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) 2019 International Union of Crystallography2019-08-30International 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 75, Part 5, 2019textweekly62002-01-01T00:00+00:005752019-08-30Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances658urn:issn:2053-2733med@iucr.orgAugust 20192019-08-30Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
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Still imageAlgorithm for distance list extraction from pair distribution functions
http://scripts.iucr.org/cgi-bin/paper?eo5099
An algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Gu, R.Banerjee, S.Du, Q.Billinge, S.J.L.2019-08-12doi:10.1107/S2053273319008647International Union of CrystallographyThe atomic pair distribution function (PDF) represents the structure of a material as a list of distances between pairs of atoms. This article presents an algorithm that can extract the distance list from a measured PDF in a highly automated manner without prior knowledge of the structure.ENpair distribution functiondistance listpeak extractionDebye scattering equationcurve fittingAn algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.text/htmlAlgorithm for distance list extraction from pair distribution functionstext5752019-08-12Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers658668Robust minimal matching rules for quasicrystals
http://scripts.iucr.org/cgi-bin/paper?eo5098
A unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real-world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Kalugin, P.Katz, A.2019-08-23doi:10.1107/S2053273319008180International Union of CrystallographyAn algorithmic procedure is proposed for extraction of physically meaningful matching rules directly from the phased diffraction data of a quasicrystal.ENquasicrystalsmatching rulesquasiperiodic tilingsA unified framework is proposed for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real-world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching rules, directly from the phased diffraction data. The construction yields precise values for the spatial density of distinct atomic positions and tolerates the presence of defects in a robust way.text/htmlRobust minimal matching rules for quasicrystalstext5752019-08-23Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers669693XGANDALF – extended gradient descent algorithm for lattice finding
http://scripts.iucr.org/cgi-bin/paper?ae5071
Serial crystallography records still diffraction patterns from single, randomly oriented crystals, then merges data from hundreds or thousands of them to form a complete data set. To process the data, the diffraction patterns must first be indexed, equivalent to determining the orientation of each crystal. A novel automatic indexing algorithm is presented, which in tests usually gives significantly higher indexing rates than alternative programs currently available for this task. The algorithm does not require prior knowledge of the lattice parameters but can make use of that information if provided, and also allows indexing of diffraction patterns generated by several crystals in the beam. Cases with a small number of Bragg spots per pattern appear to particularly benefit from the new approach. The algorithm has been implemented and optimized for fast execution, making it suitable for real-time feedback during serial crystallography experiments. It is implemented in an open-source C++ library and distributed under the LGPLv3 licence. An interface to it has been added to the CrystFEL software suite.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Gevorkov, Y.Yefanov, O.Barty, A.White, T.A.Mariani, V.Brehm, W.Tolstikova, A.Grigat, R.-R.Chapman, H.N.2019-08-30doi:10.1107/S2053273319010593International Union of CrystallographyA description and evaluation are given of XGANDALF, extended gradient descent algorithm for lattice finding, an algorithm developed for fast and accurate indexing of snapshot diffraction patterns.ENindexingXGANDALFCrystFELmultiple latticesserial crystallographySerial crystallography records still diffraction patterns from single, randomly oriented crystals, then merges data from hundreds or thousands of them to form a complete data set. To process the data, the diffraction patterns must first be indexed, equivalent to determining the orientation of each crystal. A novel automatic indexing algorithm is presented, which in tests usually gives significantly higher indexing rates than alternative programs currently available for this task. The algorithm does not require prior knowledge of the lattice parameters but can make use of that information if provided, and also allows indexing of diffraction patterns generated by several crystals in the beam. Cases with a small number of Bragg spots per pattern appear to particularly benefit from the new approach. The algorithm has been implemented and optimized for fast execution, making it suitable for real-time feedback during serial crystallography experiments. It is implemented in an open-source C++ library and distributed under the LGPLv3 licence. An interface to it has been added to the CrystFEL software suite.text/htmlXGANDALF – extended gradient descent algorithm for lattice findingtext5752019-08-30Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers694704Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement
http://scripts.iucr.org/cgi-bin/paper?ib5077
Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)2] and dicyanomercury(II) [Hg(CN)2]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)2 and Hg(CN)2, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Bučinský, L.Jayatilaka, D.Grabowsky, S.2019-08-12doi:10.1107/S2053273319008027International Union of CrystallographyContributions of different physical effects (thermal smearing, relativity, electron correlation, basis set, environment and/or atomic contributions) to the structure factors of heavy-element compounds are inspected. Relativistic Hirshfeld atom refinement yields an almost perfect agreement with reference geometries in this theoretical pilot study, showing the usefulness of the employed methodology.ENelectron densityrelativistic effectselectron correlationrelativistic Hirshfeld atom refinementquantum crystallographyQuantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)2] and dicyanomercury(II) [Hg(CN)2]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)2 and Hg(CN)2, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.text/htmlRelativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinementtext5752019-08-12Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers7057171920799Anomalous X-ray diffraction from ω nanoparticles in β-Ti(Mo) single crystals
http://scripts.iucr.org/cgi-bin/paper?wo5034
Anomalous X-ray diffraction (AXRD) is a technique which makes use of effects occurring near the energy of an absorption edge of an element present in the studied sample. The intensity of the diffracted radiation exhibits an anomalous decrease when the primary beam energy matches the energy needed to excite an electron from an atomic orbital. The characteristics of this step are sensitive to the concentration of the `anomalous' element and its spatial distribution in the sample. In the present investigation, AXRD was employed to study ω particles in a metastable β titanium alloy Ti–15Mo (in wt%). The experiments were done in an energy range around the Mo K edge at 20.0 keV, allowing investigation of the distribution of Mo in the material, which is rejected from the volume of ω particles during their diffusion-driven growth. This paper deals with diffuse scattering patterns around the (006)β diffraction maximum. It was observed that different regions of the diffuse scattering exhibited different variations of diffracted intensity with the incident photon energy near the absorption edge. Numerical simulations of diffuse scattering patterns as well as of energy dependences of the scattered intensity were performed. It was found that the observed patterns and their dependence on the primary beam energy can be explained by taking into account (a) elastic deformation of the β matrix arising from the presence of slightly misfitting ω particles and (b) the presence of a `cloud' of a higher Mo concentration around ω particles.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Šmilauerová, J.Harcuba, P.Cieslar, M.Janeček, M.Holý, V.2019-08-12doi:10.1107/S2053273319008428International Union of CrystallographyAnomalous X-ray diffraction was used to study the energy dependence of diffuse scattering around the reciprocal-lattice point h = [006]β \equiv [06{\overline 6}3]_\omega of a Ti–15Mo single crystal. The diffuse scattering as well as its energy dependence around an Mo K absorption edge were qualitatively explained by a numerical model of ω particles which elastically deform the surrounding β matrix.ENanomalous X-ray diffractionmetastable β-Ti alloysdiffuse scatteringω phaseAnomalous X-ray diffraction (AXRD) is a technique which makes use of effects occurring near the energy of an absorption edge of an element present in the studied sample. The intensity of the diffracted radiation exhibits an anomalous decrease when the primary beam energy matches the energy needed to excite an electron from an atomic orbital. The characteristics of this step are sensitive to the concentration of the `anomalous' element and its spatial distribution in the sample. In the present investigation, AXRD was employed to study ω particles in a metastable β titanium alloy Ti–15Mo (in wt%). The experiments were done in an energy range around the Mo K edge at 20.0 keV, allowing investigation of the distribution of Mo in the material, which is rejected from the volume of ω particles during their diffusion-driven growth. This paper deals with diffuse scattering patterns around the (006)β diffraction maximum. It was observed that different regions of the diffuse scattering exhibited different variations of diffracted intensity with the incident photon energy near the absorption edge. Numerical simulations of diffuse scattering patterns as well as of energy dependences of the scattered intensity were performed. It was found that the observed patterns and their dependence on the primary beam energy can be explained by taking into account (a) elastic deformation of the β matrix arising from the presence of slightly misfitting ω particles and (b) the presence of a `cloud' of a higher Mo concentration around ω particles.text/htmlAnomalous X-ray diffraction from ω nanoparticles in β-Ti(Mo) single crystalstext5752019-08-12Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers718729Local and global color symmetries of a symmetrical pattern
http://scripts.iucr.org/cgi-bin/paper?eo5096
This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Abila, A.K.De Las Peñas, M.L.A.N.Taganap, E.2019-08-23doi:10.1107/S2053273319008763International Union of CrystallographyGiven a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs, a method is described for arriving at a coloring of {\cal P} which is perfect and transitive under its global symmetry group G and where the coloring of each motif is also perfect and transitive under its own group of symmetries (local symmetries of {\cal P}). The coloring of {\cal P} is coordinated with the property that the symmetry of {\cal P} that is both a global and local symmetry effects the same permutation of the colors of {\cal P} and the corresponding motif, respectively.ENcolor symmetrylocal symmetryglobal symmetryperfect coloringstransitive perfect coloringsThis study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.text/htmlLocal and global color symmetries of a symmetrical patterntext5752019-08-23Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers730745Coordination shells and coordination numbers of the vertex graph of the Ammann–Beenker tiling
http://scripts.iucr.org/cgi-bin/paper?eo5095
The vertex graph of the Ammann–Beenker tiling is a well-known quasiperiodic graph with an eightfold rotational symmetry. The coordination sequence and coordination shells of this graph are studied. It is proved that there exists a limit growth form for the vertex graph of the Ammann–Beenker tiling. This growth form is an explicitly calculated regular octagon. Moreover, an asymptotic formula for the coordination numbers of the vertex graph of the Ammann–Beenker tiling is also proved.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Shutov, A.Maleev, A.2019-08-23doi:10.1107/S2053273319008179International Union of CrystallographyA growth form and an asymptotic formula for the coordination sequence of the vertex graph of the Ammann–Beenker tiling are obtained.ENvertex graph of the Ammann–Beenker tilingcoordination sequencescoordination shellsgrowth formThe vertex graph of the Ammann–Beenker tiling is a well-known quasiperiodic graph with an eightfold rotational symmetry. The coordination sequence and coordination shells of this graph are studied. It is proved that there exists a limit growth form for the vertex graph of the Ammann–Beenker tiling. This growth form is an explicitly calculated regular octagon. Moreover, an asymptotic formula for the coordination numbers of the vertex graph of the Ammann–Beenker tiling is also proved.text/htmlCoordination shells and coordination numbers of the vertex graph of the Ammann–Beenker tilingtext5752019-08-23Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers746757A new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactors
http://scripts.iucr.org/cgi-bin/paper?sc5131
Structural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Hoeher, A.Mergelsberg, S.Borkiewicz, O.J.Dove, P.M.Michel, F.M.2019-08-23doi:10.1107/S2053273319008623International Union of CrystallographyA novel method is introduced for in situ X-ray total scattering experiments. Two examples of the method as applied to non-classical nucleation and crystal growth studies are discussed.ENin situ X-ray total scatteringcrystallizationamorphous calcium phosphateamorphous calcium carbonatepair distribution function analysisStructural investigations of amorphous and nanocrystalline phases forming in solution are historically challenging. Few methods are capable of in situ atomic structural analysis and rigorous control of the system. A mixed-flow reactor (MFR) is used for total X-ray scattering experiments to examine the short- and long-range structure of phases in situ with pair distribution function (PDF) analysis. The adaptable experimental setup enables data collection for a range of different system chemistries, initial supersaturations and residence times. The age of the sample during analysis is controlled by adjusting the flow rate. Faster rates allow for younger samples to be examined, but if flow is too fast not enough data are acquired to average out excess signal noise. Slower flow rates form older samples, but at very slow speeds particles settle and block flow, clogging the system. Proper background collection and subtraction is critical for data optimization. Overall, this MFR method is an ideal scheme for analyzing the in situ structures of phases that form during crystal growth in solution. As a proof of concept, high-resolution total X-ray scattering data of amorphous and crystalline calcium phosphates and amorphous calcium carbonate were collected for PDF analysis.text/htmlA new method for in situ structural investigations of nano-sized amorphous and crystalline materials using mixed-flow reactorstext5752019-08-23Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers758765Using the singular value decomposition to extract 2D correlation functions from scattering patterns
http://scripts.iucr.org/cgi-bin/paper?ib5079
The truncated singular value decomposition (TSVD) is applied to extract the underlying 2D correlation functions from small-angle scattering patterns. The approach is tested by transforming the simulated data of ellipsoidal particles and it is shown that also in the case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, the TSVD is used to analyze the small-angle X-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in the presence of magnetic fields, to verify that this approach can be applied to extract model-free the scattering profiles of anisotropic scatterers from noisy data.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Bender, P.Zákutná, D.Disch, S.Marcano, L.Alba Venero, D.Honecker, D.2019-08-23doi:10.1107/S205327331900891XInternational Union of CrystallographyThe truncated singular value decomposition is applied to extract the underlying 2D correlation functions from small-angle scattering patterns.ENsmall-angle scatteringcorrelation function2D Fourier transformanisotropic nanoparticlessingular value decompositionanisotropic structuresnanoparticlesnoise filteringThe truncated singular value decomposition (TSVD) is applied to extract the underlying 2D correlation functions from small-angle scattering patterns. The approach is tested by transforming the simulated data of ellipsoidal particles and it is shown that also in the case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, the TSVD is used to analyze the small-angle X-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in the presence of magnetic fields, to verify that this approach can be applied to extract model-free the scattering profiles of anisotropic scatterers from noisy data.text/htmlUsing the singular value decomposition to extract 2D correlation functions from scattering patternstext5752019-08-23Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers766771X-ray diffraction in superabsorbing crystals: absorption intrinsic width
http://scripts.iucr.org/cgi-bin/paper?td5061
The several mathematical formulations of X-ray diffraction theory facilitate its understanding and use as a materials characterization technique, since one can opt for the simplest formulation that adequately describes the case being studied. As synchrotrons advance, new techniques are developed and there is a need for simple formulations to describe them. One of these techniques is soft resonant X-ray diffraction, in which the X-rays suffer large attenuation due to absorption. In this work, an expression is derived for the X-ray diffraction profiles of reflections where the linear absorption is far greater than primary extinction; in other words, the crystal is superabsorbing. The case is considered of a parallel plate crystal, for which the diffraction profile of the superabsorbing crystal is computed as a function of crystal size normal to the diffraction planes. For thin crystals or those with negligible absorption, the diffraction profile of a superabsorbing crystal coincides with the result of the kinematical theory. For thick crystals, the absorption intrinsic profile is obtained, described by a Lorentzian function and characterized by the absorption intrinsic width. This absorption intrinsic width is proportional to the linear absorption coefficient and its expression is similar to that for the Darwin width, while the absorption intrinsic profile is a special case of the Laue dynamical theory, and it is similar to the Ornstein–Zernike Lorentzian. The formulation of X-ray diffraction of superabsorbing crystals is simple and provides new perspectives for the soft resonant X-ray diffraction technique.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Lima, A.N.C.Miranda, M.A.R.Sasaki, J.M.2019-08-30doi:10.1107/S2053273319009732International Union of CrystallographyThis article presents an analytical description of the X-ray diffraction peak profile of superabsorbing crystals. For thick crystals, the absorption intrinsic profile is described by a Lorentzian and characterized by an absorption intrinsic width.ENsoft X-ray diffractionsuperabsorbing crystalsabsorption intrinsic widthpeak profileThe several mathematical formulations of X-ray diffraction theory facilitate its understanding and use as a materials characterization technique, since one can opt for the simplest formulation that adequately describes the case being studied. As synchrotrons advance, new techniques are developed and there is a need for simple formulations to describe them. One of these techniques is soft resonant X-ray diffraction, in which the X-rays suffer large attenuation due to absorption. In this work, an expression is derived for the X-ray diffraction profiles of reflections where the linear absorption is far greater than primary extinction; in other words, the crystal is superabsorbing. The case is considered of a parallel plate crystal, for which the diffraction profile of the superabsorbing crystal is computed as a function of crystal size normal to the diffraction planes. For thin crystals or those with negligible absorption, the diffraction profile of a superabsorbing crystal coincides with the result of the kinematical theory. For thick crystals, the absorption intrinsic profile is obtained, described by a Lorentzian function and characterized by the absorption intrinsic width. This absorption intrinsic width is proportional to the linear absorption coefficient and its expression is similar to that for the Darwin width, while the absorption intrinsic profile is a special case of the Laue dynamical theory, and it is similar to the Ornstein–Zernike Lorentzian. The formulation of X-ray diffraction of superabsorbing crystals is simple and provides new perspectives for the soft resonant X-ray diffraction technique.text/htmlX-ray diffraction in superabsorbing crystals: absorption intrinsic widthtext5752019-08-30Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aresearch papers772776The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigenda
http://scripts.iucr.org/cgi-bin/paper?ae5073
Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.Copyright (c) 2019 International Union of Crystallographyurn:issn:2053-2733Cayron, C.2019-08-30doi:10.1107/S2053273319009276International Union of CrystallographyThree equations in Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] are corrected.ENsymmetriesmetric tensorlatticepoint groupAppendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.text/htmlThe transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigendatext5752019-08-30Copyright (c) 2019 International Union of CrystallographyActa Crystallographica Section Aaddenda and errata777777