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  • 机译 Al-Co-Ni系统中准晶相和近似相凝固动力学的并排比较
    摘要:Quasicrystals and their approximants have triggered widespread interest due to the challenge of solving their complex crystal structures as well as their possibly exceptional properties. The structural motifs of approximants are similar to those of the corresponding quasicrystals, but to what extent are their crystallization pathways the same? Unfortunately, there have been very few in situ experimental investigations to answer this question. Here, by leveraging the high penetrating power of hard X-rays, synchrotron-based X-ray tomography was conducted in order to capture the nucleation and growth of a decagonal quasicrystal and its related approximant. The combination of data-driven computational analysis with new thermodynamic databases allowed the characterization, with high precision, of the constitutional and kinetic driving forces for crystallization. The experimental results prove that the growth of both crystals from a liquid is dominated by first-order kinetics. Nevertheless, and somewhat surprisingly, significant differences were observed in their rates of nucleation and growth. The reasons for such divergent behaviours are discussed in light of contemporary theories of intermetallic crystallization.
  • 机译 从具有尾部延伸的部分重叠峰的模式中进行形状和傅立叶变换的模型独立提取
    摘要:This work presents a technique for extracting the detailed shape of peaks with extended, overlapping tails in an X-ray powder diffraction pattern. The application we discuss concerns crystallite size broadening, though the technique can be applied to spectra of any origin and without regards to how the profiles are to be subsequently analyzed. Historically, the extraction of profile shapes has been difficult due to the complexity of determining the background under the peak, resulting in an offset of the low-frequency components of the Fourier transform of the peak known as the “hook” problem. The use of a carefully considered statistical weighting function in a non-linear least-squares fit, followed by summing the residuals from such a fit with the fit itself, allows one to extract the full shape of an isolated peak, without contributions from either the background or adjacent peaks. The extracted shape, consisting of the fit function recombined with the residuals, is not dependent on any specific shape model. The application of this to analysis of microstructure is performed independently of global parametric models, which would reduce the number of refined parameters; therefore the technique requires high-quality data to produce results of interest. The effectiveness of the technique is demonstrated by extraction of Fourier transforms of peaks from two sets of size-broadened materials with two differing pieces of equipment.
  • 机译 一维替换平铺中的超均匀性和反超均匀性
    摘要:This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.
  • 机译 减少动态电子散射揭示氢原子
    摘要:Compared with X-rays, electron diffraction faces a crucial challenge: dynamical electron scattering compromises structure solution and its effects can only be modelled in specific cases. Dynamical scattering can be reduced experimentally by decreasing crystal size but not without a penalty, as it also reduces the overall diffracted intensity. In this article it is shown that nanometre-sized crystals from organic pharmaceuticals allow positional refinement of the hydrogen atoms, even whilst ignoring the effects of dynamical scattering during refinement. To boost the very weak diffraction data, a highly sensitive hybrid pixel detector was employed. A general likelihood-based computational approach was also introduced for further reducing the adverse effects of dynamic scattering, which significantly improved model accuracy, even for protein crystal data at substantially lower resolution.
  • 机译 具有平移无序的晶体衍射的从头算相
    摘要:To date X-ray protein crystallography is the most successful technique available for the determination of high-resolution 3D structures of biological molecules and their complexes. In X-ray protein crystallography the structure of a protein is refined against the set of observed Bragg reflections from a protein crystal. The resolution of the refined protein structure is limited by the highest angle at which Bragg reflections can be observed. In addition, the Bragg reflections alone are typically insufficient (by a factor of two) to determine the structure ab initio, and so prior information is required. Crystals formed from an imperfect packing of the protein molecules may also exhibit continuous diffraction between and beyond these Bragg reflections. When this is due to random displacements of the molecules from each crystal lattice site, the continuous diffraction provides the necessary information to determine the protein structure without prior knowledge, to a resolution that is not limited by the angular extent of the observed Bragg reflections but instead by that of the diffraction as a whole. This article presents an iterative projection algorithm that simultaneously uses the continuous diffraction as well as the Bragg reflections for the determination of protein structures. The viability of this method is demonstrated on simulated crystal diffraction.
  • 机译 使用Timepix量子面积直接电子检测器在室温下通过电子衍射从头算结构确定有机药物化合物的纳米晶体。更正
    摘要:Corrections are made to Table 1 in the article by .
  • 机译 在宽角度范围内通过掠入射衍射调制的镜面反射强度
    摘要:Grazing-incidence X-ray diffraction (GID) is a well known technique for the characterization of crystal surfaces. A theoretical study has been performed of the sensitivity of GID to the structure of a crystal surface and distorted nanometre-thin surface layers. To simulate GID from crystals that have a complex subsurface structure, a matrix formalism of the dynamical diffraction theory has been applied. It has been found that the azimuthal rocking curves of a crystal that has a distorted subsurface, measured over a wide angular range, show asymmetric thickness oscillations with two distinguishable sets of frequencies: one corresponding to the diffraction in the single-crystal subsurface layer and the second corresponding to the diffraction in the single-crystal substrate. Therefore, azimuthal rocking curves allow characterization of the subsurface structure of a single crystal. Furthermore, thickness oscillations induced by evanescent diffraction modulate the specular reflection intensity, showing high-intensity modulations. This will potentially allow implementation of subsurface crystal characterization using, for instance, a laboratory-scale X-ray diffractometer.
  • 机译 回应Fraser&Wark关于X射线衍射新理论的评论
    • 作者:Paul F. Fewster
    • 刊名:Acta Crystallographica. Section A, Foundations and Advances
    • 2018年第Pt 5期
    摘要:The criticisms of my theory, as given by Fraser & Wark [(2018), Acta Cryst. A74, ], are built on a misunderstanding of the concept and the methodology I have used. The assumption they have made rules out my description from which they conclude that my theory is proved to be wrong. They assume that I have misunderstood the diffraction associated with the shape of a crystal and my calculation is only relevant to a parallelepiped and even that I have got wrong. It only appears wrong to Fraser & Wark because the effect I predict has nothing to do with the crystal shape. The effect though can be measured as well as the crystal shape effects. This response describes my reasoning behind the theory, how it can be related to the Ewald sphere construction, and the build-up of the full diffraction pattern from all the scatterers in a stack of planes. It is the latter point that makes the Fraser & Wark analysis incomplete. The description given in this article describes my approach much more precisely with reference to the Ewald sphere construction. Several experiments are described that directly measure the predictions of the new theory, which are explained with reference to the Ewald sphere description. In its simplest terms the new theory can be considered as giving a thickness to the Ewald sphere surface, whereas in the conventional theory it has no thickness. Any thickness immediately informs us that the scattering from a peak at the Bragg angle does not have to be in the Bragg condition to be observed. I believe the conventional theory is a very good approximation, but as soon as it is tested with careful experiments it is shown to be incomplete. The new theory puts forward the idea that there is persistent intensity at the Bragg scattering angle outside the Bragg condition. This intensity is weak (∼10−5) but can be observed in careful laboratory experiments, despite being on the limit of observation, yet it has a profound impact on how we should interpret diffraction patterns.
  • 机译 枚举钙钛矿中磁电和多铁耦合的群论方法
    摘要:A group-theoretical approach is used to enumerate the possible couplings between magnetism and ferroelectric polarization in the parent perovskite structure. It is shown that third-order magnetoelectric coupling terms must always involve magnetic ordering at the A and B sites which either transforms both as R-point or both as X-point time-odd irreducible representations (irreps). For fourth-order couplings it is demonstrated that this criterion may be relaxed allowing couplings involving irreps at X-, M- and R-points which collectively conserve crystal momentum, producing a magnetoelectric effect arising from only B-site magnetic order. In this case, exactly two of the three irreps entering the order parameter must be time-odd irreps and either one or all must be odd with respect to inversion symmetry. It is possible to show that the time-even irreps in this triad must transform as one of: X1 +, M3,5 or R5 +, corresponding to A-site cation order, A-site antipolar displacements or anion rocksalt ordering, respectively. This greatly reduces the search space for type-II multiferroic perovskites. Similar arguments are used to demonstrate how weak ferromagnetism may be engineered and a variety of schemes are proposed for coupling this to ferroelectric polarization. The approach is illustrated with density functional theory calculations on magnetoelectric couplings and, by considering the literature, suggestions are given of which avenues of research are likely to be most promising in the design of novel magnetoelectric materials.
  • 机译 一种估计由电荷密度模型得出的特性的统计误差的方法
    摘要:Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance–covariance matrix issued from the least-squares refinement. This ‘SSD methodology’ procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.
  • 机译 准晶体:我们知道什么?我们想知道什么?我们能知道些什么?
    • 作者:Walter Steurer
    • 刊名:Acta Crystallographica. Section A, Foundations and Advances
    • 2018年第Pt 1期
    摘要:More than 35 years and 11 000 publications after the discovery of quasicrystals by Dan Shechtman, quite a bit is known about their occurrence, formation, stability, structures and physical properties. It has also been discovered that quasiperiodic self-assembly is not restricted to intermetallics, but can take place in systems on the meso- and macroscales. However, there are some blank areas, even in the centre of the big picture. For instance, it has still not been fully clarified whether quasicrystals are just entropy-stabilized high-temperature phases or whether they can be thermodynamically stable at 0 K as well. More studies are needed for developing a generally accepted model of quasicrystal growth. The state of the art of quasicrystal research is briefly reviewed and the main as-yet unanswered questions are addressed, as well as the experimental limitations to finding answers to them. The focus of this discussion is on quasicrystal structure analysis as well as on quasicrystal stability and growth mechanisms.
  • 机译 NiZr合金中[...]模组件缺陷的原子尺度分析
    摘要:Some specific structures of intermetallic alloys, like approximants of quasicrystals, have their unit cells and most of their atoms located on a periodic fraction of the nodes of a unique -module [a set of the irrational projections of the nodes of a (N > 3-dimensional) lattice]. Those hidden internal symmetries generate possible new kinds of defects like coherent twins, translation defects and so-called module dislocations that have already been discussed elsewhere [Quiquandon et al. (2016). Acta Cryst. A72, 55–61; Sirindil et al. (2017). Acta Cryst. A73, 427–437]. Presented here are electron microscopy observations of the orthorhombic phase NiZr – and its low-temperature monoclinic variant – which reveal the existence of such defects based on the underlying -module generated by the five vertices of the regular pentagon. New high-resolution electron microscopy (HREM) and scanning transmission electron microscopy high-angle annular dark-field (STEM-HAADF) observations demonstrate the agreement between the geometrical description of the structure in five dimensions and the experimental observations of fivefold twins and translation defects.
  • 机译 估算X射线衍射中的结构因子
    • 作者:Paul F. Fewster
    • 刊名:Acta Crystallographica. Section A, Foundations and Advances
    • 2018年第Pt 5期
    摘要:This article takes the concepts of the ‘new diffraction theory’ [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This ‘enhancement’ effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that ‘systematically absent’ reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.
  • 机译 关于X射线衍射新理论的评论
    摘要:In an article entitled A new theory for X-ray diffraction [Fewster (2014). Acta Cryst. A70, 257–282], hereafter referred to as NTXRD, it is claimed that when X-rays are scattered from a small crystallite, whatever its size and shape, the diffraction pattern will contain enhanced scattering at angles of exactly 2θB, whatever the orientation of the crystal. It is claimed that in this way scattering from a powder, with randomly oriented crystals, gives rise to Bragg scattering even if the Bragg condition is never satisfied by an individual crystallite. The claims of the theory put forward in NTXRD are examined and they are found to be in error. Whilst for a certain restricted set of shapes of crystals it is possible to obtain some diffraction close to (but not exactly at) the Bragg angle as the crystallite is oriented away from the Bragg condition, this is generally not the case. Furthermore, contrary to the claims made within NTXRD, the recognition of the origin of the type of effects described is not new, and has been known since the earliest days of X-ray diffraction.
  • 机译 掠入射X射线衍射图的索引:纤维化薄膜的情况
    摘要:Crystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacene­quinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacene­quinone are determined.
  • 机译 在荷兰佩滕的反应堆中心改进粉末轮廓
    • 作者:Bob van LaarHenk Schenk
    • 刊名:Acta Crystallographica. Section A, Foundations and Advances
    • 2018年第Pt 2期
    摘要:With thousands of references to ‘Rietveld refinement’ it is forgotten that the method did not suddenly appear in a flash of inspiration of a single person, but was the result of the work of three individuals working in the 1960s at the Reactor Centre Netherlands at Petten, Loopstra, van Laar and Rietveld. This paper outlines the origins of ‘profile refinement’, as it was called at Petten, and also looks at why it took so long for the scientific community to recognize its importance. With the recent passing of Hugo Rietveld, the death of Bert Loopstra in 1998 and before other pioneers also disappear, it is important to set down a first-hand account.
  • 机译 完美晶体对前向衍射X射线束的空间位移
    摘要:Time-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.
  • 机译 小角X射线散射张量层析成像:三维互空间图模型,重建算法和角度采样要求
    摘要:Small-angle X-ray scattering tensor tomography, which allows reconstruction of the local three-dimensional reciprocal-space map within a three-dimensional sample as introduced by Liebi et al. [Nature (2015), 527, 349–352], is described in more detail with regard to the mathematical framework and the optimization algorithm. For the case of trabecular bone samples from vertebrae it is shown that the model of the three-dimensional reciprocal-space map using spherical harmonics can adequately describe the measured data. The method enables the determination of nanostructure orientation and degree of orientation as demonstrated previously in a single momentum transfer q range. This article presents a reconstruction of the complete reciprocal-space map for the case of bone over extended ranges of q. In addition, it is shown that uniform angular sampling and advanced regularization strategies help to reduce the amount of data required.
  • 机译 [...公式...]晶体中的模块缺陷
    摘要:An analysis is presented of the new types of defects that can appear in crystalline structures where the positions of the atoms and the unit cell belong to the same -module, i.e. are irrational projections of an N > 3-dimensional (N-D) lattice Λ as in the case of quasicrystals. Beyond coherent irrationally oriented twins already discussed in a previous paper [Quiquandon et al. (2016). Acta Cryst. A72, 55–61], new two-dimensional translational defects are expected, the translation vectors of which, being projections of nodes of Λ, have irrational coordinates with respect to the unit-cell reference frame. Partial dislocations, called here module dislocations, are the linear defects bounding these translation faults. A specific case arises when the Burgers vector B is the projection of a non-zero vector of Λ that is perpendicular to the physical space. This new kind of dislocation is called a scalar dislocation since, because its Burgers vector in physical space is zero, it generates no displacement field and has no interaction with external stress fields and other dislocations.
  • 机译 无需样品制备的高分辨率X射线衍射
    摘要:It is shown that energy-dispersive X-ray diffraction (EDXRD) implemented in a back-reflection geometry is extremely insensitive to sample morphology and positioning even in a high-resolution configuration. This technique allows high-quality X-ray diffraction analysis of samples that have not been prepared and is therefore completely non-destructive. The experimental technique was implemented on beamline B18 at the Diamond Light Source synchrotron in Oxfordshire, UK. The majority of the experiments in this study were performed with pre-characterized geological materials in order to elucidate the characteristics of this novel technique and to develop the analysis methods. Results are presented that demonstrate phase identification, the derivation of precise unit-cell parameters and extraction of microstructural information on unprepared rock samples and other sample types. A particular highlight was the identification of a specific polytype of a muscovite in an unprepared mica schist sample, avoiding the time-consuming and difficult preparation steps normally required to make this type of identification. The technique was also demonstrated in application to a small number of fossil and archaeological samples. Back-reflection EDXRD implemented in a high-resolution configuration shows great potential in the crystallographic analysis of cultural heritage artefacts for the purposes of scientific research such as provenancing, as well as contributing to the formulation of conservation strategies. Possibilities for moving the technique from the synchrotron into museums are discussed. The avoidance of the need to extract samples from high-value and rare objects is a highly significant advantage, applicable also in other potential research areas such as palaeontology, and the study of meteorites and planetary materials brought to Earth by sample-return missions.

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