http://journals.iucr.org/a/issues/2012/02/00/isscontsbdy.html Acta Crystallographica Section A: Foundations of Crystallography 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 Copyright (c) 2012 International Union of Crystallography 2012-03-01 International Union of Crystallography International Union of Crystallography http://journals.iucr.org urn:issn:0108-7673 Acta Crystallographica Section A: Foundations of Crystallography 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/html Acta Crystallographica Section A: Foundations of Crystallography, Volume 68, Part 2, 2012 text yearly 6 2002-01-01T00:00+00:00 2 68 2012-03-01 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography 167 urn:issn:0108-7673 med@iucr.org March 2012 2012-03-01 http://journals.iucr.org/logos/rss10a.gif http://journals.iucr.org/a/issues/2012/02/00/isscontsbdy.html Still image http://scripts.iucr.org/cgi-bin/paper?wl5154 An extension of the X-ray extended-range technique is described for measuring X-ray mass attenuation coefficients by introducing absolute measurement of a number of foils – the multiple independent foil technique. Illustrating the technique with the results of measurements for gold in the 38–50 keV energy range, it is shown that its use enables selection of the most uniform and well defined of available foils, leading to more accurate measurements; it allows one to test the consistency of independently measured absolute values of the mass attenuation coefficient with those obtained by the thickness transfer method; and it tests the linearity of the response of the counter and counting chain throughout the range of X-ray intensities encountered in a given experiment. In light of the results for gold, the strategy to be ideally employed in measuring absolute X-ray mass attenuation coefficients, X-ray absorption fine structure and related quantities is discussed. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Chantler, C.T. Islam, M.T. Rae, N.A. Tran, C.Q. Glover, J.L. Barnea, Z. 2012-01-05 doi:10.1107/S0108767311044990 International Union of Crystallography A new method – the multiple independent foil technique – provides data consistency tests and extends the X-ray extended-range technique for measuring X-ray mass attenuation coefficients and X-ray absorption spectroscopy. EN gold XERT high-Z materials An extension of the X-ray extended-range technique is described for measuring X-ray mass attenuation coefficients by introducing absolute measurement of a number of foils – the multiple independent foil technique. Illustrating the technique with the results of measurements for gold in the 38–50 keV energy range, it is shown that its use enables selection of the most uniform and well defined of available foils, leading to more accurate measurements; it allows one to test the consistency of independently measured absolute values of the mass attenuation coefficient with those obtained by the thickness transfer method; and it tests the linearity of the response of the counter and counting chain throughout the range of X-ray intensities encountered in a given experiment. In light of the results for gold, the strategy to be ideally employed in measuring absolute X-ray mass attenuation coefficients, X-ray absorption fine structure and related quantities is discussed. text/html New consistency tests for high-accuracy measurements of X-ray mass attenuation coefficients by the X-ray extended-range technique text 2 68 2012-01-05 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?sc5045 For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average Rwp over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Kerman, S. Campbell, B.J. Satyavarapu, K.K. Stokes, H.T. Perselli, F. Evans, J.S.O. 2012-01-05 doi:10.1107/S0108767311046241 International Union of Crystallography A structural parameter set consisting of group-theoretically derived symmetry modes facilitates an unbiased determination of a displacively distorted structure. The space-group symmetry is identified from the active symmetry modes rather than being assumed. EN symmetry-mode analysis representational analysis distortions tungsten oxide structure determination from powder data For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average Rwp over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present. text/html The superstructure determination of displacive distortions via symmetry-mode analysis text 2 68 2012-01-05 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?dm5019 Three decades after their discovery, the unique long-range structure of quasicrystals still poses a perplexing puzzle. The fact that some ancient Islamic patterns share similar quasi-periodic symmetries has prompted several scientists to investigate their underlying geometry and construction methods. However, available structural models depend heavily on local rules and hence they were unable to explain the global long-range order of Islamic quasi-periodic patterns. This paper shows that ancient designers, using simple consecutive geometry, have resolved the complicated long-range principles of quasi-periodic formations. Derived from these principles, a global multi-level structural model is presented that is able to describe the global long-range translational and orientational order of quasi-periodic formations. The proposed model suggests that the position of building units, locally and globally, is defined by one framework, and not tiled based on local rules (matching, overlapping or subdividing). In this way, quasi-periodic formations can grow rapidly ad infinitum without the need for any defects or mismatches. The proposed model, which presents a novel approach to the study of quasi-periodic symmetries, will hopefully provide a deeper understanding of the structure of quasicrystals at an atomic scale, allowing scientists to achieve improved control over their composition and structure. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Al Ajlouni, R.A. 2012-01-05 doi:10.1107/S010876731104774X International Union of Crystallography The first global structural model for describing the long-range translational and orientational order of quasi-crystalline formations in Islamic architecture is presented. It is shown that ancient designers, using simple consecutive geometry, have resolved the complicated long-range principles of quasi-periodic formations. EN quasi-periodic geometry Islamic architecture long-range order global structural models Three decades after their discovery, the unique long-range structure of quasicrystals still poses a perplexing puzzle. The fact that some ancient Islamic patterns share similar quasi-periodic symmetries has prompted several scientists to investigate their underlying geometry and construction methods. However, available structural models depend heavily on local rules and hence they were unable to explain the global long-range order of Islamic quasi-periodic patterns. This paper shows that ancient designers, using simple consecutive geometry, have resolved the complicated long-range principles of quasi-periodic formations. Derived from these principles, a global multi-level structural model is presented that is able to describe the global long-range translational and orientational order of quasi-periodic formations. The proposed model suggests that the position of building units, locally and globally, is defined by one framework, and not tiled based on local rules (matching, overlapping or subdividing). In this way, quasi-periodic formations can grow rapidly ad infinitum without the need for any defects or mismatches. The proposed model, which presents a novel approach to the study of quasi-periodic symmetries, will hopefully provide a deeper understanding of the structure of quasicrystals at an atomic scale, allowing scientists to achieve improved control over their composition and structure. text/html The global long-range order of quasi-periodic patterns in Islamic architecture text 2 68 2012-01-05 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?eo5013 Special types of number-theoretic relations, termed multiplicative congruential generators (MCGs), exhibit an intrinsic sublattice structure. This has considerable implications within the crystallographic realm, namely for the coordinate description of crystal structures for which MCGs allow for a concise way of encoding the numerical structural information. Thus, a conceptual framework is established, with some focus on layered superstructures, which proposes the use of MCGs as a tool for the quantitative description of crystal structures. The multiplicative congruential method eventually affords an algorithmic generation of three-dimensional crystal structures with a near-uniform distribution of atoms, whereas a linearization procedure facilitates their combinatorial enumeration and classification. The outlook for homometric structures and dual-space crystallography is given. Some generalizations and extensions are formulated in addition, revealing the connections of MCGs with geometric algebra, discrete dynamical systems (iterative maps), as well as certain quasicrystal approximants. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Hornfeck, W. 2012-01-12 doi:10.1107/S0108767311049853 International Union of Crystallography Certain number-theoretic relations, known as multiplicative congruential generators, are developed into quantitative crystal structure descriptors, facilitating a linearization procedure that eventually allows for a concise, fully reconstructable representation of structural information. Potential applications are related to the computational storage, retrieval and analysis of crystal structures, their algorithmic generation in the first place, and their combinatorial enumeration and classification. EN multiplicative congruential generators crystal structure descriptors algorithmic structure generation permutation structures combinatorial crystallography Special types of number-theoretic relations, termed multiplicative congruential generators (MCGs), exhibit an intrinsic sublattice structure. This has considerable implications within the crystallographic realm, namely for the coordinate description of crystal structures for which MCGs allow for a concise way of encoding the numerical structural information. Thus, a conceptual framework is established, with some focus on layered superstructures, which proposes the use of MCGs as a tool for the quantitative description of crystal structures. The multiplicative congruential method eventually affords an algorithmic generation of three-dimensional crystal structures with a near-uniform distribution of atoms, whereas a linearization procedure facilitates their combinatorial enumeration and classification. The outlook for homometric structures and dual-space crystallography is given. Some generalizations and extensions are formulated in addition, revealing the connections of MCGs with geometric algebra, discrete dynamical systems (iterative maps), as well as certain quasicrystal approximants. text/html Quantitative crystal structure descriptors from multiplicative congruential generators text 2 68 2012-01-12 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?wl5155 This work presents a theoretical analysis of image formation in a scanning transmission electron microscope equipped with electron detectors in a plane conjugate to the specimen. This optical geometry encompasses both the three-dimensional imaging technique of scanning confocal electron microscopy (SCEM) and a recently developed atomic resolution imaging technique coined real-space scanning transmission electron microscopy (R-STEM). Image formation in this geometry is considered from the viewpoints of both wave optics and geometric optics, and the validity of the latter is analysed by means of Wigner distributions. Relevant conditions for the validity of a geometric interpretation of image formation are provided. For R-STEM, where a large detector is used, it is demonstrated that a geometric optics description of image formation provides an accurate approximation to wave optics, and that this description offers distinct advantages for interpretation and numerical implementation. The resulting description of R-STEM is also demonstrated to be in good agreement with experiment. For SCEM, it is emphasized that a geometric optics description of image formation is valid provided that higher-order aberrations can be ignored and the detector size is large enough to average out diffraction from the angle-limiting aperture. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Dwyer, C. Lazar, S. Chang, L.Y. Etheridge, J. 2012-01-12 doi:10.1107/S0108767311051592 International Union of Crystallography The use of object-conjugate detectors in STEM encompasses the three-dimensional imaging technique of SCEM and the recently developed atomic resolution technique of R-STEM. Image formation in this optical geometry is analysed using geometric optics and wave optics, and the relationship between these theories is examined using Wigner distributions. It is shown that geometric optics accurately describes R-STEM and is also applicable to SCEM in a restricted sense. EN STEM SCEM R-STEM geometric optics limit Wigner distribution This work presents a theoretical analysis of image formation in a scanning transmission electron microscope equipped with electron detectors in a plane conjugate to the specimen. This optical geometry encompasses both the three-dimensional imaging technique of scanning confocal electron microscopy (SCEM) and a recently developed atomic resolution imaging technique coined real-space scanning transmission electron microscopy (R-STEM). Image formation in this geometry is considered from the viewpoints of both wave optics and geometric optics, and the validity of the latter is analysed by means of Wigner distributions. Relevant conditions for the validity of a geometric interpretation of image formation are provided. For R-STEM, where a large detector is used, it is demonstrated that a geometric optics description of image formation provides an accurate approximation to wave optics, and that this description offers distinct advantages for interpretation and numerical implementation. The resulting description of R-STEM is also demonstrated to be in good agreement with experiment. For SCEM, it is emphasized that a geometric optics description of image formation is valid provided that higher-order aberrations can be ignored and the detector size is large enough to average out diffraction from the angle-limiting aperture. text/html Image formation in the scanning transmission electron microscope using object-conjugate detectors text 2 68 2012-01-12 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?pc5005 Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210–218; Giacovazzo et al. (2011). Acta Cryst. A67, 368–382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Altomare, A. Cuocci, C. Giacovazzo, C. Moliterni, A. Rizzi, R. 2012-01-25 doi:10.1107/S0108767311053281 International Union of Crystallography The covariance between two points of an electron-density map has been calculated, no matter the correlation between the model and target structures. EN electron-density maps covariance correlation Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210–218; Giacovazzo et al. (2011). Acta Cryst. A67, 368–382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution. text/html Covariance and correlation estimation in electron-density maps text 2 68 2012-01-25 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?pc5006 This article quantitatively reconciles crystallographic and mechanics approaches to lattice refinement as part of X-ray diffraction procedures. The equivalence between the refinement based on unit-cell parameters to that based on a lattice deformation tensor is established from a fixed reference configuration. Justification for the small strain assumption, commonly employed in X-ray diffraction based stress analysis, is also derived. It is shown that relations based on infinitesimal strains are correct to within an error of quadratic order in strain. This error may be important to consider for high-precision or high-strain experiments. It is hoped that these results are of use for facilitating communication and collaboration between crystallography and experimental mechanics communities, for studies where X-ray diffraction data are the fundamental measurement. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Edmiston, J.K. Bernier, J.V. Barton, N.R. Johnson, G.C. 2012-01-27 doi:10.1107/S010876731105598X International Union of Crystallography This article quantitatively reconciles crystallographic and mechanics approaches to lattice refinement as part of X-ray diffraction procedures. It also derives finite deformation relations of reciprocal-lattice vectors, and demonstrates infinitesimal strain descriptions, commonly employed in stress analysis, to be correct with an error at quadratic order in strain. This error may be important to consider for high-precision or high-strain studies. EN finite strain lattice refinement elastic deformation This article quantitatively reconciles crystallographic and mechanics approaches to lattice refinement as part of X-ray diffraction procedures. The equivalence between the refinement based on unit-cell parameters to that based on a lattice deformation tensor is established from a fixed reference configuration. Justification for the small strain assumption, commonly employed in X-ray diffraction based stress analysis, is also derived. It is shown that relations based on infinitesimal strains are correct to within an error of quadratic order in strain. This error may be important to consider for high-precision or high-strain experiments. It is hoped that these results are of use for facilitating communication and collaboration between crystallography and experimental mechanics communities, for studies where X-ray diffraction data are the fundamental measurement. text/html Lattice refinement strategies text 2 68 2012-01-27 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography research papers 0 0 http://scripts.iucr.org/cgi-bin/paper?sc5047 In crystallography, a centred conventional lattice unit cell has its corresponding reduced primitive unit cell. This study presents the frequency distribution of the reduced unit cells of all centred lattice entries of the Protein Data Bank (as of 23 August 2011) in four unit-cell-dimension-based groups and seven interaxial-angle-based subgroups. This frequency distribution is an added layer of support during space-group assignment in new crystals. In addition, some interesting patterns of distribution are discussed as well as how some reduced unit cells could be wrongly accepted as primitive lattices in a different crystal system. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Swaminathan, K. 2012-01-12 doi:10.1107/S0108767311052263 International Union of Crystallography This study presents the frequency distribution of the reduced unit cells of all centred lattice entries of the Protein Data Bank in four unit-cell-dimension-based groups and seven interaxial-angle-based subgroups. EN crystal conventional unit cell reduced unit cell centred lattice space group frequency distribution In crystallography, a centred conventional lattice unit cell has its corresponding reduced primitive unit cell. This study presents the frequency distribution of the reduced unit cells of all centred lattice entries of the Protein Data Bank (as of 23 August 2011) in four unit-cell-dimension-based groups and seven interaxial-angle-based subgroups. This frequency distribution is an added layer of support during space-group assignment in new crystals. In addition, some interesting patterns of distribution are discussed as well as how some reduced unit cells could be wrongly accepted as primitive lattices in a different crystal system. text/html Frequency distribution of the reduced unit cells of centred lattices from the Protein Data Bank text 2 68 2012-01-12 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography short communications 0 0 http://scripts.iucr.org/cgi-bin/paper?wx5009 A new Fourier cycling phasing method is proposed based on the mathematical principle of the global minimization. In reciprocal space, the Fourier coefficient is of a mixed form of the normalized structure factors (2E_{\rm o}^2 − E_{\rm c}^2)Ec, while in direct space the Fourier map is modified with a peak-picking procedure. This method does not use any preliminary information and does not rely on any critical parameter; it can start with either randomly assigned phases or fixed phases (all zeros). This method performs significantly better than the commonly used forms of Fourier cycling. Copyright (c) 2012 International Union of Crystallography urn:issn:0108-7673 Feng, J. 2012-01-12 doi:10.1107/S0108767311052561 International Union of Crystallography An iterative phase solution based on the global minimization is proposed. EN phase problem Fourier cycling global minimization iterative phase solution A new Fourier cycling phasing method is proposed based on the mathematical principle of the global minimization. In reciprocal space, the Fourier coefficient is of a mixed form of the normalized structure factors (2E_{\rm o}^2 − E_{\rm c}^2)Ec, while in direct space the Fourier map is modified with a peak-picking procedure. This method does not use any preliminary information and does not rely on any critical parameter; it can start with either randomly assigned phases or fixed phases (all zeros). This method performs significantly better than the commonly used forms of Fourier cycling. text/html A novel iterative solution to the phase problem text 2 68 2012-01-12 Copyright (c) 2012 International Union of Crystallography Acta Crystallographica Section A: Foundations of Crystallography short communications 0 0