Acta Crystallographica Section A
http://journals.iucr.org/a/issues/2017/02/00/isscontsbdy.html
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) 2017 International Union of Crystallography2017-02-16International 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 73, Part 2, 2017textweekly62002-01-01T00:00+00:002732017-02-16Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances85urn:issn:2053-2733med@iucr.orgFebruary 20172017-02-16Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2017/02/00/isscontsbdy.html
Still imageA projection-based reformulation of the coincident site lattice Σ for arbitrary bicrystals at finite temperature
http://scripts.iucr.org/cgi-bin/paper?td5041
The coincident site lattice and, specifically, the `Σ value' of a grain boundary are a ubiquitous metric for experimental classification of grain boundaries. However, the mathematical nature of Σ – a pathological function taking values of either an integer or infinity – has been relatively unexplored. This work presents a framework for interpreting Σ as the inverse of a projection defined using the standard L2 inner product over continuous fields that represent lattices. `Pre-mollifiers' are used to introduce thermal regularization in the context of the inner product, and a closed-form analytic result is derived. For all nonzero values of the regularization parameters, the formulation is mathematically smooth and differentiable, providing a tool for computationally determining experimental deviation from measured low-Σ boundaries at finite temperatures. It is verified that accurate Σ values are recovered for sufficiently low Σ boundaries, and that the numerical result either converges towards an integer value or diverges to infinity.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Runnels, B.2017-02-07doi:10.1107/S205327331700122XInternational Union of CrystallographyA continuous-valued formulation of the coincident site lattice Σ is developed based on the L2 inner product, taking into account temperature and arbitrary lattice rotation. Results are computed for face-centered-cubic tilt bicrystals and shown either to converge to the integer-valued Σ or to diverge to infinity.ENgrain boundariescoincident site latticeThe coincident site lattice and, specifically, the `Σ value' of a grain boundary are a ubiquitous metric for experimental classification of grain boundaries. However, the mathematical nature of Σ – a pathological function taking values of either an integer or infinity – has been relatively unexplored. This work presents a framework for interpreting Σ as the inverse of a projection defined using the standard L2 inner product over continuous fields that represent lattices. `Pre-mollifiers' are used to introduce thermal regularization in the context of the inner product, and a closed-form analytic result is derived. For all nonzero values of the regularization parameters, the formulation is mathematically smooth and differentiable, providing a tool for computationally determining experimental deviation from measured low-Σ boundaries at finite temperatures. It is verified that accurate Σ values are recovered for sufficiently low Σ boundaries, and that the numerical result either converges towards an integer value or diverges to infinity.text/htmlA projection-based reformulation of the coincident site lattice Σ for arbitrary bicrystals at finite temperaturetext2732017-02-07Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Asymmetry in serial femtosecond crystallography data
http://scripts.iucr.org/cgi-bin/paper?mq5047
Serial crystallography is an increasingly important approach to protein crystallography that exploits both X-ray free-electron laser (XFEL) and synchrotron radiation. Serial crystallography recovers complete X-ray diffraction data by processing and merging diffraction images from thousands of randomly oriented non-uniform microcrystals, of which all observations are partial Bragg reflections. Random fluctuations in the XFEL pulse energy spectrum, variations in the size and shape of microcrystals, integrating over millions of weak partial observations and instabilities in the XFEL beam position lead to new types of experimental errors. The quality of Bragg intensity estimates deriving from serial crystallography is therefore contingent upon assumptions made while modeling these data. Here it is observed that serial femtosecond crystallography (SFX) Bragg reflections do not follow a unimodal Gaussian distribution and it is recommended that an idealized assumption of single Gaussian peak profiles be relaxed to incorporate apparent asymmetries when processing SFX data. The phenomenon is illustrated by re-analyzing data collected from microcrystals of the Blastochloris viridis photosynthetic reaction center and comparing these intensity observations with conventional synchrotron data. The results show that skewness in the SFX observations captures the essence of the Wilson plot and an empirical treatment is suggested that can help to separate the diffraction Bragg intensity from the background.Copyright (c) 2017 Amit Sharma et al.urn:issn:2053-2733Sharma, A.Johansson, L.Dunevall, E.Wahlgren, W.Neutze, R.Katona, G.2017-01-30doi:10.1107/S2053273316018696International Union of CrystallographyDistribution analysis of intensity observations in serial femtosecond crystallography data processing helps to separate Bragg reflections from the background detector response.ENex-Gaussian distributionserial femtosecond crystallographyBragg reflectionssystematic absencesintensity distributionSerial crystallography is an increasingly important approach to protein crystallography that exploits both X-ray free-electron laser (XFEL) and synchrotron radiation. Serial crystallography recovers complete X-ray diffraction data by processing and merging diffraction images from thousands of randomly oriented non-uniform microcrystals, of which all observations are partial Bragg reflections. Random fluctuations in the XFEL pulse energy spectrum, variations in the size and shape of microcrystals, integrating over millions of weak partial observations and instabilities in the XFEL beam position lead to new types of experimental errors. The quality of Bragg intensity estimates deriving from serial crystallography is therefore contingent upon assumptions made while modeling these data. Here it is observed that serial femtosecond crystallography (SFX) Bragg reflections do not follow a unimodal Gaussian distribution and it is recommended that an idealized assumption of single Gaussian peak profiles be relaxed to incorporate apparent asymmetries when processing SFX data. The phenomenon is illustrated by re-analyzing data collected from microcrystals of the Blastochloris viridis photosynthetic reaction center and comparing these intensity observations with conventional synchrotron data. The results show that skewness in the SFX observations captures the essence of the Wilson plot and an empirical treatment is suggested that can help to separate the diffraction Bragg intensity from the background.text/htmlAsymmetry in serial femtosecond crystallography datatext2732017-01-30Copyright (c) 2017 Amit Sharma et al.Acta Crystallographica Section Aresearch papers00Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to l-alanine, naphthalene and xylitol
http://scripts.iucr.org/cgi-bin/paper?ae5026
In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206–214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of l-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of l-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol−1 K−1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Hoser, A.A.Madsen, A.Ø.2017-01-30doi:10.1107/S2053273316018994International Union of CrystallographyThe performance of a lattice-dynamical model refined against elastic Bragg scattering data is tested on l-alanine, naphthalene and xylitol.ENlattice dynamicsthermodynamicsrefinementBragg scatteringIn the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206–214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of l-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of l-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol−1 K−1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.text/htmlDynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to l-alanine, naphthalene and xylitoltext2732017-01-30Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00A theoretical investigation of orientation relationships and transformation strains in steels
http://scripts.iucr.org/cgi-bin/paper?ae5027
The identification of orientation relationships (ORs) plays a crucial role in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama–Wassermann (NW) and Kurdjumov–Sachs (KS). The defining feature of these and other OR models is the matching of directions and planes in the parent face-centred cubic γ phase to ones in the product body-centred cubic/tetragonal α/α′ phase. In this article a novel method that identifies transformation strains with ORs is introduced and used to develop a new strain-based approach to phase-transformation models in steels. Using this approach, it is shown that the transformation strains that leave a close-packed plane in the γ phase and a close-packed direction within that plane unrotated are precisely those giving rise to the NW and KS ORs when a cubic product phase is considered. Further, it is outlined how, by choosing different pairs of unrotated planes and directions, other common ORs such as the ones by Pitsch and Greninger–Troiano can be derived. One of the advantages of our approach is that it leads to a natural generalization of the NW, KS and other ORs for different ratios of tetragonality r of the product body-centred tetragonal α′ phase. These generalized ORs predict a sharpening of the transformation textures with increasing tetragonality and are thus in qualitative agreement with experiments on steels with varying alloy concentration.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Koumatos, K.Muehlemann, A.2017-02-07doi:10.1107/S2053273316020350International Union of CrystallographyA unified approach to derive transformation strains and orientation-relationship models in steels is presented. This unified approach is used to derive the Nishiyama–Wassermann, Kurdjumov–Sachs and other models, and extend them naturally to the situation of a tetragonal α′ phase.ENorientation relationshipsNishiyama–WassermannKurdjumov–SachsPitschGreninger–TroianoBaininverse Greninger–Troianosteelratio of tetragonalitytransformation strainsf.c.c. to b.c.c. transformationsf.c.c. to b.c.t. transformationsThe identification of orientation relationships (ORs) plays a crucial role in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama–Wassermann (NW) and Kurdjumov–Sachs (KS). The defining feature of these and other OR models is the matching of directions and planes in the parent face-centred cubic γ phase to ones in the product body-centred cubic/tetragonal α/α′ phase. In this article a novel method that identifies transformation strains with ORs is introduced and used to develop a new strain-based approach to phase-transformation models in steels. Using this approach, it is shown that the transformation strains that leave a close-packed plane in the γ phase and a close-packed direction within that plane unrotated are precisely those giving rise to the NW and KS ORs when a cubic product phase is considered. Further, it is outlined how, by choosing different pairs of unrotated planes and directions, other common ORs such as the ones by Pitsch and Greninger–Troiano can be derived. One of the advantages of our approach is that it leads to a natural generalization of the NW, KS and other ORs for different ratios of tetragonality r of the product body-centred tetragonal α′ phase. These generalized ORs predict a sharpening of the transformation textures with increasing tetragonality and are thus in qualitative agreement with experiments on steels with varying alloy concentration.text/htmlA theoretical investigation of orientation relationships and transformation strains in steelstext2732017-02-07Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Hyperbolic crystallography of two-periodic surfaces and associated structures
http://scripts.iucr.org/cgi-bin/paper?kx5056
This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group–subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol {\sf {2223}} and a {\sf {22222}} surface decoration.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Pedersen, M.C.Hyde, S.T.2017-02-07doi:10.1107/S2053273316019112International Union of CrystallographyThe intrinsic, hyperbolic crystallography of the two-periodic, genus-two HCB and SQL surfaces is presented. All discrete groups containing the translations of the Euclidean embeddings of these surfaces are derived and examples of applications are given.ENhyperbolic geometryhyperbolic crystallographyconstant mean curvature surfacesThis paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group–subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol {\sf {2223}} and a {\sf {22222}} surface decoration.text/htmlHyperbolic crystallography of two-periodic surfaces and associated structurestext2732017-02-07Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00B7 as a supergroup of crystal and quasicrystal symmetries
http://scripts.iucr.org/cgi-bin/paper?td5040
In sharp contrast to the generation of a finite group that includes all the 14 types of Bravais lattices as its subgroups [Hosoya (2000). Acta Cryst. A56, 259–263; Hosoya (2002). Acta Cryst. A58, 208], it was proved that a signed permutation group Bk may be interpreted as the supergroup of both crystal and quasicrystal symmetries. Minimal dimension k = 6 is adequate for lattices referred to their three non-coplanar shortest vectors, or for symmetry groups of most quasicrystal types. If one prefers complete, well defined semi-reduced lattice descriptions or needs a dodecagonal group, the B7 supergroup is necessary. All considered matrix groups correspond to isometric transformations in extended k-bases and may be easily derived from B7 and projected onto three-dimensional crystallographic space. Three models of extended bases are proposed: semi-reduced, cyclic and axial. In all cases additional basis vectors are strictly (functionally) related to three original basis vectors.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Stróż, K.2017-02-07doi:10.1107/S2053273316019586International Union of CrystallographyThe practical generation of all Bravais and quasicrystal symmetries from a finite group is described.ENcrystal symmetryquasicrystal symmetrysupergroupsprojectionextended basesIn sharp contrast to the generation of a finite group that includes all the 14 types of Bravais lattices as its subgroups [Hosoya (2000). Acta Cryst. A56, 259–263; Hosoya (2002). Acta Cryst. A58, 208], it was proved that a signed permutation group Bk may be interpreted as the supergroup of both crystal and quasicrystal symmetries. Minimal dimension k = 6 is adequate for lattices referred to their three non-coplanar shortest vectors, or for symmetry groups of most quasicrystal types. If one prefers complete, well defined semi-reduced lattice descriptions or needs a dodecagonal group, the B7 supergroup is necessary. All considered matrix groups correspond to isometric transformations in extended k-bases and may be easily derived from B7 and projected onto three-dimensional crystallographic space. Three models of extended bases are proposed: semi-reduced, cyclic and axial. In all cases additional basis vectors are strictly (functionally) related to three original basis vectors.text/htmlB7 as a supergroup of crystal and quasicrystal symmetriestext2732017-02-07Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00The phase problem for one-dimensional crystals
http://scripts.iucr.org/cgi-bin/paper?sc5101
The phase problem for diffraction amplitudes measured from a one-dimensional crystal is examined. In the absence of any a priori information, the solution to this problem is shown to be unique up to a parameterized, low-dimensional set of solutions. Minimal additional a priori information is expected to render the solution unique. The effects of additional information such as positivity, molecular envelope and helical symmetry on uniqueness are characterized. The results are pertinent to structural studies of polymeric and rod-like biomolecular assemblies that form one-dimensional, rather than three-dimensional, crystals. This shows the potential for ab initio phasing of diffraction data from single such assemblies measured using new X-ray free-electron laser sources. Such an approach would circumvent the complicated inversion of cylindrically averaged diffraction that is necessary in traditional X-ray fibre diffraction analysis.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Millane, R.P.2017-02-16doi:10.1107/S2053273316020386International Union of CrystallographyThe properties of the phase problem for a one-dimensional crystal and implications for imaging single, rod-like molecules are examined.ENphase problemone-dimensional crystalsXFELsThe phase problem for diffraction amplitudes measured from a one-dimensional crystal is examined. In the absence of any a priori information, the solution to this problem is shown to be unique up to a parameterized, low-dimensional set of solutions. Minimal additional a priori information is expected to render the solution unique. The effects of additional information such as positivity, molecular envelope and helical symmetry on uniqueness are characterized. The results are pertinent to structural studies of polymeric and rod-like biomolecular assemblies that form one-dimensional, rather than three-dimensional, crystals. This shows the potential for ab initio phasing of diffraction data from single such assemblies measured using new X-ray free-electron laser sources. Such an approach would circumvent the complicated inversion of cylindrically averaged diffraction that is necessary in traditional X-ray fibre diffraction analysis.text/htmlThe phase problem for one-dimensional crystalstext2732017-02-16Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aresearch papers00Douglas (Doug) Dorset (1942–2016)
http://scripts.iucr.org/cgi-bin/paper?es0425
Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Baugh, L.Disko, M.Lamberti, W.Strohmaier, K.Duax, W.Fryer, J.Hovmöller, S.Zou, X.Marks, L.Nicolopoulos, S.2017-01-30doi:10.1107/S2053273316020210International Union of CrystallographyObituary for Douglas (Doug) DorsetENobituaryelectron crystallographytext/htmlDouglas (Doug) Dorset (1942–2016)text2732017-01-30Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Aobituaries00Report of the Executive Committee for 2015
http://scripts.iucr.org/cgi-bin/paper?es0419
The report of the Executive Committee for 2015 is presented.Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Dacombe, M.2017-02-13doi:10.1107/S2053273316011128International Union of CrystallographyThe report of the Executive Committee for 2015 is presented.ENInternational Union of CrystallographyExecutive CommitteeThe report of the Executive Committee for 2015 is presented.text/htmlReport of the Executive Committee for 2015text2732017-02-13Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Ainternational union of crystallography00Crystallography: A Very Short Introduction. By A. M. Glazer. Oxford University Press, 2016. Pp. 168. Price GBP 7.99. ISBN 9780198717591.
http://scripts.iucr.org/cgi-bin/paper?xo0056
Copyright (c) 2017 International Union of Crystallographyurn:issn:2053-2733Lecomte, C.2017-01-30doi:10.1107/S2053273316018829International Union of CrystallographyENbook reviewcrystallographytext/htmlCrystallography: A Very Short Introduction. By A. M. Glazer. Oxford University Press, 2016. Pp. 168. Price GBP 7.99. ISBN 9780198717591.text2732017-01-30Copyright (c) 2017 International Union of CrystallographyActa Crystallographica Section Abook reviews00