-motivated approach for designing perovskites with ferroic and magnetoelectric couplings is proposed. The results highlight which kinds of magnetic orderings and structural distortions need to coexist within the same structure to produce the desired couplings.enMAGNETOELECTRIC COUPLINGS; MULTIFERROIC COUPLINGS; PEROVSKITES; IMPROPER FERROELECTRICITY; GROUP THEORY; IRREP ANALYSIS; ANHARMONIC COUPLINGSA group-theoretical approach is used to enumerate the possible couplings between magnetism and ferroelectric polarization in the parent Pm{\overline 3}m perovskite structure. It is shown that third-order magnetoelectric coupling terms must always involve magnetic ordering at the A and B sites which either transforms both as R-point or both as X-point time-odd irreducible representations (irreps). For fourth-order couplings it is demonstrated that this criterion may be relaxed allowing couplings involving irreps at X-, M- and R-points which collectively conserve crystal momentum, producing a magnetoelectric effect arising from only B-site magnetic order. In this case, exactly two of the three irreps entering the order parameter must be time-odd irreps and either one or all must be odd with respect to inversion symmetry. It is possible to show that the time-even irreps in this triad must transform as one of: X1+, M3,5− or R5+, corresponding to A-site cation order, A-site antipolar displacements or anion rocksalt ordering, respectively. This greatly reduces the search space for type-II multiferroic perovskites. Similar arguments are used to demonstrate how weak ferromagnetism may be engineered and a variety of schemes are proposed for coupling this to ferroelectric polarization. The approach is illustrated with density functional theory calculations on magnetoelectric couplings and, by considering the literature, suggestions are given of which avenues of research are likely to be most promising in the design of novel magnetoelectric materials.text/htmlA group-theoretical approach to enumerating magnetoelectric and multiferroic couplings in perovskitestext4742018-07-05Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers308med@iucr.orgJuly 20183212053-2733Ted Janssen (1936–2017)
http://scripts.iucr.org/cgi-bin/paper?es5003
urn:issn:2053-2733Souvignier, B.2018-06-06doi:10.1107/S2053273318007088International Union of CrystallographyObituary for Ted Janssen.enOBITUARY; N-DIMENSIONAL CRYSTALLOGRAPHY; APERIODIC STRUCTURES; SUPERSPACE APPROACHtext/htmlTed Janssen (1936–2017) text744Acta Crystallographica Section A: Foundations and Advances2018-06-06403obituaries2053-2733July 2018med@iucr.org4042053-2733Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films
http://scripts.iucr.org/cgi-bin/paper?wo5026
Crystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Simbrunner, J.Simbrunner, C.Schrode, B.Röthel, C.Bedoya-Martinez, N.Salzmann, I.Resel, R.2018-07-05doi:10.1107/S2053273318006629International Union of CrystallographyCrystal structure solutions from fibre-textured crystals within thin films are frequently achieved by grazing-incidence X-ray diffraction experiments. In the present work, analytical mathematical expressions are derived for the indexing of experimental diffraction patterns.enGRAZING-INCIDENCE X-RAY DIFFRACTION; THIN FILMS; INDEXING; SPECULAR SCAN; MATHEMATICAL CRYSTALLOGRAPHYCrystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.text/htmlIndexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin filmstext744https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-07-05373research papers2053-2733July 2018med@iucr.org3872053-2733A method to estimate statistical errors of properties derived from charge-density modelling
http://scripts.iucr.org/cgi-bin/paper?ae5043
Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Fournier, B.Guillot, B.Lecomte, C.Escudero-Adán, E.C.Jelsch, C.2018-05-03doi:10.1107/S2053273318004308International Union of CrystallographyErrors on molecular properties including the topology of electron density and electrostatics are estimated from a sample of deviating models generated using the variance–covariance matrix issued at the end of the charge-density refinement.enMONTE CARLO METHODS; ELECTRON DENSITY; UNCERTAINTY; TOPOLOGY; INTERMOLECULAR INTERACTIONSEstimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.text/htmlA method to estimate statistical errors of properties derived from charge-density modellingtext743https://creativecommons.org/licenses/by/2.0/ukActa Crystallographica Section A: Foundations and Advances2018-05-03170research papers2053-2733May 2018med@iucr.org1832053-2733Comments on A new theory for X-ray diffraction
http://scripts.iucr.org/cgi-bin/paper?ae5039
In an article entitled A new theory for X-ray diffraction [Fewster (2014). Acta Cryst. A70, 257–282], hereafter referred to as NTXRD, it is claimed that when X-rays are scattered from a small crystallite, whatever its size and shape, the diffraction pattern will contain enhanced scattering at angles of exactly 2θB, whatever the orientation of the crystal. It is claimed that in this way scattering from a powder, with randomly oriented crystals, gives rise to Bragg scattering even if the Bragg condition is never satisfied by an individual crystallite. The claims of the theory put forward in NTXRD are examined and they are found to be in error. Whilst for a certain restricted set of shapes of crystals it is possible to obtain some diffraction close to (but not exactly at) the Bragg angle as the crystallite is oriented away from the Bragg condition, this is generally not the case. Furthermore, contrary to the claims made within NTXRD, the recognition of the origin of the type of effects described is not new, and has been known since the earliest days of X-ray diffraction.https://creativecommons.org/licenses/by/2.0/ukurn:issn:2053-2733Fraser, J.T.Wark, J.S.2018-07-18doi:10.1107/S2053273318003959International Union of CrystallographyFewster [(2014), Acta Cryst. A70, 257–282] claimed that a new theory of X-ray diffraction is required, and that small crystallites will give rise to scattering at angles of exactly twice the Bragg angle, whatever their orientation. This article demonstrates that this theory is in error.enDIFFRACTION THEORY; POWDER DIFFRACTION; SMALL CRYSTALSIn an article entitled A new theory for X-ray diffraction [Fewster (2014). Acta Cryst. A70, 257–282], hereafter referred to as NTXRD, it is claimed that when X-rays are scattered from a small crystallite, whatever its size and shape, the diffraction pattern will contain enhanced scattering at angles of exactly 2θB, whatever the orientation of the crystal. It is claimed that in this way scattering from a powder, with randomly oriented crystals, gives rise to Bragg scattering even if the Bragg condition is never satisfied by an individual crystallite. The claims of the theory put forward in NTXRD are examined and they are found to be in error. Whilst for a certain restricted set of shapes of crystals it is possible to obtain some diffraction close to (but not exactly at) the Bragg angle as the crystallite is oriented away from the Bragg condition, this is generally not the case. Furthermore, contrary to the claims made within NTXRD, the recognition of the origin of the type of effects described is not new, and has been known since the earliest days of X-ray diffraction.text/htmlComments on A new theory for X-ray diffractiontext5742018-07-18Acta Crystallographica Section A: Foundations and Advanceshttps://creativecommons.org/licenses/by/2.0/uk2053-2733research papers447med@iucr.orgSeptember 20184562053-2733