Acta Crystallographica Section A via MedWorm.com

Computation of small-angle scattering profiles with three-dimensional Zernike polynomials

Acta Crystallographica Section A — Thu, 09 Feb 2012 05:00:00 +0100

Small-angle X-ray scattering (SAXS) methods are extensively used for characterizing macromolecular structure and dynamics in solution. The computation of theoretical scattering profiles from three-dimensional models is crucial in order to test structural hypotheses. Here, a new approach is presented to efficiently compute SAXS profiles that are based on three-dimensional Zernike polynomial expansions. Comparison with existing methods and experimental data shows that the Zernike method can be used to effectively validate three-dimensional models against experimental data. For molecules with large cavities or complicated surfaces, the Zernike method more accurately accounts for the solvent contributions. The program is available as open-source software at http://sastbx.als.lbl.gov. (Source: ...

Higher-dimensional crystallography of N-fold quasiperiodic tilings

Acta Crystallographica Section A — Wed, 08 Feb 2012 05:00:00 +0100

Crystallography and periodic average structures (PASs) of two-dimensional (2D) quasiperiodic tilings with N-fold symmetry (N-QPTs with N = 7, 8, 9, 10, 11, 12, 13, 15) were studied using the higher-dimensional approach. By identifying the best (most representative) PASs for each case, it was found that the complexity of the PASs and the degree of average periodicity (DAP) strongly depend on the dimensionality and topology of the hypersurfaces (HSs) carrying the structural information. The distribution of deviations from periodicity is given by the HSs projected upon physical space. The 8-, 10- and 12-QPTs with their 2D HSs have the highest DAP. In the case of the 7-, 9-, 11-, 13- and 15-QPTs, the dimensionality of the HSs is greater than two, and is therefore reduced in the projection upon...

Phase retrieval in protein crystallography

Acta Crystallographica Section A — Tue, 07 Feb 2012 05:00:00 +0100

Solution of the phase problem is central to crystallographic structure determination. An oversampling method is proposed, based on the hybrid input–output algorithm (HIO) [Fienup (1982). Appl. Opt. 21, 2758–2769], to retrieve the phases of reflections in crystallography. This method can extend low-resolution structures to higher resolution for structure determination of proteins without additional sample preparation. The method requires an envelope of the protein which divides a unit cell into the density region where the proteins are located and the non-density region occupied by solvents. After a few hundred to a few thousand iterations, the correct phases and density maps are recovered. The method has been used successfully in several cases to retrieve the phases from the experiment...

Mathematical aspects of molecular replacement. II. Geometry of motion spaces

Acta Crystallographica Section A — Tue, 07 Feb 2012 05:00:00 +0100

Molecular replacement (MR) is a well established computational method for phasing in macromolecular crystallography. In MR searches, spaces of motions are explored for determining the appropriate placement of rigid models of macromolecules in crystallographic asymmetric units. In the first paper of this series, it was shown that this space of motions, when endowed with an appropriate composition operator, forms an algebraic structure called a quasigroup. In this second paper, the geometric properties of these MR search spaces are explored and analyzed. This analysis includes the local differential geometry, global geometry and symmetry properties of these spaces. (Source: Acta Crystallographica Section A)

Lattice refinement strategies

Acta Crystallographica Section A — Fri, 27 Jan 2012 05:00:00 +0100

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, f...

Covariance and correlation estimation in electron-density maps

Acta Crystallographica Section A — Wed, 25 Jan 2012 05:00:00 +0100

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 poin...

A novel iterative solution to the phase problem

Acta Crystallographica Section A — Thu, 12 Jan 2012 05:00:00 +0100

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. (Source: Acta Crystallographica Section A)

Frequency distribution of the reduced unit cells of centred lattices from the Protein Data Bank

Acta Crystallographica Section A — Thu, 12 Jan 2012 05:00:00 +0100

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. (Source: Acta Crystallographica Section A)

Image formation in the scanning transmission electron microscope using object-conjugate detectors

Acta Crystallographica Section A — Thu, 12 Jan 2012 05:00:00 +0100

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 geometr...

Quantitative crystal structure descriptors from multiplicative congruential generators

Acta Crystallographica Section A — Thu, 12 Jan 2012 05:00:00 +0100

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 clas...

New consistency tests for high-accuracy measurements of X-ray mass attenuation coefficients by the X-ray extended-range technique

Acta Crystallographica Section A — Sat, 07 Jan 2012 00:12:21 +0100

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 r...

The global long-range order of quasi-periodic patterns in Islamic architecture

Acta Crystallographica Section A — Thu, 05 Jan 2012 05:00:00 +0100

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 q...

The superstructure determination of displacive distortions via symmetry-mode analysis

Acta Crystallographica Section A — Thu, 05 Jan 2012 05:00:00 +0100

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 a...

Laue centennial

Acta Crystallographica Section A — Tue, 20 Dec 2011 05:57:49 +0100

(Source: Acta Crystallographica Section A)

The success story of crystallographyThis Laue centennial article has also been published in Zeitschrift für Kristallographie [Schwarzenbach (2012). Z. Kristallogr.227, 52–62].

Acta Crystallographica Section A — Tue, 20 Dec 2011 05:00:00 +0100

This article presents the limited, subjective view of its author and a limited selection of references. The bulk of the article covers the history of X-ray structure determination from the NaCl structure to aperiodic structures and macromolecular structures. The theoretical foundations were available by 1920. The subsequent success of crystallography was then due to the development of diffraction equipment, the theory of the solution of the phase problem, symmetry theory and computers. The many structures becoming known called for the development of crystal chemistry and of data banks. Diffuse scattering from disordered structures without and with partial long-range order allows determination of short-range order. Neutron and electron scattering and diffraction are also mentioned. (Source:...

Optical properties of X-rays – dynamical diffractionThis Laue centennial article has also been published in Zeitschrift für Kristallographie [Authier (2012). Z. Kristallogr.227, 36–51].

Acta Crystallographica Section A — Tue, 20 Dec 2011 05:00:00 +0100

The first attempts at measuring the optical properties of X-rays such as refraction, reflection and diffraction are described. The main ideas forming the basis of Ewald's thesis in 1912 are then summarized. The first extension of Ewald's thesis to the X-ray case is the introduction of the reciprocal lattice. In the next step, the principles of the three versions of the dynamical theory of diffraction, by Darwin, Ewald and Laue, are given. It is shown how the comparison of the dynamical and geometrical theories of diffraction led Darwin to propose his extinction theory. The main optical properties of X-ray wavefields at the Bragg incidence are then reviewed: Pendellösung, shift of the Bragg peak, fine structure of Kossel lines, standing waves, anomalous absorption, paths of wavefields insi...

Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussionsThis Laue centennial article has also been published in Zeitschrift für Kristallographie [Eckert (2012). Z. Kristallogr.227, 27–35].

Acta Crystallographica Section A — Tue, 20 Dec 2011 05:00:00 +0100

The discovery of X-ray diffraction is reviewed from the perspective of the contemporary knowledge in 1912 about the nature of X-rays. Laue's inspiration that led to the experiments by Friedrich and Knipping in Sommerfeld's institute was based on erroneous expectations. The ensuing discoveries of the Braggs clarified the phenomenon (although they, too, emerged from dubious assumptions about the nature of X-rays). The early misapprehensions had no impact on the Nobel Prizes to Laue in 1914 and the Braggs in 1915; but when the prizes were finally awarded after the war, the circumstances of `Laue's discovery' gave rise to repercussions. Many years later, they resulted in a dispute about the `myths of origins' of the community of crystallographers. (Source: Acta Crystallographica Section A)

Crystallography from Haüy to Laue: controversies on the molecular and atomistic nature of solidsThis Laue centennial article has also been published in Zeitschrift für Kristallographie [Kubbinga (2012). Z. Kristallogr.227, 1–26].

Acta Crystallographica Section A — Tue, 20 Dec 2011 05:00:00 +0100

The history of crystallography has been assessed in the context of the emergence and spread of the molecular theory. The present paper focuses on the 19th century, which saw the emancipation of crystallography as a science sui generis. Around 1800, Laplace's molecularism called the tune in the various sciences (physics, chemistry, biology, crystallography). In crystallography, two schools opposed each other: that of Weiss, in Berlin, and that of Haüy, in Paris. Symmetry proved essential. It will be shown how the lattice theory arose in an essentially molecular framework and how group theory imposed itself. The salt hydrates suggested the idea of (two or more) superimposed molecular lattices. Gradually it became clear that an ultimate lattice theory ought to be atomic. The experiments of L...

Charge transfer on the metallic atom-pair bond, and the crystal structures adopted by intermetallic compounds

Acta Crystallographica Section A — Wed, 30 Nov 2011 05:00:00 +0100

It has been argued in our recent papers that the heat of formation of intermetallic compounds is mostly concentrated in the nearest neighbor unlike atom-pair bonds, and that the positive term in Miedema's equation is associated with charge transfer on the bond to maintain electroneutrality. In this paper, taking examples of some well populated crystal-structure types such as MgCu2, AsNa3, AuCu3, MoSi2 and SiCr3 types, the effect of such charge transfer on the crystal structures adopted by intermetallic compounds is examined. It is shown that the correlation between the observed size changes of atoms on alloying and their electronegativity differences is supportive of the idea of charge transfer between atoms. It is argued that the electronegativity and valence differences need to be of the...

X-ray diffraction from nonperiodic layered structures with correlations: analytical calculation and experiment on mixed Aurivillius films

Acta Crystallographica Section A — Thu, 24 Nov 2011 05:00:00 +0100

X-ray diffraction from films consisting of layers with different thicknesses, structures and chemical contents is analysed. The disorder is described by probabilities for different sequences of layers. Closed analytical expressions for the diffracted X-ray intensity are obtained when the layers form a stationary Markov chain. The proposed model is applied to the diffraction data from epitaxial sodium bismuth titanate thin films with Aurivillius structure possessing such one-dimensional disorder. In this case, the disorder is caused by a random stacking of three and four perovskite units separated by bismuth oxide interlayers. The results of analytical calculations are in good agreement with the experimental data and indicate that the incorporation of sodium in the Bi4Ti3O12 phase causes th...

The application of eigensymmetries of face forms to X-ray diffraction intensities of crystals twinned by `reticular merohedry'

Acta Crystallographica Section A — Thu, 24 Nov 2011 05:00:00 +0100

This paper is an extension of a previous treatment of `twins by merohedry' with full lattice coincidence [Σ = 1, Klapper & Hahn (2010). Acta Cryst. A66, 327–346] to `twins by reticular merohedry' with partial lattice coincidence (Σ > 1). Again, the sets of symmetrically equivalent reflections {hkl} are considered as sets of equivalent faces (face forms) {hkl}, and the behaviour of the oriented eigensymmetries of these forms under the action of a twin operation is used to determine the X-ray reflection sets, the intensities of which are affected or not affected by the twinning. The following cases are treated: rhombohedral obverse/reverse Σ3 twins, cubic Σ3 (spinel) twins, tetragonal Σ5 twins (twin elements m′(120), 2′[{\overline 2}10]) and hexagonal Σ7 twins (m′(12{\overline ...

Direct phasing from Patterson syntheses by δ recycling

Acta Crystallographica Section A — Thu, 17 Nov 2011 05:00:00 +0100

The direct methods origin-free modulus sum function [Rius (1993). Acta Cryst. A49, 406–409] includes in its definition the structure factor G(Φ) of the squared crystal structure expressed in terms of Φ, the set of ϕ phases of the normalized structure factors E's of the crystal structure of unit-cell volume V. Here the simpler sum function variant S_{\rm P}^{\prime} = ∑HE−H∫VδP,Δ(Φ)exp(i2πHr)dV extended over all H reflections is introduced which involves no G's and in which the δP,Δ function corresponds to δP = FT−1{(E_{\bf H}^2 - \langle E^2\rangle)exp[iϕH(Φ)]} (where FT = Fourier transform) with all values smaller than Δ = 2.5σP equated to zero (\sigma_{\rm P}^2 is the variance of δP calculable from the experimental intensities). The new phase estimates are obtain...

New version of the theoretical databank of transferable aspherical pseudoatoms, UBDB2011 – towards nucleic acid modelling

Acta Crystallographica Section A — Thu, 17 Nov 2011 05:00:00 +0100

This study shows that on the basis of the UBDB2011 databank electrostatic interaction energies can be estimated and structure refinements carried out. However, some method limitations are apparent. (Source: Acta Crystallographica Section A)

Scattering amplitudes and static atomic correction factors for the composition-sensitive 002 reflection in sphalerite ternary III–V and II–VI semiconductors

Acta Crystallographica Section A — Fri, 11 Nov 2011 07:00:00 +0100

Modified atomic scattering amplitudes (MASAs), taking into account the redistribution of charge due to bonds, and the respective correction factors considering the effect of static atomic displacements were computed for the chemically sensitive 002 reflection for ternary III–V and II–VI semiconductors. MASAs were derived from computations within the density functional theory formalism. Binary eight-atom unit cells were strained according to each strain state s (thin, intermediate, thick and fully relaxed electron microscopic specimen) and each concentration (x = 0, …, 1 in 0.01 steps), where the lattice parameters for composition x in strain state s were calculated using continuum elasticity theory. The concentration dependence was derived by computing MASAs for each of these binary ...

Diffuse scattering in relaxor ferroelectrics: true three-dimensional mapping, experimental artefacts and modelling

Acta Crystallographica Section A — Fri, 11 Nov 2011 05:00:00 +0100

The available body of experimental data in terms of the relaxor-specific component of diffuse scattering is critically analysed and a collection of related models is reviewed; the sources of experimental artefacts and consequent failures of modelling efforts are enumerated. Furthermore, it is shown that the widely used concept of polar nanoregions as individual static entities is incompatible with the experimental diffuse scattering results. Based on the synchrotron diffuse scattering three-dimensional data set taken for the prototypical ferroelectric relaxor lead magnesium niobate–lead titanate (PMN–PT), a new parameterization of diffuse scattering in relaxors is presented and a simple phenomenological picture is proposed to explain the unusual properties of the relaxor behaviour. The...

Grazing-incidence small-angle X-ray scattering: application to the study of quantum dot lattices

Acta Crystallographica Section A — Fri, 11 Nov 2011 05:00:00 +0100

The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determination, including lattice type, lattice parameters, the type and degree of disorder in the quantum dot positions and the distributions of the quantum dot sizes. Applications of the developed models are demonstrated using experimentally measured data from several types of quantum dot lattices formed by a self-assembly process. (Source: Acta Crystallographica Section A)

On QM/MM and MO/MO cluster calculations of all-atom anisotropic displacement parameters for molecules in crystal structures

Acta Crystallographica Section A — Fri, 11 Nov 2011 05:00:00 +0100

The practical aspects of ab initio calculation of anisotropic displacement parameters (ADPs) for molecules in crystal structures are investigated. Computationally efficient approaches to calculate ADPs are QM/MM or MO/MO methods, where quantum chemical calculations are split into a high-level and a low-level part. Such calculations allow geometry optimizations and subsequent frequency calculations of a central molecule in a cluster of surrounding molecules as found in the crystal lattice. The frequencies and associated displacements are then converted into ADPs. A series of such calculations were performed with different quantum chemical methods and basis sets on the three zwitterionic amino-acid structures of l-alanine, l-cysteine and l-threonine, where high-quality low-temperature X-ray ...

Prices of IUCr journals

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

(Source: Acta Crystallographica Section A)

Fundamentals of Crystallography, 3rd edition. By C. Giacovazzo, H. L. Monaco, G. Artioli, D. Viterbo, M. Milaneso, G. Ferraris, G. Gilli, P. Gilli, G. Zanotti and M. Catti. Edited by C. Giacovazzo. IUCr Texts on Crystallography No. 15, IUCr/Oxford University Press, 2011. Pp. xxi + 842. Price (hardback) GBP 90.00. ISBN 978-0-19-957365-3.

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

(Source: Acta Crystallographica Section A)

Computer-simulated X-ray three-beam pinhole topographs for spherical silicon crystals

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

X-ray three-beam pinhole topograph images for spherical silicon crystals were computer-simulated based on the n-beam Takagi–Taupin (T–T) equation. They were compared with those for parallel-plate crystals. The procedure to integrate the n-beam T–T equation for a crystal with an arbitrary shape has been validated in a separate paper [Okitsu et al. (2011), Acta Cryst. A67, 550–556] from comparison between experimentally obtained and computer-simulated six-beam pinhole topographs for a channel-cut silicon crystal. (Source: Acta Crystallographica Section A)

On the polarization state of X-rays generated using a rotating four-quadrant X-ray phase retarder system

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

A method of calculating the polarization state of X-rays transmitted through a rotating four-quadrant X-ray phase retarder system is described using Jones calculus. This method was applied to correcting the polarization states of X-rays incident on a channel-cut silicon crystal. Details and results of this experiment are given in a separate paper [Okitsu et al. (2011), Acta Cryst. A67, 550–556]. (Source: Acta Crystallographica Section A)

Polarization-dependent X-ray six-beam pinhole topographs for a channel-cut silicon crystal

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

It was pointed out in a previous paper [Okitsu et al. (2006), Acta Cryst. A62, 237–244] that an n-beam Takagi–Taupin (T–T) equation can be solved for a crystal of arbitrary shape. The procedure to integrate the n-beam T–T equation is to let all the Fourier coefficients of the electric susceptibility be zero at positions inside the Borrmann pyramid but outside the crystal. The efficiency of this simple procedure is verified in the present paper by showing qualitative and quantitative agreements between experimentally obtained and computer-simulated X-ray six-beam pinhole topographs for a channel-cut silicon crystal. (Source: Acta Crystallographica Section A)

A multi-dataset data-collection strategy produces better diffraction data

Acta Crystallographica Section A — Tue, 18 Oct 2011 04:00:00 +0100

A multi-dataset (MDS) data-collection strategy is proposed and analyzed for macromolecular crystal diffraction data acquisition. The theoretical analysis indicated that the MDS strategy can reduce the standard deviation (background noise) of diffraction data compared with the commonly used single-dataset strategy for a fixed X-ray dose. In order to validate the hypothesis experimentally, a data-quality evaluation process, termed a readiness test of the X-ray data-collection system, was developed. The anomalous signals of sulfur atoms in zinc-free insulin crystals were used as the probe to differentiate the quality of data collected using different data-collection strategies. The data-collection results using home-laboratory-based rotating-anode X-ray and synchrotron X-ray systems indicate ...

A Fourier transform method for powder diffraction based on the Debye scattering equation

Acta Crystallographica Section A — Sun, 16 Oct 2011 08:46:57 +0100

A fast Fourier transform algorithm is introduced into the method recently defined for calculating powder diffraction patterns by means of the Debye scattering equation (DSE) [Thomas (2010). Acta Cryst. A66, 64–77]. For this purpose, conventionally used histograms of interatomic distances are replaced by compound transmittance functions. These may be Fourier transformed to partial diffraction patterns, which sum to give the complete diffraction pattern. They also lead to an alternative analytical expression for the DSE sum, which reveals its convergence behaviour. A means of embedding the DSE approach within the reciprocal-lattice–structure-factor method is indicated, with interpolation methods for deriving the peak profiles of nanocrystalline materials outlined. Efficient calculation o...

Common arc method for diffraction pattern orientation

Acta Crystallographica Section A — Thu, 13 Oct 2011 04:00:00 +0100

Very short pulses of X-ray free-electron lasers opened the way to obtaining diffraction signal from single particles beyond the radiation dose limit. For three-dimensional structure reconstruction many patterns are recorded in the object's unknown orientation. A method is described for the orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, and hence named the common arc orientation method. The present implementation of the algorithm optionally takes into account Friedel's law, handles missing data and is capable of determining the point group of symmetric objects. Its performance is demonstrated on simulated diffraction data sets and verification of the results indicates a ...

Form, symmetry and packing of biomacromolecules. V. Shells with boundaries at anti-nodes of resonant vibrations in icosahedral RNA viruses

Acta Crystallographica Section A — Thu, 13 Oct 2011 04:00:00 +0100

The RNA viruses cowpea chlorotic mottle, satellite tobacco mosaic, pariacoto and MS2, already considered in part IV of this series of papers [Janner, A. (2011a), Acta Cryst. A67, in the press], are investigated further, with the aim to arrive at a possible physical basis for their structural properties. The shell structure of the filled capsid is analyzed in terms of successive spherical boundaries of the sets of icosahedral equivalent chains. By inversion in the sphere enclosing the capsid, the internal boundaries are transformed into external ones, which are more easily visualized. This graphical procedure reveals the presence of regularly spaced shells with boundaries fitting with anti-nodal surfaces of the virus considered as an elastic resonator. The centers of gravity of the various ...

Form, symmetry and packing of biomacromolecules. IV. Filled capsids of cowpea, tobacco, MS2 and pariacoto RNA viruses

Acta Crystallographica Section A — Thu, 13 Oct 2011 04:00:00 +0100

Four icosahedral RNA viruses are considered: the cowpea chlorotic mottle virus, the satellite tobacco mosaic virus, the pariacoto virus and the MS2 bacteriophage. The validity of the phenomenological rules derived in previous publications (crystallographic scaling, indexed forms enclosing axial-symmetric clusters, packing lattices of viral crystals) is confirmed and shown to apply equally well to the coat proteins as to the (ordered) RNA chains. (Source: Acta Crystallographica Section A)

Some Beq are more equivalent than others

Acta Crystallographica Section A — Thu, 13 Oct 2011 04:00:00 +0100

Crystallographic structural models for macromolecules have typically included an isotropic displacement parameter Biso for each atom. In cases where the structural model instead includes anisotropic displacement parameters Uij, the derived quantity Beq can be substituted for Biso for many purposes. Beq is not, however, the best predictor of the value Biso that would hypothetically have been obtained by direct refinement of an isotropic model. A new entity Best is proposed that represents an estimate for Biso that minimizes the Kullback–Leibler divergence from a paired anisotropic model. In general B_{{\rm est}}/B_{{\rm eq}} < 1, with the difference between the two values becoming larger for atoms that are more anisotropic. Although this difference does not affect direct refinement of eit...

Structure of ice Ih and ice Ic as described in the language of Delaunay simplices

Acta Crystallographica Section A — Thu, 13 Oct 2011 04:00:00 +0100

Classification of the Delaunay simplex forms is carried out for the ideal structures of ice Ih and ice Ic. Classification according to the number of edges of different length reveals six types of simplices, while classification according to the number and mutual positions of edges of the unit length (equal to the length of the hydrogen bond) reveals five types of indices. Ice Ic is composed of simplices of three types (one of which has the form of a perfect tetrahedron), ice Ih from six simplices. Degeneracy is removed in computer models of slightly distorted ice by means of insignificant shifting of water molecules from their ideal positions. This makes it possible to provide the unambiguous partition of the crystal structure into Delaunay simplices. It is found that degeneracy removal re...

Radial integrals for the magnetic form factor of 5d transition elements

Acta Crystallographica Section A — Tue, 02 Aug 2011 23:00:00 +0100

The radial integrals, 〈jL〉, where L = 0, 2, 4, for several electronic configurations in the 5d electrons of transition metal atoms and ions are calculated using radial wavefunctions from the pseudo-relativistic Hartree–Fock method in the Cowan program. The resultant values are fitted to Gaussian analytical expressions with four exponential terms, and the fitted coefficients are tabulated. This table can be used to interpret the magnetic form factor measurements for 5d transition metals. (Source: Acta Crystallographica Section A)

Anisotropy of extinction: extrapolation to the kinematical limit by γ-ray diffraction

Acta Crystallographica Section A — Tue, 19 Jul 2011 23:00:00 +0100

A direct experimental approach to the problem of anisotropic extinction is presented. Structure-factor measurements from a vanadium and a niobium crystal, performed with four γ-ray wavelengths in the range 0.02–0.06 Å, substantiate the adequacy of Zachariasen's theory [Acta Cryst. (1967), 23, 558–564] in high-energy diffraction, which provides a theoretical basis for the extrapolation to zero extinction values. Fitting of the theoretical curve to the observed points, placed on a common scale, allows determination of the kinematical structure-factor value without the need for a particular model of anisotropy in the mosaic structure. (Source: Acta Crystallographica Section A)

Iteratively reweighted least squares in crystal structure refinements

Acta Crystallographica Section A — Tue, 19 Jul 2011 23:00:00 +0100

The use of robust techniques in crystal structure multipole refinements of small molecules as an alternative to the commonly adopted weighted least squares is presented and discussed. As is well known, the main disadvantage of least-squares fitting is its sensitivity to outliers. The elimination from the data set of the most aberrant reflections (due to both experimental errors and incompleteness of the model) is an effective practice that could yield satisfactory results, but it is often complicated in the presence of a great number of bad data points, whose one-by-one elimination could become unattainable. This problem can be circumvented by means of a robust least-squares regression that minimizes the influence of outliers. This work is aimed at showing the capability of a robust regres...

About the hybrid Fourier syntheses: a probabilistic approach

Acta Crystallographica Section A — Wed, 13 Jul 2011 23:00:00 +0100

The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst. A66, 347–361]. New Fourier coefficients were devised which were the basis of a new ab initio method for the solution of the phase problem (i.e. VLD, vive la difference). In this paper we study the joint probability distribution functions P(F, Fp, FQ), where FQ is the structure factor corresponding to the ideal hybrid Fourier synthesis ρQ = τρ − ωρp and τ and ω are any pair of real numbers. New Fourier coefficients for the calculations of any hybrid synthesis are obtained, and the properties of the corresponding electron-density maps are discussed. The first applications show the correctness of our theoretical approach and sugges...

Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison

Acta Crystallographica Section A — Thu, 07 Jul 2011 20:04:43 +0100

The advent of X-ray free-electron lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10−2 photons per pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance. (Source: Acta Crystallographica Section A)

Atomic resolution imaging using the real-space distribution of electrons scattered by a crystalline material

Acta Crystallographica Section A — Tue, 05 Jul 2011 23:00:00 +0100

We present an alternative atomic resolution incoherent imaging technique derived from scanning transmission electron microscopy (STEM) using detectors in real space, in contrast to conventional STEM that uses detectors in diffraction space. The images obtained from various specimens have a resolution comparable to conventional high-angle annular dark-field (HAADF) STEM with good contrast, which seems to be very robust with respect to thickness, focus and imaging conditions. The results of the simulations are consistent with the experimental results and support the interpretation of the real-space STEM image contrast as being a result of aberration-induced displacements of the high-angle scattered electrons. (Source: Acta Crystallographica Section A)

Mathematical aspects of molecular replacement. I. Algebraic properties of motion spaces

Acta Crystallographica Section A — Tue, 05 Jul 2011 23:00:00 +0100

Molecular replacement (MR) is a well established method for phasing of X-ray diffraction patterns for crystals composed of biological macromolecules of known chemical structure but unknown conformation. In MR, the starting point is known structural domains that are presumed to be similar in shape to those in the macromolecular structure which is to be determined. A search is then performed over positions and orientations of the known domains within a model of the crystallographic asymmetric unit so as to best match a computed diffraction pattern with experimental data. Unlike continuous rigid-body motions in Euclidean space and the discrete crystallographic space groups, the set of motions over which molecular replacement searches are performed does not form a group under the operation of ...

Direct methods: a paradox with regard to the convergence of random phase trials toward solutions

Acta Crystallographica Section A — Tue, 05 Jul 2011 23:00:00 +0100

A frustrating observation, based on an Rmin variance analysis within the `shake and bake' framework of direct methods phasing, is described. The variance of Rmin can on occasion identify large subsets of phases that have a significantly lower mean phase error than the entire direct methods phase set of otherwise unsuccessful phasing trials for which the overall phase error occasionally dips below 75 or 80°. This is the first time, other than for a handful of Σ1 phase indications in optimal situations, that a priori phase estimates have been attained for large numbers of E values, prior to solving the structure. Although the a priori variance of Rmin is a useful tool for identifying such phases, the a posteriori phase refinement shifts indicated by its minimum often prevent a successful c...

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application

Acta Crystallographica Section A — Tue, 05 Jul 2011 23:00:00 +0100

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1–13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830–838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyze...

Ninth Ewald Prize

Acta Crystallographica Section A — Thu, 16 Jun 2011 23:00:00 +0100

The ninth Ewald Prize has been awarded to Professor E. Dodson, Professor C. Giacovazzo and Professor G. M. Sheldrick for the enormous impact they have made on structural crystallography. (Source: Acta Crystallographica Section A)

High-resolution study of (222, 113) three-beam diffraction in Ge

Acta Crystallographica Section A — Thu, 16 Jun 2011 23:00:00 +0100

The results of high-resolution analysis of the (222, >113) three-beam diffraction in Ge are presented. For monochromatization and angular collimation of the incident synchrotron beam a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes was used in an attempt to experimentally approach plane-wave incident conditions. Using this setup, for various azimuthal angles the polar angular curves which are very close to theoretical computer simulations for the plane monochromatic wave were measured. The effect of the strong two-beam 222 diffraction was observed for the first time with the maximum reflectivity close to 60% even though the total reflection of the incident beam into a forbidden reflection was not achieved owing to absorption. The structure factor of ...

Linear transformations of variance/covariance matrices

Acta Crystallographica Section A — Thu, 16 Jun 2011 23:00:00 +0100

Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance matrix. For the transformation of second-rank tensors it is suggested that the 3 \times 3 matrix is re-written into a 9 \times 1 vector. The transformation of the corresponding variance/covariance matrix is then straightforward and easily implemented into computer software. This method is applied in the transformation of anisotropic displacement parameters, the calculation of equivalent isotropic displacement parameters, the comparison of refinements in different space-group settings and the ca...

Estimation of the variance in any point of an electron-density map for any space group

Acta Crystallographica Section A — Thu, 16 Jun 2011 23:00:00 +0100

In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210–218] a mathematical expression of the variance at any point of the unit cell has been described. The formulas were derived in P1 for any type of Fourier synthesis (observed, difference and hybrid) under the following hypothesis: the current phases are distributed on the trigonometric circle about the correct values according to von Mises distributions. This general hypothesis allows the variance expressions to be valid at any stage of the phasing process. In this paper the method has been extended to any space group, no matter whether centric or acentric. The properties of the variance generated by space-group symmetry are described; in particular it is shown that the variance is strictly connected with the implication ...

Addressing the amorphous content issue in quantitative phase analysis: the certification of NIST standard reference material 676a

Acta Crystallographica Section A — Thu, 16 Jun 2011 23:00:00 +0100

A non-diffracting surface layer exists at any boundary of a crystal and can comprise a mass fraction of several percent in a finely divided solid. This has led to the long-standing issue of amorphous content in standards for quantitative phase analysis (QPA). NIST standard reference material (SRM) 676a is a corundum (α-Al2O3) powder, certified with respect to phase purity for use as an internal standard in powder diffraction QPA. The amorphous content of SRM 676a is determined by comparing diffraction data from mixtures with samples of silicon powders that were engineered to vary their specific surface area. Under the (supported) assumption that the thickness of an amorphous surface layer on Si was invariant, this provided a method to control the crystalline/amorphous ratio of the silicon...

Seitz notation for symmetry operations of space groups

Acta Crystallographica Section A — Wed, 25 May 2011 23:00:00 +0100

Space-group symmetry operations are given a geometric description and a short-hand matrix notation in International Tables for Crystallography, Volume A, Space-Group Symmetry. We give here the space-group symmetry operations subtables with the corresponding Seitz (R∣t) notation for each included symmetry operation. (Source: Acta Crystallographica Section A)

Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. II. Developing and assessing new Debye–Waller factors

Acta Crystallographica Section A — Wed, 25 May 2011 23:00:00 +0100

Two new anharmonic forms for the Debye–Waller factor, aimed at modelling curvilinear and asymmetric motion, have been introduced. These forms permit the refinement of structures with these types of anharmonic motion using a small number of additional parameters. Molecular-dynamics-derived numerical probability density functions (PDFs) have been used to assess the merit of these new functions in real space. The comparison is favourable particularly for the curvilinear PDF based on a parabolic coordinate system change of a trivariate Gaussian distribution. The initial results also suggest that high-order even terms from the Gram–Charlier series may be important for modelling methyl-group libration. The molecular-dynamics data sets provide useful insights into the nature of anharmonic the...

Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. I. Study of positional parameters

Acta Crystallographica Section A — Wed, 25 May 2011 23:00:00 +0100

Molecular-dynamics-derived numerical probability density functions (PDFs) have been used to illustrate the effect of different models for thermal motion on the parameters refined in a crystal structure determination. Specifically, anharmonic curved or asymmetric PDFs have been modelled using the traditional harmonic approximation and the anharmonic Gram–Charlier series treatment. The results show that in cases of extreme anharmonicity the mean and covariance matrix of the harmonic treatment can deviate significantly from physically meaningful values. The use of a Gram–Charlier anharmonic PDF gives means and covariance matrices closer to the true (numerically determined) anharmonic values. The physical significance of the maxima of the anharmonic distributions (the most probable or mode...

The similarity types of primitive parallelohedra in Ed, 2 ≤ d ≤ 5

Acta Crystallographica Section A — Wed, 25 May 2011 23:00:00 +0100

The similarity types of parallelohedra are defined and a complete classification of the primitive parallelohedra in E^d, 2 \le d \le 5, is given. (Source: Acta Crystallographica Section A)

Relaxation of the resolution requirements for direct-methods phasing

Acta Crystallographica Section A — Wed, 18 May 2011 23:00:00 +0100

Shake-and-bake phasing methods have permitted the ab initio solution of crystal structures containing more than 1000 independent non-H light atoms (C, N, O). The success of these procedures is critically dependent upon having diffraction data measured to at least 1.2 Å resolution. A new target function R2(ϕh) is introduced into the shake-and-bake procedure along with a real difference map strategy whereby this resolution limit can be appreciably lowered toward 1.5 Å. These improvements, when applied to moderately high resolution data, may now allow one the possibility to solve structures that are twice as large as could have been solved previously. (Source: Acta Crystallographica Section A)

Anomalous extinction of X-rays diffracted in strongly deformed crystals

Acta Crystallographica Section A — Wed, 18 May 2011 23:00:00 +0100

The extinction concept is extended for very thin non-ideal crystals. It is shown that for a large gradient, the integrated reflected intensity exhibits a prominent extinction minimum. This anomaly is an interbranch effect, occurring for crystals with thicknesses of the order of the interbranch extinction length. Different possibilities for applying this newly developed extinction theory to X-ray integrated wave topography are discussed. (Source: Acta Crystallographica Section A)

The development of Laue techniques for single-pulse diffraction of chemical complexes: time-resolved Laue diffraction on a binuclear rhodium metal-organic complex

Acta Crystallographica Section A — Thu, 12 May 2011 04:22:13 +0100

A modified Laue method is shown to produce excited-state structures at atomic resolution of a quality competitive with those from monochromatic experiments. The much faster data collection allows the use of only one or a few X-ray pulses per data frame, which minimizes crystal damage caused by laser exposure of the samples and optimizes the attainable time resolution. The method has been applied to crystals of the α-modification of Rh2(μ-PNP)2(PNP)2 (BPh4)2 [PNP = CH3N(P(OCH3)2)2, Ph = phenyl]. The experimental results show a shortening of the Rh—Rh distance in the organometallic complex of 0.136 (8) Å on excitation and are quantitatively supported by quantum-mechanical (QM)/molecular-mechanics (MM) theoretical calculations which take into account the confining effect of the cryst...

Kinematic diffraction on a structure with periodically varying scattering function

Acta Crystallographica Section A — Mon, 09 May 2011 23:00:00 +0100

A theory is developed to describe the kinematic diffraction response of a crystal when it is subjected to a periodically varying external perturbation. It is shown that if a part of the local electron density varies linearly with an external stimulus, the diffracted signal is not only a function of the stimulation frequency Ω, but also of its double 2Ω. These frequency components can provide, under certain conditions, selective access to partial diffraction contributions that are normally summed up in the interference pattern. A phasing process applied to partial diffraction terms would allow recovery of the substructure actively responding to the stimulus. Two ways of frequency filtering are discussed (demodulation and correlation) with respect to extracting information from such an exp...

On the symmetry and the signature of atomic mechanisms in multiferroics: the example of Ba2CoGe2O7

Acta Crystallographica Section A — Mon, 11 Apr 2011 23:00:00 +0100

The systematic use of symmetry arguments, with inclusion of magnetic symmetry, is scarce in the investigation of magnetic materials. This is an unfortunate situation particularly when multiferroics are being studied. The lack of a consistent complete symmetry framework often prevents the distinction of what is the signature of a specific atomic mechanism and what is symmetry-forced and therefore common to any possible underlying microscopic model. Here the recently reported magnetoelectric properties of Ba2CoGe2O7 [Murakawa et al. (2010). Phys. Rev. Lett. 105, 137202] are discussed as an extreme example of this situation, and it is shown how three of the four magnetoelectric responses that have been reported for this compound can be predicted by symmetry considerations without appealing to...

Faulting in finite face-centered-cubic crystallites

Acta Crystallographica Section A — Mon, 11 Apr 2011 23:00:00 +0100

The effects that planar faults have on the powder diffraction peak profiles of a face-centered cubic (f.c.c.) material are studied considering the case of small crystallites. In doing so a new method to calculate the planar probability correlation function of a faulted crystallite is presented which considers the finite extent of the planar sequence. The resulting correlation function is demonstrated to be dependent on the position of a fault in a crystallite through its proximity to a crystallite boundary. The average correlation function found considering equal probability of a fault existing on each plane in a crystallite is compared with that found by solving a system of recursion relations. The broadened subcomponents of the f.c.c. powder profiles are shown to be related to the correl...

Precession electron diffraction of Mn2O3 and PbMnO2.75: solving structures where X-rays fail

Acta Crystallographica Section A — Wed, 06 Apr 2011 23:00:00 +0100

The structure solutions of the two phases Mn2O3 and PbMnO2.75 by precession electron diffraction (PED) are presented. In the powder samples used these structures could not be solved by X-ray diffraction because Mn2O3 is a minority phase in an MnO2 powder and the complex structure of PbMnO2.75 leads to severe peak overlap in the powder diffraction pattern. The influence of different parameters on the structure solution is studied, i.e. the number of reflections measured, precession angle, resolution limit and Lorentz-type correction. It is shown that the number of reflections is the most important parameter for successful structure solution from PED data. (Source: Acta Crystallographica Section A)

Pseudo extra reflection conditions

Acta Crystallographica Section A — Wed, 06 Apr 2011 23:00:00 +0100

The extra reflection conditions as given in Volume A of International Tables for Crystallography may not be rigorously fulfilled if the thermal vibrations and positional or static disorder of the atoms are not isotropic. Although small in most cases, the intensities of reflections violating the extra reflection conditions can become measurable for large thermal and positional anisotropy. It would be useful to have an inventory of these `pseudo extra reflection conditions' for all space groups in the early stage of structure investigation. The subject is demonstrated with the aid of four significant examples and the possibility of predicting without calculation the status of the largest part of the extra reflection conditions is discussed. (Source: Acta Crystallographica Section A)

A charge-flipping algorithm to handle incomplete data

Acta Crystallographica Section A — Wed, 06 Apr 2011 23:00:00 +0100

Missing data are a general hindrance for all iterative, dual-space methods of structure determination. Charge flipping is no exception; its real-space perturbation may turn out to be too strong if the amount of diffraction data is not sufficient. To handle this situation, we introduce a variant of the basic algorithm which combines the original charge-flipping density modification in real space, the reflector of the Fourier-modulus projection in reciprocal space and the parameterless iteration scheme of averaged alternating reflections (AAR). This simple algorithm is a balance of increased perturbations and full negative feedback, with the extra freedom that it can be fine-tuned by a different treatment of different unobserved reflections. The efficiency of the method was tested using seve...

Exact direct-space asymmetric units for the 230 crystallographic space groups

Acta Crystallographica Section A — Wed, 30 Mar 2011 23:00:00 +0100

It is well known that the direct-space asymmetric unit definitions found in the International Tables for Crystallography, Volume A, are inexact at the borders. Face- and edge-specific sub-conditions have to be added to remove parts redundant under symmetry. This paper introduces a concise geometric notation for asymmetric unit conditions. The notation is the foundation for a reference table of exact direct-space asymmetric unit definitions for the 230 crystallographic space-group types. The change-of-basis transformation law for the conditions is derived, which allows the information from the reference table to be used for any space-group setting. We also show how the vertices of an asymmetric unit can easily be computed from the information in the reference table. (Source: Acta Crystallog...

Response to Olczak's comment on Probability density functions of the average and difference intensities of Friedel opposites

Acta Crystallographica Section A — Tue, 29 Mar 2011 23:00:00 +0100

A response is given to to Olczak's comment about the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669–675]. (Source: Acta Crystallographica Section A)

Comment on Probability density functions of the average and difference intensities of Friedel opposites by Shmueli & Flack (2010)

Acta Crystallographica Section A — Tue, 29 Mar 2011 23:00:00 +0100

A comment is made on the discussion of probability density functions (p.d.f.s) and simulations of Friedel intensity differences in Shmueli & Flack [Acta Cryst. (2010), A66, 669–675]. (Source: Acta Crystallographica Section A)

About the σA estimate

Acta Crystallographica Section A — Tue, 29 Mar 2011 23:00:00 +0100

The resolution parameter σA is currently used for evaluating the degree of similarity between a model and the target structure. Here, quasi-Wilson distributions are used to represent the local statistics of the normalized amplitudes both for the target and for the model structure. The study uses the joint probability distribution approach to provide (i) a description of the statistical properties of the σA parameter; (ii) a deeper insight into the role, for the σA estimate, of the high-order moments of the target and of the model structure-factor distributions; and (iii) new statistical formulas for estimating σA. The theoretical results have been checked using test proteins. (Source: Acta Crystallographica Section A)

The quality of precession electron diffraction data is higher than necessary for structure solution of unknown crystalline phases

Acta Crystallographica Section A — Tue, 29 Mar 2011 23:00:00 +0100

Four crystal structures are solved from precession electron diffraction data using either the highest-quality experimental data available or voluntarily deteriorated data. The data quality was lowered by changing the intensity of each individual reflection by as much as a factor of 2, even for strong reflections, while taking care to keep strong reflections strong and weak reflections weak. The crystals have been chosen for their different characteristics, ranging from small to large unit cells, low to high symmetry, and containing heavy and light atoms. In each case the structure solution succeeded with the deteriorated data provided that the completeness of the data was high enough. The accuracy of the atom positions obtained for the cations was comparable to that for the best experiment...

Conditional ambiguity of one-dimensional crystal structures determined from a minimum of diffraction intensity data

Acta Crystallographica Section A — Fri, 25 Mar 2011 00:00:00 +0100

When the number of intensities greatly exceeds the number of unknown atomic coordinates, the problem of obtaining a crystal structure from the intensities is overdetermined and, for a sufficiently small structure, a chemically meaningful solution can be found by direct methods. A difficulty in determining a structure has been historically attributed to the non-uniqueness of such a structure owing to multiple, or homometric, structures that yield the same set of intensities. The number of homometric structures has not been rigorously analyzed owing to the complexity of this problem. By using the method of elementary symmetric polynomials with a new origin definition, one-dimensional crystal structures of a small number of identical atoms (N < 5), determined from a minimum (N − 1) of the l...

Non-crystallographic nets with freely acting, non-abelian local automorphism groups

Acta Crystallographica Section A — Fri, 25 Mar 2011 00:00:00 +0100

Non-crystallographic (NC) nets are defined as periodic nets whose automorphism groups are not isomorphic to any isometry group in Euclidean space. This work focuses on a simple class of NC nets, restricted to nets with non-abelian, freely acting local automorphism groups. A general method is presented to derive such NC nets from crystallographic nets and some non-trivial examples are explored. It is shown that the labelled quotient graph of these nets does not necessarily possess non-trivial automorphisms which exchange cycles having the same net voltage. However, barycentric representations of these nets systematically display vertex collisions. (Source: Acta Crystallographica Section A)

Simultaneous determination of highly precise Debye–Waller factors and multiple structure factors for chemically ordered tetragonal FePd

Acta Crystallographica Section A — Thu, 24 Mar 2011 00:00:00 +0100

Accurate Debye–Waller (DW) factors and low-index structure factors up to 222 of chemically ordered FePd have been measured at 120 K. Ordered FePd has a simple tetragonal unit cell (tP2, P4/mmm) with Fe and Pd atoms at 0, 0, 0 and at {1\over 2}, {1\over 2}, {1\over 2}, respectively, requiring the measurement of four different DW factors. It was possible to simultaneously determine all four DW factors and several low-order structure factors using different, special off-zone-axis multi-beam convergent-beam electron diffraction patterns with high precision and accuracy. The different diffraction conditions exhibit different levels of sensitivity to changes in DW and structure factors. Here the sensitivity of different off-zone-axis convergent-beam electron diffraction patterns with respect...

Translation calibration of inverse-kappa goniometers in macromolecular crystallography

Acta Crystallographica Section A — Tue, 15 Mar 2011 00:00:00 +0100

Precise and convenient crystal reorientation is of experimental importance in macromolecular crystallography (MX). The development of multi-axis goniometers, such as the ESRF/EMBL mini-κ, necessitates the corresponding development of calibration procedures that can be used for the setup, maintenance and troubleshooting of such devices. While traditional multi-axis goniometers require all rotation axes to intersect the unique point of the sample position, recently developed miniaturized instruments for sample reorientation in MX are not as restricted. However, the samples must always be re-centred following a change in orientation. To overcome this inconvenience and allow the use of multi-axis goniometers without the fundamental restriction of having all axes intersecting in the same point...

Variance of electron-density maps in space group P1

Acta Crystallographica Section A — Tue, 15 Mar 2011 00:00:00 +0100

The expected mean-square error of electron-density maps (observed and difference) is traditionally estimated as a function of the variance of the observed amplitudes. The usual purpose is to evaluate the reliability of the structural parameters suggested by the final electron-density maps. Accordingly, such calculations are performed after the refinement stage, when the phases are considered perfectly determined. In this paper a mathematical expression for the variance (observed, difference and hybrid) is obtained for each point of an electron-density map for the space group P1 under a different hypothesis: the current phases are distributed on the trigonometric circle about the correct values, according to von Mises distributions. The variance calculation may then be performed at any stag...

Structure of planar defects in tilted perovskites

Acta Crystallographica Section A — Fri, 11 Mar 2011 00:32:12 +0100

A mathematical framework is developed to describe tilted perovskites using a tensor description of octahedral deformations. The continuity of octahedral tilts through the crystal is described using an operator which relates the deformations of adjacent octahedra; examination of the properties of this operator upon application of symmetry elements allows the space group of tilted perovskites to be obtained. It is shown that the condition of octahedral continuity across a planar defect such as an anti-phase boundary or domain wall necessarily leads to different octahedral tilting at the defect, and a method is given to predict the local tilt system which will occur in any given case. Planar boundaries in the rhombohedral R3c a−a−a− tilt system are considered as an example. (Source: Act...

Grazing-incidence small-angle X-ray scattering from a random rough surface: a self-consistent wavefunction approximation

Acta Crystallographica Section A — Thu, 10 Mar 2011 00:00:00 +0100

An attempt is made to go beyond the distorted-wave Born approximation addressed to the grazing-incidence small-angle X-ray (GISAX) scattering from a random rough surface. The integral wave equation adjusted with the Green function formalism is applied. To find out an asymptotic solution of the non-averaged integral wave equation in terms of the Green function formalism, the theoretical approach based on a self-consistent approximation for the X-ray wavefunction is elaborated. Such an asymptotic solution allows one to describe the reflected X-ray wavefield everywhere in the scattering (θ, ϕ) angular range, in particular below the critical angle θcr for total external reflection (θ is the grazing scattering angle with the surface, ϕ is the azimuth scattering angle; θ0 is the grazing in...

Structure-factor analysis of femtosecond microdiffraction patterns from protein nanocrystals

Acta Crystallographica Section A — Fri, 18 Feb 2011 00:22:04 +0100

A complete set of structure factors has been extracted from hundreds of thousands of femtosecond single-shot X-ray microdiffraction patterns taken from randomly oriented nanocrystals. The method of Monte Carlo integration over crystallite size and orientation was applied to experimental data from Photosystem I nanocrystals. This arrives at structure factors from many partial reflections without prior knowledge of the particle-size distribution. The data were collected at the Linac Coherent Light Source (the first hard-X-ray laser user facility), to which was fitted a hydrated protein nanocrystal injector jet, according to the method of serial crystallography. The data are single `still' diffraction snapshots, each from a different nanocrystal with sizes ranging between 100 nm and 2 µm...

Form, symmetry and packing of biomacromolecules. III. Antigenic, receptor and contact binding sites in picornaviruses

Acta Crystallographica Section A — Wed, 16 Feb 2011 00:00:00 +0100

The relation between serotype differentiation and crystallographic symmetry, revealed by the contact fingerprint diagrams investigated in Part II [Janner (2010). Acta Cryst. A66, 312–326] for the human rhinovirus, is extended to the Picornaviridae family. The approach, outlined in Part I [Janner (2010). Acta Cryst. A66, 301–311] and Part II for biomacromolecules packed in a crystal and based on concepts such as packing lattice, kissing points and crystal-packing parameters, can directly be applied to the picornaviruses. In particular, the contact fingerprint diagrams of 20 different virus strains have been derived. In these cases, as for the rhinovirus, these diagrams are serotype/strain specific, justifying the name fingerprint. The molecular basis for the serotype variability, and th...

Verification of structural and electrostatic properties obtained by the use of different pseudoatom databases

Acta Crystallographica Section A — Wed, 26 Jan 2011 15:56:19 +0100

The existing pseudoatom databases (ELMAM, Invariom, UBDB and ELMAM2) enable structure refinement to be performed with the use of aspherical scattering factors computed from the transferable aspherical atom model (TAAM) as an alternative to independent atom model refinement. In addition, electrostatic properties can be estimated with the help of the databases. The quality of the structural and electrostatic properties obtained from the individual databases was tested. On the basis of a 100 K high-resolution single-crystal X-ray diffraction experiment on l-His–l-Ala dihydrate and 23 K high-resolution data for l-Ala [Destro & Marsh (1988). J. Phys. Chem. 92, 966–973], the structural properties, electron-density distributions and molecular electrostatic potentials obtained from differe...

Importance of the consideration of anharmonic motion in charge-density studies: a comparison of variable-temperature studies on two explosives, RDX and HMX

Acta Crystallographica Section A — Wed, 26 Jan 2011 00:00:00 +0100

Extremely accurate X-ray data were obtained for the explosive RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) at three different temperatures (20, 120 and 298 K). Collected reflections were integrated using the latest version of the program VIIPP which uses separate Kα1/Kα2 contributions to the profile fitting during integration. For each temperature both anharmonic and harmonic descriptions of the atomic thermal motion were utilized in the model refinements along with the multipole expansion of the electron density. H atoms were refined anisotropically and agree well with a previous neutron study. Topological analysis [Bader (1990). Atoms in Molecules: A Quantum Theory. The International Series of Monographs of Chemistry, edited by J. Halpern & M. L. H. Green. Oxford: Clarendon Press] o...

Interference fringes in multiple Bragg–Laue mode

Acta Crystallographica Section A — Wed, 26 Jan 2011 00:00:00 +0100

have been measured from the lateral surface of an Si plane-parallel crystal by changing the distance L between the incident point of X-rays and the crystal edge for two sample crystals with different thicknesses H. The period of the interference fringes becomes large when the distance L becomes large or the thickness H becomes small. When the ratio L/H is larger than 15, a shorter period of oscillation appears in addition to the interference fringes. These variations are explained by considering the beams in multiple Bragg–Laue modes based on the dynamical theory of diffraction. When L/H is less than 15, the measured fringes are well reproduced by taking account of interference between beams in the Bragg–Laue and the Bragg–Bragg–Laue modes. The short period of the oscillations obs...

Notes for authors 2011

Acta Crystallographica Section A — Wed, 15 Dec 2010 00:00:00 +0100

(Source: Acta Crystallographica Section A)

Isomorphism of lattices of subgroups of the layer and rod groups with sublattices of subgroups of the space groups

Acta Crystallographica Section A — Wed, 15 Dec 2010 00:00:00 +0100

Following a brief overview of current knowledge on lattices of subgroups of the space groups, it is shown that in the case of reducible space groups those lattices contain sublattices which are lattice isomorphic to the lattices of subgroups of layer and rod groups. Both sublattices involve the sublattice consisting of equitranslational subgroups. (Source: Acta Crystallographica Section A)

Euclidian embeddings of periodic nets: definition of a topologically induced complete set of geometric descriptors for crystal structures

Acta Crystallographica Section A — Wed, 15 Dec 2010 00:00:00 +0100

Crystal-structure topologies, represented by periodic nets, are described by labelled quotient graphs (or voltage graphs). Because the edge space of a finite graph is the direct sum of its cycle and co-cycle spaces, a Euclidian representation of the derived periodic net is provided by mapping a basis of the cycle and co-cycle spaces to a set of real vectors. The mapping is consistent if every cycle of the basis is mapped on its own net voltage. The sum of all outgoing edges at every vertex may be chosen as a generating set of the co-cycle space. The embedding maps the cycle space onto the lattice L. By analogy, the concept of the co-lattice L* is defined as the image of the generators of the co-cycle space; a co-lattice vector is proportional to the distance vector between an atom and the ...

Patterson-function direct methods for structure determination of organic compounds from powder diffraction data. XVI

Acta Crystallographica Section A — Tue, 07 Dec 2010 00:00:00 +0100

A new type of direct methods (DM) called Patterson-function DM are presented that directly explore the Patterson instead of the modulus function. Since they work with the experimental intensities, they are particularly well suited for handling powder diffraction data. These methods are based on the maximization of the sum function SP ∝ ∑H(IH − 〈I〉)G–H(Φ) in terms of the Φ phases of the structure factors. The quantity accessible from the experiment is IH, the equidistributed multiplet intensity of reflection H, and 〈I〉 is the average intensity taken over all non-systematically absent reflections. G–H(Φ) is the calculated structure-factor amplitude of the squared structure that includes the positivity and the atomicity of the density function in its definition. The SP su...

PVMR: assembling small helix fragments as structural solutions for molecular replacement

Acta Crystallographica Section A — Tue, 07 Dec 2010 00:00:00 +0100

A new real-space implementation of the molecular-replacement method is described. The method locates the search model in the target crystal by maximizing the matching between the search-model vectors and the Patterson self and cross vectors. In previous work, a new rotation function was introduced for the molecular-replacement method [Jiang (2008). Acta Cryst. D64, 561–566]. This rotation function is calculated by matching the search model directly with both the Patterson self and cross vectors in real space. All the matches are summed and averaged to enhance the overall signal-to-noise ratio for a given orientation of the search model. Recently, to avoid the dependence of the weights derived from the linear regression on the properties of the search model and the target crystal structur...

Practical applications of averages and differences of Friedel opposites

Acta Crystallographica Section A — Tue, 07 Dec 2010 00:00:00 +0100

The practical use of the average and difference intensities of Friedel opposites at different stages of structure analysis has been investigated. It is shown how these values may be properly and practically used at the stage of space-group determination. At the stage of least-squares refinement, it is shown that increasing the weight of the difference intensities does not improve their fit to the model. The correct form of the coefficients for a difference electron-density calculation is given. In the process of structure validation, it is further shown that plots of the observed and model difference intensities provide an objective method to evaluate the fit of the data to the model and to reveal insufficiencies in the intensity measurements. As a further tool for the validation of struct...

Report of the Executive Committee for 2009

Acta Crystallographica Section A — Tue, 30 Nov 2010 00:00:00 +0100

(Source: Acta Crystallographica Section A)

On the allowed values for the triclinic unit-cell angles

Acta Crystallographica Section A — Thu, 25 Nov 2010 00:00:00 +0100

This short article questions and investigates the possible range of values for the three angles of a unit cell in the triclinic system. Although no constraints are reported in manuals and tables for crystallography, the three angles are not really independent; the range of allowed values is calculated and presented in this paper. (Source: Acta Crystallographica Section A)

Generation of (3 + d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures

Acta Crystallographica Section A — Thu, 18 Nov 2010 00:00:00 +0100

A complete table of (3 + 1)D, (3 + 2)D and (3 + 3)D superspace groups (SSGs) has been enumerated that corrects omissions and duplicate entries in previous tables of superspace groups and Bravais classes. The theoretical methods employed are not new, though the implementation is both novel and robust. The paper also describes conventions for assigning a unique one-line symbol for each group in the table. Finally, a new online data repository is introduced that delivers more complete information about each SSG than has been presented previously. (Source: Acta Crystallographica Section A)

Geometric properties of nucleic acids with potential for autobuilding

Acta Crystallographica Section A — Thu, 11 Nov 2010 10:58:59 +0100

We describe a simple method, starting from a list of electron-density `blobs', for identifying backbone phosphates and nucleic acid bases based on properties of the local electron-density distribution. This knowledge should be useful for the automated building of nucleic acid models into electron-density maps. We show that the distances and angles involving C1′ and the P atoms, using the pseudo-torsion angles \eta' and \theta\,' that describe the …P—C1′—P—C1′… chain, provide a promising basis for building the nucleic acid polymer. These quantities show reasonably narrow distributions with asymmetry that should allow the direction of the phosphate backbone to be established. (Source: Acta Crystallographica Section A)

Coincidence lattices in the hyperbolic plane

Acta Crystallographica Section A — Thu, 11 Nov 2010 00:00:00 +0100

The problem of coincidences of lattices in the space {\bb R}^{p,q}, with p + q = 2, is analyzed using Clifford algebra. We show that, as in {\bb R}^n, any coincidence isometry can be decomposed as a product of at most two reflections by vectors of the lattice. Bases and coincidence indices are constructed explicitly for several interesting lattices. Our procedure is metric-independent and, in particular, the hyperbolic plane is obtained when p = q = 1. Additionally, we provide a proof of the Cartan–Dieudonné theorem for {\bb R}^{p,q}, with p + q = 2, that includes an algorithm to decompose an orthogonal transformation into a product of reflections. (Source: Acta Crystallographica Section A)

Ab initio reconstruction of difference densities by charge flipping

Acta Crystallographica Section A — Thu, 11 Nov 2010 00:00:00 +0100

The charge-flipping algorithm in its band-flipping variant is capable of ab initio reconstructions of scattering densities with positive and negative values. It is shown that the method can be applied to reconstructions of difference electron densities of superstructures, i.e. densities obtained as a difference between the true scattering density and the average density over two or more subcells of the true structure. The amplitudes of reflections lying on the reciprocal lattice of the subcell are not required for the procedure. A series of examples shows applications of the method to the solution of superstructures in periodic crystals or quasicrystals as well as the application to ab initio solution of modulation of an incommensurately modulated structure from satellite reflections only ...

SHELX makes an impact

Acta Crystallographica Section A — Tue, 19 Oct 2010 19:10:48 +0100

(Source: Acta Crystallographica Section A)

Prices of IUCr journals

Acta Crystallographica Section A — Mon, 18 Oct 2010 23:00:00 +0100

(Source: Acta Crystallographica Section A)

David H. Templeton (1920–2010)

Acta Crystallographica Section A — Mon, 18 Oct 2010 23:00:00 +0100

(Source: Acta Crystallographica Section A)

Is there a fundamental upper limit for the significance I/σ(I) of observations from X-ray and neutron diffraction experiments?

Acta Crystallographica Section A — Mon, 18 Oct 2010 23:00:00 +0100

The answer is yes. A fundamental limit exists, which is not strongly applicable to individual reflections but to a sufficiently large set of reflections such as any set for structure determination. The limit originates from Poisson statistics which gives a minimum (average) error. The proposed limit of significance and a proposed decrease in significance due to data processing are also tested by monitoring W = {\langle I_{hkl}^{1/2} \rangle/ \langle \sigma (I_{hkl}) \rangle} for raw and for Bragg data. Since Poisson statistics are the lower limit for the experimental standard uncertainties, it is expected that W < 1 for raw and Bragg data, and that W decreases upon data processing. W also gives a measure of systematic errors in the experimental data as W \simeq 1 characterizes pure Poisson...

Simultaneous determination of highly precise Debye–Waller factors and structure factors for chemically ordered NiAl

Acta Crystallographica Section A — Wed, 13 Oct 2010 23:00:00 +0100

Accurate Debye–Waller (DW) factors and several low-index structure factors of chemically ordered β-NiAl at different temperatures have been measured using an off-zone-axis multi-beam convergent-beam electron diffraction method. The temperature dependences of DW factors of Ni and Al atoms are compared with previous experimental measurements and theoretical calculations. The temperature below which the DW factor of Ni becomes smaller than that of Al was found to be lower than previously reported. Structure factors are determined with an accuracy of 0.05% and compared with prior reports. (Source: Acta Crystallographica Section A)

Determination of Debye–Waller factor and structure factors for Si by quantitative convergent-beam electron diffraction using off-axis multi-beam orientations

Acta Crystallographica Section A — Wed, 13 Oct 2010 23:00:00 +0100

Debye–Waller (DW) factors and structure factors have been measured for Si using convergent-beam electron diffraction (CBED) experiments with a transmission electron microscope equipped with a field-emission gun and a post-column energy-filtering device. Si has been used here to evaluate the accuracy of multi-beam near-zone-axis orientations for the simultaneous refinement of DW factors and multiple structure factors. Strong dynamic interactions among different beams are obtained by tilting the crystal to specific four- or six-beam orientations near major zone axes, which provide sufficient sensitivity to determine accurate DW factors and structure factors. The DW factors of Si were measured using four-beam conditions near the [001] zone axis for temperatures ranging from 96 to 300 K. A...

Probability density functions of the average and difference intensities of Friedel opposites

Acta Crystallographica Section A — Wed, 13 Oct 2010 23:00:00 +0100

Trigonometric series for the average (A) and difference (D) intensities of Friedel opposites were carefully rederived and were normalized to minimize their dependence on \sin(\vartheta)/\lambda. Probability density functions (hereafter p.d.f.s) of these series were then derived by the Fourier method [Shmueli, Weiss, Kiefer & Wilson (1984). Acta Cryst. A40, 651–660] and their expressions, which admit any chemical composition of the unit-cell contents, were obtained for the space group P1. Histograms of A and D were then calculated for an assumed random-structure model and for 3135 Friedel pairs of a published solved crystal structure, and were compared with the p.d.f.s after the latter were scaled up to the histograms. Good agreement was obtained for the random-structure model and a quali...

Double-slit dynamical diffraction of X-rays in ideal crystals (Laue case)

Acta Crystallographica Section A — Mon, 04 Oct 2010 23:00:00 +0100

The theoretical investigation of double-slit dynamical X-ray diffraction in ideal crystals shows that, on the exit surface of crystals, interference fringes similar to Young's fringes are formed. An expression for the period of the fringes was obtained. The visibility of the fringes depending on temporal and spatial coherent properties of the incident beam is studied. The polarization state of the incident beam also affects the visibility of the fringes, which in turn depends on the size of the slits. The deviation from Bragg's exact angle causes a shift of the fringes and can also affect the amplitude of the intensity. One of the parameters on which the visibility of the fringes depends is the source–crystal distance. The proposed scheme can be used as a Rayleigh X-ray interferometer. U...

X-ray diffraction peaks from correlated dislocations: Monte Carlo study of dislocation screening

Acta Crystallographica Section A — Mon, 04 Oct 2010 23:00:00 +0100

X-ray diffraction peak profiles are calculated by the Monte Carlo method for arbitrarily correlated dislocations without making any approximations or simplifications. The arrangement of dislocations in pairs with opposite Burgers vectors provides screening of the long-range strains. Moreover, any screening can be modeled by appropriate distribution of the dislocation pairs. Analytical description of the peak profiles is compared with the Monte Carlo results. Symmetric peaks due to screw dislocations and asymmetric peaks due to edge dislocations are simulated and analyzed. (Source: Acta Crystallographica Section A)

The influence of different Student's T mosaic distributions on the extinction factor in mosaic crystals

Acta Crystallographica Section A — Mon, 04 Oct 2010 23:00:00 +0100

During the preparation of versatile tables for the secondary extinction factor Yμ of cylindrical and spherical mosaic crystals expressed as functions of the Bragg angle θ, absorption coefficient times radius μρ and reduced radius τ0 = σ0ρ [σ0 = (2π)1/2Q/η], or of θ, τ0 and ξ0 = μ/σ0, five kinds of Student's Tn probability functions T1, T2, T3, T4, T∞ for describing the mosaic distribution of crystals have been tested. T1 is Lorentzian (L) and T∞ is close to Gaussian (G). The influence of these different mosaic distributions upon the reflection power ratio, the integrated reflection power ratio (the area under the rocking curve) and the extinction factor Yμ in cylindrical crystals has been thoroughly investigated. For a weakly absorbing cylindrical crystal with τ0 = 30,...

Volume of intersection of two balls in orientation space

Acta Crystallographica Section A — Mon, 27 Sep 2010 23:00:00 +0100

Orientations deviating from an ideal orientation by angles not exceeding a given limit constitute a ball in the metric space of orientations. Such balls arise in crystallographic computations, and in some cases intersections of the balls are of interest. This paper provides an analytical formula for calculation of the volume of the intersection of two balls from their radii and the distance between their centers. The formula is used to determine the volumes of the intersections of balls corresponding to misorientations of coincident lattices. (Source: Acta Crystallographica Section A)

Magnetic space and superspace groups, representation analysis: competing or friendly concepts?

Acta Crystallographica Section A — Mon, 27 Sep 2010 23:00:00 +0100

Although encoded in theoretical works, relationships between the diffraction symmetry of magnetic structures and magnetic space/superspace groups are often ignored in practical applications. It is shown that magnetic symmetry operations have a direct impact through the rotation parts in the diffraction symmetry of the crystal and can be used to simplify calculations of magnetic structure factors. Besides, the translation parts can introduce specific systematic extinctions of magnetic reflections. Another point is that the efficiency and stability of refinement of magnetic crystal structures, in analogy with the refinement of nuclear structures, depend on direct application of the magnetic symmetry in the structure-factor formula. Magnetic symmetry also allows diffractionally independent ma...

Data scaling and temperature calibration in time-resolved photocrystallographic experiments

Acta Crystallographica Section A — Thu, 23 Sep 2010 10:20:09 +0100

Experiments in which structural changes in crystals are induced by pulsed-laser exposure involve an increase in sample temperature due to the dissipation of the deposited excess energy. The heat increase is especially pronounced when a large number of pulses is needed, as in pseudo-steady-state experiments conducted at conventional sources, but not negligible in synchrotron studies in which very short laser exposures may be adequate. The relative scaling of the light-ON and light-OFF data and the correction for temperature differences between the two sets are discussed. (Source: Acta Crystallographica Section A)

X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism

Acta Crystallographica Section A — Tue, 21 Sep 2010 23:00:00 +0100

The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoff's integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection Rcoh(θ) and transmission Tcoh(θ) coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height–height correlation function. In the limiting cases when the correlation length \xi is equal to zero or infinity, analytical formulae for the reflection Rcoh(θ) and transmission Tcoh(θ) coefficients of the specular wave are obtained. It is important that in the case...

Simple tilings by polyhedra with five- and six-sided faces

Acta Crystallographica Section A — Tue, 21 Sep 2010 23:00:00 +0100

Thirteen tilings of space by simple polyhedra with five- and six-sided faces (`fullerenes') are reported in which there are up to 11 kinds of vertex (vertex 11-transitive). All tilings contain dodecahedra and one or more of nine other kinds of tile. The duals are tilings by tetrahedra and include the four simplest of the known Frank–Kasper intermetallic structure phases. A fifth structure involving just the Frank–Kasper coordination polyhedra has a higher average coordination number than any known or postulated Frank–Kasper phase. (Source: Acta Crystallographica Section A)

Structural transitions in solids

Acta Crystallographica Section A — Thu, 12 Aug 2010 09:04:34 +0100

(Source: Acta Crystallographica Section A)

Crystallography of Quasicrystals. By Walter Steurer and Sofia Deloudi. Springer Series in Materials Sciences No. 126. Springer, 2009. Pp. xiv + 384. Price (hardback) EUR 128.35. ISBN 978-3-642-01898-5, e-ISBN 978-3-642-01899-2, doi 10.1007/978-3-642-01899-2.

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

(Source: Acta Crystallographica Section A)

Polarization effects and phase equilibria in high-energy-density polyvinylidene-fluoride-based polymers

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

Using first-principles calculations, the phase diagrams of polyvinylidene fluoride (PVDF) and its copolymers under an applied electric field are studied and phase transitions between their nonpolar α and polar β phases are discussed. The results show that the degree of copolymerization is a crucial parameter controlling the structural phase transition. In particular, for tetrafluoroethylene (TeFE) concentration above 12%, PVDF–TeFE is stabilized in the β phase, whereas the α phase is stable for lower concentrations. As larger electric fields are applied, domains with smaller concentrations (\leq 12%) undergo a transition from the α to the β phase until a breakdown field of ~600 MV m−1 is reached. These structural phase transitions can be exploited for efficient storage of ele...

Interactive visualization of quantum-chemistry data

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

Simulation and computation in chemistry studies have improved as computational power has increased over recent decades. Many types of chemistry simulation results are available, from atomic level bonding to volumetric representations of electron density. However, tools for the visualization of the results from quantum-chemistry computations are still limited to showing atomic bonds and isosurfaces or isocontours corresponding to certain isovalues. In this work, we study the volumetric representations of the results from quantum-chemistry computations, and evaluate and visualize the representations directly on a modern graphics processing unit without resampling the result in grid structures. Our visualization tool handles the direct evaluation of the approximated wavefunctions described as...

Integral modeling approach to study the phase behavior of complex solids: application to phase transitions in MgSiO3 pyroxenes

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

A combination of electronic structure calculations, classical molecular dynamics simulations and metadynamics is proposed to study the phase behavior of complex crystals. While the former provide accurate energetics for thermodynamic properties, molecular dynamics and metadynamics simulations may reveal new metastable phases and provide insight into mechanisms and kinetics of the respective structural transformations. Here, different simulation methods are used to investigate the polymorphism of MgSiO3 pyroxenes (enstatites) up to high pressures and temperatures. A number of displacive phase transitions are observed within the three basic structure types clino-, ortho- and protoenstatite using classical molecular dynamics simulations. Transitions between these types require a change of sta...

Addressing chemical diversity by employing the energy landscape concept

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

Exploring the structural diversity of a chemical system rests on three pillars. First, there is the global exploration of its energy landscape that allows one to predict which crystalline modifications can exist in a chemical system at a given temperature and pressure. Next, there is the development of new synthesis methods in solid-state chemistry, which require only very low activation energies such that even metastable modifications corresponding, for example, to minima on the landscape surrounded by low barriers can be realized. Finally, there is the theoretical design of optimal synthesis routes, again based on the study of the system's energy landscape. In this paper the energy landscape approach to the prediction of stable and metastable compounds as a function of temperature and pr...

Crystal fingerprint space – a novel paradigm for studying crystal-structure sets

Acta Crystallographica Section A — Wed, 11 Aug 2010 23:00:00 +0100

The initial aim of the crystal fingerprint project was to solve a very specific problem: to classify and remove duplicate crystal structures from the results generated by the evolutionary crystal-structure predictor USPEX. These duplications decrease the genetic diversity of the population used by the evolutionary algorithm, potentially leading to stagnation and, after a certain time, reducing the likelihood of predicting essentially new structures. After solving the initial problem, the approach led to unexpected discoveries: unforeseen correlations, useful derived quantities and insight into the structure of the overall set of results. All of these were facilitated by the project's underlying idea: to transform the structure sets from the physical configuration space to an abstract, high...

A special class of simple 24-vertex polyhedra and tetrahedrally coordinated structures of gas hydrates

Acta Crystallographica Section A — Wed, 04 Aug 2010 23:00:00 +0100

It is established that the eight-dimensional lattice E8 and the Mathieu group M12 determine a unique sequence of algebraic geometry constructions which define a special class of simple 24-vertex, 14-face polyhedra with four-, five- and six-edge faces. As an example, the graphs of the ten stereohedra that generate most known tetrahedrally coordinated water cages of gas hydrates have been derived a priori. A structural model is proposed for the phase transition between gas hydrate I and ice. (Source: Acta Crystallographica Section A)

Space fullerenes: a computer search for new Frank–Kasper structures

Acta Crystallographica Section A — Wed, 04 Aug 2010 23:00:00 +0100

A Frank–Kasper structure is a 3-periodic tiling of the Euclidean space {\bb E}^3 by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank–Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank–Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank–Kasper–Sullivan, Shoemaker–Shoemaker, Sadoc–Mosseri and Deza–Shtogrin. (Source: Acta Crystallographica Section A)

Geometric parameters of isotropic ensembles of right cylinders from the small-angle-scattering correlation function

Acta Crystallographica Section A — Wed, 04 Aug 2010 23:00:00 +0100

The scattered intensity of ensembles of right homogeneous quasi-diluted cylinders with constant oval right section (RS) and volume fraction ϕ are analyzed using the small-angle-scattering (SAS) correlation function (CF) γ(r) = γ(r, ϕ) in the isotropic two-phase approximation. A relation between the CF of the cylinder RS, β0(r), and the CF of the single cylinder of height H, γ0(r, H), allows the calculation of the explicit cylinder parameters of height, surface area, RS surface area, RS perimeter and volume. This is accomplished by evaluating the first two derivatives of γ0(r) at r = 0. Without the assumption of an oval RS, neither H nor the RS surface area can be uniquely determined. (Source: Acta Crystallographica Section A)

Mode crystallography of distorted structures

Acta Crystallographica Section A — Thu, 22 Jul 2010 07:31:52 +0100

The description of displacive distorted structures in terms of symmetry-adapted modes is reviewed. A specific parameterization of the symmetry-mode decomposition of these pseudosymmetric structures defined on the setting of the experimental space group is proposed. This approach closely follows crystallographic conventions and permits a straightforward transformation between symmetry-mode and conventional descriptions of the structures. Multiple examples are presented showing the insight provided by the symmetry-mode approach. The methodology is shown at work, illustrating its various possibilities for improving the characterization of distorted structures, for example: detection of hidden structural correlations, identification of fundamental and marginal degrees of freedom, reduction of ...

On R factors for dynamic structure crystallography

Acta Crystallographica Section A — Wed, 21 Jul 2010 23:00:00 +0100

In studies of dynamic changes in crystals in which induced metastable species may have lifetimes of microseconds or less, refinements are most sensitive if based on the changes induced in the measured intensities. Agreement factors appropriate for such refinements, based on the ratios of the intensities before and after the external perturbation is applied, are discussed and compared with R factors commonly applied in static structure crystallography. (Source: Acta Crystallographica Section A)

Diffusion-equation method for crystallographic figure of merits

Acta Crystallographica Section A — Wed, 21 Jul 2010 23:00:00 +0100

Global optimization methods play a significant role in crystallography, particularly in structure solution from powder diffraction data. This paper presents the mathematical foundations for a diffusion-equation-based optimization method. The diffusion equation is best known for describing how heat propagates in matter. However, it has also attracted considerable attention as the basis for global optimization of a multimodal function [Piela et al. (1989). J. Phys. Chem. 93, 3339–3346]. The method relies heavily on available analytical solutions for the diffusion equation. Here it is shown that such solutions can be obtained for two important crystallographic figure-of-merit (FOM) functions that fully account for space-group symmetry and allow the diffusion-equation solution to vary depend...

Interbranch transient beating of X-ray intensities in deformed crystals

Acta Crystallographica Section A — Tue, 25 May 2010 23:00:00 +0100

X-ray dynamical diffraction in a deformed crystal is studied using the interbranch resonance concept. It is shown that appreciable beating of the X-ray intensities may be induced by a lattice distortion that produces interbranch transformations of the local dispersion surface. In X-ray plane-wave topography, this effect may be observed as interference fringes arising around the kinematical image of a defect. It is predicted that such interbranch fringes can be induced by edge dislocations. (Source: Acta Crystallographica Section A)

Structure factor for decorated Penrose tiling in physical space

Acta Crystallographica Section A — Tue, 25 May 2010 23:00:00 +0100

The structure factor for an arbitrarily decorated Penrose tiling has been calculated in the average unit cell description. The obtained formula uses only the physical coordinates of the atoms decorating a structure. The final equation can be easily extended so that it can describe the other physical properties of a structure. Its usefulness is demonstrated by its use in the Al–Ni–Co alloy structure-refinement process. (Source: Acta Crystallographica Section A)

Multipole electron-density modelling of synchrotron powder diffraction data: the case of diamond

Acta Crystallographica Section A — Tue, 18 May 2010 23:00:00 +0100

Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with li...

Comparative refinement of correct and incorrect structural models of tetrabutylammonium tetrabutylborate – pitfalls arising from poor-quality data

Acta Crystallographica Section A — Wed, 12 May 2010 23:00:00 +0100

This paper demonstrates how numerical parameters usually used to assess the quality of a crystal structure solution (R, wR and S) may be misleading when studying a model refined against poor-quality data. Weakly diffracting crystals of tetrabutylammonium tetrabutylborate, a low-density organic salt comprising isoelectronic cations and anions, were measured using Cu and Mo Kα radiation. Along with the correct structural model, six erroneous structural models were constructed and refined against the same data. For both data sets it was found that models based on an incorrect unit-cell choice give lower values of R and wR than the correct one, thus apparently being in better agreement with measured data. Closer inspection of the measured data shows that this is in fact not the case. (Source:...

Three-beam X-ray rocking curves calculated from computer-simulated pinhole topographs

Acta Crystallographica Section A — Wed, 12 May 2010 23:00:00 +0100

X-ray rocking curves are reported which have been obtained by fast-Fourier-transforming X-ray amplitudes in three-beam pinhole topographs. The topographs were computer-simulated based on the Takagi–Taupin equation with the condition of spherical-wave X-ray incidence. This is another strategy for calculating three-beam rocking curves, which are usually calculated based on the Ewald–Laue dynamical theory. (Source: Acta Crystallographica Section A)

Combined structure-factor phase measurement and theoretical calculations for mapping of chemical bonds in GaN

Acta Crystallographica Section A — Fri, 07 May 2010 15:10:33 +0100

We report here accurate low-order structure-factor phases and amplitudes for gallium nitride (GaN) in the wurtzite structure. The measurement accuracy is up to 0.1% for amplitude and 0.2° for phases. By combining these with high-order structure factors from electronic structure calculation, charge-density maps were obtained. Fine bonding features suggest that the Ga—N bonds are polar and covalent, with charge transfer from Ga to N; however, the polarity effect is extremely small. (Source: Acta Crystallographica Section A)

Non-periodicity in nanoparticles with close-packed structures

Acta Crystallographica Section A — Thu, 06 May 2010 23:00:00 +0100

Experimentally it is observed that nanomaterials from II–VI compounds like CdS have a high density of stacking faults. It is argued that these are not crystal defects but rather that they represent a characteristic feature of nanomaterials. (Source: Acta Crystallographica Section A)

Two-wave approximation in surface effects in asymmetric Laue crystals

Acta Crystallographica Section A — Thu, 06 May 2010 23:00:00 +0100

This paper is a study of surface effects, e.g. roughness or asymmetrical cut, in the Laue diffraction of X-rays by crystals, based on the Takagi–Taupin equations. By means of Riemann–Green integrals, first a formal solution has been obtained when the entrance and the exit surfaces are arbitrary. Then a coordinate transformation mapping a propagation domain with arbitrary boundaries into a rectangular domain with straight boundaries is given. Potential measurement errors in \gamma-ray wavelength and silicon lattice-parameter measurements by double-crystal diffractometry and X-ray interferometry, respectively, are outlined and anticipated by studying, in the two-wave approximation, the reflection peak shift and extra phase originating from an asymmetrically cut crystal. A relationship be...

High-resolution study of dynamical diffraction phenomena accompanying the Renninger (222/113) case of three-beam diffraction in silicon

Acta Crystallographica Section A — Thu, 06 May 2010 23:00:00 +0100

X-ray optical schemes capable of producing a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes have been evaluated and utilized to study high-resolution diffraction phenomena in the Renninger (222/113) case of three-beam diffraction in silicon. The effect of the total reflection of the incident beam into the nearly forbidden reflected beam was observed for the first time with the maximum 222 reflectivity at the 70% level. We have demonstrated that the width of the 222 reflection can be varied many times by tuning the azimuthal angle by only a few µrad in the vicinity of the three-beam diffraction region. This effect, predicted theoretically more than 20 years ago, is explained by the enhancement of the 222 scattering amplitude due to the vi...

Louis Delbaere (1943–2009)

Acta Crystallographica Section A — Fri, 16 Apr 2010 15:21:35 +0100

(Source: Acta Crystallographica Section A)

A general expression of the polarization factor for multi-diffraction processes

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

A general expression of the polarization factor of multi-diffracted beams is formulated. By assigning the diffracted beam direction of each diffraction process as the y axis of a Cartesian coordinate system, the polarization factor of multi-diffraction processes can be easily calculated for polarized and unpolarized beams without being limited by the number of diffraction processes. The method can be applied to processes with more than three scattering events such as multiple diffraction and extinction. (Source: Acta Crystallographica Section A)

Complex quasiperiodic self-similar tilings: their parameterization, boundaries, complexity, growth and symmetry

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

A class of quasiperiodic tilings of the complex plane is discussed. These tilings are based on β-expansions corresponding to cubic irrationalities. There are three classes of tilings: Q3, Q4 and Q5. These classes consist of three, four and five pairwise similar prototiles, respectively. A simple algorithm for construction of these tilings is considered. This algorithm uses greedy expansions of natural numbers on some sequence. Weak and strong parameterizations for tilings are obtained. Layerwise growth, the complexity function and the structure of fractal boundaries of tilings are studied. The parameterization of vertices and boundaries of tilings, and also similarity transformations of tilings, are considered. (Source: Acta Crystallographica Section A)

Interference fringes in multiple Bragg–Laue mode and mirage fringes from bent crystals

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

Interference fringes are measured in the diffraction from the surface as well as from the lateral surface of an Si single-crystal strip which is deformed in cantilever bending as a function of the tip displacement. The interference fringes are observed only when the bending strain is applied. Both interference fringes change conspicuously by increasing the bending strain. The number of the interference fringes changes, and the positions and heights of the peaks in the fringes change. These variations can be explained by the change of the interference between the beams in multiple Bragg–Laue modes and those of mirage diffraction based on the dynamical theory of diffraction. (Source: Acta Crystallographica Section A)

Magnetic short-range order diffuse scattering in quasicrystals

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

An analytical expression is derived for the short-range order (SRO) magnetic neutron diffuse scattering intensity in quasicrystals, and it is applied to a fictitious model of spin-orientation disorder in the Penrose pattern. The SRO diffuse scattering intensity depends on the overlapped volume of the occupation domains which are separated from each other by distances less than the correlation length and the SRO correlation functions. Analytical results for four different spin arrangements in the Penrose pattern are compared with numerical ones. The corresponding analytical and numerical results for all the cases are quite similar, suggesting the validity of the analytical expression. (Source: Acta Crystallographica Section A)

Short-range order diffuse scattering in quasicrystals

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

A theory for the diffuse scattering intensity owing to short-range order (SRO) in quasicrystals is given. The diffuse scattering intensity can be calculated based on higher-dimensional cluster models of quasicrystals. It is determined by the overlapped area (or volume) of occupation domains separated from each other by distances up to the correlation length and the SRO correlation functions. It is applied to a random atom distribution in phason flip sites in the Penrose pattern. To confirm the validity of the derived formula, analytical and numerical results for this case have been compared. Both results give similar diffuse scattering intensity, suggesting the validity of the theory. (Source: Acta Crystallographica Section A)

On the effect of neglecting anharmonic nuclear motion in charge density studies

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

The effect of neglecting anharmonic nuclear motion when it is definitely present is studied. To ensure the presence of anharmonic nuclear motion a model was used that was previously refined against experimental data including anharmonic nuclear motion, and these calculated structure factors were used as observed data for a multipole refinement. It was then studied how the neglect of anharmonic nuclear motion and noise in the data affects the usual crystallographic quality measure R, the density parameters and the residual density distribution. It is demonstrated that the neglect of anharmonic nuclear motion leads to a characteristic imprint onto the residual density distribution in terms of residual density peaks and holes, in terms of the whole residual density distribution and in terms o...

The application of eigensymmetries of face forms to anomalous scattering and twinning by merohedry in X-ray diffraction

Acta Crystallographica Section A — Thu, 15 Apr 2010 23:00:00 +0100

The face form (crystal form) {hkl} which corresponds to an X-ray reflection hkl is considered. The eigensymmetry (inherent symmetry) of such a face form can be used to derive general results on the intensities of the corresponding X-ray reflections. Two cases are treated. (i) Non-centrosymmetric crystals exhibiting anomalous scattering: determination of reflections hkl for which Friedel's rule is strictly valid, i.e. I(hkl) = I(\bar h\bar k\bar l) (Friedel pair, centric reflection), or violated, i.e. I(hkl) ≠ I(\bar h \bar k \bar l) (Bijvoet pair, acentric reflection). It is shown that those reflections hkl strictly obey Friedel's rule, for which the corresponding face form {hkl} is centrosymmetric. If the face form {hkl} is non-centrosymmetric, Friedel's rule is violated due to anomalou...

Electron beam–specimen interactions and their effect on high-angle annular dark-field imaging of dopant atoms within a crystal

Acta Crystallographica Section A — Tue, 30 Mar 2010 23:00:00 +0100

A Bloch wave model based on perturbation theory is used to analyse high-angle annular dark-field (HAADF) imaging of a substitutional and interstitial W atom in [111]-oriented body-centred-cubic Fe. For the substitutional atom the 1s Bloch state is scattered to high angles thereby producing HAADF dopant atom contrast. Intraband scattering of the 1s state is the strongest individual Bloch wave transition but collective interband scattering of the non-1s states to the 1s state leads to variations in the high-angle scattering with depth of the dopant atom. The non-1s states are Coulomb attracted towards the W atom thereby giving rise to an `atom focusing' effect similar to channelling. For the interstitial atom, which in the [111] orientation does not overlap with an atom column of the host la...

The difference electron density: a probabilistic reformulation

Acta Crystallographica Section A — Tue, 30 Mar 2010 23:00:00 +0100

The joint probability distribution function P(E, Ep), where E and Ep are the normalized structure factors of the target and of a model structure, respectively, is a fundamental tool in crystallographic methods devoted to crystal structure solution. It plays a central role in any attempt for improving phase estimates from a given structure model. More recently the difference electron density ρq = ρ − ρp has been revisited and methods based on its modifications have started to play an important role in combination with electron density modification approaches. In this paper new coefficients for the difference electron density have been obtained by using the joint probability distribution function P(E, Ep, Eq) and by taking into account both errors in the model and in measurements. The f...

The role of the tangent bundle for symmetry operations and modulated structures

Acta Crystallographica Section A — Tue, 30 Mar 2010 23:00:00 +0100

An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be derived. Euclidean symmetry operations associated with the tangent bundle are generalized and their usefulness for the determination of the intrinsic translation part in helicoidal axes and glide planes is illustrated. Finally, a novel representation of space groups is shown to be independent of any origin point. (Source: Acta Crystallographica Section A)

Opechowski–Guccione-like symbols labelling magnetic space groups independent of tabulated (0, 0, 0)+ sets

Acta Crystallographica Section A — Fri, 26 Mar 2010 16:17:56 +0100

For the magnetic space-group types with a black and white lattice two sets of symbols have been proposed: the BNS symbols [Belov et al. (1957). Sov. Phys. Crystallogr. 2, 311–322] and the OG symbols [Opechowski & Guccione (1965). Magnetism, edited by G. T. Rado & H. Suhl, Vol. II, Part A, pp. 105–165. New York: Academic Press]. Whereas generators of the group can be read off the BNS symbol, International Tables for X-ray Crystallography (1952) must be consulted to interpret the OG symbols. In the cases where the black and white lattice is centred, it is shown how the OG symbols can be modified so that generators of the group can be deduced directly from the symbol. (Source: Acta Crystallographica Section A)

Form, symmetry and packing of biomacromolecules. II. Serotypes of human rhinovirus

Acta Crystallographica Section A — Fri, 26 Mar 2010 00:00:00 +0100

The differentiation of the human rhinovirus into serotypes, all having very similar structures and the same architecture, is shown to be related to the packing of the viruses in the crystal and to its space-group symmetry. The molecular crystallographic properties (here described in terms of a molecular lattice ΛM instead of the form lattice ΛF considered in previous publications) appear to be compatible with the crystal structure and with the packing lattice ΛP, introduced in Part I [Janner (2010). Acta Cryst. A66, doi:10.1107/S0108767310001674]. On the basis of the enclosing forms of the capsid, a sphere packing is considered, where the spheres touch at kissing points. Residues of each of the four coat proteins (VP1, VP2, VP3, VP4), having a minimal distance from the kissing points, d...

Form, symmetry and packing of biomacromolecules. I. Concepts and tutorial examples

Acta Crystallographica Section A — Fri, 26 Mar 2010 00:00:00 +0100

The aim of this paper is to relate morphological properties of single biomacromolecules based on molecular enclosing forms indexed by an appropriate form lattice to the symmetry of the crystal where the molecules are periodically packed. Similar to the way in which the `molécule intégrante' of Haüy permitted a molecular interpretation of the law of rational indices of crystal growth forms, alternative molecular enclosing forms, indexed by a so-called packing lattice, allow one to bridge the gap between form and crystal lattices. In this first part, selected tutorial examples illustrate the validity of the approach and the crystallographic compatibility between molecular and crystal structures. In particular, integral molecular lattices are shown to imply the observed axial ratios betwee...

Orthorhombic sphere packings. III. Trivariant lattice complexes with mirror symmetry

Acta Crystallographica Section A — Fri, 26 Mar 2010 00:00:00 +0100

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that refer to the 18 orthorhombic trivariant lattice complexes with mirror symmetry. In total, sphere packings of 51 different types have been found. Only for 28 of these types is the maximal inherent symmetry of their sphere packings orthorhombic. Some crystal structures that can be described by means of sphere packings are listed. (Source: Acta Crystallographica Section A)

Dynamical structural science

Acta Crystallographica Section A — Wed, 17 Feb 2010 16:18:31 +0100

(Source: Acta Crystallographica Section A)

Ultrafast X-ray diffraction in liquid, solution and gas: present status and future prospects

Acta Crystallographica Section A — Tue, 16 Feb 2010 00:00:00 +0100

In recent years, the time-resolved X-ray diffraction technique has been established as an excellent tool for studying reaction dynamics and protein structural transitions with the aid of 100 ps X-ray pulses generated from third-generation synchrotrons. The forthcoming advent of the X-ray free-electron laser (XFEL) will bring a substantial improvement in pulse duration, photon flux and coherence of X-ray pulses, making time-resolved X-ray diffraction even more powerful. This technical breakthrough is envisioned to revolutionize the field of reaction dynamics associated with time-resolved diffraction methods. Examples of candidates for the first femtosecond X-ray diffraction experiments using highly coherent sub-100 fs pulses generated from XFELs are presented in this paper. They include...

Analysis of time-resolved X-ray scattering data from solution-state systems

Acta Crystallographica Section A — Tue, 16 Feb 2010 00:00:00 +0100

As ultrafast time-resolved studies of liquid systems with the laser pump/X-ray scattering probe method have come of age over the past decade, several groups have developed methods for the analysis of such X-ray scattering data. The present article describes a method developed primarily with a focus on determining structural parameters in the excited states of medium-sized molecules (\sim30 atoms) in solution. The general methodology is set in a maximum-likelihood framework and is introduced through the analysis of the photoactive platinum compound PtPOP, in particular the structure of its lowest triplet excited state (^3A_{2{u}}). Emphasis is put on structure determination in terms of model comparisons and on the information content of difference scattering signals as well as the related e...