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  • International Union of Crystallography (IUCr)
  • Annual Reviews
  • 1980-1984  (3,969)
  • 1982  (2,129)
  • 1981  (1,840)
  • 1
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    Anisotropies diamagnétiques moléculaires expérimentales des composés aromatiques condensés (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 211-219 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For explaining diamagnetic effects observed in condensed aromatic compounds, their molecular diamagnetic anisotropies must be known. A method is proposed which, on the basis of relatively accurate structural data and of two experimental crystal anisotropies, allows the determination of molecular anisotropies in the plane and perpendicular to it. For monoclinic compounds whose magnetic tensor has no revolution symmetry, it is necessary to correct to first order the orientation of the principal magnetic axes of the crystal with respect to revolution symmetry. The proposed method is applied and discussed in the case of ten condensed aromatic compounds which crystallize in the orthorhombic and monoclinic systems. It yields, in some cases, molecular anisotropies very different from those suggested by different authors. One very simplified model produces results which fit in with the molecular anisotropies obtained as long as the arrangement of the rings is not too complex.
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    URL: http://dx.doi.org/10.1107/S0567739481000508
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  • 2
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    Investigation and interpretation of diffuse X-ray scattering in Li3N (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 219-226 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Diffuse X-ray scattering in Li3N has been investigated in the range 293 to 880 K with monochromatic Mo Kα radiation. Crystal and film were fixed during the exposure. Diffuse intensity in the form of rods and discs was found. It increased with increasing temperature but without change of its features. The diffuse intensity distribution was calculated for various temperatures on the basis of an anisotropic shell model. Good agreement with the experimental results was achieved. The anharmonic effects detected in the difference electron density were studied taking into account split positions for the Li ions. This simulation leads to only minor changes in the calculated intensity distribution which indicates that the diffuse intensity of Li3N is mainly caused by harmonic lattice vibrations.
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  • 3
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    Anomalous dispersion calculations near to and on the long-wavelength side of an absorption edge (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 267-268 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent experimental measurements have revealed systematic differences between measured values of f' and those calculated by the method of Cromer & Liberman [J. Chem. Phys. (1970), 53, 1891-1898] when the incident X-ray is near to and on the long-wavelength side of an edge. The source of the discrepancy has been identified and some previously published values of f' are corrected. These corrections also apply to Table 2.3.1 in International Tables for X-ray Crystallography, Vol. IV [(1974), Birmingham: Kynoch Press].
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    URL: http://dx.doi.org/10.1107/S0567739481000600
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  • 4
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    Notes And News (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 269-269 
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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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  • 5
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    Deriving the equilibrium conformation in molecular crystals by the quasi-harmonic procedure: some critical remarks (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 335-342 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Owing to progress in lattice-dynamical computing routines, free-energy calculations for perfect molecular crystals are no longer prohibitive in the quasi-harmonic approximation. Thus the consistent derivation of an equilibrium conformation at various temperatures and pressures, and even the stability range of various phases, may become a routine possibility, starting from semi-empirical potentials only. An example of such conformational calculations is given and discussed for the tetragonal phase of adamantane at 163 and 1 K. The effect of vibrational energy (even zero-point) and entropy upon molecular orientation and position in the unit cell is shown not to be negligible by several examples. This precludes the possibility of calculating the cell parameters on free-energy grounds and the molecular coordinates by considering the minimum packing energy. For crystals with molecules fixed by symmetry, the quasi-harmonic approximation becomes particularly appropriate, since in this case for any unit cell the first derivatives of energy with respect to any molecular shift are zero. Some critical steps of such calculations are examined and discussed, especially in connection with converging processes. No particular problem is encountered in sampling the Brillouin zone, because only a limited number of points is necessary. Convergence of lattice sums to obtain packing energy is more critical, although for most practical purposes a maximum packing distance of 15 Å is sufficient. The real difficulties of these calculations consist in the need of considering many degrees of freedom at once, and also in the inadequacy of present-day semi-empirical potentials.
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  • 6
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    Third-order elastic constants of orthorhombic calcium formate (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 361-364 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: All 20 independent third-order elastic constants (TOEC) of orthorhombic calcium formate, Ca(HCOO)2, Ca2+. C2H2O2-4, space group Pcab, have been determined with the aid of stress-induced shifts of ultrasonic resonance frequencies. Longitudinal and transverse effects possess negative values indicating the high stability of calcium formate over a wide pressure range. The anisotropy of TOEC, characterized by --c111 〉 --c333 〉 --c222, corresponds with the anisotropy of second-order elastic constants (c11 〉 c33 〉 c22). The value 5.22 for the pressure derivative of the inverse bulk compressibility coincides with the quasi- invariant value of ca 5 observed in most stable cubic crystals so far investigated. There exists a pronounced departure from third-order Cauchy relations: the 'transverse' constants exceed the corresponding 'shear' components considerably in absolute magnitude in accordance with the behaviour of the second-order Cauchy relations. These effects are explained as originating from the non-centrosymmetric formate ions. A comparison of TOEC of calcium formate and cubic calcium fluoride confirms the typical contribution of the formate ions to the third-order elastic behaviour.
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  • 7
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    The ultrastructure of pyroxenoid chain silicates. III. Intersecting defects in a synthetic iron–manganese pyroxenoid (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 281-286 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A synthetic pyroxenoid of nominal composition MnFeSi2O6 has been produced in the glassy state and examined by high-resolution electron microscopy after periods of annealing of from two to sixteen hours at 1070 K. Initially highly defective structures exhibiting large chain repeat distances are produced, but on further annealing the five-tetrahedra chain repeat of rhodonite predominates. (110)-type stacking faults are frequently observed. In most eases these faults involve considerable disruption of the lattice, but in certain instances the stacking fault displacement is equal to the rhodonite lattice repeat and the faults are visible only if the chain periodicity varies. In the latter case, the structure shows a two-dimensional ability to accommodate defects, and models for this, involving chain breaking and/or chain branching, are proposed.
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  • 8
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    The three-colored three-dimensional space groups (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 286-292 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This article contains a table of the groups of combined geometrical and color-permutational symmetry operations that leave a certain kind of three-colored, three-dimensionally periodic object apparently unchanged. The asymmetric units - 'motifs' - of the object are all either geometrically congruent to, or are mirror images of, one another. Each motif has a 'color' representing a scalar quality of some kind, and three different colors of motifs are assumed to occur in the object. Two types of three-colored space groups exist: type I in which all of the geometrical lattice translations leave all the motifs unchanged in color, and type II in which at least one of the geometrical lattice translations requires a permutation of the three colors in order to restore the original appearance. There are 88 three-colored space groups of type I, and 341 of type II. Type I can belong only to the trigonal, hexagonal and cubic systems; type II can belong to any system, except the cubic. A notation for the three-colored, three-dimensional space groups is proposed. It is based on similar principles to those used in the article on colored point groups by Harker [Acta Cryst. (1976), A32, 133-139].
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  • 9
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    The Fourier transforms of a coiled coil and a toroidal helix (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 309-314 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Fourier transform of a finite coiled coil containing an integral number of repeat units is evaluated analytically. The special cases where the coiled coil reduces either to a pure helix or to a toroidal helix are specifically included.
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  • 10
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    Diffraction of X-rays by magnetic materials. II. Measurements on antiferromagnetic Fe2O3 (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 324-331 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two of the magnetic superlattice Bragg reflections of a single crystal of hematite (Fe2O3) have been measured by diffraction of X-rays produced from a conventional source, and compared to the intensities expected from the photon-spin scattering. Several orientations of the spins relative to the beams have been realized by rotating the crystal and by changing its temperature through the Morin (spin-flip) transition; in some of the measurements, the polarization produced by the monochromator was enhanced and this produced a visible asymmetry in the dependence of the intensities on the spin direction. The variations of the intensities during these changes of configuration are characteristic of magnetic scattering; the observed variations, as well as the absolute intensities, agree with the theory apart from some discrepancies. These may be due to intense multiple-scattering effects, and to some possible anomalies in the spin direction near the sample surface. As an application of this technique, changes of the direction of magnetization when a magnetic field is applied to the weakly ferromagnetic room-temperature phase have been investigated.
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  • 11
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    The application of the molecular replacement method in studies on the quaternary structure of haemoglobin (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 407-413 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It has been found that the crystallization of oxyhaemoglobin from polyethylene glycol solutions [Grabowski et al. (1978). Biochem. J. 171, 277-279] yields at least three different forms of isomorphous crystals (P21212, a = 96.66, b = 97.88, c = 65.40 Å). 3.5 Å resolution data have been collected for two of the three identified forms. The orientations and positions of the αβ haemoglobin dimers within the asymmetric units of these crystals have been established by the molecular replacement method with computing techniques different from those used by Ward, Wishner, Lattman & Love [J. Mol. Biol. (1975), 98, 161-171] in their studies of human deoxyhaemoglobin crystals obtained from polyethylene glycol solutions. The calculations have been performed also with diffraction data from deoxyhaemoglobin and fluoromethaemoglobin + inositol hexaphosphate crystallized from polyethylene glycol by Fermi & Perutz [J. Mol. Biol. (1977), 144, 421-431]. In all cases, the individual dimers have been positioned independently and it is shown that, in the methods using a fast rotation function, three- and multidimensional residual-type translation functions may be directly applied to the structure determination of those complex structures in which the structure of only one of the two subunits present in the asymmetric unit is known. It is also shown that in all crystals studied the haemoglobin dimers are arranged in the \cal Y conformation, which seems to exclude the possibility of the full oxygenation of haemoglobin crystallized from polyethylene glycol solutions.
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  • 12
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    A simple computer method for the orientation of single crystals of any structure using Laue back-reflection X-ray photographs (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 430-436 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple computer program for the simulation and analysis of X-ray back-reflection Laue photographs of a single crystal with any structure and orientation has been developed in Fortran IV. Comparison of computer plots of the calculated patterns with the photographs enables rapid identification of approximate orientation. The program may ultimately be used to index an orientation from the identification of at least three spots from the photographs. The procedure incorporating use of the program requires only minimal knowledge of crystallography or computer methods.
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    URL: http://dx.doi.org/10.1107/S0567739481000910
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  • 13
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    The effect of data truncation on the measurability of Bijvoet differences (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 153-162 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Theoretical expressions for the complementary cumulative function of the Bijvoet ratio X applicable to a truncated data set are worked out for a non-centrosymmetric crystal containing P anomalous scatterers in the unit cell [P = 1 and many (MN and MC cases)] besides a large number of normal scatterers. These expressions contain the truncation limit yt as a parameter of the distribution. The results obtained are used to discuss the effect of data truncation arising from the non-observability of extremely weak reflections on the measurability of Bijvoet differences.
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    URL: http://dx.doi.org/10.1107/S0567739481000429
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  • 14
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    On the application of phase relationships to complex structures. XIX. Magic-integer representation of a large set of phases: the MAGEX procedure (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 566-572 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Long one-dimensional magic-integer sequences are used to express the phases of 10-20 primary reflexions. The magic-integer representation of phases is extended to other secondary reflexions through strong triple- phase relationships involving one secondary and two primary reflexions. In the MAGEX procedure multiple magic-integer representations of the secondaries are sought and the error involved in their subsequent use in a conventional ψ map is much reduced. In view of the large number of primary reflexions the indices of the terms included in the ψ map are large and maps may be computed at up to 220 points. Further reflexions, in batches of ten or so, may be added to the initial set by the further use of magic integers and small-scale maps. When the base of estimated phases is sufficiently large then the phase information is extended by the controlled use of the tangent formula. Examples of the successful application of MAGEX are described.
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  • 15
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    Antiphase périodique orientationnelle et transformation de phase dans le fluosilicate de fer (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 578-584 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: FeSiF6.6H2O above 240 K is described following the structural model previously proposed for MgSiF6.6H2O above 300 K: periodic antiphase built on the ordered monoclinic cell of the low-temperature form. In the present case a progressive ordering is observed and the antiphase boundaries are no longer planar but exhibit steps which lead to a mean boundary canted with respect to the c hexagonal axis (space group P3). Above 240 K a phase transformation occurs with a threefold twinning and a significant lattice deformation. The monoclinic cell (P21/c) is described.
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  • 16
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    Improved technique for peak integration for crystallographic data collected with position-sensitive detectors: a dynamic mask procedure (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 594-604 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A technique for improving the precision of crystal data collected on films or with electronic position-sensitive detectors is proposed. The extent of each medium or strong reflection is computed independently, after smoothing and filtering the individual intensities, producing a variable 'dynamic mask'. A method of calculating universal background profiles, which preserves the data and limits the necessary storage, is introduced. The method was applied to data collected with X-ray precession and oscillation techniques and to neutron data collected with a fiat-cone diffractometer equipped with a linear detector. In all cases substantial improvement in the precision of weaker reflections was observed. The overall quality of the data was particularly enhanced in the neutron diffraction case.
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  • 17
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    Ferroelastic phases in Pb3(PO4)2–Pb3(AsO4)2; X-ray and optical experiments (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 145-153 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Mixed crystals Pb3(PO4)2--Pb3(AsO4)2 are ferroelastic at low temperatures. The phase diagram contains three different phases a (paraelastic), \tt b and \tt c (both ferroelastic). The transformation \tt a-\tt b is first order for Pb3(PO4)2 and approaches second-order behaviour with increasing As content. The spontaneous strains and the birefringence follow approximately a Curie-Weiss law, with a corresponding order-parameter exponent β = ¼. The mutual high-temperature phases give diffuse X-ray reflections due to inelastic scattering. The soft-mode model is discussed for these results.
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  • 18
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    Exact method for the calculation of pseudorotation parameters P, τm and their errors. A comparison of the Altona–Sundaralingam and Cremer–Pople treatment of puckering of five-membered rings (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 421-425 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A comparison of the two methods available for describing the puckering of five-membered rings - the Altona-Sundaralingam (A-S) [Altona & Sundaralingam (1972). J. Am. Chem. Soc. 94, 8205-8212] pseudorotation parameters τm, P and the Cremer-Pople (C-P) [Cremer & Pople (1975). J. Am. Chem. Soc. 97, 1354-1358] puckering parameters q, φ - shows that they are the same for all practical purposes but both have minor shortcomings. In the A-S method, the value of τm is somewhat dependent on the choice of the origin atom, while in the C-P method the normal to the mean plane, rather than being fixed, precesses as the ring puckering changes. We present here an exact procedure for obtaining the A-S parameters τm, P that correspond to the amplitude and phase of the Fourier wave of period 4π/5, thus making τm independent of the origin atom. Formulae are also given for the estimation of the standard deviations in the A-S and C-P parameters.
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  • 19
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    A statistical interpretation of rotation and translation functions in reciprocal space (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 426-430 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Rotation and translation functions in reciprocal space, commonly used to find the orientation of a known molecular fragment and/or its position in the unit cell, are all identical or closely related to the function Q(R,t) = 〈|Eh|2|Ehp(R,t)|2〉h, where |Eh| is the observed normalized structure factor and Ehp(R,t) is the normalized structure factor for the partial structure, calculated for orientation R and position t. In this paper, this function is derived from statistical considerations without referring to a Patterson synthesis. From the centrosymmetric and noncentrosymmetric probability density functions, Q(R,t) = 1 + 2p2 and Q(R,t) = 1 + p2 are obtained, respectively, where p2 is the fraction of atoms (scattering power) that has been placed in the correct orientation and position in the unit cell. Alternative search functions, for instance using |Eh|4 instead of |Eh|2, are discussed.
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  • 20
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    An X-ray measurement of charge asphericity in vanadium metal (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 697-701 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For b.c.c. vanadium metal the integrated intensities of 80 independent reflections were measured by using a spherically shaped single crystal 0.241 (3) mm in diameter with Ag Kα radiation. It was confirmed that there are very small differences in integrated intensities between paired reflections, and these differences can be measured significantly beyond the experimental error. The ratios of the paired reflections are small than those obtained from platy crystals [Weiss & DeMarco (1965). Phys. Rev. A. 140, 1223-1225] but are in good agreement with those recalculated recently by means of the APW method [Wakoh & Kubo (1980). J. Phys. F. 10, 2707-2715].
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  • 21
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    A charge density study of copper by γ-ray diffractometry on imperfect single crystals (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 711-722 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: 19 absolute atomic scattering factors were measured for imperfect copper single crystals with an accuracy of the order of ±0.05 electrons for reflections with sin θ/λ ≤ 0.7 Å-1. This data set is of significantly higher accuracy than those measured earlier with X-rays for imperfect single crystals. The experimental form factors for low momentum transfer are significantly smaller than the free-atom values. The corresponding deformation density shows a small pile up of charge between nearest-neighbour atoms. At the present level of experimental accuracy, none of the available band-structure calculations provides a satisfactory description of the measured form factors over the whole range of momentum transfer where effects due to bonding can be expected.
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  • 22
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    The superspace groups for incommensurate crystal structures with a one-dimensional modulation (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 625-636 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A complete list of (3 + 1)-dimensional superspace groups is presented. These groups describe the symmetry of incommensurate crystal structures with a one-dimensional modulation. A short discussion is given of applications. Extinction rules and Bravais types are tabulated in order to facilitate the determination of the superspace-group symmetry.
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    On the application of phase relationships to complex structures. XVIII. RANTAN–random MULTAN (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 642-644 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: To overcome the disadvantages of a small starting set in MULTAN a technique is described whereby a large number of phases are given random values with low weights and then refined by a weighted tangent formula. The effectiveness of the process depends quite critically on assigning suitable weights to phase estimates and on a fairly tight control of the refinement. Examples of the application of the method are given for a number of structures, many of which are difficult to solve by direct methods.
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    Optimum choice of wavelengths in the anomalous scattering technique with synchrotron radiation (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 636-641 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.
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    Elastic constants of acenaphthene determined from studies of thermal diffuse scattering of X-rays (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 645-649 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The absolute values of all the nine elastic constants of acenaphthene single crystals, C12H10, belonging to the orthorhombic system, have been determined by the photographic method from the measurement of the intensities of thermal diffuse scattering observed in a series of Laue photographs taken with monochromatized Cu Kα radiation having no higher harmonics of λKα. The direct beam was recorded photographically after being absorbed through nickel foils of known thickness, its intensity being reduced by a factor of 106. Diffuse scattering domains near the reciprocal-lattice nodes 400, 080, 004, 105, 014 and 072 were investigated extensively. The diffusely scattered intensities were corrected for the general scattering, polarization and skew factors. Corrections for absorption, divergence and second-order diffuse scattering were found negligible. The values of the elastic constants in units of GN m-2, with e.s.d.'s in parentheses, are C11 = 11.05 (50); C22 = 10.26 (30); C33 = 9.40 (23); C44 = 4.25 (08); C55 = 3.69 (07); C66 = 4.87 (10); C12 = -1.93 (20); C13 = 3.34 (12); C23 = 2.34 (13). The accuracy of experimentally determined values of the elastic constants is discussed.
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    Des dangers d'utiliser sans précaution des tables de sous-groupes maximum; retour au théorème d'Hermann (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 649-652 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Most tables of space subgroups of space groups are devoted to maximal subgroups. Although available tables of maximal subgroups are complete with regard to translationengleich subgroups, they are inaccurate concerning klassengleich subgroups. As a matter of fact, these tables do not show that several klassengleich subgroups relevant to the same set of basis vectors may be distinguished by non-congruous origins.
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    A linear equation for products of normalized structure factors. II. Tensor formalism (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 658-661 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: New, finite and exact relationships between products of two normalized structure factors, with coefficients which are a function of the squared moduli of structure factors, are presented. The equations allow new linear relationships between the cosine and sine of triple-phase invariants to be set up. The meaning of the new equations is discussed in connexion with the direct calculation of cosines of triple-phase invariants and the results show, for simple one-dimensional model structures, that it is possible to obtain exact solutions.
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    A phase-difference approach to EXAFS analysis of germanium polymorphs (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 653-658 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two germanium polymorphs of the diamond type and the ST-12 structure were used to investigate the accuracy of extended X-ray absorption fine structure (EXAFS) analysis with a phase-difference method. This method gives similar accuracies to both conventional curve-fitting and Fourier-transform methods in determining the difference of the first- neighbor distances for these two polymorphs. The number of first-shell atoms of the ST-12 structure was determined to be 4.0 ± 0.2 with the diamond-type phase as a standard. In addition, the first-neighbor coordination of amorphous germanium was analyzed with this method. These results suggest that the phase-difference method is useful for structure analysis of materials and that it is especially useful for structure analyses under high pressure.
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    A new type of satellite in plagioclases (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 754-762 
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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 type of satellite has been observed in plagioclases CaxNa1 - x[Al1 + xSi3 - xO8] with 0.5 ≤ x ≤ 1. Their intensities are such that they could be observed only by applying a special focusing technique. They appear in the neighbourhood of some strong reflections with h + k = 2n, l = 2n. It is shown that the new satellites are most probably caused by a three-dimensional array of domains of two structures, differing only by small displacements of the atoms. Since the translation lattices of the two structures have the same geometry it is concluded that the two structures are twins of an acentric plagioclase correlated with a centre of symmetry. The size of the domains is 80 Å approximately. The diffraction of such submicroscopically intergrown twins is calculated for lamellae and blocks and compared qualitatively with the experimental results. The approximate periodicity of the domains could be destroyed by very long exposure to X-rays.
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    The thermodynamic approach to the structure analysis of crystals (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 742-754 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a previous paper [Khachaturyan, Semenovskaya & Vainshtein (1979). Soy. Phys. Crystallogr. 24, 519- 524], the thermodynamic formulation of the procedure of crystal structure determination from the intensity array of X-ray reflections was proposed. This approach requires the introduction of analogues of such thermodynamic functions as the free energy, entropy, temperature and so on, and it is reduced to the solution of the specific 'kinetic equation'. It was shown that the equilibrium state of the system is described by the distribution of the scattering substance density which at low temperature corresponds to the true structure of the crystal. The problem of crystal structure determination is thus reduced to determination of the equilibrium distribution of the scattering substance. The Önsager equation formalism was applied to derive 'kinetic equations' describing the relaxation of the system to its equilibrium state. The test of the proposed procedure exemplified by the solution of the 'kinetic equation' to determine the crystal structure of l-proline, C5H9NO2, with 32 atoms per unit cell is considered.
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    Estimates of the standard deviations of ring-puckering coordinates (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 764-765 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Expressions are derived for estimating the standard deviations of Cremer-Pople ring-puckering coordinates, with the assumption that the e.s.d.'s of the atomic positions are approximately isotropic.
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    Co-editor of Acta Crystallographica (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 767-767 
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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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    A table of maxima and minima of the Bessel functions Jn(Z) for n = 0 to n = 30 (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 765-766 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Maxima and minima are tabulated for the Bessel functions Jn(x) for values of n from 0 to 30 [i.e. zeros of J'n(x)]. The first six points are recorded for each function. The table considerably extends the range of earlier tables available in the literature. It should have applications in the interpretation of diffraction patterns from helical or wave-form structures or features, and has been used in connection with some electron microscope images.
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    DELCRI, an enantiomorph-specific figure of merit (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 684-689 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A figure of merit DELCRI, with estimates Δ3 for the absolute values of the triplet phase sums φ3, is described for the selection of numerical values of symbols used in a symbolic addition procedure. From tests with a number of structures crystallizing in polar space groups this figure of merit was found to enable the selection of enantiomorph-specific phase sets.
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    The use of phase combination in the refinement of phosphoglycerate kinase at 2.5 Å resolution (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 491-500 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The combination of phase information obtained by the method of isomorphous replacement with that calculated from a partial model of the structure has proved to be a powerful tool in the interpretation of the structure of horse muscle phosphoglycerate kinase. That the combined phases are an improvement on the calculated or isomorphous ones is evidenced by more readily interpretable electron density maps, which show only a low level of feedback from incorrectly located atoms. Several different types of Fourier syntheses have been calculated using the combined phase angles and an essentially qualitative evaluation of their relative merits is presented.
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    Representation of bicrystal invariant translations (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 500-506 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: All complete pattern shift lattice (DSC-lattice) translations of one lattice with respect to the second lattice of a bicrystal are described as a group. It is shown that the matrix representation of this group can be used to solve topological problems connected with secondary grain boundary dislocations (SGBD's) such as finding the step in the boundary associated with the SGBD. We have formulated this problem by establishing the 'step vector' S associated with the Burgers vector b of the SGBD in a cubic bicrystal. The problem is then solved in 2D, and the way to generalize to 3D is indicated.
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    Correlative microdomain model for shortrange-ordered alloy structures. II. Applications to special cases (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 511-516 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general theory of the diffuse scattering which has previously been developed on the basis of a microdomain model [Hashimoto (1974). Acta Cryst. A30, 792-798] is applied to the three special cases in which the microdomains have the ordered structures denoted by L12, L10 and L11. The practical intensity formula is presented in each case, which can be used to obtain, from the observed X-ray intensity distribution, the statistical nature of the microdomains; the average size, the size distribution, the number density and the spatial interdomain correlation.
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    Space-group notation with an explicit origin (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 517-525 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A set of symbols based on the minimum subset of Seitz matrices required to generate the complete symmetry may be derived for each of the three-dimensional crystallographic space groups. This has a number of desirable properties including explicit information on the choice of origin. It also leads to a simple and general algorithmic procedure for generating equivalent positions.
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    Electric field gradients and charge density in lithium nitride (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 507-510 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The magnitudes of the electric field gradients at all atomic positions in Li3N are known from NQR experiments. High-temperature NQR data indicate the gradients at Li(1) and Li(2) to be of opposite sign. In this paper, we calculate the field gradients from X-ray data and refine the parameters of the multipole deformation functions together with scale, extinction and temperature factors against X-ray and NQR data simultaneously, assuming various sign combinations for the gradients at Li(1), Li(2) and N. Despite an ill-defined scale factor of the X-ray intensities, negative signs at both Li(2) and N are obtained, and the sign at Li(1) is thus positive. The same signs are obtained from an ionic point-charge model. The extinction correction is important and dependent on the assumed signs. The model deformation map for the signs +, -, - at Li(1), Li(2) and N shows nearly spherical Li ions, whereas N appears to be strongly polarized perpendicular to c. With the assumption of the incorrect negative sign at Li(1), a strongly polarized Li(1) ion but approximately the same reliability indices for the X-ray data are obtained. Inclusion of NQR data in the charge-density refinement results in a better definition of the quadrupolar components of the deformation density close to the atomic centres.
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    Diffracted intensities from partially ordered layer structures with layer shift: two dimensional (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 525-529 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general expression for the diffracted intensities from an aggregate of partially disordered layer structures consisting of plane lattice layers displaced randomly along a and b by arbitrary fractions a/qa and b/qb has been worked out. The approach is similar to that of Wilson [X-ray Optics (1962). London: Methuen] and has been followed by Ray, De & Bhattacherjee [Clay Miner. (1980), 15, 393]. The expression is very general in nature and is suitable for studying the variation of intensities from such crystallites with any amount of displacements. Numerical computations for several cases have been carried out and results discussed. It is concluded that the peak will broaden and background increase as the magnitudes and probabilities of disorder increase.
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    A linear equation for products of normalized structure factors. I. Fourier formalism (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 548-552 
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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 relationship between products of two structure factors with coefficients calculated as the Fourier transform of a modified Patterson function is presented. The relation is alternatively expressed in terms of triple phase invariants and also a new weighted form of Sayre's equation [Sayre (1952). Acta Cryst. 5, 60-65] emerges as a special case. The advantages of the new equations with respect to Sayre's equation are discussed and, with simple one-dimensional models, examples of direct calculation of the cosines of triple-phase invariants are included.
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    Intermolecular energy, structure and stability of regular stacks of tetrathiafulvalene (TTF) and tetracyanoquinodimethane (TCNQ) (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 529-535 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The lattice energy of isolated, regular tetrathiafulvalene (C6H4S4) and tetracyanoquinodimethane (C12H4N4) segregated and mixed stacks was minimized for four structural parameters; a longitudinal and transverse slip of neighbouring molecules relative to each other, a rotation of a neighbouring molecule perpendicular to the molecular planes and the perpendicular distance between two neighbouring molecules. The van der Waals and repulsive interactions only were calculated from atom-atom potentials. The absolute minima of the lattice energies were achieved at stack structures slipped longitudinally with all stack parameters deviating less than about 0.1 Å from their observed mid-range values. The mixed stack proved to be less stable than the segregated stack only by about some tenths of a kJ mo1-1. Additional local minima were found for the segregated tetrathiafulvalene stack and for the mixed stack, which are not (yet) observed experimentally. The eclipsed tetrathiafulvalene stack and the tetracyanoquinodimethane stack with transverse slip, both of these observed experimentally, could not be predicted within a one-dimensional isolated stack model.
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    X-ray study of the paracrystalline nature of crystallized 70S ribosome lamellae (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 536-547 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: If a mixed organic solvent is added to a ribosome solution and stored at 277 K in a crystallization chamber, thin lamellae of a few μm diameter can be obtained. Under the electron microscope, tetragonal face-centred macrocells of b = 40 and c = 55 nm are visible. These findings are substantiated by X-ray small- and wide-angle diffraction which leads to macrocells of b = 42 and c = 52 nm and establishes the third dimension of the macrocell with a = 42 nm. Mainly 0kl reflections appear. From their line widths, it follows that each lamella consists of at least 15 × 15 × 15 macrocells with small paracrystalline distortions gs - 1.5%, whilst their 6 × 8 × 12 subcells with a0 = 7.1, b0 = 5.3 and c0 = 4.3 nm have large fibrillary distortions in the bc plane, similar to the aggregation of microparacrystals in stretched and annealed polymers. With a new method, the folding root of the Q function projected on the b axis can be analysed. Two compounds are placed in each macrocell, each consisting of about 136 cylinders of about 2.0 nm diameter and 7 nm length. They are aligned to fibrils of different lengths orthogonal to the bc plane and occupy about 47% of the macrocell. The residual volume is filled up with an 'amorphous phase' as in semicrystalline polymers. A comprehensive study of the existing literature leads to the conclusion that the 'crystalline phase' consists of two 70S ribosome tetramers and that the cylinders are obviously parts of two-stranded helices, whilst most of the RNA proteins are in the 'amorphous phase'. The biological significance of the ribosome crystals and the paracrystalline sublattice is described in detail in the Discussion.
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    A useful algorithm in lattice geometry (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 553-557 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An efficient algebraic algorithm is described for determining unit cells. It can be directly implemented on a digital computer. Two practical examples of its use are given: the determination of a unit cell on the (hkl) plane and the enumeration of the lattice points contained in a non-primitive cell. Both examples can be performed easily by hand; when performed by computer, they achieve a considerably higher computational speed than any other known methods.
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    The negative-quartet relation from electron-density considerations (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 573-578 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: On the basis of electron-density considerations, graphic explanations are given of triplets and positive and negative quartets. It is shown that the number of useful negative relations will always be much smaller than the number of useful positive relations.
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    Neutron diffraction study of thermal parameters in UX3 compounds (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 558-565 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The intensities of the weak superlattice reflections in the UX3 compounds, where X = Ru, Rh, Ge, and Sn, have been measured by neutron diffraction. These compounds have the ordered AuCu3 structure. Excellent fits to the observed intensities are obtained by introducing anisotropic second-order and fourth-order (anharmonic) terms to describe the probability distribution function at the X atom site. The ratio of the magnitude of the mean-square thermal vibration parallel to and perpendicular to the unique tetragonal axis of the X atom appears to depend on whether p bonding (UGe3, USn3) or d bonding (URu3, URh3) occurs with the U electrons. In UGe3 data out to Q = 13 Å-1 show the need to include a fourth-order anharmonic term. The form of this anharmonicity suggests an attractive potential between the nearest- neighbor U-X atoms.
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    The temperature dependence of correlated atomic vibrations in the Debye model (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 851-856 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Within the Debye approximation the temperature-dependent correlations of atomic vibrations are shown to involve essentially a single integral which is a function of two parameters. A tabulation of this integral is presented, together with high- and low-temperature expansions. A comparison with much more elaborate calculations for real crystals suggests that the simple method described might be accurate to 2̃0%.
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    Some implications of accurate thermal parameters for beryllium (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 848-850 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Authoritative values for the parameters of harmonic thermal motion have been used as criteria for various least-squares refinements of the structure model for beryllium metal. A change in the absolute scale of Brown [Philos. Mag. (1972), 26, 1377-1394] improves the correspondence of the associated data with the true thermal parameters. Contraction of the core-electron distribution upon bonding is a possible implication of the rescaled data.
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    Direct observation of TDS profiles from perfect silicon single crystals on a neutron diffractometer (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 863-871 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: TDS profiles convoluted with the instrument resolution were obtained by forming differences between diffraction profiles measured with neutrons of wavelength 0.60 Å on three perfect Si crystals of different thickness. The profiles were measured with two detector apertures for the reflections 022, 004, 044, 026, 008 and 066. From these measurements TDS correction factors α and hence a correction term ΔB for the temperature parameter of Si were derived. The temperature parameter of Si was determined for two temperatures, 92 and 292 K, as B92 = 0.212 (3) Å2 and B292 = 0.422 (3) Å2, respectively, from the refinement of 100 symmetry-inequivalent reflections measured with neutrons of wavelength 0.53 Å on an imperfect Si crystal.
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    Joint X-ray and neutron data refinement of structural and charge density parameters (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 857-863 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure for joint refinement of X-ray and neutron data is described in which structural, charge density and extinction parameters are adjusted simultaneously in order to arrive at the best least-squares solution with respect to all available diffraction data. This X + N refinement is applied to previously collected low-temperature data on oxalic acid dihydrate, C2H2O4.2H2O, and results are compared with the X-ray-only refinement, and an X-ray refinement with neutron values for the hydrogen structural parameters. The X + N model deformation density shows higher peak heights in the lone-pair regions than the X- ray-only model density and resembles more closely the X-N deformation maps. Though the X + N maps are more strongly model dependent, they contain less noise, provide an analytical description of the deformation density and, unlike the X-N density, can be obtained in principle with a less than complete data set. The estimate of the goodness-of-fit for each of the data sets requires an apportioning of the joint parameters, which in this study is based on the relative magnitude of the least-squares derivatives.
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    Numerical structure factor calculation of orientationally disordered molecules (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 899-903 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure factor of librating or orientationally disordered molecules with isotropic Gaussian distribution functions is calculated exactly by numerical integration. The computer program with an example is described. The results are compared with approximation methods which correspond to a cumulant expansion of the structure factor. The application to the refinement of the plastic phases of C2Cl6 and SF6 is shown. The influence of anharmonic distributions is considered. The method is compared to the analysis with spherical cubic harmonics.
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    Simultaneous Bragg diffraction of X-rays from liquid-phase epitaxial thin films (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 876-889 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Multiple simultaneous Bragg diffraction effects of X-rays in quaternary III-V liquid-phase epitaxial thin layers are investigated with both photographic and counter detection methods. For the photographic investigation, a divergent source is used. The geometric aspects of this type of diffraction, affected by lattice mismatch between epitaxial layers and substrates, are discussed for cases involving five-, six- and eight-beam reflections. The lattice mismatches in directions parallel and perpendicular to the interface normal of InGaAsP/ InP, determined from a single divergent-beam photograph, are obtained. For the counter detection study, a collimated incident beam and several single and double heterojunction samples, with large lattice mismatches are used. A kinematical treatment for a general n-beam diffraction, from double- and triple-layer systems, is derived to account for the measured intensities.
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    Investigation of long-range order in protein crystals by X-ray diffraction (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 871-875 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The rate and mechanisms of growth and the final quality of crystals are related to lattice disorders and can be studied from the analysis of X-ray diffraction patterns. Crystals of proteins and other biological macromolecules display features which are different from those of inorganic crystals. In this work the long-range order of protein crystals is probed via the mosaic spread, with a special camera constructed for this purpose. The very small mosaic spread measured indicates almost perfect long-range order in the crystal, suggesting the absence of dislocations. This is compatible with the weak binding energies and mechanical softness of protein crystals. If indeed such crystals do not incorporate dislocations, accumulation of strain may be a possible mechanism for the cessation of growth of protein crystals. Microscopic observations of crystal growth support this idea.
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    The influence of crystal and sample symmetries on the orientation distribution function of the crystallites in polycrystalline materials (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 889-899 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the most general case the orientation distribution of crystals in a polycrystalline sample is to be described by a function of orthogonal transformations which splits up into two functions of rotations corresponding to right- and left-handed crystals. The properties of these functions are influenced by crystal and sample symmetry. The rotational subgroup of crystal symmetry leads to symmetry relations which may be written in the form of selection rules. Elements of the second kind of the crystal symmetry give rise to a determinability condition, according to which the texture function may be split into a part \tilde{f}(g) which can be determined from polycrystal diffraction experiments and a part \tilde{\tilde{f}}(g) which cannot. The determinability condition may take on three different forms according to whether the crystal symmetry contains a centre of inversion, a mirror plane or a \bar 4 inversion axis. In the case of normal scattering the Laue symmetry is to be considered instead of the true crystal symmetry. The sample symmetry is to be described by a black-white or Shubnikov group containing four kinds of elements which give rise to four kinds of symmetry conditions in the function f(g). The sample symmetry may be a conventional one consisting of one-to-one relationships between crystal orientations. It may, however, also be a non-conventional one defined by an integral relation between an infinite number of crystal orientations.
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    Examination of semiempirical atom–atom potential functions for Cl...Cl non-bonded interactions (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 908-913 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Three semiempirical atom-atom potential functions suggested by different authors to describe non-bonded Cl...Cl interactions are examined via calculation of some thermodynamic properties of hexachloro- benzene, C6Cl6, and p-dichlorobenzene, C6H4Cl2, crystals. All thermodynamic quantities are evaluated with the cell model as a statistical mechanical basis. The calculation results provide some evidence to support the existence of positional disorder in the high-temperature phases of p-dichlorobenzene.
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    Cell reduction and lattice symmetry determination (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 913-915 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Simple inspection of the reduced form of a unit cell can fail to detect the correct lattice symmetry, because of the effects of measurement errors, computer rounding errors and uncertainties in interpretation of almost equal numbers. A procedure which is insensitive to these effects consists of the generation of a list of lattice vectors sorted on length, together with angles between pairs of them. The list includes the edges, face diagonals and body diagonals of the reduced cell, and the sums and differences of any of these which are similar in length. The correct unit cell is easily recognized in the vector list.
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    The plastic phase of hexachloroethane, C2Cl6: a neutron powder and single-crystal investigation (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 904-908 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Bragg intensity data extracted from energy-integrated neutron measurements were treated by a conventional split-atom model, with a series expansion in cubic harmonic functions, and by a Gaussian approximation for the molecular librations. The trigonal molecular axes are found to be smeared out close to cubic [111] axes with the Cl atoms near the [100] axes. With the three models mentioned consistent data are obtained for the root-mean-square translational amplitude: 0.4 Å, and the librational amplitude: 19.6°; both at 423 K. Data and results for three different temperatures are given.
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    Extinction corrections for a highly perfect crystal (SrTiO3) (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 916-920 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Accurate neutron-diffraction data from a highly perfect crystal of SrTiO3 have been used to assess the extinction model of Becker & Coppens [Acta Cryst. (1974), A30, 129-147, 148-153; Acta Cryst. (1975), A31, 417--425] in refining reliable thermal parameters from data very strongly affected by extinction. The model incorporates approximations not evidently reasonable in this case - namely, the (usual) kinematical approximation and the mosaic-block description of crystal microstructure. However, it is shown that a careful choice of parameterization within the overall motel (e.g. between a Gaussian and a Lorentzian function for the distribution of mosaic-block orientations) can yield a uniformly good description of the extinction per se - except for reflections extinguished by more than about 90% on intensity. The refined thermal parameters are in remarkably good agreement with values obtained independently from lattice-dynamical calculations.
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    Space-group notation with an explicit origin; erratum (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 921-921 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Hall [Acta Cryst. (1981). A37, 517-525] there are two errors in Table 7 on page 524. The proposed notation for proposed orders 144 and 157 should be P\bar 3 and \bar P32.
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    Notes and News (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 921-921 
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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 effect of data truncation on the measurability of Bijvoet differences; erratum (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 921-921 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Table 2 of Parthasarathy & Ponnuswamy [Acta Cryst. (1981), A37, 153-162], for every value of k, the row against yt = 0.3 for P = 1 and the row against yt = 0.3 for P = MC are to be interchanged. All relevant information is given in the Abstract.
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    Report of Executive Committee for 1980 (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 922-941 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    World Directory of Crystallographers Sixth Edition (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 943-944 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Election of Officers of the Union and Chairmen of Commissions (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 943-943 
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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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    Prices of Acta Crystallographica and Journal of Applied Crystallography (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 942-943 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Diffraction and resonance analysis. (In Russian.) by G. S. Zhdanov, A. S. Ilyushin and S. V. Nikitina (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 944-944 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Direct methods in crystallography by C. Giacovazzo (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 944-944 
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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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    Editorial. Division of Acta Crystallographica (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 1-2 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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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 d2 by A. Pies and A. Weiss (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 944-944 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    On the evaluation of root-mean-square errors in atomic coordinates in protein crystallography (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 432-438 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The calculation of standard deviations for atomic coordinates in human deoxyhaemoglobin A on the basis of various reciprocal-space residuals has shown the resulting values to be in good agreement with each other. Evidence is presented that such calculations may be more reliable than is commonly accepted. It is also shown that Wilson's statistics may be applied successfully to low- and high-angle protein diffraction data.
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    The origin of the crystallographic pedigree (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 443-453 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The origin of the crystallographic pedigree [Haisa (1978). Acta Cryst. A34, 753-759] is shown to be the Fm3m family, by examining crystal structures of chemical elements and compounds. The family is maintained by making the most of the relevant symmetry sites over the structures of a (Strukturbericht A1), ab (B1), ac (C1), abc (L21), abd, ae, abe, ace (J11), abce (J21), abcde, bcef (D89), abcef (H58), cdf, bdef (D8a), abdef; acefh (D84), ai (D2f), abcgj, abdfk and abcejl types in Wyckoff notation. The descent in site symmetry from Oh to its subgroups may be caused by the balance of the interactions between the neighbors of atomic contents which can be estimated from the lifting of the degeneracy of the nearest-neighbor distances, or the coordination index. When the interactions become out of balance, a descent of the space group through Pm3m, Im3m and P63/mmc to their subgroups occurs to form the crystallographic pedigree.
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    The use of Karle–Hauptman determinants in small-structure determinations. II (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 464-470 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper presents the results of an investigation into the usefulness of Karle-Hauptman determinants for the solution of the phase problem in small structures. The algorithm is discussed in some detail. Results for five test structures are given. For all test structures starting sets of about 25 reflexions with an acceptable phase error of 25° or less could be obtained. Various attempts to extend these starting sets in order to solve the structures are reported. In the writing of the program compatibility with the MULTAN system has been the authors' intention.
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    The kinematical theory of X-ray spherical-wave diffraction (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 454-463 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that the Fraunhofer approximation, used in the kinematical theory of X-ray diffraction, may fail for a wide variety of crystals with different perfection. The kinematical theory describing the diffraction pattern in the general case is developed. The case of spherical-wave diffraction by a plane parallel crystal is considered in detail. The intensity distribution and the diffraction line width are ascertained to be essentially dependent on the region of diffraction in which the observation plane is located. On the other hand, the diffraction pattern geometry is independent of the diffraction region and is determined only by the crystal structure and the optics of diffraction. The geometry of the diffraction pattern recorded by the divergent-beam method is analysed in detail.
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    A density-modification method for the improvement of poorly resolved protein electron-density maps (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 21-29 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An efficient computer procedure has been developed for the extraction of regions of contiguous, well-connected high density from a three-dimensional electron-density map. This procedure may be used to generate an extended model volume, from a smaller volume based on a starting atomic model. The starting model may, for example, only include main-chain atoms for a protein, or may omit uninterpretable segments of chain. The procedure may also be used to extract regions of contiguous density where no model exists. The extended model volume is used to produce a properly scaled model electron density. Calculated structure factors are obtained from the scaled model electron density by fast Fourier transform, and combined, with appropriate weights, with the existing phase information to give improved phase angles. Calculation of a new electron-density map with the new phase angles initiates the next step of a cyclic procedure which converges rapidly. The procedure has been applied to the structure determination of tyrosyl-tRNA synthetase. It has led to identification of most of the available amino-acid sequence in the electron density, and a revised tracing of the main polypeptide chain. Evidence for improvement in phase angles is obtained from electron-density difference maps for substrate and inhibitor binding, in which a reduction in background density is observed.
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    Lattice dynamical calculations of the mean square amplitudes of crystalline biphenyl (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 29-33 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The molecular mean-square-amplitude matrix of crystalline biphenyl, C12H10, is calculated with an intermolecular potential of the atom-atom type. The effect of the presence of the low-lying torsional mode, which interacts with translational modes, is discussed. The Born S-matrix method is used, and proves to be an excellent approximation, which takes about of the computer time of the exact calculation. The resulting amplitudes are in fair agreement with experiment, and show that the extremely high amplitude of libration about the long molecular axis may be satisfactorily explained without assuming a double-well shape for the torsional potential.
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    Experimental correction for primary and secondary extinction. I. Method (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 642-647 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The energy transfer equations are used to solve secondary extinction in a parallel-sided crystal slab in Laue geometry. Practical formulas are given for determination of the refiectivity per unit length, σ(ε), from the measured absolute powers of the diffracted and direct beams at rocking angle ε = θ- θB. The calculation assumes non-divergent beams, and the experimental tolerances are considered in detail. The primary extinction factor is defined by yp(ε) = σ(ε)/σkin(ε), where σkin is the kinematical reflectivity. When yp 〉 0.5 it may be approximated by yp ∼ exp[-(αδ)2], where α is about 0.5 and δ is the average size of the coherent domains when measured in units of the extinction distance Λ, δ = D/Λ. The extinction distance can be varied by changing the X-ray wavelength or polarization, and yp(ε) can be determined from two measurements.
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    Treatment for the intensity problem of n-beam kinematical reflections in a dynamical formalism (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 41-48 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The use of exponential functions as an approximation for reflection powers leads the intensity problem of n-beam kinematical diffraction to an eigenvalue problem. It is solved in the way similar to an n-beam Borrmann dynamical diffraction problem. Besides the intensities of Bragg-reflected beams, the excitation of modes concerning the intensity attenuation is also calculated for highly absorbing infinitely thick crystals. Experiments of multiple reflection from GaAs, InAs and InP single crystals for Cu Kα radiation were carried out. Comparison between the experimental and calculated reflected intensities for several 2-, 3-, 4-, 5- and 8-beam cases are given and discussed.
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    On the application of phase relationships to complex structures. XXI. An extension to the MAGEX procedure (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 683-685 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the previously described MAGEX procedure [Hull, Viterbo, Woolfson & Zhang Shao-Hui (1981). Acta Cryst. A37, 566-572] trial phases found from a ψ map were refined by a parameter-shift process which maximized a function depending on the overall satisfaction of the triple-phase relationships. Advantages have been found in using a different function which has a somewhat stronger physical basis. Two algorithms are described which may be used either for centrosymmetric structures or for individual reflexions which can take only restricted phase values.
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    Low-resolution neutron diffractometry with a position-sensitive multidetector (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 670-679 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A data reduction system for neutron crystallography using a two-dimensional planar multidetector is described. The method is based on an a priori calculation of the intensity distribution for each reflection for any crystal orientation. The orientation matrix of the crystal has to be known. From the calculated intensity distribution a mask is derived for each reflection. The detection elements of the detector which are inside the mask are summed to determine the intensity of that reflection and the cells outside are used to determine the background. The size of the mask is adapted to the relative height of the measured intensity of the reflector compared to the background. The theoretical intensity distribution for each reflection is calculated in reciprocal space from the primary-beam divergence and wavelength spread and the crystal mosaic spread, on the basis of the kinematic theory of diffraction. The derivation of the necessary equations, i.e. the determination of the resolution function of the instrument, is presented. Some typical results of data collection are also presented. The advantages of this data collection method are the safe determination of weak reflections, the easy discrimination of reflections which nearly overlap, the determination of crystal mosaic spread, and the discrimination of inelastic scattering in the proximity of intense reflections.
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    High-resolution electron microscopy of McGillite. II. Polytypism and disorder (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 695-702 
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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 series of polytypes of a sheet silicate mineral, mcGillite, has been found using high-resolution electron microscopy. Their crystal structures are described in terms of the stacking sequence of the one-layer monoclinic structure [Iijima (1982) Acta Cryst. A38, 685-694]. Multiplicity of the polytypes results from regular occurrences of the 120° rotation twinning on the basal (001) plane. The two- and three-layer polytypes found in the present study are both monoclinic and are different from two-layer schallerite and three-layer friedelite, belonging to the family of manganpyrosmalite and being reported as trigonal.
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    Determination of the position of even the lighter anomalous scatterers in a crystal structure by means of a two-wavelength technique (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 710-717 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For identical anomalous scatterers among a majority of normal scatterers the structure-factor amplitudes are estimated from intensity data obtained either with two wavelengths at one side of the absorption edge or with one wavelength at either side. Direct methods (or a Patterson synthesis) will allow the localization of these anomalous scatterers. Test calculations on the known structure of the iron-containing protein ferredoxin, simulating the effects of synchrotron radiation, show the feasibility of the procedure.
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    A comment on the method of determination of the polarization ratio for crystal-monochromated X-rays by Vincent & Flack (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 739-740 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By reference to previously unpublished tests, the validity of the experimental procedure proposed by Vincent & Flack [Acta Cryst. (1980), A36, 614-620] for the measurement of the polarization factor is questioned.
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    Electric field gradients and charge density in corundum, α-Al2O3 (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 733-739 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The charge density in α-Al2O3 has been refined with respect to X-ray structure factors [complete spheres for both Mo Kα and Ag Kα radiations with (sin θ/λ)max = 1.19 and 1.495 Å-1 respectively] and electric-field gradient tensors at both atomic sites, using Hirshfeld- type deformation functions. Atomic charges from a κ refinement are + 1.32 (5) for Al and -0.88 (8) e for O. The charge distribution of O is polarized towards the four Al neighbours, and metal-metal bonds are clearly absent. Quadrupole coupling constants and asymmetry parameters of the field-gradient tensors cannot be determined from the structure factors. They define the quadrupolar deformations near the atomic centers, and the X-ray data define the charge density between the atoms. The orientational parameters of the tensors and the signs of their largest eigenvalues can be qualitatively retrieved from the X-ray data. The refinement of anisotropic secondary-extinction parameters may, however, destroy this information. Refinement with respect to the field gradients affects mainly the quadrupolar deformation terms, and has little influence on the X-ray scale factor (i.e. monopolar terms) and computed electrostatic fields (i.e. dipolar terms). Properties of the charge density with different angular symmetries are thus only weakly correlated.
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    Electron microscopy of Li2O–Al2O3–SiO2 glass ceramics (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 741-743 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A combination of high-resolution electron microscopy and electron diffraction methods is used to obtain microstructural information of lithium-bearing glass ceramics, Li2O-Al2O3-4SiO2 with TiO2 as a nucleating agent (system A), and of the commercial system 0.68Li2O3 Al2O3 6.1SiO2 0.13ZnO 0.03Na2O 0.01K2O 0.11TiO2 0.077ZrO2 (system D). The experiments reveal the presence of small amounts of γ-spodumene in system A. In system D, the volume fraction of residual glass is estimated and the microstructure of various nucleating agents is elucidated.
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    Notes and News (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 749-750 
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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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    A matrix method for lattice symmetry determination (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 748-749 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general approach for the determination of metric lattice symmetry has been successfully tested on 3̃0 000 lattices from the National Bureau of Standards Crystal Data File. The central focus of the method is on the determination of matrices relating any primitive cell of the lattice to itself rather than on determining reduced cells or conventional cells. The method can conveniently be used in routine structure work as it readily detects the highest possible metric symmetry within any specified range of cell-parameter errors.
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    Matrix isolation spectroscopy by A. J. Barnes, W. J. Orville-Thomas, A. Müller and R. Gaufrés (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 751-751 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    High-resolution electron microscopy of the incommensurate structure in Sr2Nb2O2 (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 780-789 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The incommensurate structure of strontium diniobate, Sr2Nb2O7, is formed below 488 K with a one-dimensional lattice modulation along the [100] direction. A model of the atom displacements due to this lattice modulation has been proposed from an analysis of the systematic extinction of the extra reflections due to the incommensurate structure. High-resolution electron microscopy clearly reveals the lattice modulation in the incommensurate phase. The observed images are well interpreted by image simulation of the proposed model.
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    The temperature dependence of the Debye–Waller factor near a phase transition: CsPbCl3 (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 790-796 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By fitting effective one-particle potentials to Bragg neutron diffraction intensities measured by Sakata, Harada, Cooper & Rouse [Acta Cryst. (1980), A36, 7-15] for the cubic perovskite caesium lead chloride, CsPbCl3, it has been established that, contrary to the results of Sakata et al., the effective one-particle potentials for the Cl ion are neither independent of temperature nor of a highly anharmonic form. To the resolution limit of the data, collected out to sin θ/λ = 0.58 Å-1, the one-particle probability density function of the Cl ion is singly peaked. It is proposed that the strong temperature dependence of the effective one-particle potentials, and the accompanying anomalous temperature behaviour observed for the mean-square displacements of the Cl and Cs ions above the anti-ferrodistortive phase transition temperature, result from soft-mode vibrations. The temperature dependence of the mean-square displacement in the presence of soft modes is derived and it is shown for the first time that a significant temperature-invariant component will be the main additional effect at temperatures well above the critical temperature. The Cl and Cs ions in CsPbCl3 obey this derived mean-square displacement relationship.
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    The zeolite A debate: how wrong is a nearly correct space group? (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 821-825 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The apparent contradiction between NMR and X-ray results concerning the Si, A1 distribution in zeolite A is quantitatively analysed. It is concluded that the Fm{\bar 3}c structure model, based on X-ray refinements, is compatible with the NMR data if a cautious chemical-shift assignment is applied. The appropriate use of crystallographic approximations and their symmetry is discussed.
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    A theory for the evaluation of small-angle scattering diagrams of quasi radially symmetric particles considering polydispersity and deviations from radial symmetry (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 835-840 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general theory has been developed describing the scattering intensity of a polydisperse dilute ensemble of particles. These particles are assumed to be mainly radially symmetric. Deviations from radial symmetry are treated quantitatively using an expansion of the electron density in terms of multipole components. The particle radii are assumed to have a Gaussian-like distribution. The electron density of the particle core is allowed to be different from that of the solvent. As a practical application of this theory a Fortran 77 program was written which determines the radial electron density profile, the standard deviation of the radii, and additional parameters describing the deviations from spherical symmetry directly from the measured intensity.
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    Theoretical considerations on phase determination by three-beam interference (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 841-848 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For φ-scan experiments rotating the crystal through a three-beam case the rocking-curve: profiles have been calculated on the basis of the dynamical theory of X-ray diffraction. Divergence and wavelength spread of the incident beam have been taken into account. It is shown that for centrosymmetric crystal structures the asymmetry of the profiles is related to the sign of the triple product of the structure factors F({\bar {\bf h}})F(g)F(h - g) which are involved in a three-beam case. If anomalous absorption ('double Borrmann' effect) can be neglected the typical asymmetry is independent of the diffraction geometry (Laue or Bragg case). For Laue geometry and thick crystals (μ0 t 〉 1) corrections are necessary. For centrosymmetric structures it may be possible to determine the phase sum of a triplet by inspection of the rocking curve without computer calculations. The general features of the rocking curve are discussed and a physical interpretation is given.
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    The reflectivity of a pyrolytic graphite monochromator (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 859-863 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that a pyrolytic graphite monochromator crystal scatters X-rays as a mosaic crystal in accordance with the Darwin formulism, both for reflecting power and integrated intensity, over a range in wavelength from 0.5 to 1.54 Å. The scattering cannot be considered kinematic and, from estimates of the reflectivities parallel and perpendicular to the diffraction plane, polarization ratios are calculated which are in accord with published values. A simple description of the scattering process is given. The variation of polarization ratio with mosaic spread is discussed.
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    The electronic state of O2− in MgO studied by the Compton profile method (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 155-161 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The electronic state of the O2- ion in MgO is studied in detail by measuring the isotropic Compton profile and profiles in crystal directions [100], [110], and [111]. The theoretical profiles are calculated using linear combinations of local orbitals orthogonalized to each other symmetrically. The orthogonalization is performed with the 'exact' cluster method. Nine different local wave functions of the O2- ion have been used as the basis of the calculations. The experimental and theoretical profiles as well as their Fourier transforms are compared with each other. The orthogonalized Watson +1 potential-well wave function and the orthogonalized LCAO band function of Pantelides, Mickish & Kunz [Phys. Rev. B. (1974), 10, 5203- 5212] were found to describe best the ionic state of O2- even though neither of the functions gives complete agreement with the experiment.
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    Six regular polygons at a four-connected vertex (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 165-166 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Six angles are formed between four straight lines meeting at a point in space. Since there is one relationship between them. only certain combinations of six regular polygons will fit together at such a point. Some of these are enumerated.
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    An X-ray diffraction study of lithium (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 163-165 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An accurate X-ray diffraction investigation has been carried out on two single crystals of lithium. The data from crystal 1 were obtained at temperatures of 248 and 296 K, and those for crystal 2 in the temperature range 293 to 423 K. The measured integrated intensities have been analysed for the presence of anharmonicity in the atomic vibrations by using a temperature factor based on a one-particle potential of the form V(u) = ½ αu2 + γu4 + δ(u4x + uy4 + uz4 - u4). An average value for the parameter δ of 290 ± 140 eV nm-4 was found. No significant value of γ was found in the analysis of data from crystal 1, but a value of -360 ± 40 eV nm-4 was obtained from the higher-temperature data of crystal 2.
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    Structural studies on A-cation-deficient perovskite-related phases. I. ThNb4O12, thorium/vacancy ordering in slow-cooled samples (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 177-186 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The A-cation-deficient perovskite, Th0.25NbO3, i.e. ThNb4O12, when slowly cooled from the melt, presents an interesting hierarchy of ordering phenomena. The associated diffraction effects have been studied with electron microscopy/diffraction and X-ray diffraction techniques. Three main types of ordering processes occur, with different degrees of long-range order. A primary ordering of thorium atoms into alternate (001)p planes of A-cation sites (cell ap × bp × 2cp, P4/mmm) exhibits well-established long-range ordering. A secondary ordering of thorium atoms within the (001)p planes (cell 3\sqrt{2\alpha_{p}} × \sqrt{2b_{p}} × 4cp, Immm) is short range in nature and gives rise to superlattice reflections in the form of diffuse rods directed along g(110)p and g(\bar 110)p. The length of the rods corresponds to correlation lengths of only 20-30 Å between {110}p planes of thorium atoms, and the thorium/ vacancy ordering is adequately described by a sinusoidal modulation model, with accompanying modulated displacements of niobium and oxygen atoms. Thirdly, a system of octahedral tilts about [110]p or [\bar 110]p axes is described by a cell \sqrt{2\alpha _{p}} × \sqrt{2b_{p}} × 2cp, Pmam. Independent models for thorium/ vacancy ordering and octahedral tilts have been refined with the intensities of the corresponding groups of satellites measured from precession photographs. The complete model for ThNb4O12 can be described in the unit cell 3\sqrt{2\alpha _{p}} × \sqrt{2b_{p}} × 4cp, P2mm. The superlattice reflections arising from the octahedral tilts are split into groups of four satellites in the form of crosses, owing to microdomain formation in ThNb4O12, with domain boundaries parallel to (100)p and (010)p and with average widths of 2̃5 Å.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000424
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    The effect of crystal bending on direct phasing of electron diffraction data from cytosine (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 207-211 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Limiting conditions for the crystal structure analysis of organics using electron diffraction intensity data from elastically bent microcrystals are shown for a representative aromatic structure, cytosine, C4H5N3O. In a projection down the longest unit-cell axis, the normalized structure-factor magnitudes are greatly changed by slight bends, making the diffraction data useless for crystal structure analysis. This alteration of intensity is less severe for a projection down the shortest cell axis and allows a correct structure analysis for bends comparable to those measured experimentally. The correct crystal orientation, moreover, is only achieved by epitaxial growth and not solution growth.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000461
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  • 99
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    Pseudoatom expansions of the first-row diatomic hydride electron densities (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 225-239 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Representations of high-quality molecular electron densities are studied. An evaluation of restricted radial functions is made using a least-squares figure of merit, the molecular dipole and quadrupole moments, the electric fields at the nuclei, the electric-field gradients at the nuclei, an approximate energy and difference-density maps. For the heavy atom, a satisfactory representation has a fixed core function with a variable population and requires optimized dipolar core polarization functions, and an additional monopole term. The heavy-atom valence regions, and the H require expansions to at least the quadrupole level, with one Slater-type radial function per multipole and all exponents optimized. Additional valence radial functions and higher multipoles are required to give completely satisfactory difference-density maps but do not consistently improve the physical properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000515
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  • 100
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    A procedure for joint refinement of macromolecular structures with X-ray and neutron diffraction data from single crystals (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 239-247 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is presented for the stereochemically restrained least-squares refinement of macromolecular structures with neutron and X-ray diffraction data from single crystals. This procedure has been tested by refining a model of ribonuclease A using neutron data to minimal spacings of 2.8 Å and X-ray data from within 2.0 Å spacings. Joint X-ray and neutron refinement is well conditioned and tends to avoid false minima that may occur when a medium-resolution structure is refined solely with the neutron structure factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482000527
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