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  • Articles  (123,163)
  • Springer  (84,068)
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  • International Union of Crystallography (IUCr)
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  • 2005-2009  (65,849)
  • 1985-1989
  • 1975-1979  (55,457)
  • 1945-1949  (1,857)
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  • 101
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    The magnetic structure of Bi2Fe4O9 – analysis of neutron diffraction measurements (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 662-666 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The compound Bi2Fe4O9 belongs to the space group Pbam ( D92h), with two formula units per unit cell. Neutron diffraction measurements showed that it is paramagnetic at room temperature and undergoes a transition to an antiferromagnetic state at TN = (264 ± 3) K in agreement with previous susceptibility and Mössbauer measurements. Analysis of the 80 K neutron diffraction pattern yielded a magnetic structure with the following features: (a) The basic translations ao, bo, co of the chemical lattice change into antitranslations in the magnetic lattice. (b) The spins are perpendicular to co. (c) The magnetic structure belongs to the PC2/m space group and is a basis vector to an irreducible space under the Pbam irreducible representations, in accord with Landau's theory of second-order phase transition. The position parameters of the Fe3+ ions in the unit cell were refined. The magnetic moment of the compound was found to be (4.95 ± 0.08) μB, compared with the value of 5 μB for the Fe3+ free ion. The temperature dependence of the { 131 } magnetic reflection peak intensity was measured and found to be in agreement with the sublattice magnetization predicted by the molecular field approximation.
    Type of Medium: Electronic Resource
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  • 102
    Electronic Resource
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    The short-range-order structure of α-phase Cu–Al alloys (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 667-681 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A three-dimensional X-ray diffuse scattering investigation of the short-range order in a-phase Cu-Al alloys, and its dependence on alloy composition, quenching temperature and isothermal annealing at 250°C, has been carried out. The Cowley-Warren order coefficients were determined after separation of the size effects using a procedure based on the Boric-Sparks quadratic approximation of atomic displacements. These short-range-order coefficients were analyzed in terms of the complete spectrum of nearest-neighbor atomic configurations, without the necessity of invoking a specific model for the characteristic feature(s) of the local-order structure. Although in the composition range investigated the equilibrium condition is a short-range-ordered structure, the nearest-neighbor configurations bear a marked resemblance to the long-period anti-phase-shift structures which have been found in alloys with more Al. Because essentially all of the most highly ordered configurations were found to exist isolated from each other in a 9.13 at.% Al alloy, it is concluded that they represent inherently stable, spatial arrangements of the atoms. In alloys containing 13.56 and 14.76 at.% Al, connected ordered configurations, or small ordered domains, were detected, and this effect increases markedly with increasing Al content. Isothermal annealing at 250°C of a Cu-14.76 at.% Al alloy quenched from 650°C results in a net disordering process; however, superimposed on this, in the early stages of annealing, is an enhancement of the population density of an atomic configuration confined to planes of the { 111 } type. This is interpreted as evidence for occurrence of the Suzuki mechanism. It is argued that the body of published experimental observations on this alloy system is better understood if one recognizes the existence of stacking faults, and their interaction with the matrix, in addition to that of short-range order.
    Type of Medium: Electronic Resource
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  • 103
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    Experimental study of disordered mica structures by high-resolution electron microscopy (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 709-719 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Disorder in stacking sequences of mica minerals, predominantly 1M muscovite from York, Ontario and biotite from Mitchell Co., North Carolina, was observed using high-resolution electron microscopy. The specimens were prepared by sectioning the flakes of mica in the microtome with a diamond knife, so that crystals were viewed down the direction parallel to the Si-O layers. Disordered sequences of the layers, as well as ordered crystals, are best described by citing the positions of tunnels between alkali ions lying in the interlayers, since these individual sites are resolved in electron micrographs of micas. An evaluation of the usefulness of one-dimensional lattice fringe images for studying disordered states in crystals is also discussed by comparing them with structure images of corresponding crystals. Intimate intergrowths of different mica polytypes on a scale of tens of ångströms raise questions as to the definition of origins of unit cells and therefore polytypes.
    Type of Medium: Electronic Resource
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  • 104
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    The crystal structure of η-Cu3Si precipitates in silicon (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 684-698 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal structure of Cu-Si precipitates in silicon has been studied by means of transmission electron diffraction and microscopy. The precipitates are shown to be of the equilibrium Cu3Si phase, probably of the low-temperature η” form. Consistent with earlier X-ray diffraction data for this phase, the crystal structure of the precipitates is determined to be based on a trigonally distorted b.c.c. arrangement. The lattice is orthorhombic (C), and is a two-dimensional long-period superlattice, which it is suggested is based on the intermediate-temperature η' phase; lattice parameters aη” = 76.76, bη” = 7.00, cη” = 21.94 Å. On the basis of the diffraction data for the precipitates, it is suggested that the ηand η' phases are both trigonal, space groups R{\bar 3}m and R{\bar 3} respectively, with lattice parameters aη = 2.47 Å, αη = 109.74° and aη' = 4.72 Å, αη' = 95.72°.
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  • 105
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    A Bayesian three-stage model in crystallography (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 728-738 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A Bayesian method of statistical analysis is presented, one which provides a more powerful approach than classical least squares in circumstances where hitherto the latter technique has been applied. The general principles of the method are discussed and applications to crystallographic refinement and primary reduction of diffractometer data given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001503
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  • 106
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    Unique phase determination on the basis of Bijvoet ratios by means of resonant neutron scattering (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 747-750 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new two-wavelength Bijvoet-pair method is proposed, which allows unique experimental determination of anomalous phases without absorption correction and scaling of the Bragg intensities, if the resonant atom structure is known. The method consists of measuring Bijvoet ratios at two wavelengths λ1 and λ2, for which the real and imaginary dispersion terms in the anomalous scattering amplitude fulfil the conditions: b′A(λ1) = -b′A(λ2) and b′′A(λ1) = b′′A(λ2). These conditions can be fulfilled with resonant neutron scattering by nuclei like 113Cd, 149Sm or 157Gd, but not with resonant X-ray or Mössbauer γ-ray scattering. A first application of the method to experimental phase determination for a small structure, Cd-histidine, is described.
    Type of Medium: Electronic Resource
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  • 107
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    Surface and defect properties of solids, Vol. 6 by M. W. Roberts and J. M. Thomas (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 831-832 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001734
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  • 108
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    Convergence of Brillouin zone summations (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 823-824 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple method to overcome convergence problems in Brillouin zone summations of lattice dynamical properties is proposed, which makes use of evenly spread sample points and gives a special treatment to points close to the Brillouin zone origin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001667
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  • 109
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    L'association des familles de Wyckoff dans les changements de repère conventionnel des groupes spatiaux et les passages aux sous-groupes spatiaux (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 811-819 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper is the continuation of another paper devoted to the systematic derivation of space subgroups and changes in standard setting of space groups. In the present paper, the correspondence of the sets of equivalent positions in such transitions is examined. Any set WG of general positions of the space group G splits up into ig/G sets Wg of general positions of the space subgroup g (ig/G is the index of subgroup g): there is a one-to-one correspondence between the Wg sets and the complexes of g in the partition of G; the coordinates of each Wg are obtained, as a function of coordinates of WG, from generating the symmetry operation of the corresponding complex. Miscellaneous examples of splitting of the WG set are investigated in the transitions: I422-P222, Fddd-Bb, P{\bar 1}-P{\bar 1}, I23-F23, P6222-P222. Any set WGP of special positions of G is the result of the superposition of general positions on particular points of point symmetry P. Such superpositions arise in the connected sets of g; there are three ways of grouping the positions in these sets: superposition in one set which turns into one special set WgP, superposition of several general sets which become one general set Wg, and mixed inner-outer superposition which leads to one special set of positions Wgp, their point groups being any subgroup p of P. These properties are illustrated by example of the transition P6222-P222 (10 types of special sets WgP). In the changes in standard setting in a given space group, each general or special set is connected with only one set; if the change of setting is associated with any symmetry operation of the space group, each set of positions is applied to itself.
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  • 110
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    A test for rigid-body vibrations based on a generalization of Hirshfeld's `rigid-bond' postulate (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 828-829 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple test for the validity of the rigid-body model for molecular vibrations in crystals is proposed.
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    URL: http://dx.doi.org/10.1107/S0567739478001692
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  • 111
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    A note on On the diffraction of X-rays by face-centred cubic crystals containing extrinsic stacking faults by C. J. Howard (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 830-830 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The intensity of X- ray scattering from f.c.c. crystals containing extrinsic stacking faults with two fault parameters [see Howard (1977). Acta Cryst. A33, 29-32] has been calculated.
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  • 112
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    An ambiguity in indexing Renninger diagrams and the distinction between some opposite directions in cubic crystals (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 825-826 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the course of a discussion of the nature of an ambiguity in the indexing of Renninger peaks the possibility was discovered of distinguishing some opposite directions in a cubic crystal without recourse to anomalous scattering. A multiple-diffraction experiment performed on a (111) Ge plate rotated about [222] enabled distinction between the [1{\bar 1}0] and [0{\bar 1}1] directions to be made. The azimuthal angles counted from alternative zero meridians containing [1{\bar 1}0] or [0{\bar 1}1] are the same, but give rise to peaks indexed hkl and 2 - l,2 - h,2 - k respectively. However, dynamically equivalent situations 222, hkl/(2 - h,2 - k,2 - l) and 222, (2 - l,2 - h,2 - k)/lhk are geometrically different, being distinguished as Bragg-Laue and Bragg-Bragg, respectively, or vice versa.
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  • 113
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    Dynamic density and structure factors for rigid molecules with large librations (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 905-908 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For rigid molecules which undergo large librations, the dynamic density and the dynamic molecular scattering factor are derived. The general case is treated where translations and librations of the molecule are coupled (no site symmetry). The dynamic molecular scattering factor is an integral which cannot generally be solved, and temperature factors generally do not appear. For the special case of statistically independent translations and librations, a temperature factor for the translations of the molecule is obtained. Moreover, temperature factors are obtained for density units which are spherically symmetric, since the motions of these density units can be described by translations only. The possible cases for which spherically symmetric density units can be assumed and, hence, temperature factors can be applied, are discussed.
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  • 114
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    Refinement of large structures by simultaneous minimization of energy and R factor (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 931-935 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An improved method of crystallographic structure refinement, especially suitable for large molecules, is described, it is based on simultaneous minimization of a realistic potential-energy function and a crystallographic residual. The method has already proved its worth in the final stages of refinement of two structures; an application to crude wiremodel coordinates of a small protein is described and evaluated.
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  • 115
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    Aspects of symmetry in electron diffraction patterns and optical transforms of very small homo-atomic aggregates using computer simulation (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 853-859 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The study investigates the reasons why it may happen that the first simulation of an electron diffraction pattern is not always centrosymmetrical whereas the second one is bound to be so. The formal link between the two simulations is established. A number of examples are given.
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  • 116
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    Positional errors in (partial) structure models; their influence on the residual R2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 860-863 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Algebraic expressions are evaluated, from which the influence of small discrepancies between atomic positions in a structure model and the corresponding atomic sites in the observed structure on R2 can be calculated. Theory and experiment are in good agreement. It is demonstrated that because of the effect of small positional errors, R2 as a function of the size of a structure model does not necessarily show a monotonic decrease. The path of R2 may even contain additional minima.
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  • 117
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    Intermolecular interactions in crystals of carboxylic acids. IV. Empirical interatomic potential functions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 842-853 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An intermolecular force field for carboxylic acids has been derived by a least-squares fit of the parameters of non-bonded atom-atom potentials and a hydrogen-bond potential to experimental data. The latter include heats of dimerization and dimer structures of formic, acetic and propionic acid, and heats of sublimation and crystal structures of acetic, α and β-oxalic, α and β-fumaric and isophthalic acid. It was found that (exp - 6 - 1) atom-atom potentials and the Lippincott-Schroeder potential for the hydrogen bonds reproduce fairly well the experimental energies as well as the structures. The transferability of the potentials was studied with respect to the crystal structure of allene dicarboxylic acid and to the crystal structure and the lattice energy of formic acid, and was found to be good. A comparison is made with the results of other authors.
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  • 118
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    On the application of phase relationships to complex structures. XVI. A random approach to structure determination (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 883-892 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: With triple-phase relationships treated as linear equations it is possible to refine a set of phases from given initial values. Phases so obtained are better than those found by refining to self-consistency with the tangent formula. An investigation of the radius of convergence of the least-squares refinement process showed that a substantially correct solution may often be found even starting with random phases. Systems containing up to 300 phases have been investigated and the results and their implications are discussed. It is concluded that the random approach can, at the very least, be used to obtain 70--100 phases as a good starting point for phase development. There is also the possibility of obtaining a sufficient number of phases directly to define a reasonably complex structure, especially with a computer augmented by an array processor. A problem which can arise with linear equations, as with the tangent formula, is that the phases obtained do not adequately define the enantiomorph and give an E map with a pseudo centre of symmetry. Two methods of overcoming this problem are described.
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  • 119
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    Difference Fourier refinement of metaquohemerythrin (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1014-1019 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A model for metaquohemerythrin from Themiste dyscritum has been refined in the crystallographic sense of the term by difference Fourier methods at 2.8 and 2.5 Å resolution. Fourteen cycles of refinement reduced R from an initial value of 0.385 for the 9461 reflections from 10 to 2.8 Å to 0.253 for 16 363 reflections from 10 to 2.5 Å resolution. On the basis of peaks in difference maps, 49 water molecules have been added to the model for a total of 3833 atoms in the asymmetric unit.
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  • 120
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    Crystal powder statistics. II. Line profiles in diffraction spectra of identical crystals and of Gaussian samples. Crystal size distributions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1006-1013 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The average interference function ({\cal J}hkl(ΔS)) of a powder sample containing perfect crystals at a reciprocal distance ΔS from the peak is evaluated both for the case of identical parallelepiped crystals and for a Gaussian sample [probability of thickness d along a given crystal direction = C1 exp (-C2d2)]. In the latter case ({\cal J}hkl(ΔS)) decreases as 1/ΔS2 for large ΔS, by analogy with the Bernoullian model [Ailegra, Bassi & Meille (1978). Acta Cryst. A34, 652-655] although with a smaller amplitude, for a fixed integrated intensity and half-peak width. It is shown that the Gaussian interference function, or line profile, cannot be given by any real sample, at least if its crystals neither contain holes nor have concave surfaces. Number and weight probability distributions are calculated both for the Bernoullian and for the Gaussian crystal-size statistics. As expected from the calculated line profiles, the Bernoullian statistics correspond to a larger weight percentage of crystals smaller than the average.
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  • 121
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    Clarification of discussion on constrained refinement (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1020-1021 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Pawley's [Acta Cryst. (1976). A32, 921-922] disproof of the C & D method of applying constraints in crystallographic refinements [Chesick & Davidon (1975). Acta Cryst. A31, 586-591] is incorrect. Nevertheless, the C & D method is incorrect. Both the method and its disproof clearly fail for the particular case of linear least-squares with linear constraints. The method can be corrected in this case but not for the non-linear case.
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  • 122
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    On `non-stoichiometric phases' in thin films of rare-earth oxides (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1025-1027 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Kaul & Saxena [Acta Cryst. (1977), A33, 992-996] have reported the existence of long-range and short-range order in a non-stoichiometric phase 'LnOx' (Ln = rare earth). It is shown that the experiments they are describing are indeed the oxidation of the rare-earth hydride LnH2 into the rare-earth cubic C-type sesquioxide. The interpretation they give of their experiments is to be discarded entirely.
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  • 123
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    High-flux micro-resonators for X-ray and γ-ray lasers (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1028-1029 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that a small single crystal may resonate at a wide range of X- and γ-ray frequencies. Such a resonator should produce roughly 1011 times greater radiative flux density per photon than previous designs.
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    A phase transition in a 3D growth-disorder model; erratum (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1030-1030 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The following corrections should be made in Welberry & Miller [Acta Cryst. (1978). A34, 120-123]. 1. Equation (2) on p. 121 should read: E(σ) = - \sum_{{\rm all_{sites}}} σi,j,k [J(σi - 1, j, k + 1 + σ i,j + 1, k - 1 + σi + 1 j - 1, k) + K (σi - 1, j,k + σi,j - 1,k + σi,j,k - 1) + L(σi - 1, j,kσi,j - 1, kσi,j,k - 1)]. 2. The expression for J on p. 121 should be J = 1/8 In [a(1 - a)/b(1 - b)]. 3. In the second paragraph of the second column on p. 121 'J and - K' should be replaced by 'K and -J'. All information is given in the Abstract.
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    Prices of Acta Crystallographica and Journal of Applied Crystallography (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 1047-1048 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    An X-ray diffuse-scattering study of the ordered, cubic, F\overline{4}3m phase of adamantane (tricyclo[3.3.1.13,7]decane) (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 242-249 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray diffuse-scattering experiments at 295 and 218 K on adamantane crystals, grown by annealing, show that its space group is F{\bar 4}3m, and that it is not orientationally disordered. A re-analysis of previous X-ray Bragg-scattering data shows that the conclusion of Fm3m, with orientational disorder, for sublimation-grown crystals is not statistically significant. The Bragg intensities are much less sensitive to orientational disorder than the diffuse scattering. The diffuse scattering shows short-range correlation effects interpretable as pairs of neighbouring molecules tending to adopt local configurations characteristic of the low-temperature P{\bar 4}21c phase, i.e. symmetry breaking in F{\bar 4}3m.
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    Pairs in P21: probability distributions which lead to unique estimates of the two-phase structure seminvariants in the interval (–π,π) (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 230-241 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Conditional probability distributions of the two-phase structure seminvariant φ12 = φh1kl1 - φh2kl2 in P21, given the values of one or more two-phase structure seminvariants, as well as appropriately chosen sets of structure factor magnitudes |E|, are derived. These distributions yield unique and reliable estimates, in the whole interval (-π,π), of the values of these seminvariants. In the case that a given structure seminvariant specifies the enantiomorph, the values of the remaining seminvariants are consistent with this choice of enantiomorph. In any event, the variance of any distribution of the kind described here is much smaller, in favorable cases, than that of a distribution which assumes as known magnitudes |E| alone, reflecting the fact that previously derived phase information severely limits the possible values of other phases.
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    A neutron investigation of the low-temperature structure of RbH3(SeO3)2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 268-274 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal structure of RbH3(SeO3)2 has been determined in the low-temperature phase (space group P21) with neutron diffraction. The crystal undergoes an improper ferroelectric phase transition at 158 K and the unit cell is doubled below the transition temperature. This transition is induced by the condensation of a soft mode at the Brillouin zone boundary. Imposing the symmetry of the soft-mode eigenvector on the static displacements from the high-temperature positions (space group P212121) results in a reduction, by a factor of four, of the number of positional parameters required to describe the low-temperature structure. The crystal is constructed of two types of chains consisting of SeO3 groups connected by hydrogen bonds, and the order parameter for the transition is shown to be the rigid rotations of the SeO3 tetrahedra belonging to one type of chain. The atomic displacements necessary to produce the observed spontaneous polarization are shown to be too small to be observed in the present experiment, and the precise mechanism responsible for the spontaneous polarization remains unknown.
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    Stable calculation of coordinates from distance information (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 282-284 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new method is described for the calculation of Cartesian coordinates for n points given the n × n matrix of interpoint distances. The algorithm is faster than some earlier methods, and it is remarkably stable with respect to both numerical roundoff errors and errors in the given distance matrix. The resultant coordinates have their origin near the center of mass and axes approximately along the three principal rotational axes. The calculation is described of distances to the center of mass directly from the distance matrix. Results of computer trials of the algorithm are given.
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    The electron stationary picture method for high-speed measurement of reflection intensities from crystals with large unit cells (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 289-296 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method for measuring X-ray intensity data from crystals with large unit ceils is presented. The method takes full advantage of the capabilities of the multiwire area detector diffractometer. This diffractometer is a high-speed data collection system utilizing a multiwire proportional chamber that can detect photons from all simultaneously occurring reflections and record the diffraction pattern as a two-dimensional histogram in a computer mass core memory. In the electronic stationary picture method of data collection, reflection intensities are extracted from a sequence of electronic pictures each of which is exposed while the crystal is stationary. Between successive pictures the crystal is rotated about a fixed axis by a small constant angle of approximately 0.05°. Because the integrated intensity of each reflection is extracted from several consecutive pictures, advance prediction of detector coordinates and picture number is required for all reflections and the data-extraction computer program is necessarily complex. Expressions are derived for reflection detector coordinates and setting angles, the system hardware and software are described, the data collection procedure is outlined, and the quality of 7 × 105 reflection intensities measured during six months of operation is analyzed.
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    Primary extinction for finite crystals. Square-section parallelapiped (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 321-326 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The results are given for the calculation of the profile function of the scattering curve and the calculated primary extinction factor for a crystal in the form of a square-section parallelepiped as a function of its size τ, expressed in extinction length units. The calculations are based on the equations of the dynamical theory of diffraction. Asymmetry of the scattering curve and a shift of its principal maximum to larger angles, with τ and the Bragg angle increasing, are found. Approximate expressions for calculating the primary extinction factor as a function of τ are given.
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    A graph theoretical basis for structural chemistry. I. Structures based on trivalent graphs with 10 vertices (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 275-282 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper is the first in a series concerned with a particular graph theoretical scheme for enumeration and derivation of structures of prescribed form. The problem spoken to by this work is that of finding a unique formal procedure for generating all distinct (i.e. non-isomorphic) graphs of a given number of vertices and prescribed valency. Here the scheme is outlined as applied to a search for regular trivalent graphs, some of which correspond to trivalent polyhedra. A systematic procedure for obtaining the number of equivalence classes of the adjacency matrices associated with trivalent graphs of n points is described. The procedure is of general applicability, though no proof of its correctness is offered. Instead, a number of examples are discussed, and its application is illustrated. The scheme is based on consideration of unique matrices associated with graphs which in turn are determined so that the corresponding binary code obtained by reading the rows of the matrix from left to right and from top to bottom represents the smallest possible binary code. Part of the scheme consists in finding all acceptable matrices, testing them for isomorphism, and selecting those which satisfy additional restrictions and ensure that the derived graph represents a structure of interest.
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    A neutron diffraction study of the wavelength dependence of extinction in UO2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 336-341 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron diffraction measurements have been carried out on a single crystal of UO2 examined at four different wavelengths; 0.85, 1.12, 1.54 and 1.84 Å. The Bragg intensities were analysed for the wavelength dependence of extinction using both the Cooper-Rouse and the Becker-Coppens formulations. Both treatments showed that the crystal is of type I (i.e. r 〉〉 λg, where r is the domain radius, λ the wavelength and g the mosaic-spread parameter). The value of g is the same, within one standard deviation, for each wavelength; its magnitude is appreciably less than for other crystals (SrF2,ZnS,ZnTe,KCl) which have been examined by neutron diffraction at a number of wavelengths. Keeping the isotropic temperature factor for uranium fixed at 0.28 Å2, the value of 0.55 ± 0.02 Å2 is derived for the temperature factor of oxygen. There are no significant differences between the values of the extinction parameters and temperature factors obtained using the Cooper-Rouse treatment and the Becker-Coppens treatment based on either a Gaussian or a Lorentzian mosaic-spread distribution.
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    On extrinsic faults in face-centred cubic crystals (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 344-346 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Application of the matrix intensity equation of X-ray diffraction is discussed for the second problem of extrinsic faults in face-centred cubic crystals, discussed by Howard [Acta Cryst. (1977), A33, 29-32]. The second problem is generalized to the case that the probability with which inserted layers follow layers of the original crystal differs from that with which inserted layers follow previously inserted layers. The Q matrix for the case is obtained and the results of intensity calculation are shown.
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    About sequences of maximal subgroups, a few answers to a question from Bertaut: erratum (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 348-348 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Billiet [Acta Cryst. (1977). A33, 1007-1008] the printer has omitted line 17. The last sentence of the first paragraph should read: One knows, at the present time, no complete and definitive answer to this question, but may invoke some general elements which are likely to occur in the resolution of this problem.
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    Crystal form and structure edited by C. J. Schneer (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 349-350 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Concerning an unnecessary approximation made by Zachariasen in treating the perfect-crystal Bragg case (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 343-344 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An approximation in Zachariasen's [Theory of X-Ray Diffraction in Crystals (1945). New York: John Wiley] treatment of X-ray diffraction from a perfect plane-parallel crystal in the Bragg case is pointed out and eliminated. The corresponding unapproximated expression for the transmitted beam is also given. It transpires that Zachariasen's approximation leads to significant errors for 'thin' crystals (i.e. those for which the path length is less than or of the order of the extinction length). Some illustrations of the nature of the error are given.
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    Liquid crystals by S. Chandrasekhar (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 351-351 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Physics of semiconductors edited by F. G. Fumi (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 352-352 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Pendellösung effects as a tool for examining minute strains with a triple-crystal X-ray spectrometer (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 362-367 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Plane-wave Pendellösung effects are shown to be effective and very sensitive for analyzing minute strains in silicon crystals with dimensions normally used for practical applications. In a triple-crystal silicon X-ray spectrometer with an angular beam divergence of less than 0.1" the Pendellösung effect is very pronounced for sample thicknesses up to 1.2 mm. Strain fields are shown for silicon crystals implanted with 60 keV phosphorus ions for doses down to 1013 ion cm-2 and the limit of resolution is one order of magnitude less.
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    Cesium hydrogen tartrate and anomalous dispersion of cesium (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 368-371 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Cesium hydrogen (+)-tartrate is orthorhombic, P212121, a = 8.076 (3), b = 11.621 (5), c = 7.692 (3) Å, Z = 4, Dx = 2.594 g cm-3, at 22°C. Its structure, nearly the same as that of ammonium hydrogen tartrate, was refined to R = 0.016 for 2442 reflections (F2 〉 3σ) out to d = 0.66 Å. Our least-squares program was modified to treat anomalous-dispersion terms as independent adjustable parameters, and f" for cesium was determined as 2.22 (6) e for Mo Kα radiation. In the determination of absolute configuration or polarity, refinement of f" for a heavy atom has the advantage that one can detect inversion twinning, as well as save on computational time.
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    LALS: a linked-atom least-squares reciprocal-space refinement system incorporating stereochemical restraints to supplement sparse diffraction data (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 3-11 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: LALS is a computer program for the refinement of molecular structures. It is primarily intended for helical macromolecules but has applicability in other fields. The refinement uses as data, X-ray structure factors, usually from fibre diffraction studies, and/or stereochemical information, including a comprehensive short-contact search. Various other geometrical constraints and restraints may be placed on the molecular conformation. As parameters of the refinement, LALS uses primarily dihedral angles about single bonds, assuming bond lengths and angles to be fixed and known. This greatly reduces the number of parameters from conventional atom-position refinements, as is necessary in systems where data are sparse. LALS has been used successfully to investigate the structures of a large number of more or less ordered polynucleotides, polysaccharides and other fibrous materials.
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    Modeling of face-centered cubic solid solutions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 65-73 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A computer program has been written to simulate binary face-centered cubic solutions by interchanging the atoms until the populations in 18 shells are in agreement with the short-range order parameters obtained from diffuse X-ray measurements. Comparisons are made between the intensity maps from the model and from the data for most of the published work. We conclude that the published data are of reasonable quality, although sometimes the alphas are somewhat too large or the intensity maps contain artifacts. Computer simulation can be useful in rectifying errors in the experimental parameters.
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    The electron density and bonding in beryllium metal as studied by Fourier methods (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 61-65 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The bonding in Be metal is studied by calculation of valence and deformation density maps from data collected by Brown [Philos. Mag. (1972), 26, 1377-1394]. The deformation maps show clearly that the predominant interaction is bonding through the tetrahedral holes of the h.c.p. lattice. The valence-density maps generally agree with least-squares-model maps published by Stewart [Acta Cryst. (1977), A33, 33-38], though differences in detail exist which may result from incomplete space filling of the least-squares model functions. The experimental densities are interpreted in terms of the hybrid-orbital model of Altmann, Coulson & Hume-Rothery [Proc. R. Soc. London Ser. A, (1957), 240, 145-155] as corresponding to (sp2)a (sp)b hybridization of the Be atoms with b 〉 a. Agreement with a theoretical density obtained by the augmented plane wave calculation of lnoue & Yamashita [J. Phys. Soc. Jpn. (1973), 35, 677-683] supports both theoretical and experimental procedures.
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    Thermal expansion and phase separation of MoSCl (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 137-138 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The lattice parameter of MoSCI was determined at different temperatures from 30 to 437°C with X-ray diffraction methods. The coefficient of thermal expansion of this cubic compound was determined from the above data. At 550°C it was found that the compound irreversibly transforms to α-MoO3, which belongs to the orthorhombic system.
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    Generalized temperature-factor formulation with application to cadmium selenide and other wurtzites (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 130-136 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The generalized temperature factor is formulated within the framework of the one-particle potential in terms of functions derived from the harmonic functions of Stewart. This formulation is then applied to the wurtzite structure and projection analysis is used to eliminate one component of the potential. Inclusion of the generalized temperature factor in the structure-factor expression for wurtzitc leads to the appearance of harmonically forbidden reflections and the loss of equivalence of non-symmetry-related reflections which occur at the same Bragg angle. The results of a room-temperature X-ray experiment with cadmium selenide are interpreted within the above model to yield cubic anharmonic parameters |β332| = |β337| = |β313| = (0.13 ± 0.01) × 10-12 erg A-3. These are used to estimate the anharmonic effect on the position parameter u. Some general conclusions are drawn regarding the possibility of observing similar effects in other wurtzite structures.
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    A description of electron diffraction from higher-order Laue zones (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 138-139 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The usual Bloch wave description of electron diffraction from higher-order Laue zones requires the solution of a quadratic eigenvalue equation. In this note we show that in the high-energy case this eigenvalue equation reduces to linear form.
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    The relationship between cell volume, mean bond length and effective ionic radius (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 139-140 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: If ionic radii are calculated so as to predict accurately mean interatomic distances, then the relationship between cell volume and the cube of the cation radius for a series of isotypic compounds is non-linear.
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    Electron-density studies. III. A re-evaluation of the electron distribution in crystalline silicon (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 183-193 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Highly accurate absolute measurements of the X-ray structure factors of silicon [Aldred & Hart, Proc. R. Soc. London, Ser. A, (1973). 332, 223-238] have been used to analyse a number of models for the electron distribution. Initially, the valence-electron distribution (with the neon core assumed to be unmodified from that of the isolated silicon atoms) was built up with a radial basis of the form rn exp (-ζr) and non-sphericity was allowed for by inclusion of octupole and hexadecapole terms. Improved representation was achieved with related models in which deformations from the total isolated-atom electron density were refined instead. The exact shape of the deformation electron density in the region of the bond was sensitively dependent on the monopole deformation term. The anomalous-dispersion contributions (Δf') to the scattering factors were refined and found to be in agreement with recent interferometric measurements, but not with recent calculations. The octupole density term is slightly sharper at 293.2 than at 92.2 K, and the structure factor for the 222 reflection is predicted to be larger at the higher temperature. These effects may be due to a failure of the convolution approximation or to uncertainties in the anharmonic corrections to the structure-factor data.
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    Electron-density studies. IV. A comparison of techniques for charge-density analysis and their application to s-triazine (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 194-203 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Some techniques for charge-density analysis proposed by R. F. Stewart have been compared by application to s-triazine, with X-ray data and neutron structural parameters. There is strong correlation between population coefficients for density basis functions which overlap heavily with each other, and in extreme cases individual populations are indeterminate. Multipole expansions centred on the nuclei are better defined than sets of orbital products which include two-centre terms. Trigonal octupole functions centred on the carbon and nitrogen nuclei give a marked improvement in the description of the scattering experiment provided the exponents which determine the radial variation of the density functions are optimized. The optimum exponent varies with the length of the multipole expansion. New algorithms developed for these studies give improved computational efficiency.
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    Electron-density studies. V. The electron density in melamine (2,4,6-triamino-s-triazine) with and without exponent refinement (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 203-216 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electron density distribution in melamine has been studied with X-ray diffraction data and neutron structural parameters. The at-rest valence density is represented as a set of nuclear-centred multipole density functions with Slater-type radial functions. Two series of analyses were compared, the first with the radial exponents fixed at the standard molecular values and the second with these exponents as variable parameters. Exponent refinement allows a marked improvement in the fit of the model to the data. The population coefficients of the multipole terms are better defined when the exponents are optimized. On chemically similar atoms the populations of the monopole terms are inversely related to the exponents. The carbon atom parameters agree to high precision. Exponents for the ring and amine nitrogens differ and small differences within each set are related to the hydrogen-bond and packing environment. The exponents and electron density near the nucleus are relatively low for hydrogens involved in hydrogen bonding. The most significant deformation functions in the multipole expansion have a symmetry compatible with nearest-neighbour geometry. Differences between populations are related to distortions from the idealized geometry or to hydrogen-bonding interactions. The inclusion of a hydrogen dipole deformation term with a large exponent results in internally consistent populations which are correlated with N-H stretching amplitudes in the structure. This suggests that the convolution approximation is invalid at this level of structure refinement.
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    Pairs in P21: probability distributions which lead to estimates of the two-phase structure seminvariants in the vicinity of ±π/2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 224-229 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The second sequence of nested neighborhoods of the two-phase structure seminvariant φ12 - φh1kl2 - φh1kl2 in the space group P21 is defined, and conditional probability distributions associated with the first four neighborhoods derived. In the favorable case that the variance of a distribution happens to be small, the distribution yields a particular reliable value for φ12. The most reliable estimates are obtained when φ12 ∼ ± π/2, thus facilitating enantiomorph specification in this space group.
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    Pairs in P21: probability distributions which lead to estimates of the two-phase structure seminvariants in the vicinity of 0 or π (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 216-223 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The first sequence of nested neighborhoods of the two-phase structure seminvariant φ12 = φh1k1 -- φh2k2 in the space group P21 is defined, and conditional probability distributions associated with the first four neighborhoods derived. In the favorable case that the variance of a distribution happens to be small, the distribution yields a particularly reliable value for φ12. The most reliable estimates are obtained when φ12 ∼ 0 or π.
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    Long- and short-range ordering in LiTbS2 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 250-253 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electron-microscope studies have been performed on single crystals of LiTbS2. Samples cooled from 1000°C show diffuse intensity bands in the diffraction patterns, arising from short-range ordering of Li and Tb. After annealing at 500°C, the ordering range increases and three superstructures are observed. On the basis of the observed diffraction patterns and bright and dark-field images the range and the nature of the ordering is discussed.
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    Electron-density studies. II. Further comments on the electron density in diamond (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 173-183 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray powder diffraction data for diamond have been re-analysed, in terms of an 'at rest' deformation-density model of monopole, octupole, hexadecapole and hexacontatettarapole terms of exponential form. The values of the parameters describing the third and fourth-order terms, and the refinement indices, are no different from those of an 'at rest' valence-density model. Unlike earlier analyses, however, the model is consistent with experimental measurements of the absolute scale, and with independently determined values of the Debye-Waller parameter. The predicted values of physical properties such as the gradient of the electric-field gradient at the carbon nucleus are shown to be strongly model-dependent. It is noted that the fit to the data, and in particular to the observed structure factor of the overlapping 333-511 reflection, is poor for all published charge-density analyses. Recent theoretical (crystal 'Hartree-Fock') calculations indicate, within the convolution and harmonic approximations, an experimental B value of 0.172 ± 0.006 Å2 and a scale factor of 1.004 ± 0.002. These theoretical results are, however, in poor agreement with the experimental structure factors.
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    Errors in deformation-density and valence-density maps: the scale-factor contribution (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 254-256 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A formulation for the variance-covariance estimate of the deformation or valence density is given for a centrosymmetric crystal, taking into account correlations with the scale factor, when this is determined by the usual scaling procedure. It is shown that, when heavy atoms are present in the crystal, the scaling procedure is likely to result in better precision than an independent experimental determination of the scale factor.
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    Strukturmöglichkeiten für Pentahalogenide mit Doppeloktaeder-Molekülen (MX5)2 bei dichtester Packung der Halogenatome (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 256-267 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal structures of the dimeric pentahalides (MX5)2 have a close-packed arrangement of halogen atoms in which one fifth of the octahedral holes are occupied by metal atoms. From considerations of the geometrical possibilities of arranging the molecules and thereby resulting symmetry restrictions, the possible space groups and structures are elucidated with the aid of group-subgroup relationships. It is shown that only certain space groups can be achieved. Among the centrosymmetric space groups these include: 1. C2/m, C2/c and C{\bar 1} for hexagonal close packing when octahedral holes are occupied between layers A and B but not between B and A; 2. Pnma, Pnmn, Pnab, C2/m, P2/m, P21/m, P21/a and P{\bar 1} for h.c.p. when holes between all pairs of layers are occupied; 3. P21/m, P21/a and P{\bar 1} for the double hexagonal close packing; 4. I41/a, Bbmb, Fddd and the monoclinic and triclinic space groups for cubic close packing. The more important arrangements are illustrated and their expected cell dimensions are given. The results are compared with the known structures of the pentachlorides of Nb, Ta, Mo, W, U and Re, (NbBr5)2, β-(PaBr5)2, and also (WSCl4)2 and (WSBr4)2. It is deduced that the previously published structure of niobium pentaiodide is probably in error. Predictions are made for likely structures of (TaI5)2, α-(PaBr5)2, (PaI5)2 and (UBr5)2.
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    Diffraction from dislocations and grain boundaries – an optical analogue study (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 284-288 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Optical transforms of the models of atomic configurations around edge and screw dislocations in f.c.c. and b.c.c. lattices as well as grain boundaries have been obtained with the help of a laser diffractometer. The models used were based on computer simulation studies of other workers. It has been observed that the intensity at the reciprocal lattice points splits into annular haloes or takes the 'figure of eight' shape in some cases. The directional dependence of the splitting has been compared with the existing theories. It has also been observed that with ordering of the dislocations at the grain boundaries, the diffraction pattern resembles that of a single dislocation.
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    Elimination of extinction by a temperature gradient (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 329-336 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Experiments with crystals of a KNCS. C12H24O6 complex show that the integrated intensities of reflections showing strong extinction can be raised to their expected kinematic values when the crystal is subjected to a temperature gradient. The intensity increases are accompanied by a broadening of the diffraction peaks and are reversible with no detectable hysteresis. These observations seem to be incompatible with the mosaic-crystal model. Local variations in the extinction behaviour have been detected by using a fine incident beam and suggest inhomogeneity of crystal texture. The intensity increases are probably connected with a reduction in the mean size of the perfect crystal domains, i.e. with a decrease of the mean spatial correlation length within the crystal.
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    Fourier transforms of Gaussian orbital products (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 341-343 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An expression for the Fourier transform of two-centre Gaussian orbital products is obtained which is identical in form with expressions for overlap integrals. The one-centre transform is a special case, and is obtained in a trivial way from the two-centre expression. Explicit expressions of the transform for all combinations up to ff products are given.
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    α, β and γ forms of p-dichlorobenzene: calculation of crystal structure and potential energy (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 346-348 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new potential function for non-bonded atom. . . atom interactions of chlorine atoms has been used to calculate equilibrium crystal structures and potential energies of the three polymorphs of solid p-dichlorobenzene.
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    Quantum theory of the solid state (Parts A and B) by J. Callaway (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 349-349 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Neutron scattering in chemistry by G. E. Bacon (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 350-350 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Crystallographic computing techniques edited by F. R. Ahmed (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 350-351 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    The plastic deformation of simple ionic crystals by M. T. Sprackling (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 351-352 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Crystal field effects in metals and alloys: Proceedings of the international conference held in Zurich, Sept. 1976 edited by A. Furrer (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 352-352 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Structural relations between vanadium, niobium, tantalum hydrides and deuterides (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 389-399 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The phase diagrams and crystal structures of V, Nb, Ta (= M) hydrides and deuterides show a close relationship, with some substantial differences at lower temperatures. At high temperatures ( ̃500 K) H atoms form a disordered solid solution at tetrahedral interstices of a b.c.c. metal lattice in the composition range MHx with 0 〈 x ∼ 1 (α-MH). At lower temperatures (3̃00 K) the composition is limited to a non-stoichiometric solid solution MH0.5-MH. The H ordering in ζ-NbH (β-TaH structure, composition MH0.5, space group C222) and γ-NbH (MH, I{\bar 4}m2) is closely related to β-NbH (MH,Cccm). The symmetry is lowered to B2/m (β-VH structure, MH0.5) for a similar distribution of H at octahedral interstices. The crystal structures can be characterized by the translation vectors T1 (½ ½ ½) and T2 (0 ½ ½) between nearest H atoms, α-MH exhibits a short-range order with a preference of T1 and T2 between neighbouring H atoms. In MH0.5-MHss the percentage [T] of T1 and T2 translations changes with composition and temperature. The different low- temperature phases and the order-disorder transitions can be characterized by the ratio [T1]/([T1] + [T2 ]).
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    Interaction energies at twin boundaries and effects of the dihedral reentrant and salient angles on the growth morphology of twinned crystals (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 406-413 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Twin-boundary energies are calculated with the Lennard-Jones 6-12 potential function for the (110) and (310)-twin laws of orthorhombic even n-alkane crystals. In agreement with experiment, the calculations show that the higher the interaction energy along the twin boundary, the higher the probability of observing the corresponding twin. According to the values of the reentrant angles, the adsorption sites near the twin boundary may act as permanent growth sites (kinks) where growth takes place spontaneously and leads to a crystal elongated in the direction of the twin boundary.
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    Physical significance of triplets in direct methods (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 421-427 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Direct methods of phase determination frequently make use of the triplet formula, φ(h) ∼ (φ(h - k) + φ(k)). This expression is derived by a probability approach which has no easily visualized connection with an actual crystal structure. In this paper the positions of electron-dense planes are related to the positions of peaks in the two-term E map of E(k) and E(h - k). The connection between φ(h) and [φ(k) + φ(h - k)] is then easily visualized. A consideration of spurious peaks in the two-term E map suggests that the probability that φ(-h) + φ(k) + φ(h - k) sums to zero is increased by a small value of |E(2k - h)/E(h)l and may be decreased by a large value of this ratio. The relation between symmetry and aberrancy is briefly considered.
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    La détermination systématique des sous-groupes spatiaux et des changements de repère conventionnel des groupes spatiaux (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 414-421 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: After usual properties of space subgroups have been described, the sufficient condition is given for a space group g to be any subgroup of a space group G: the translation vectors a, b, c of the conventional unit cell of g(o,a,b,c) must belong to the lattice of G and the 'generators' of equivalent general positions of g must be enclosed in the set of general positions of G. In order to verify this criterion, it is necessary to obtain the coordinates of general positions of g in the reference standard setting of G(O,A,B,C); it is necessary to know the coordinates of origin o and the components of vectors a, b, c in terms of the reference setting (O,A,B,C). Then, all the possibilities of a space group of standard symbol \cal s being any subgroup of a space group of standard symbol \cal l can be characterized. Classification of the standard settings of subgroups is established: different settings of the same subgroup and settings of conjugated subgroups.
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    The thermal-motion correction for bond angles (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 428-431 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Expressions for the thermal-motion correction of bond angles are derived by determining the mean angle. Thus the joint distribution of the three relevant nuclei is used in the harmonic approximation of the nuclear vibrations. To calculate the correction in practice, the coupling tensors among the three relevant atoms must be known, these being a characteristic feature of the joint distribution. Since the coupling tensors cannot be measured, they must be determined from simple models of motion or from the interatomic force constants. The model of rigid-body motions can be applied in many cases, and for this model it is shown that the angle correction can be calculated from the corrected bond lengths. Approximate expressions for upper and lower bounds of the angle correction are derived.
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    Définition algébrique des groupes de symetrie (d'isométries) des cristaux et autres objets parfaits de l'espace à n dimensions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 432-441 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Using isomorphism properties of translation groups, an intrinsic definition of the classes of perfect objects belonging to n dimensional space, such as crystals, semicrystals, non-crystals and perfect gas, is given. Through the partition of space group G with respect to its (invariant) translation sub-group T, its point group is defined, an isomorph of the group of classes G/T. Examples are given, with symmorphic or non-symmorphic objects in spaces E2, E3, E4 and En. Moreover, the unsuitable expression 'Bravais lattice' should be changed into 'Bravais type of cell'.
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    Determination of third-order elastic constants from stress-shifted resonance frequencies, observed by diffraction of light. Examples: aluminium alums of K, NH4, Cs and CH3NH3 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 442-446 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Resonance frequencies of thick plane-parallel plates are easily detected by diffraction of light with an accuracy better than 1 p.p.m. The method, which has been earlier employed for the determination of thermoelastic properties, proved to be sufficiently sensitive also for the measurement of stress-induced shifts of resonance frequencies, and is therefore suited for the determination of third-order elastic constants. The technique is easier to handle and much less expensive than other methods in use today. The complete sets of third-order elastic constants for KAl(SO4)2.12H2O, NH4Al(SO4)2.12H2O, CsAl(SO4)2.12H2O and CH3NH3Al(SO4)2.12H2O have been measured. All constants possess negative values. These alums exhibit a behaviour similar to that of the structurally related caesium halides, with the exception of ammonium alum which shows anomalously small constants.
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    Overlapping Patterson peaks and direct methods: the structure of prostratin (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 450-453 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A genralized discussion of direct methods of solving the phase problem leads to the suggestion that overlapping vectors in the Patterson function may be the cause of failures in these methods. A simple removal of these overlapping vectors is proposed, which produces modified |E| values. There were used with the program MULTAN to solve the structure of a prostratin derivative, C22H28O6, which had otherwise resisted solution.
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    Direct phase determination of triple products from Bijvoet inequalities. II. A probabilistic approach (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 447-450 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Probability calculations confirm a recently proposed formula for the calculation of sin \bar \phihk from Bijvoet inequalities, where \bar \phihk is the average phase of the triple products FhFkF{\bf {\bar h + k}} and F{\bf {\bar h}}, F{\bf {\bar k}}F{\bf {\bar h + k}} [paper I: Kroon, Spek & Krabbendam (1977), Acta Cryst. A33, 382-3851. In paper I it was shown that {\bar \phi}hk could be calculated quite accurately without knowledge of the positions of the anomalous scatterers, provided an appropriate scaling procedure was applied. If the magnitudes of the individual structure factors are considered in addition to the magnitudes of the triple products, an improved formula is obtained which leads to even better results without any scaling procedure. The efficacy of the improved formula is demonstrated by test calculations for the same structure as in paper I (space group P1, two Br ions): (i) the phases of 5139 triple products formed from 322 reflexions (observed) with |E| 〉 1.2 are calculated with a mean error in {\bar \phi}hk of 16° (paper I: 21°), (ii) the phases of 3832 triple products formed from 258 reflexions (calculated) with |E| 〉 1.2 are calculated with a mean error in {\bar \phi}hk of 8° (paper I: 14°). 447
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    Optical selected-area diffraction patterns of high-resolution electron-microscope images for crystal analysis (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 453-459 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Optical selected-area diffraction patterns made from high-resolution electron micrographs of crystals have been used as a source of diffraction information from areas as small as a single unit cell of the crystal. The intensities of the electron diffraction pattern of the specimen crystal and the optical diffraction patterns of high-resolution electron-microscope images have been discussed by electron optical image formation theory taking account of spherical aberration and defocusing of the objective electron lens and it is concluded that the optical diffraction pattern may be identical with the electron diffraction pattern if the electron micrograph is photographed under optimum conditions. Optical diffraction patterns from areas of 80, 30 and 10 Å in diameter of labradorite feldspar have been taken and the orientation of two adjoining grains, 30 Å in diameter, has been determined. The diffraction pattern from a unit-cell area has also been taken and compared with the calculated intensity.
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    Etude cristallographique de la transition de phase du benzil (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 459-462 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Benzil exhibits a solid-solid phase transition at 83.3 〈 Tc 〈 83.4 K. The low-temperature lattice is complex triclinic: there are three kinds of domain and the space group is a pseudo-symmetry group P321. The lattice of each domain is triclinic, pseudo-hexagonal, with the three domains arranged around a pseudo-threefold axis.
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    Interpretation of pseudo-extinctions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 473-474 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Equations for the interpretation of pseudo- (non-space-group) extinctions are given.
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    On the probability of measuring the intensity of a reflexion as negative (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 474-475 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Infrequently quoted statistical results relating to taxi queues etc. are modified to obtain the probability of obtaining an observed number of counts Ro = To - Bo when the 'true' numbers of counts are R, T and B for reflexion, total and background respectively and To and Bo have the expected Poisson distributions. The expression, valid for negative as well as positive values of Ro, is p(Ro) = exp {-(B + T)}(T/B)Ro2IRo{2(BT)1/2}, where ln(x) is the hyperbolic Bessel function of the first kind. If the negative values of Ro are included, Ro is an unbiased estimator of R. In no case is R1/2 an unbiased estimator of R1/2, so that Patterson and R2 methods are preferred to usual electron-density and R1 methods in structure determination whenever they are appropriate.
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    Effects of incorrect phases on difference density distributions (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 476-477 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The effect of incorrect phases on difference density distributions is illustrated with the example of thiourea (space group P21ma). Two difference density maps with phases from the free-atom model (R = 0.030) and a molecular model of the charge distribution (R = 0.017) are calculated. These maps show deviations as large as 0.2 e Å-3 in the peak heights.
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    A simple refinement of density distributions of bonding electrons. VIII. Comparison of experimental and theoretical scattering curves for bond charges in urea and thiourea (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 475-476 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Gaussian scattering curves for bond charges in urea and thiourea whose parameters were determined from 123 K X-ray data are compared with those derived theoretically. A fairly close agreement among the different scattering curves was found.
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    The use of molecular-orbital calculations on model systems for the prediction of bridging-bond-angle variations in siloxanes, silicates, silicon nitrides and silicon suffides (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 463-472 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: CNDO/2 molecular-orbital calculations are shown to predict trends in bridging angle, ∠T-Y-T, with reasonable accuracy for gas-phase molecules of the type TX3YTX3, where Y is an anion (= O, OH, S, NH) bridging the tetrahedrally coordinated cations T(= C, Si, Al, Be, B) and where X are the nonbridging anions (= H, F). For example, calculated equilibrium ∠T-O-T are 100, 125 and 150° in CH3OCH3, SiH3OCH3 and SiH3OSiH3, respectively, compared to experimental values of 111, 121 and 144°. The equilibrium ∠Si-O-Si in SiH3OSiH3 is also in close agreement with the average value of this angle (148°) in the silica polymorphs. The SiH3YTH3 molecule is proposed as a model system for studying bridging bond angles in silicates and is found to give bridging-angle trends in reasonable agreement with those observed in Si-containing solids. In particular, calculations on SiH3YSiH3 predict LSi-Y-Si to decrease from 150 to 130 to 109° as Y is changed from O to NH to S, in agreement with observed average angles of 144, 120 and 110°, respectively, in silicates, silicon nitrides and silicon sulfides. For SiH3OSiH3 the equilibrium ∠Si-O-Si is calculated to increase as the Si-O bond distance decreases, at a rate within a factor of two of that observed for the silica polymorphs. Calculations on clusters with Be or B replacing Si invariably lead to predicted equilibrium ∠Si -O-T values from 125 to 105°, in accord with the small angles that tend to be observed for such bridge bonds in minerals. Since Si(3d) orbitals are excluded in these calculations, it is apparent that the observed angular trends can be explained without invoking d-p π bonding. Inspection of one and two-center energy components of the CNDO/2 total energy also shows that the form of the Si-T interaction is not that of a nonbonded repulsion.
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    Eleventh International Congress of Crystallography. General Lectures and Open Meeting of the Commission on Journals (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 477-477 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Scanning electron microscopy, 1976, Vol. 1 edited by O. Johari (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 478-478 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Intermediate quantum theory of solids by A. O. E. Animalu (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 478-479 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Radial crystal charts, `A' and `B' by K. M. Gurappa (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 480-480 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Landolt–Börnstein. Numerical data and functional relationships in science and technology. Group III. Crystal and solid state physics. Vol. 7. Crystal structure data of inorganic compounds. Part f by W. Pies and A. Weiss (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 480-480 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Absorption-weighted mean path lengths for spheres (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 489-491 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Accurate values ( ̃0.05%) of the absorption-weighted mean path lengths for spheres as a function of μR and θ have been calculated by differentiation of the table of values of absorption corrections [Dwiggins (1975). Acta Cryst. A31, 395-396].
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    X-ray measurement of the root-mean-square displacement of the atoms in cadmium single crystals (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 497-500 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The root-mean-square displacements ua and uc of the cadmium atoms in single crystals in the a and c directions, respectively, were determined by the use of Bragg intensities obtained with Mo Kα radiation. The results [ua = 0.121 (1), uc = 0.196 (1) Å] are compared with other X-ray measurements.
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    Anharmonic contributions to Bragg diffraction. I. Copper and aluminium (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 500-505 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Anharmonic contributions to the atomic motion in copper and aluminium single crystals have been deter- mined from measurements of the elastic scattering of recoil-less γ-rays at temperatures up to 1200 K for copper and 900 K for aluminium. The results are compared with theoretical predictions.
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    On the treatment of negative intensity observations (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 517-525 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is described which produces sensible estimates of structure factor moduli from intensity observations, whether the latter are positive or negative. Preliminary applications of the method to data from the protein phosphorylase b are summarized.
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    The extension concept and its role in the probabilistic theory of the structure seminvariants (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 525-528 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By embedding the structure seminvariant T and symmetry-related variants of T in suitable structure invariants Q the values of which, because of the space-group-dependent relations among the phases, are related to T, one reduces the probabilistic theory of the structure seminvariants to that of the structure invariants, which is well developed. The structure invariants Q are said to be extensions of the structure seminvariant T.
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    The vicissitudes of the low-quartz crystal setting or the pitfalls of enantiomorphism (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 584-594 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Based on a literature study, the following proposals endeavour to combine the advantages of previous conventions for setting low-quartz crystals: (1) Knowing that symmetry axes are parallel to the edges of the smallest hexagonal cell, place Oz along the 3-axis and Ox, Oy, Ou along the macroscopic 2-axes. (2) Direct the polar axes positively toward the s and x faces, if present, or toward the positive charge developed on extension by piezoelectric test. (3) Match the hand of the coordinate system to that of the structural screw; thus, the right-handed coordinate system (RHCS) for the known right screw (RS) of laevorotatory quartz. (4) Let the coordinate axis that coincides with a 2-axis in the structure be Ox[100]. These rules result in both enantiomorphs obeying Lang's mnemonic rule and being in the r(+) setting, in which {10{\bar 1}1} symbolizes the major rhombohedron r, defined by Iobs(10{\bar 1}1) 〉 Iobs(01{\bar 1}1). Low quartz has only one structure. It should be published only for the RS (P3121) and in the RHCS: anyone can visualize the LS enantiomorph by plotting the atomic coordinates in the LHCS. This policy should apply to any enantiomorphous substance with known absolute configuration. If a crystal structure, determined in the RHCS, turns out to have a LS, transform to LHCS and publish the new coordinates, which also fit the standard RS in RHCS, but add, 'Known only as LS' or 'Observed as LS'.
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    Mixed-layer characteristics in real humite structures (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 607-609 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Transmission electron micrographs resolving (100) lattice fringes of clinohumite revealed faults parallel to (100). A simplified model of humite minerals, which interprets them as layers of forsterite and brucite-sellaite, was used for analysis of the faults. These compositional faults produce one or two unit layers of humite and/or chondrodite interlayered between the regular sequence of clinohumite along a*. Thus, nonstoichiometric compositions of humite minerals can be explained as mixed layers.
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    Electron microscopy study of ordering of potassium ions in cubic KSbO3 (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 625-634 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Ordered and disordered states of potassium ions in (111) tunnels in the structure of cubic KSbO3 have been studied by high-resolution electron microscopy. N-beam calculations for the images of both the ordered and disordered states reproduce well the observed images. The disordered state changes into the ordered state under electron irradiation during the observations. Electron diffraction from the specimens and optical diffraction from the images show diffuse spots due to small domains of the long-range-ordered state, but no other diffuse scattering due to short-range order has been observed.
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    A simple refinement of density distributions of bonding electrons. III. Experimental static electron densities for the diborane molecule (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 621-625 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: From recently refined models of the electron density distribution in the diborane molecule, static density sections are calculated and presented as difference densities ρ(molecule at rest) - ρ(isolated atoms at rest). The sections obtained are compared with corresponding ones derived from quantum-chemical calculations by Laws, Stevens and Lipscomb.
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    Reproduction of IUCr publications (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 639-639 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Rare gas solids. Vol. II edited by M. L. Klein and J. A. Venables (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 639-640 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Electron distribution and charge transfer in the ammonium ion (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 656-662 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A re-analysis of the single-crystal X-ray data of Adrian & Feil [Acta Cryst. (1969), A25, 438-444] for ammonium fluoride has shown that there is a transfer of negative charge from the 'surface' of the ammonium ion to the central nitrogen. In addition to charge transfer, models used in the analysis allow for non-rigid-body motion of the ammonium ion and asphericity in the hydrogen electron densities. This asphericitiy has been represented in two different ways, one involving a floated monopole and the other a polarized distribution centred on the neutron-determined position. Both models give comparable fits to the data and similar charge- transfer parameters are obtained, so that the floated-monopole model is considered adequate for obtaining properties of the total molecular electron distribution. However, the dipole model is to be preferred if information about the hydrogen pseudo-atom is desired. The present analysis is compared with previous ones employing structure factors derived from molecular wavefunctions for the ammonium ion. These previous analyses are less successful than might be expected and this is attributed to their over-simplified treatment of the ammonium ion as a rigid body and their neglect of crystal-field effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001400
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    Electronic Resource
    The projection of molecular charge density into spherical atoms. I. Density basis functions for first-row atoms (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 641-648 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electron population analyses of several molecular one-electron density functions have been studied by least-squares projection methods into several atomic-density basis functions. All studies have been restricted to spherically symmetrical functions, which have been fitted to the atomic-density functions for the ground-state atoms hydrogen through neon. It is found that when the atom-density basis functions are split into inner (K shell) and outer (L shell) parts, then the atomic charges reflect polarity of the molecule reasonably well and, moreover, are relatively independent of the orbital bases used in spanning the molecular wave function. The standard density basis sets given here can be used for a similar electron population analysis of accurate X-ray diffraction data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001370
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