Acta Crystallographica Section A
http://journals.iucr.org/a/issues/2015/05/00/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) 2015 International Union of Crystallography2015-08-27International 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 71, Part 5, 2015textyearly62002-01-01T00:00+00:005712015-08-27Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section A: Foundations and Advances473urn:issn:2053-2733med@iucr.orgAugust 20152015-08-27Acta Crystallographica Section Ahttp://journals.iucr.org/logos/rss10a.gif
http://journals.iucr.org/a/issues/2015/05/00/isscontsbdy.html
Still imageInterpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens
http://scripts.iucr.org/cgi-bin/paper?ib5033
The interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is examined. It is found that in general there are odd symmetries in experimental electron nanodiffraction patterns. Using simulation, it is demonstrated that this effect can be attributed to dynamical scattering, rather than other divergences from the ideal experimental conditions such as probe-forming lens aberrations and camera noise. The departure of opposing diffracted intensities from Friedel's law in the phase grating formalism is calculated using a general structure factor for disordered materials. On the basis of this, a simple correction procedure is suggested to recover the kinematical angular symmetries, and thus readily interpretable information that reflects the symmetries of the original projected object. This correction is numerically tested using both the phase object and multislice calculations, and is demonstrated to fully recover all the kinematical diffracted symmetries from a simulated atomic model of a metallic glass.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Liu, A.C.Y.Lumpkin, G.R.Petersen, T.C.Etheridge, J.Bourgeois, L.2015-07-09doi:10.1107/S2053273315011845International Union of CrystallographyThe interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is discussed. It is demonstrated that dynamical scattering decreases the angular symmetry of the diffraction pattern from that obtained in the kinematical approximation, and that this effect dominates over other experimental parameters such as probe-forming lens aberrations and camera noise. The decrease in angular symmetry of the diffraction pattern is demonstrated using the phase grating and multislice formalisms. A method is demonstrated whereby the dynamical data can be corrected to recover the kinematical result.ENamorphous materialselectron nanodiffractionshort-range orderscanning transmission electon microscopyFriedel symmetryThe interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is examined. It is found that in general there are odd symmetries in experimental electron nanodiffraction patterns. Using simulation, it is demonstrated that this effect can be attributed to dynamical scattering, rather than other divergences from the ideal experimental conditions such as probe-forming lens aberrations and camera noise. The departure of opposing diffracted intensities from Friedel's law in the phase grating formalism is calculated using a general structure factor for disordered materials. On the basis of this, a simple correction procedure is suggested to recover the kinematical angular symmetries, and thus readily interpretable information that reflects the symmetries of the original projected object. This correction is numerically tested using both the phase object and multislice calculations, and is demonstrated to fully recover all the kinematical diffracted symmetries from a simulated atomic model of a metallic glass.text/htmlInterpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimenstext5712015-07-09Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers473482Solution of the phase problem at non-atomic resolution by the phantom derivative method
http://scripts.iucr.org/cgi-bin/paper?mq5035
For a given unknown crystal structure (the target), n random structures, arbitrarily designed without any care for their chemical consistency and usually uncorrelated with the target, are sheltered in the same unit cell as the target structure and submitted to the same space-group symmetry. (These are called ancil structures.) The composite structures, whose electron densities are the sum of the target and of the ancil electron densities, are denoted derivatives. No observed diffraction amplitudes are available for them: in order to emphasize their unreal nature, the term phantom is added. The paper describes the theoretical basis by which the phantom derivative method may be used to phase the target structure. It may be guessed that 100–300 ancil structures may be sufficient for phasing a target structure, so that the phasing technique may be denoted as the multiple phantom derivative method. Ancil phases and amplitudes may be initially combined with observed target magnitudes to estimate amplitudes and phases of the corresponding phantom derivative. From them suitable algorithms allow one to obtain poor target phase estimates, which are often improved by combining the indications arising from each derivative. Probabilistic criteria are described to recognize the most reliable target phase estimates. The method is cyclic: the target phase estimates just obtained are used to improve amplitudes and phases of each derivative, which, in their turn, are employed to provide better target phase estimates. The method is a fully ab initio method, because it needs only the experimental data of the target structure. The term derivative is maintained with reference to SIR–MIR (single isomorphous replacement–multiple isomorphous replacement) techniques, even if its meaning is different: therefore the reader should think of the phantom derivative method more as a new method than as a variant of SIR–MIR techniques. The differences are much greater than the analogies. The paper also describes how phantom derivatives may be used for improving structure models obtained via other ab initio or non-ab initio techniques. The method is expected to be insensitive to the structural complexity of the target and to the target experimental data resolution, provided it is better than 4–6 Å.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Giacovazzo, C.2015-08-28doi:10.1107/S2053273315013856International Union of CrystallographyThe method of multiple phantom derivatives allows one to solve ab initio and at non-atomic resolution the crystallographic phase problem for a target structure by using random structures with the same unit cell and space-group symmetry: the composite structures, called derivatives, are devoid of experimental data. The method is also suitable for extending and refining phases obtained by other techniques.ENab initio solutionphasing methodsderivative structureFor a given unknown crystal structure (the target), n random structures, arbitrarily designed without any care for their chemical consistency and usually uncorrelated with the target, are sheltered in the same unit cell as the target structure and submitted to the same space-group symmetry. (These are called ancil structures.) The composite structures, whose electron densities are the sum of the target and of the ancil electron densities, are denoted derivatives. No observed diffraction amplitudes are available for them: in order to emphasize their unreal nature, the term phantom is added. The paper describes the theoretical basis by which the phantom derivative method may be used to phase the target structure. It may be guessed that 100–300 ancil structures may be sufficient for phasing a target structure, so that the phasing technique may be denoted as the multiple phantom derivative method. Ancil phases and amplitudes may be initially combined with observed target magnitudes to estimate amplitudes and phases of the corresponding phantom derivative. From them suitable algorithms allow one to obtain poor target phase estimates, which are often improved by combining the indications arising from each derivative. Probabilistic criteria are described to recognize the most reliable target phase estimates. The method is cyclic: the target phase estimates just obtained are used to improve amplitudes and phases of each derivative, which, in their turn, are employed to provide better target phase estimates. The method is a fully ab initio method, because it needs only the experimental data of the target structure. The term derivative is maintained with reference to SIR–MIR (single isomorphous replacement–multiple isomorphous replacement) techniques, even if its meaning is different: therefore the reader should think of the phantom derivative method more as a new method than as a variant of SIR–MIR techniques. The differences are much greater than the analogies. The paper also describes how phantom derivatives may be used for improving structure models obtained via other ab initio or non-ab initio techniques. The method is expected to be insensitive to the structural complexity of the target and to the target experimental data resolution, provided it is better than 4–6 Å.text/htmlSolution of the phase problem at non-atomic resolution by the phantom derivative methodtext5712015-08-28Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers483512Theoretical analysis of reflection high-energy electron diffraction (RHEED) and reflection high-energy positron diffraction (RHEPD) intensity oscillations expected for the perfect layer-by-layer growth
http://scripts.iucr.org/cgi-bin/paper?lk5005
Predictions from two theoretical models, allowing one to determine the phase of intensity oscillations, are compared for reflected beams of electrons and positrons. Namely, results of the precise dynamical calculations are compared with results obtained using a simplified approach. Within the simplified model, changes in the specularly reflected beam intensity, expected to occur during the deposition of new atoms, are described with the help of interfering waves and the effect of refraction, and respective approximate analytical formulas are employed to determine the phase of the oscillations. It is found that the simplified model is very useful for understanding the physics ruling the appearance of intensity oscillations. However, it seems that the model with the realistic potential is more suitable for carrying out interpretations of experimental data.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Mitura, Z.2015-07-09doi:10.1107/S2053273315010608International Union of CrystallographyThe importance of the phenomenon of the refraction of waves in the behaviour of the phase shift of intensity oscillations for RHEED and RHEPD is discussed using a simple model of the interference of two waves along with the precise dynamical diffraction theory.ENRHEEDRHEPDdynamical diffraction theorynanolayersPredictions from two theoretical models, allowing one to determine the phase of intensity oscillations, are compared for reflected beams of electrons and positrons. Namely, results of the precise dynamical calculations are compared with results obtained using a simplified approach. Within the simplified model, changes in the specularly reflected beam intensity, expected to occur during the deposition of new atoms, are described with the help of interfering waves and the effect of refraction, and respective approximate analytical formulas are employed to determine the phase of the oscillations. It is found that the simplified model is very useful for understanding the physics ruling the appearance of intensity oscillations. However, it seems that the model with the realistic potential is more suitable for carrying out interpretations of experimental data.text/htmlTheoretical analysis of reflection high-energy electron diffraction (RHEED) and reflection high-energy positron diffraction (RHEPD) intensity oscillations expected for the perfect layer-by-layer growthtext5712015-07-09Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers513518A study of X-ray multiple diffraction by means of section topography
http://scripts.iucr.org/cgi-bin/paper?lk5006
The results of theoretical and experimental study are presented for the question of how the X-ray multiple diffraction in a silicon single crystal influences the interference fringes of section topography for the 400 reflection in the Laue case. Two different cases of multiple diffraction are discovered for zero and very small values of the azimuthal angle for the sample in the form of a plate with the surface normal to the 001 direction. The cases are seen on the same topogram without rotation of the crystal. Accurate computer simulations of the section topogram for the case of X-ray multiple diffraction are performed for the first time. It is shown that the structure of interference fringes on the section topogram in the region of multiple diffraction becomes more complicated. It has a very sharp dependence on the azimuthal angle. The experiment is carried out using a laboratory source under conditions of low resolution over the azimuthal angle. Nevertheless, the characteristic inclination of the interference fringes on the tails of the multiple diffraction region is easily seen. This phenomenon corresponds completely to the computer simulations.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Kohn, V.G.Smirnova, I.A.2015-07-09doi:10.1107/S2053273315012176International Union of CrystallographyThe theoretical and experimental study of two different cases of X-ray multiple diffraction by means of section topography for 400 diffraction in a silicon single crystal is described. Accurate computer simulations of the section topogram for the case of X-ray multiple diffraction are performed for the first time. The experiment is carried out using a laboratory source under conditions of low resolution over the azimuthal angle.ENX-ray diffractionsection topographymultiple diffractioncomputer simulationslaboratory studyThe results of theoretical and experimental study are presented for the question of how the X-ray multiple diffraction in a silicon single crystal influences the interference fringes of section topography for the 400 reflection in the Laue case. Two different cases of multiple diffraction are discovered for zero and very small values of the azimuthal angle for the sample in the form of a plate with the surface normal to the 001 direction. The cases are seen on the same topogram without rotation of the crystal. Accurate computer simulations of the section topogram for the case of X-ray multiple diffraction are performed for the first time. It is shown that the structure of interference fringes on the section topogram in the region of multiple diffraction becomes more complicated. It has a very sharp dependence on the azimuthal angle. The experiment is carried out using a laboratory source under conditions of low resolution over the azimuthal angle. Nevertheless, the characteristic inclination of the interference fringes on the tails of the multiple diffraction region is easily seen. This phenomenon corresponds completely to the computer simulations.text/htmlA study of X-ray multiple diffraction by means of section topographytext5712015-07-09Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers519525Image definition evaluation functions for X-ray crystallography: a new perspective on the phase problem
http://scripts.iucr.org/cgi-bin/paper?mq5033
The core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribution by straightforward Fourier synthesis is usually hindered due to the well known phase problem and the finite resolution of diffraction data. In analogy with optical imaging systems, the reconstructed electron-density map may be regarded as the image of the real electron-density distribution in crystals. Inspired by image definition evaluation functions applied in the auto-focusing process, two evaluation functions are proposed for the reconstructed electron-density images. One of them is based on the atomicity of the electron-density distribution and properties of Fourier synthesis. Tests were performed on synthetic data of known structures, and it was found that this evaluation function can distinguish the correctly reconstructed electron-density image from wrong ones when diffraction data of atomic resolution are available. An algorithm was established based on this evaluation function and applied in reconstructing the electron-density image from the synthetic data of known structures. The other evaluation function, which is based on the positivity of electron density and constrained power spectrum entropy maximization, was designed for cases where only diffraction data of rather limited resolution are available. Tests on the synthetic data indicate that this evaluation function may identify the correct phase set even for a data set with resolution as low as 3.5 Å. Though no algorithm for structure solution has been figured out based on the latter function, the results presented here provide a new perspective on the phase problem.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Li, H.He, M.Zhang, Z.2015-07-22doi:10.1107/S2053273315012103International Union of CrystallographyThe phase problem of X-ray crystallography is surveyed from a perspective of image definition evaluation functions. The reconstructed electron-density maps are taken as the images of the real electron distribution in crystals, and two image definition evaluation functions are proposed to identify the correct phase set.ENphase problemimage definition evaluation functionspower spectrum entropyiteration algorithmscharge-density mapsThe core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribution by straightforward Fourier synthesis is usually hindered due to the well known phase problem and the finite resolution of diffraction data. In analogy with optical imaging systems, the reconstructed electron-density map may be regarded as the image of the real electron-density distribution in crystals. Inspired by image definition evaluation functions applied in the auto-focusing process, two evaluation functions are proposed for the reconstructed electron-density images. One of them is based on the atomicity of the electron-density distribution and properties of Fourier synthesis. Tests were performed on synthetic data of known structures, and it was found that this evaluation function can distinguish the correctly reconstructed electron-density image from wrong ones when diffraction data of atomic resolution are available. An algorithm was established based on this evaluation function and applied in reconstructing the electron-density image from the synthetic data of known structures. The other evaluation function, which is based on the positivity of electron density and constrained power spectrum entropy maximization, was designed for cases where only diffraction data of rather limited resolution are available. Tests on the synthetic data indicate that this evaluation function may identify the correct phase set even for a data set with resolution as low as 3.5 Å. Though no algorithm for structure solution has been figured out based on the latter function, the results presented here provide a new perspective on the phase problem.text/htmlImage definition evaluation functions for X-ray crystallography: a new perspective on the phase problemtext5712015-07-22Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers526533Neutron interferometric measurement and calculations of a phase shift induced by Laue transmission
http://scripts.iucr.org/cgi-bin/paper?vk5004
This study investigates the phase shift induced by Laue transmission in a perfect Si crystal blade in unprecedented detail. This `Laue phase' was measured at two wavelengths in the vicinity of the Bragg condition within a neutron interferometer. In particular, the sensitivity of the Laue phase to the alignment of the monochromator and interferometer (rocking angle) and beam divergence has been verified. However, the influence of fundamental quantities, such as the neutron–electron scattering length, on the Laue phase is rather small. The fascinating steep phase slope of 5.5° [(220) Bragg peak] and 11.5° [(440) Bragg peak] per 0.001 arcsec deviation from the Bragg angle has been achieved. The results are analysed using an upgraded simulation tool.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Potocar, T.Zawisky, M.Lemmel, H.Springer, J.Suda, M.2015-07-22doi:10.1107/S205327331501205XInternational Union of CrystallographyIn this study, the phase shift induced by Laue transmission in a perfect Si crystal blade is investigated. This `Laue phase', with a fascinating steep slope, was measured in the vicinity of the Bragg condition within a neutron interferometer.ENNeutron interferometryperfect crystal interferometerlarge-area interferometerdynamical diffractionbeam deflectionneutron–electron scattering lengthsThis study investigates the phase shift induced by Laue transmission in a perfect Si crystal blade in unprecedented detail. This `Laue phase' was measured at two wavelengths in the vicinity of the Bragg condition within a neutron interferometer. In particular, the sensitivity of the Laue phase to the alignment of the monochromator and interferometer (rocking angle) and beam divergence has been verified. However, the influence of fundamental quantities, such as the neutron–electron scattering length, on the Laue phase is rather small. The fascinating steep phase slope of 5.5° [(220) Bragg peak] and 11.5° [(440) Bragg peak] per 0.001 arcsec deviation from the Bragg angle has been achieved. The results are analysed using an upgraded simulation tool.text/htmlNeutron interferometric measurement and calculations of a phase shift induced by Laue transmissiontext5712015-07-22Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers534541Three new crystal structures in the Na–Pb system: solving structures without additional experimental input
http://scripts.iucr.org/cgi-bin/paper?ae5007
The structures of three Na–Pb compounds, γ, δ and δ′, have remained incompletely solved for nearly 60 years. The space group, lattice parameters and positions of the Pb atoms of these three structures have been determined, but the positions of the Na atoms are still unknown. In this work, the First-Principles Assisted Structure Solution (FPASS) method [Meredig & Wolverton (2013). Nat. Mater. 12, 123–127] has been used to complete the description of these three structures using only experimental information available from the literature as input. The paper also discusses the relative advantages of constrained crystal structure prediction tools, like FPASS, in comparison to conventional crystal structure prediction methods in reference to their abilities to complete the solution of other unsolved structures.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Ward, L.Michel, K.Wolverton, C.2015-08-28doi:10.1107/S2053273315012516International Union of CrystallographyThree compounds in the Na–Pb binary system are solved using the First-Principles Assisted Structure Solution method.ENNa–Pb binarystructure solutionFPASSThe structures of three Na–Pb compounds, γ, δ and δ′, have remained incompletely solved for nearly 60 years. The space group, lattice parameters and positions of the Pb atoms of these three structures have been determined, but the positions of the Na atoms are still unknown. In this work, the First-Principles Assisted Structure Solution (FPASS) method [Meredig & Wolverton (2013). Nat. Mater. 12, 123–127] has been used to complete the description of these three structures using only experimental information available from the literature as input. The paper also discusses the relative advantages of constrained crystal structure prediction tools, like FPASS, in comparison to conventional crystal structure prediction methods in reference to their abilities to complete the solution of other unsolved structures.text/htmlThree new crystal structures in the Na–Pb system: solving structures without additional experimental inputtext5712015-08-28Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers542548Hexagonal projected symmetries
http://scripts.iucr.org/cgi-bin/paper?pc5052
In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern.Copyright (c) 2015 International Union of Crystallographyurn:issn:2053-2733Oliveira, J.F.Castro, S.B.S.D.Labouriau, I.S.2015-08-28doi:10.1107/S2053273315012905International Union of CrystallographyA list of the three-dimensional lattices that can be projected so as to obtain a two-dimensional hexagonal pattern is established.ENSymmetric patternsprojected patternshexagonal symmetriesIn the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern.text/htmlHexagonal projected symmetriestext5712015-08-28Copyright (c) 2015 International Union of CrystallographyActa Crystallographica Section Aresearch papers549558