Acta Crystallographica Section A
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.enCopyright (c) 2023 International Union of Crystallography2022-11-25International Union of CrystallographyInternational Union of Crystallographyhttp://journals.iucr.orgurn:issn:2053-2733Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A: Foundations and Advances, Volume 79, Part 1, 2023textweekly62002-01-01T00:00+00:001792022-11-25Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances465urn:issn:2053-2733med@iucr.orgNovember 20222022-11-25Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
//journals.iucr.org/a/issues/2023/01/00/index.html
Still imageGeographic style maps for two-dimensional lattices
http://scripts.iucr.org/cgi-bin/paper?uv5012
This paper develops geographic style maps containing two-dimensional lattices in all known periodic crystals parameterized by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of two-dimensional lattices is a square with identified edges or a punctured sphere. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualize hundreds of thousands of lattices of real crystal structures from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Bright, M.Cooper, A.I.Kurlin, V.2023-01-01doi:10.1107/S2053273322010075International Union of CrystallographyContinuous invariant-based maps visualize for the first time all two-dimensional lattices extracted from hundreds of thousands of known crystal structures in the Cambridge Structural Database.ENtwo-dimensional latticesreduced basisobtuse superbaseisometrycomplete invariantsmetric tensorcontinuityThis paper develops geographic style maps containing two-dimensional lattices in all known periodic crystals parameterized by recent complete invariants. Motivated by rigid crystal structures, lattices are considered up to rigid motion and uniform scaling. The resulting space of two-dimensional lattices is a square with identified edges or a punctured sphere. The new continuous maps show all Bravais classes as low-dimensional subspaces, visualize hundreds of thousands of lattices of real crystal structures from the Cambridge Structural Database, and motivate the development of continuous and invariant-based crystallography.text/htmlGeographic style maps for two-dimensional latticestext1792023-01-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Determination of the superlattice structure factor by X-ray diffraction using a temperature gradient
http://scripts.iucr.org/cgi-bin/paper?iv5026
The influence of a temperature gradient directed perpendicular to the crystal surface on the diffraction focusing of a spherical X-ray wave in a superlattice is studied for the Laue geometry. It is shown that different satellites can be focused on the exit surface of the crystal by a smooth change in the gradient value, which can become the basis for the experimental determination of the structure factor of the superlattice.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Levonyan, L.Manukyan, H.2023-01-01doi:10.1107/S2053273322009925International Union of CrystallographyA method is described for determining the structure factor of a superlattice by measuring the value of the temperature gradient that provides diffraction focusing of radiation from a point source of X-rays.ENsuperlatticespherical X-ray wavefocusingtemperature gradientThe influence of a temperature gradient directed perpendicular to the crystal surface on the diffraction focusing of a spherical X-ray wave in a superlattice is studied for the Laue geometry. It is shown that different satellites can be focused on the exit surface of the crystal by a smooth change in the gradient value, which can become the basis for the experimental determination of the structure factor of the superlattice.text/htmlDetermination of the superlattice structure factor by X-ray diffraction using a temperature gradienttext1792023-01-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Lorentz factor for time-of-flight neutron Bragg and total scattering
http://scripts.iucr.org/cgi-bin/paper?ib5112
The three fundamental origins of the Lorentz factor for neutron time-of-flight powder diffraction are revisited. A detailed derivation of the Lorentz factor is presented in the context of diffuse scattering modelling in reciprocal space when perfect periodicity is assumed, and the total scattering pattern is constructed in its discrete form – the factor in this case becomes 1/Q2 (or d2). Discussion is also presented with respect to practical data reduction where a vanadium measurement is usually taken as the normalization factor (to account for various factors such as detector efficiency), and it is shown that the existence of the Lorentz factor is independent of such a normalization process.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Zhang, Y.Liu, J.Tucker, M.G.2023-01-01doi:10.1107/S2053273322010427International Union of CrystallographyThe Lorentz factor for the integrated intensity of time-of-flight neutron scattering is discussed in detail, including that for Bragg diffraction and total scattering. It is shown that normalization using a vanadium measurement does not, in practice, influence the existence of the Lorentz factor.ENLorentz factorvanadium normalizationBragg diffractiontotal scatteringThe three fundamental origins of the Lorentz factor for neutron time-of-flight powder diffraction are revisited. A detailed derivation of the Lorentz factor is presented in the context of diffuse scattering modelling in reciprocal space when perfect periodicity is assumed, and the total scattering pattern is constructed in its discrete form – the factor in this case becomes 1/Q2 (or d2). Discussion is also presented with respect to practical data reduction where a vanadium measurement is usually taken as the normalization factor (to account for various factors such as detector efficiency), and it is shown that the existence of the Lorentz factor is independent of such a normalization process.text/htmlLorentz factor for time-of-flight neutron Bragg and total scatteringtext1792023-01-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Introduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbacks
http://scripts.iucr.org/cgi-bin/paper?ae5120
In a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136–146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λJ for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Macetti, G.Genoni, A.2023-01-01doi:10.1107/S2053273322010221International Union of CrystallographyA weighting scheme for the X-ray restrained/constrained wavefunction approach is proposed. Test calculations were carried out with both theoretical and experimental X-ray diffraction data to assess advantages and drawbacks of the proposed approach in the different cases.ENX-ray restrained/constrained wavefunctionweighting schemereflection distributionquantum crystallographyIn a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136–146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λJ for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.text/htmlIntroduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbackstext1792023-01-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Electron density and thermal motion of diamond at elevated temperatures
http://scripts.iucr.org/cgi-bin/paper?pl5020
The electron density and thermal motion of diamond are determined at nine temperatures between 100 K and 1000 K via synchrotron powder X-ray diffraction (PXRD) data collected on a high-accuracy detector system. Decoupling of the thermal motion from the thermally smeared electron density is performed via an iterative Wilson–Hansen–Coppens–Rietveld procedure using theoretical static structure factors from density functional theory (DFT) calculations. The thermal motion is found to be harmonic and isotropic in the explored temperature range, and excellent agreement is observed between experimental atomic displacement parameters (ADPs) and those obtained via theoretical harmonic phonon calculations (HPC), even at 1000 K. The Debye temperature of diamond is determined experimentally to be ΘD = 1883 (35) K. A topological analysis of the electron density explores the temperature dependency of the electron density at the bond critical point. The properties are found to be constant throughout the temperature range. The robustness of the electron density confirms the validity of the crystallographic convolution approximation for diamond in the explored temperature range.Copyright (c) 2023 International Union of Crystallographyurn:issn:2053-2733Beyer, J.Grønbech, T.B.E.Zhang, J.Kato, K.Brummerstedt Iversen, B.2023-01-01doi:10.1107/S2053273322010154International Union of CrystallographyThe electron densities and atomic displacement parameters of diamond are determined from 100 K to 1000 K using synchrotron powder X-ray diffraction.ENX-ray electron densitysynchrotron powder X-ray diffractiondiamondconvolution approximationThe electron density and thermal motion of diamond are determined at nine temperatures between 100 K and 1000 K via synchrotron powder X-ray diffraction (PXRD) data collected on a high-accuracy detector system. Decoupling of the thermal motion from the thermally smeared electron density is performed via an iterative Wilson–Hansen–Coppens–Rietveld procedure using theoretical static structure factors from density functional theory (DFT) calculations. The thermal motion is found to be harmonic and isotropic in the explored temperature range, and excellent agreement is observed between experimental atomic displacement parameters (ADPs) and those obtained via theoretical harmonic phonon calculations (HPC), even at 1000 K. The Debye temperature of diamond is determined experimentally to be ΘD = 1883 (35) K. A topological analysis of the electron density explores the temperature dependency of the electron density at the bond critical point. The properties are found to be constant throughout the temperature range. The robustness of the electron density confirms the validity of the crystallographic convolution approximation for diamond in the explored temperature range.text/htmlElectron density and thermal motion of diamond at elevated temperaturestext1792023-01-01Copyright (c) 2023 International Union of CrystallographyActa Crystallographica Section Aresearch papers00