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Cryst
Kinds of Cryst Selected AbstractsComments on papers reporting IR-spectra and other data of alleged L-alanine alaninium nitrate and L-alanine sodium nitrate crystalsCRYSTAL RESEARCH AND TECHNOLOGY, Issue 7 2009M. Fleck Abstract We argue that the IR- and Raman-spectra of "L-alanine alaninium nitrate" given in "Investigation on the growth, optical behaviour and factor group of an NLO crystal: L-Alanine Alaninium nitrate" by Aravindan et al., Cryst. Res. Technol. 42, 1097 (2007), actually concern L-Alanine. Correspondingly, the data presented in "A comparative study on the growth and characterization of nonlinear optical amino acid crystals: L-Alanine (LA) and L-alanine alaninium nitrate (LAAN)" by Aravindan et al., Spectrochim. Acta A 71, 297 (2008), seems to be erroneous, as is "Synthesis, Growth, and Characterization of a New Semiorganic Nonlinear Optical Crystal: L-Alanine Sodium Nitrate (LASN)", Sethuraman, et al., Cryst. Growth Des. 8, 1863 (2008). In these papers properties and data were reported for L-Alanine compounds that actually are L-Alanine crystals and, in addition, unit cell parameters were given that seem to have been copied from other papers. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Ab initio structure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density eliminationJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2010Frank Fleischer Comprehensive tests on the density-modification methods charge flipping [Oszlányi & Süt, (2004). Acta Cryst. A60, 134,141] and low-density elimination [Shiono & Woolfson (1992). Acta Cryst. A48, 451,456] for solving crystal structures are performed on simulated diffraction data of periodic structures and quasicrystals. A novel model-independent figure of merit, which characterizes the reliability of the retrieved phase of each reflection, is introduced and tested. The results of the performance tests show that the quality of the phase retrieval highly depends on the presence or absence of an inversion center and on the algorithm used for solving the structure. Charge flipping has a higher success rate for solving structures, while low-density elimination leads to a higher accuracy in phase retrieval. The best results can be obtained by combining the two methods, i.e. by solving a structure with charge flipping followed by a few cycles of low-density elimination. It is shown that these additional cycles dramatically improve the phases not only of the weak reflections but also of the strong ones. The results can be improved further by averaging the results of several runs and by applying a correction term that compensates for a reduction of the structure-factor amplitudes by averaging of inconsistently observed reflections. It is further shown that in most cases the retrieved phases converge to the best solution obtainable with a given method. [source] EXPO2009: structure solution by powder data in direct and reciprocal spaceJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2009Angela Altomare The program EXPO2009 is the evolution of EXPO2004 [Altomare, Caliandro, Camalli, Cuocci, Giacovazzo, Moliterni & Rizzi (2004). J. Appl. Cryst. 37, 1025,1028]. EXPO2009 performs all the steps of ab initio structure solution by powder data: indexing, space-group determination, estimation of the reflection integrated intensities, structure solution by direct/Patterson methods and/or by a direct-space/hybrid approach, and model refinement by the Rietveld technique. New procedures have been introduced in EXPO2009 for enhancing the structure solution process, particularly in the case of low-resolution data and/or organic compounds, when traditional approaches like direct methods may fail. The EXPO2009 graphical interface has been optimized and made very user friendly. [source] Advances in powder diffraction pattern indexing: N-TREOR09JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2009Angela Altomare Powder pattern indexing can still be a challenge, despite the great recent advances in theoretical approaches, computer speed and experimental devices. More plausible unit cells, belonging to different crystal systems, are frequently found by the indexing programs, and recognition of the correct one may not be trivial. The task is, however, of extreme importance: in case of failure a lot of effort and computing time may be wasted. The classical figures of merit for estimating the unit-cell reliability {i.e.M20 [de Wolff (1968). J. Appl. Cryst.1, 108,113] and FN [Smith & Snyder (1979). J. Appl. Cryst.12, 60,65]} sometimes fail. For this reason, a new figure of merit has been introduced in N-TREOR09, the updated version of the indexing package N-TREOR [Altomare, Giacovazzo, Guagliardi, Moliterni, Rizzi & Werner (2000). J. Appl. Cryst. 33, 1180,1186], combining the information supplied by M20 with additional parameters such as the number of unindexed lines, the degree of overlap in the pattern (the so-called number of statistically independent observations), the symmetry deriving from the automatic evaluation of the extinction group, and the agreement between the calculated and observed profiles. The use of the new parameters requires a dramatic modification of the procedures used worldwide: in the approach presented here, extinction symbol and unit-cell determination are simultaneously estimated. N-TREOR09 benefits also from an improved indexing procedure in the triclinic system and has been integrated into EXPO2009, the updated version of EXPO2004 [Altomare, Caliandro, Camalli, Cuocci, Giacovazzo, Moliterni & Rizzi (2004). J. Appl. Cryst. 37, 1025,1028]. The application of the new procedure to a large set of test structures is described. [source] CRUNCH: a phase refinement program for high-resolution macromolecular structuresJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2000David A. Langs A phase refinement program for high-resolution macromolecular structures is described. The mean phase error of an initial structural solution can often be as large as 60° prior to attempting a refinement, but the CRUNCH program procedure may allow one to reduce this phase error to 10 or 20° for all data prior to actually inspecting any map to see how well it may fit a structural model. The procedure is similar to the real/reciprocal space refinement loop incorporated in the half-baked algorithm described by Sheldrick [Sheldrick & Gould (1995). Acta Cryst. B51, 423,431.] Refinement results are presented for nine different structures which diffract to better than 1.2,Ĺ resolution. The program and test data are available via anonymous ftp (nexus.hwi.buffalo.edu). [source] Form, symmetry and packing of biomacromolecules.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2010The 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 ,M instead of the form lattice ,F considered in previous publications) appear to be compatible with the crystal structure and with the packing lattice ,P, introduced in Part I [Janner (2010). Acta Cryst. A66, 301,311]. 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, define a set of kissing point related (KPR) residues. In this set only four different residues occur, one for each coat protein, ordered into symmetric clusters {already classified in a previous publication [Janner (2006). Acta Cryst. A62, 270,286]} and indexed by neighbouring lattice points of ,P (or equivalently of ,M). The indexed KPR residues allow a fingerprint characterization of the five rhinovirus serotypes whose structures are known (HRV16, HRV14, HRV3, HRV2 and HRV1A). In the fingerprint they occur as internal (if inside the given capsid), as external (if belonging to the neighbouring viruses) or as a contact residue (if at a kissing point position). The same fingerprint, periodically extended, permits a coarse-grained reconstruction of the essential properties of the crystal packing, invariant with respect to the space group of the serotype. [source] Molecular crystal global phase diagrams.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010In the first part of this series [Keith et al. (2004). Cryst. Growth Des.4, 1009,1012; Mettes et al. (2004). Acta Cryst. A60, 621,636], a method was developed for constructing global phase diagrams (GPDs) for molecular crystals in which crystal structure is presented as a function of intermolecular potential parameters. In that work, a face-centered-cubic center-of-mass lattice was arbitrarily adopted as a reference state. In part two of the series, experimental crystal structures composed of tetrahedral point group molecules are classified to determine what fraction of structures are amenable to inclusion in the GPDs and the number of reference lattices necessary to span the observed structures. It is found that 60% of crystal structures composed of molecules with point-group symmetry are amenable and that eight reference lattices are sufficient to span the observed structures. Similar results are expected for other cubic point groups. [source] Molecular crystal global phase diagrams.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010In previous parts of this series [Mettes et al. (2004). Acta Cryst. A60, 621,636; McClurg & Keith (2010). Acta Cryst. A66, 38,49] a method for constructing global phase diagrams (GPDs) for molecular crystals was developed and the method was applied to single-component ordered crystal structures of tetrahedral molecules. GPDs are useful for visualizing what types of crystal structures a given molecule may assume depending on molecular form/interaction. Their construction uses group-theoretical methods which enumerate all possible symmetry breakings during a statistical mechanical high-to-low temperature search. In this work these results are expanded upon by outlining a method to determine a sufficiently rich parameter space to represent the experimentally observed crystal structures in a data set derived from the Cambridge Structural Database. This is significant because previous work (Mettes et al., 2004) did not specify the number of parameters needed for GPDs. Although there are suggestions in the literature that thousands of parameters are required to adequately describe tetrahedral molecule intermolecular potentials, it is found that 15 parameters are sufficient to represent the structures of the test data. The origin of this difference and its implications for determining GPD parameter values from a more detailed intermolecular potential and for interpreting GPD parameter values are discussed. [source] Improving the direct-methods sign-unconstrained S-FFT algorithm.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009In order to extend the application field of the direct-methods S-FFT phase-refinement algorithm to density functions with positive and negative peaks, the equal-sign constraint was removed from its definition by combining ,2 with an appropriate density function mask [Rius & Frontera (2008). Acta Cryst. A64, 670,674]. This generalized algorithm (S2 -FFT) was shown to be highly effective for crystal structures with at least one moderate scatterer in the unit cell but less effective when applied to structures with only light scatterers. To increase the success rate in this second case, the mask has been improved and the convergence rate of S2 -FFT has been investigated. Finally, a closely related but simpler phase-refinement function (Sm) combining , (instead of ,2) with a new mask is introduced. For simple cases at least this can also treat density peaks in the absence of the equal-sign constraint. [source] On a minimum tetrahedron in a three-dimensional lattice.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2009Part I. Lattices with a shortest basis fulfilling b The problem of a representative body of a three-dimensional lattice is considered. The cell fulfilling a + b + c = min is clearly not unique: even five mutually non-congruent such cells can exist in some lattices [Gruber (1973). Acta Cryst. A29, 433,440]. The idea that this number could be reduced by replacing the cell (i.e. a parallelepiped) by another, possibly more suitable, geometrical object is considered. For this object a lattice tetrahedron fulfilling the condition a + b + c + d + e + f = min is chosen, a to f being the lengths of its edges. It is called the minitetrahedron of the lattice. In this article, the problem is solved in detail for lattices that can be generated by a basis a, b, c fulfilling |a| + |b| + |c| = min, b,·,c, 0, a,·,c, 0, a,·,b, 0. It turns out that in this case not more than two mutually non-congruent minitetrahedra can exist. Necessary and sufficient conditions for the uniqueness are found. They have the form of inequalities between the lengths of the edges and diagonals of the parallelepiped formed by the vectors a, b, c. A procedure for determining all minitetrahedra of a given lattice is shown. Some results are illustrated graphically and all assertions are proved mathematically. [source] Concise intensity statistics of Friedel opposites and classification of the reflectionsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2009U. Shmueli A previous extensive analysis of the mean-square intensity difference of Friedel opposites [Shmueli et al. (2008). Acta Cryst. A64, 476,483] is here concisely re-examined and confirmed by purely statistical methods. The analysis applies to noncentrosymmetric crystals only. For special reflections and centered lattices both mean-square intensity difference and average intensity of Friedel opposites depend on the centering factor of the crystal lattice and/or on the isotropy subgroup of the reflection. A complete classification of the reflections, based on the above intensity statistics, is presented. It is also shown that the experimentally important Bijvoet ratio is found to depend only on the chemical composition of the unit-cell content and the wavelength of the radiation. [source] Correcting electron-density resolution bias in reciprocal spaceACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009Angela Altomare Fourier syntheses are always affected by series-termination errors, which generate sets of positive and negative ripples around each main peak in the map. The interaction among the ripples distorts the profile of the map and moves peaks away from their correct positions. In a previous paper [Altomare et al. (2008). Acta Cryst. A64, 326,336] an algorithm was described which reduces the resolution bias by removing the effects of the ripples in direct space. In this paper the correction is performed in reciprocal space: the effect of the ripples on the atomic scattering factors is calculated and subtracted from the usual atomic scattering factors. The modified scattering factors are used to calculate new structure factors, from which more accurate electron-density maps may be obtained. The experimental tests show that the procedure minimizes the effects of the resolution bias and provides atomic positions that are more accurate than those provided by traditional approaches. [source] Convergence study of a Schrödinger-equation algorithm and structure-factor determination from the wavefunctionACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2008Kostas Bethanis The algorithm [Bethanis, Tzamalis, Hountas & Tsoucaris (2002). Acta Cryst. A58, 265,269] which reformulates the quantum-mechanical problem of solving a Schrödinger (S) equation in a crystallographic context has been upgraded and tested for many aspects of convergence. The upgraded algorithm in reciprocal space aims at determining a wavefunction ,H such that (a) ,H fulfils the S equation within certain precision and (b) ,H minimizes by least squares the differences between the calculated structure factors from the wavefunction and the observed ones. Calculations have been made with three molecules (11, 41 and 110 non-H atoms in the asymmetric unit) for different numbers of initially given phases. Three main questions have been addressed: (I) Does the iterative calculation of the wavefunction converge? (II) Do the calculated wavefunctions converge to a unique set of ,H values independent of the initial random set of ,H? (III) Is the calculated ,H set a good approximation of a wavefunction able to produce within certain errors the correct values of the phases of the structure factors? Concerning questions (I) and (II), our results give a strong hint about fast convergence to a unique wavefunction independent of the arbitrary starting wavefunction. This is an essential prerequisite for practical applications. For question (III) in the case closer to the ab initio situation, the final mean phase error, respectively, for the three structures is 3, 26 and 28°. The combination of (a) and (b) in the upgraded algorithm has been proved crucial especially for the results concerning the larger structures. [source] Reconstruction of an object from its symmetry-averaged diffraction patternACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2008Veit Elser The problem of reconstructing an object from diffraction data that has been incoherently averaged over a discrete group of symmetries is considered. A necessary condition for such data to uniquely specify the object is derived in terms of the object support and the symmetry group. An algorithm is introduced for reconstructing objects from symmetry-averaged data and its use with simulations is demonstrated. The results demonstrate the feasibility of structure determination using a recent proposal for aligning molecules by means of their anisotropic dielectric interaction with an intense light field [Spence et al. (2005). Acta Cryst. A61, 237,245]. [source] Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering dataACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2007Jean-Michel Gillet A possible model of one-electron reduced density matrices is presented, adapted from the Hansen,Coppens pseudo-atomic description of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909,913]. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated. [source] Application of maximum likelihood to direct methods: the probability density function of the triple-phase sums.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2006The maximum-likelihood method is applied to direct methods to derive a more general probability density function of the triple-phase sums which is capable of predicting negative values. This study also proves that maximization of the origin-free modulus sum function S yields, within the limitations imposed by the assumed approximations, the maximum-likelihood estimates of the phases. It thus represents the formal theoretical justification of the S function that was initially derived from Patterson-function arguments [Rius (1993). Acta Cryst. A49, 406409]. [source] Polarization-dependent six-beam X-ray pinhole topographsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2006Kouhei Okitsu X-ray six-beam pinhole topograph images were obtained for a silicon crystal with incident synchrotron X-rays. The polarization state of X-rays incident on the sample crystal was controlled by using a four-quadrant phase-retarder system [Okitsu et al. (2002). Acta Cryst. A58, 146,154] that can be rotated around the transmitted beam axis to generate arbitrarily polarized X-rays. Quantitative agreement was found between the experimental and computer-simulated topograph images based on the n -beam Takagi,Taupin dynamical theory under the assumption that the polarization state of the incident X-rays was identical with the experiment. This result confirmed the validity of the computer algorithm to solve the n -beam dynamical theory and the proper operation of the rotating four-quadrant phase-retarder system simultaneously. [source] Application of modern tensor calculus to engineered domain structures.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2006The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper [Kopský (2006), Acta Cryst. A62, 4764], we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described. [source] X-ray diffraction by a crystal in a permanent external electric field: electric-field-induced structural response in ,-GaPO4ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2006Semen Gorfman For the first time, site-selective distortion has been investigated for two different structural units in the ternary compound ,-GaPO4 under the influence of a permanent external electric field. Based on 54 measured reflection intensities, the electric-field-induced distortion of PO4 and GaO4 tetrahedra in ,-GaPO4 crystals is evaluated using a model of pseudoatomic displacements introduced recently [Gorfman, Tsirelson & Pietsch (2005). Acta Cryst. A61, 387396]. A stronger variation of the P,O bond lengths in the PO4 tetrahedron was found compared to the bonds in the GaO4 tetrahedron. The different distortions of the tetrahedra owing to the electric field were analysed in terms of the valence charge density of ,-GaPO4 and its topological characteristics. The larger charge of the P pseudoatom compared to the Ga atom was recognized as the main reason for the higher sensitivity of the PO4 tetrahedron to a permanent external electric field. [source] Ab initio structure solution by charge flipping.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2005The original charge flipping algorithm [Oszlnyi & St (2004). Acta Cryst. A60,34141] is an amazingly simple structure solution method which works ab initio on high-resolution X-ray diffraction data. In this paper, a new version of the algorithm is presented that complements the phase exploration in reciprocal space. Instead of prescribing observed moduli of all structure factors, weak reflections are treated separately. For these reflections, calculated moduli are accepted unchanged and calculated phases are shifted by a constant ,, = ,/2. This means that the observed data of weak reflections are not used in the iteration, except for the knowledge that they are indeed weak. The improvement is drastic, in some cases the success rate is increased by a factor of ten, in other cases a previously unsolvable structure becomes solvable by the modified algorithm. [source] SPEDEN: reconstructing single particles from their diffraction patternsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2004Stefan P. Hau-Riege SPEDEN is a computer program that reconstructs the electron density of single particles from their X-ray diffraction patterns, using a single-particle adaptation of the holographic method in crystallography [Szöke, Szöke & Somoza (1997). Acta Cryst. A53, 291,313]. The method, like its parent, is unique because it does not rely on `back' transformation from the diffraction pattern into real space and on interpolation within measured data. It is designed to deal successfully with sparse, irregular, incomplete and noisy data. It is also designed to use prior information for ensuring sensible results and for reliable convergence. This article describes the theoretical basis for the reconstruction algorithm, its implementation, and quantitative results of tests on synthetic and experimentally obtained data. The program could be used for determining the structures of radiation-tolerant samples and, eventually, of large biological molecular structures without the need for crystallization. [source] On a fast calculation of structure factors at a subatomic resolutionACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2004P. V. Afonine In the last decade, the progress of protein crystallography allowed several protein structures to be solved at a resolution higher than 0.9,Ĺ. Such studies provide researchers with important new information reflecting very fine structural details. The signal from these details is very weak with respect to that corresponding to the whole structure. Its analysis requires high-quality data, which previously were available only for crystals of small molecules, and a high accuracy of calculations. The calculation of structure factors using direct formulae, traditional for `small-molecule' crystallography, allows a relatively simple accuracy control. For macromolecular crystals, diffraction data sets at a subatomic resolution contain hundreds of thousands of reflections, and the number of parameters used to describe the corresponding models may reach the same order. Therefore, the direct way of calculating structure factors becomes very time expensive when applied to large molecules. These problems of high accuracy and computational efficiency require a re-examination of computer tools and algorithms. The calculation of model structure factors through an intermediate generation of an electron density [Sayre (1951). Acta Cryst.4, 362,367; Ten Eyck (1977). Acta Cryst. A33, 486,492] may be much more computationally efficient, but contains some parameters (grid step, `effective' atom radii etc.) whose influence on the accuracy of the calculation is not straightforward. At the same time, the choice of parameters within safety margins that largely ensure a sufficient accuracy may result in a significant loss of the CPU time, making it close to the time for the direct-formulae calculations. The impact of the different parameters on the computer efficiency of structure-factor calculation is studied. It is shown that an appropriate choice of these parameters allows the structure factors to be obtained with a high accuracy and in a significantly shorter time than that required when using the direct formulae. Practical algorithms for the optimal choice of the parameters are suggested. [source] A revised proof of the metric properties of optimally superimposed vector setsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2002Boris Steipe A revised proof is given that the root-mean-square deviation between more than two vector sets after optimal superposition induces a metric. This corrects an error in a previous manuscript [Kaindl & Steipe (1997). Acta Cryst. A53, 809]. [source] Systematic intensity errors caused by spectral truncation: origin and remedyACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2001A. T. H. Lenstra The wavelength dispersion of graphite(002)-monochromated X-ray beams has been determined for a Cu, a Mo and an Rh tube. The observed values for ,,, were 0.03, 0.14 and 0.16, respectively. The severe reduction in monochromaticity as a function of wavelength is determined by the absorption coefficient , of the monochromator. ,(monochromator) varies with ,3. For an Si monochromator with its much larger absorption coefficient, ,,, values of 0.03 were found, regardless of the X-ray tube. This value matches a beam divergence defined by the size of the focus and of the crystal. This holds as long as the monochromator acts as a mirror, i.e.,(monochromator) is large. In addition to monochromaticity, homogeneity of the X-ray beam is also an important factor. For this aspect the mosaicity of the monochromator is vital. In cases like Si, in which mosaicity is practically absent, the reflected X-ray beam shows an intensity distribution equal to the mass projection of the filament on the anode. Smearing by mosaicity generates a homogeneous beam. This makes a graphite monochromator attractive in spite of its poor performance as a monochromator for , < 1,Ĺ. This choice means that scan-angle-induced spectral truncation errors are here to stay. These systematic intensity errors can be taken into account after measurement by a software correction based on the real beam spectrum and the applied measuring mode. A spectral modeling routine is proposed, which is applied on the graphite-monochromated Mo K, beam. Both elements in that spectrum, i.e. characteristic ,1 and ,2 emission lines and the Bremsstrahlung, were analyzed using the 6318 reflection of Al2O3 (s = 1.2,Ĺ,1). The spectral information obtained was used to calculate the truncation errors for intensities measured in an ,2, scan mode. The results underline the correctness of previous work on the structure of NiSO4·6H2O [Rousseau, Maes & Lenstra (2000). Acta Cryst. A56, 300,307]. [source] Upgrading the twin variables algorithm for large structuresACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2000K. Bethanis Phase extension from lower to higher resolution by using an upgraded TWIN variables algorithm [Hountas & Tsoucaris (1995). Acta Cryst. A51, 754,763] in protein molecules with close to 1000 non-H atoms is presented. Three points of this procedure are of particular interest. (i) The use of a set of auxiliary variables providing a satisfactory fit for many kinds of constraints: the new algorithm works efficiently despite the extreme `dilution' of very limited initial phase information into a much larger set of auxiliary variables. (ii) The extension of this auxiliary variables set beyond the resolution of the observed data, which enhances the phase extension in a so-called `super-resolution' sphere. (iii) The use of the crystallographic symmetry as a new figure of merit and as a reliable test for the correctness of the phase-extension process allows an efficient screening. [source] Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculationsACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2010Jacco Van De Streek This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data. 241 experimental organic crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the experimental and the minimized crystal structures were subjected to statistical analysis. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 experimental crystal structures are reproduced very well: the average r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095,Ĺ (0.084,Ĺ for the 225 ordered structures). R.m.s. Cartesian displacements above 0.25,Ĺ either indicate incorrect experimental crystal structures or reveal interesting structural features such as exceptionally large temperature effects, incorrectly modelled disorder or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect. [source] Modulation functions of incommensurately modulated Cr2P2O7 studied by the maximum entropy method (MEM)ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2010Liang Li The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. [(2006), Acta Cryst. B62, 556,566]. Chromium pyrophosphate, Cr2P2O7, contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of ,,0.01,Ĺ for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities. [source] Revision of the structure of Cs2CuSi5O12 leucite as orthorhombic PbcaACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2010A. M. T. Bell The crystal structure of a hydrothermally synthesized leucite analogue Cs2CuSi5O12 has been determined and refined using the Rietveld method from high-resolution synchrotron X-ray and neutron powder diffraction data. This structure is based on the topology and cation-ordering scheme of the Pbca leucite structure of Cs2CdSi5O12, and exhibits five ordered Si sites and one ordered Cu tetrahedrally coordinated (T) site. This structure for Cs2CuSi5O12 is topologically identical to other known leucite structures and is different from that originally proposed by Heinrich & Baerlocher [(1991), Acta Cryst. C47, 237,241] in the tetragonal space group . The crystal structure of a dry-synthesized leucite analogue Cs2CuSi5O12 has also been refined; this has the cubic pollucite structure with disordered T sites. [source] Towards a more reliable symmetry determination from powder diffraction: a redetermination of the low-temperature structure of 4-methylpyridine- N -oxideACTA CRYSTALLOGRAPHICA SECTION B, Issue 6 2009Palatinus The low-temperature structure of 4-methylpyridine- N -oxide was previously determined in symmetry P41 [Damay et al. (2006), Acta Cryst. B62, 627,633]. Using a recently published symmetry-determination method it was found that the true symmetry of the structure is P41212. The structure was refined in the new space group using X-ray and neutron data. The previously published structure is close to the newly refined structure, but the new structure is in agreement with the results of rotational tunneling spectroscopy, and, in contrast to the structure in symmetry P41, does not require a twofold degeneracy of the tunneling bands. [source] Structures of the pseudo-trigonal polymorphs of Cu2(OH)3Cl.ACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2009Corrigendum An error in the paper by Malcherek & Schlter (2009), Acta Cryst. B65, 334341, is corrected. [source] | ||||||||||