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  • International Union of Crystallography (IUCr)  (1,489)
  • 1980-1984
  • 1975-1979  (1,489)
  • 1978  (1,489)
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  • 1980-1984
  • 1975-1979  (1,489)
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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 43-47 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The real part, f' of the anomalous dispersion correction to atomic structure factors was measured by using Pendellösung fringes for Si 220 and {\bar 22}0 reflections in the wavelength range from Cu Kα1 to Rh Kα1. In order to avoid ambiguity in the Thomson-scattering term due to the nature of the bonding, the quantity (f'X - f'Ag) was compared with the available theoretical calculations. In this expression, f'X and f'Ag are the corrections for radiation X and Ag Kα1, which is used as the standard, respectively. The present experimental results fit best the values calculated by Cromer & Liberman [J. Chem. Phys. (1970), 53, 1891-1898].
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  • 2
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 61-65 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The bonding in Be metal is studied by calculation of valence and deformation density maps from data collected by Brown [Philos. Mag. (1972), 26, 1377-1394]. The deformation maps show clearly that the predominant interaction is bonding through the tetrahedral holes of the h.c.p. lattice. The valence-density maps generally agree with least-squares-model maps published by Stewart [Acta Cryst. (1977), A33, 33-38], though differences in detail exist which may result from incomplete space filling of the least-squares model functions. The experimental densities are interpreted in terms of the hybrid-orbital model of Altmann, Coulson & Hume-Rothery [Proc. R. Soc. London Ser. A, (1957), 240, 145-155] as corresponding to (sp2)a (sp)b hybridization of the Be atoms with b 〉 a. Agreement with a theoretical density obtained by the augmented plane wave calculation of lnoue & Yamashita [J. Phys. Soc. Jpn. (1973), 35, 677-683] supports both theoretical and experimental procedures.
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  • 3
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 88-90 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Earlier neutron-diffraction measurements [Willis (1964), Proc. Br. Ceram. Soc. 1, 9-19] on a single crystal of UO2.12 at 800°C showed that interstitial oxygen atoms enter the UO2 lattice at two kinds of site, which are displaced by about 1 Å along the (110) and (111) directions from the cubic-coordinated interstitial sites. It was also shown that the solution of oxygen is accompanied by the formation of vacancies in the normal oxygen sites, but that the uranium sublattice remains undisturbed. A new analysis of the same data has been carried out, which introduces constraints between some of the parameters and allows a more satisfactory treatment of the anharmonic motion of the oxygen atoms. The new analysis leads to a much more precise determination of the occupation numbers of the (110) and (111) oxygen atoms and of the normal oxygen vacancies. The simplest model to account for these new results is the so-called 2:2:2 configuration of oxygen defects.
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  • 4
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 91-94 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The planar bonding in graphite is interpreted in terms of the deformation density approach. The calculated ratio of the 100 and 110 structure factors is in good agreement with experimental results. This suggests possibly a general means of comparing bonding effects in structures where either the strength of the bonding or the atomic environment is similar and where the bonding parameters in one of the structures are known.
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  • 5
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 120-123 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that a model of growth disorder, describing the way in which substitutional disorder can be introduced into binary solid solutions at growth, exhibits a phase transition. In a particular case it is shown that the distribution in 2D sections of the crystal corresponds to the simple pair-interaction Ising model on a triangular lattice.
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  • 6
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 116-120 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Lattice fringes corresponding to (00.3) spacings of the 126R polytype of SiC have been obtained in the electron microscope. A number of 10.l reflections were allowed to pass through the objective aperture to obtain the lattice fringes showing a periodicity of ̃105 Å (one third of the c parameter of the hexagonal cell) and each unit-cell block is subdivided into smaller blocks corresponding to the spacings of 6H, 15R, 21R etc. The stacking sequence of these blocks has been used to work out the detailed structure of the 126R polytype. It has been suggested that the lattice resolution technique in conjunction with X-ray diffraction is likely to prove a useful method for determining difficult polytypic structures.
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  • 7
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 173-183 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray powder diffraction data for diamond have been re-analysed, in terms of an 'at rest' deformation-density model of monopole, octupole, hexadecapole and hexacontatettarapole terms of exponential form. The values of the parameters describing the third and fourth-order terms, and the refinement indices, are no different from those of an 'at rest' valence-density model. Unlike earlier analyses, however, the model is consistent with experimental measurements of the absolute scale, and with independently determined values of the Debye-Waller parameter. The predicted values of physical properties such as the gradient of the electric-field gradient at the carbon nucleus are shown to be strongly model-dependent. It is noted that the fit to the data, and in particular to the observed structure factor of the overlapping 333-511 reflection, is poor for all published charge-density analyses. Recent theoretical (crystal 'Hartree-Fock') calculations indicate, within the convolution and harmonic approximations, an experimental B value of 0.172 ± 0.006 Å2 and a scale factor of 1.004 ± 0.002. These theoretical results are, however, in poor agreement with the experimental structure factors.
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  • 8
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 242-249 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray diffuse-scattering experiments at 295 and 218 K on adamantane crystals, grown by annealing, show that its space group is F{\bar 4}3m, and that it is not orientationally disordered. A re-analysis of previous X-ray Bragg-scattering data shows that the conclusion of Fm3m, with orientational disorder, for sublimation-grown crystals is not statistically significant. The Bragg intensities are much less sensitive to orientational disorder than the diffuse scattering. The diffuse scattering shows short-range correlation effects interpretable as pairs of neighbouring molecules tending to adopt local configurations characteristic of the low-temperature P{\bar 4}21c phase, i.e. symmetry breaking in F{\bar 4}3m.
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  • 9
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 309-317 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structures of (Na,K)NbO3 solid solutions have been determined by using the neutron powder-profile refinement technique: phases K and L at room temperature, and G and F at higher temperatures. In each case approximate values have been found for position parameters and temperature factors. The structural models proposed by Ahtee & Glazer [Acta Cryst. (1976), A32, 434-446] based on the lattice parameters and intensities of difference reflexions have been found to be substantially correct. Indications of vibrational modes have been found in the sequential phase transitions of Na0.90K0.10NbO3.
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  • 10
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 318-321 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Following the theoretical approach of Bansigir and Iyengar, the expression for p44 for the crystals of CsC1 type is developed. Polarizabilities of some ions at 5890 Å are evaluated with experimental values of p44 and are found to be in good agreement with reported values. Polarizabilities of the ions in CsI at different wavelengths in the range 3000 to 5890 Å are also evaluated.
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  • 11
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 329-336 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Experiments with crystals of a KNCS. C12H24O6 complex show that the integrated intensities of reflections showing strong extinction can be raised to their expected kinematic values when the crystal is subjected to a temperature gradient. The intensity increases are accompanied by a broadening of the diffraction peaks and are reversible with no detectable hysteresis. These observations seem to be incompatible with the mosaic-crystal model. Local variations in the extinction behaviour have been detected by using a fine incident beam and suggest inhomogeneity of crystal texture. The intensity increases are probably connected with a reduction in the mean size of the perfect crystal domains, i.e. with a decrease of the mean spatial correlation length within the crystal.
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  • 12
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 343-344 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An approximation in Zachariasen's [Theory of X-Ray Diffraction in Crystals (1945). New York: John Wiley] treatment of X-ray diffraction from a perfect plane-parallel crystal in the Bragg case is pointed out and eliminated. The corresponding unapproximated expression for the transmitted beam is also given. It transpires that Zachariasen's approximation leads to significant errors for 'thin' crystals (i.e. those for which the path length is less than or of the order of the extinction length). Some illustrations of the nature of the error are given.
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  • 13
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 348-348 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Billiet [Acta Cryst. (1977). A33, 1007-1008] the printer has omitted line 17. The last sentence of the first paragraph should read: One knows, at the present time, no complete and definitive answer to this question, but may invoke some general elements which are likely to occur in the resolution of this problem.
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 350-350 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 296-308 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The MoO3 structure is analysed by means of multi-slice calculations for crystals up to 80 Å thick. It is shown that for such thin crystals convergent-beam patterns can be simply analysed. This allows crystal thickness to be readily determined and opens up the way to more precise structure factor measurements. Many-beam calculations are also used to analyse unit-cell and symmetry data obtained by convergent-beam diffraction/microscopy observations of '101' domains in molybdenum trioxide, showing that [MoO6] octahedra in domains are more nearly regular than in MoO3. This is supported by analysis of thermal diffuse scattering. The '101' domain structure has space group Cmcm and unit-cell parameters identical to those of the molybdenum oxide-hydroxide Mo4O10(OH)2. A qualitative comparison of calculated and observed intensities for the space-group-forbidden 100 reflexions of MoO3 indicates the presence of epitaxically deposited surface layers. This observation, together with the evidence of a hydroxylated domain structure, suggests that thin crystals are formed with epitaxic hydroxyl layers which diffuse into the bulk structure when the crystals are heated.
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 289-296 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method for measuring X-ray intensity data from crystals with large unit ceils is presented. The method takes full advantage of the capabilities of the multiwire area detector diffractometer. This diffractometer is a high-speed data collection system utilizing a multiwire proportional chamber that can detect photons from all simultaneously occurring reflections and record the diffraction pattern as a two-dimensional histogram in a computer mass core memory. In the electronic stationary picture method of data collection, reflection intensities are extracted from a sequence of electronic pictures each of which is exposed while the crystal is stationary. Between successive pictures the crystal is rotated about a fixed axis by a small constant angle of approximately 0.05°. Because the integrated intensity of each reflection is extracted from several consecutive pictures, advance prediction of detector coordinates and picture number is required for all reflections and the data-extraction computer program is necessarily complex. Expressions are derived for reflection detector coordinates and setting angles, the system hardware and software are described, the data collection procedure is outlined, and the quality of 7 × 105 reflection intensities measured during six months of operation is analyzed.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 336-341 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron diffraction measurements have been carried out on a single crystal of UO2 examined at four different wavelengths; 0.85, 1.12, 1.54 and 1.84 Å. The Bragg intensities were analysed for the wavelength dependence of extinction using both the Cooper-Rouse and the Becker-Coppens formulations. Both treatments showed that the crystal is of type I (i.e. r 〉〉 λg, where r is the domain radius, λ the wavelength and g the mosaic-spread parameter). The value of g is the same, within one standard deviation, for each wavelength; its magnitude is appreciably less than for other crystals (SrF2,ZnS,ZnTe,KCl) which have been examined by neutron diffraction at a number of wavelengths. Keeping the isotropic temperature factor for uranium fixed at 0.28 Å2, the value of 0.55 ± 0.02 Å2 is derived for the temperature factor of oxygen. There are no significant differences between the values of the extinction parameters and temperature factors obtained using the Cooper-Rouse treatment and the Becker-Coppens treatment based on either a Gaussian or a Lorentzian mosaic-spread distribution.
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 346-348 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new potential function for non-bonded atom. . . atom interactions of chlorine atoms has been used to calculate equilibrium crystal structures and potential energies of the three polymorphs of solid p-dichlorobenzene.
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  • 19
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 349-350 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 20
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 352-352 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 21
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Gaussian scattering curves for bond charges in urea and thiourea whose parameters were determined from 123 K X-ray data are compared with those derived theoretically. A fairly close agreement among the different scattering curves was found.
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  • 22
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 479-479 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 23
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 517-525 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is described which produces sensible estimates of structure factor moduli from intensity observations, whether the latter are positive or negative. Preliminary applications of the method to data from the protein phosphorylase b are summarized.
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  • 24
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 528-533 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A class of determinantal equations for the scale factor, the temperature factors and quantitative chemical contents of the unit cell is derived assuming non-penetrating atoms but without making use of statistical arguments. A new method for the determination of the scale and Debye-Waller factors is developed on the basis of these equations and applied to the structure factors of Al(OH)3, giving results with errors of about 2%.
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  • 25
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 428-431 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Expressions for the thermal-motion correction of bond angles are derived by determining the mean angle. Thus the joint distribution of the three relevant nuclei is used in the harmonic approximation of the nuclear vibrations. To calculate the correction in practice, the coupling tensors among the three relevant atoms must be known, these being a characteristic feature of the joint distribution. Since the coupling tensors cannot be measured, they must be determined from simple models of motion or from the interatomic force constants. The model of rigid-body motions can be applied in many cases, and for this model it is shown that the angle correction can be calculated from the corrected bond lengths. Approximate expressions for upper and lower bounds of the angle correction are derived.
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  • 26
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    Acta crystallographica 34 (1978), S. 450-453 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A genralized discussion of direct methods of solving the phase problem leads to the suggestion that overlapping vectors in the Patterson function may be the cause of failures in these methods. A simple removal of these overlapping vectors is proposed, which produces modified |E| values. There were used with the program MULTAN to solve the structure of a prostratin derivative, C22H28O6, which had otherwise resisted solution.
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  • 27
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    Acta crystallographica 34 (1978), S. 442-446 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Resonance frequencies of thick plane-parallel plates are easily detected by diffraction of light with an accuracy better than 1 p.p.m. The method, which has been earlier employed for the determination of thermoelastic properties, proved to be sufficiently sensitive also for the measurement of stress-induced shifts of resonance frequencies, and is therefore suited for the determination of third-order elastic constants. The technique is easier to handle and much less expensive than other methods in use today. The complete sets of third-order elastic constants for KAl(SO4)2.12H2O, NH4Al(SO4)2.12H2O, CsAl(SO4)2.12H2O and CH3NH3Al(SO4)2.12H2O have been measured. All constants possess negative values. These alums exhibit a behaviour similar to that of the structurally related caesium halides, with the exception of ammonium alum which shows anomalously small constants.
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  • 28
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    Acta crystallographica 34 (1978), S. 625-634 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Ordered and disordered states of potassium ions in (111) tunnels in the structure of cubic KSbO3 have been studied by high-resolution electron microscopy. N-beam calculations for the images of both the ordered and disordered states reproduce well the observed images. The disordered state changes into the ordered state under electron irradiation during the observations. Electron diffraction from the specimens and optical diffraction from the images show diffuse spots due to small domains of the long-range-ordered state, but no other diffuse scattering due to short-range order has been observed.
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  • 29
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    Acta crystallographica 34 (1978), S. 638-639 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In lnternationale Tabellen zur Bestimmung der Kristallstrukturen (IT) [Vol. I. (1935), Berlin: Borntraeger] Carl Hermann followed the Mallard classification into crystal systems. The 'trigonal system' did not enter the IT until 1952 - a step backwards.
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  • 30
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    Acta crystallographica 34 (1978), S. 698-701 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Phase refinement based on minimization of C = Σh, k |EhEkE-h-k | [1 -- cos(φh + φk + φ-h-k)]2 has been tested on several known structures (space group P21) containing elements of pseudo-centrosymmetry. C always has a maximum for a consistent centric phase set provided that some invariants have a phase of 180°. Thus C will have a minimum for a noncentric phase set, and the phases do not turn centric during the refinement as often is the case when the ordinary tangent formula is applied. The hydrochloride of the insect alkaloid adaline (space group P21), whose cell constants and hitherto unpublished atomic positions are given, is one of the examples upon which the destruction of centrosymmetry is demonstrated. The destruction of centrosymmetry was indicated by the largest maximum of a one-dimensional modified F2 synthesis along the unique axis.
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  • 31
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    Acta crystallographica 34 (1978), S. 724-727 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new method is given for the calculation of integrals IlLL2 (k) = {{1}\over{4\pi}} ∫ Rα(r1)Rβ(r2) {{r^{L_{2}_{1}}\over{r^{L_{\beta}_{2}}} jl(kr1)PL(cos θ1) dV which are needed to evaluate orientation-dependent scattering factors for the overlap electron density between orbitals on stationary atoms at rα and rβ, where r1 = r - rα, r2 = r - rβ and Rα(r1) and Rβ(r2) are Slater-type radial functions. The integration may be reduced to the sum of an algebraic term and a one-dimensional numeric integration between 0 and R, where R = rβ - rα.
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  • 32
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    Acta crystallographica 34 (1978), S. 728-738 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A Bayesian method of statistical analysis is presented, one which provides a more powerful approach than classical least squares in circumstances where hitherto the latter technique has been applied. The general principles of the method are discussed and applications to crystallographic refinement and primary reduction of diffractometer data given.
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  • 33
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    Acta crystallographica 34 (1978), S. 751-753 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of analysing the X-ray diagrams of imperfect membrane lattices with degrees of stacking disorder between 2 and 6% is presented. The method is, however, generally applicable to partially disordered lattices of centrosymmetric membranes. This can also be extended to the case of asymmetric membranes occurring in one orientation only, or in pairs, back-to-back. The procedure allows the determination of the statistical quantities characteristic of the partially disordered lattices and the separation of the diffuse scattering component. As a direct consequence, the refinement of membrane electron density projections becomes feasible and an example is presented for erythrocyte membrane lattices. A one-dimensional model of the refined electron density profile of the erythrocyte membrane is used to calculate numerically the X-ray scattering for a partially disordered lattice of N membrane units. A residual of 15% is obtained with this model and the difference between the observed and calculated values can be minimized further with the proposed refinement procedure.
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  • 34
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    Notes: The crystal structures of phases, previously designated as 11L, 9L and 16L, which were commonly found in the title systems are suggested from their high-resolution two-dimensional electron-microscope images. Two types of blocks are found which are composed of five and six layers of pentavalent-metal oxide octahedra and are closely related to the pyrochlore structure. The 11L structure is of rhombohedral {\tt ABCABC} stacking of the former type of block, and the 9L structure is of hexagonal {\tt B}_{0}{\tt A}_{0}^{\prime}{\tt B}_{0}{\tt A}_{0}^{\prime} stacking of the latter type of block. The 16L structure is found to be an alternate stacking of the two types of blocks. The method of stacking of the blocks is the same for the three structures and is found to be favorable from the point of view of local charge balance.
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  • 35
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    Acta crystallographica 34 (1978), S. 782-791 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The newly developed fast Fourier least-squares algorithm [Agarwal (1978). Acta Cryst. A34, 791-809] has been used to refine the structure of rhombohedral 2-Zn pig insulin at a resolution of 1.5 Å. The CPU time required for each cycle of refinement was about 3 min on an IBM 370/168 computer. After 67 cycles of refinement the conventional R factor was 0.113 for 11 890 terms. The procedure used in the refinement is described and an analysis of the results presented. From the experience learned in this refinement a procedure is suggested which should provide faster convergence and require considerably fewer refinement cycles.
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  • 36
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    Acta crystallographica 34 (1978), S. 809-811 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that correlation between the third-cumulant coefficients in noncentrosymmetric structures restricts the number of coefficients which can be refined. In the space group P1 all ten coefficients of one atom have to be kept fixed.
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  • 37
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    Acta crystallographica 34 (1978), S. 825-826 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the course of a discussion of the nature of an ambiguity in the indexing of Renninger peaks the possibility was discovered of distinguishing some opposite directions in a cubic crystal without recourse to anomalous scattering. A multiple-diffraction experiment performed on a (111) Ge plate rotated about [222] enabled distinction between the [1{\bar 1}0] and [0{\bar 1}1] directions to be made. The azimuthal angles counted from alternative zero meridians containing [1{\bar 1}0] or [0{\bar 1}1] are the same, but give rise to peaks indexed hkl and 2 - l,2 - h,2 - k respectively. However, dynamically equivalent situations 222, hkl/(2 - h,2 - k,2 - l) and 222, (2 - l,2 - h,2 - k)/lhk are geometrically different, being distinguished as Bragg-Laue and Bragg-Bragg, respectively, or vice versa.
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  • 38
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    Acta crystallographica 34 (1978), S. 863-870 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Suitable weighting schemes for use in tangent-formula phase development and refinement are discussed, and a statistically based weighting scheme, which can easily be incorporated in existing computer programs, is proposed. Examples of the use of this method in structure solution and completion are presented for a previously unknown structure and for several structures which had been difficult to solve by other methods. In addition a method is given for subtracting the contribution of heavy atoms from observed |E| values on a statistical basis which is very useful when the presence of such atoms leads to problems in defining the enantiomorph. These methods add greatly to the power of the MUL TAN computer program.
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  • 39
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    Acta crystallographica 34 (1978), S. 860-863 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Algebraic expressions are evaluated, from which the influence of small discrepancies between atomic positions in a structure model and the corresponding atomic sites in the observed structure on R2 can be calculated. Theory and experiment are in good agreement. It is demonstrated that because of the effect of small positional errors, R2 as a function of the size of a structure model does not necessarily show a monotonic decrease. The path of R2 may even contain additional minima.
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  • 40
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    Acta crystallographica 34 (1978), S. 883-892 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: With triple-phase relationships treated as linear equations it is possible to refine a set of phases from given initial values. Phases so obtained are better than those found by refining to self-consistency with the tangent formula. An investigation of the radius of convergence of the least-squares refinement process showed that a substantially correct solution may often be found even starting with random phases. Systems containing up to 300 phases have been investigated and the results and their implications are discussed. It is concluded that the random approach can, at the very least, be used to obtain 70--100 phases as a good starting point for phase development. There is also the possibility of obtaining a sufficient number of phases directly to define a reasonably complex structure, especially with a computer augmented by an array processor. A problem which can arise with linear equations, as with the tangent formula, is that the phases obtained do not adequately define the enantiomorph and give an E map with a pseudo centre of symmetry. Two methods of overcoming this problem are described.
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  • 41
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    Acta crystallographica 34 (1978), S. 922-931 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: With high-resolution electron microscopy new crystal structures were found in the binary system of Nb2O5WO3 oxides. The compounds are proposed to have the mole ratios 4Nb2O5. 22WO3 and 4Nb2O5. 50WO3. The crystal structures are ascribed to intimate intergrowths of two known structures, the ReO3 type and tetragonal tungsten bronze type. The latter grows coherently in the host lattice of the former, forming regularly arranged slabs. The coherent intergrowth of the tetragonal tungsten bronze structures is described as the 'rotation operation' on the ReO3-type structure.
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  • 42
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    Acta crystallographica 34 (1978), S. 909-921 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray data on silicon, tetracyanoethylene, p-nitropyridine N-oxide and ammonium thiocyanate are refined with a generalized aspherical-atom formalism as introduced by Stewart, but modified to have a spherical valence more similar to the unperturbed HF valence shell. Several types of radial dependences of the multipole functions are tested and criteria are developed for judging the adequacy of the aspherical-atom refinement. The aspherical-atom model leads to a significant decrease in the least-squares error function, a reduction of features in the residual map, and an improvement in thermal parameters when comparison is made with the neutron results or when the rigid-bond postulate proposed by Hirshfeld is applied. Positional parameters are often improved except in the case of terminal atoms for which discrepancies, attributed to correlation between dipole-population and positional parameters, are sometimes observed. Deformation maps based on the aspherical-atom least-squares parameters contain less noise than X -- N maps and benefit from inclusion of calculated values of weak structure amplitudes in the summation. In the cases studied, deformation maps including terms beyond the experimental resolution do not yield additional information.
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  • 43
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    Acta crystallographica 34 (1978), S. 946-949 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple method is described for the interpretation of Weissenberg photographs and the determination of triclinic cell parameters from a single setting of the crystal. The theoretical approach is followed by an example illustrating the procedure. A comparison of these results with those derived from diffractometer measurements is made.
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  • 44
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    Acta crystallographica 34 (1978), S. 1025-1027 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Kaul & Saxena [Acta Cryst. (1977), A33, 992-996] have reported the existence of long-range and short-range order in a non-stoichiometric phase 'LnOx' (Ln = rare earth). It is shown that the experiments they are describing are indeed the oxidation of the rare-earth hydride LnH2 into the rare-earth cubic C-type sesquioxide. The interpretation they give of their experiments is to be discarded entirely.
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  • 45
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    Acta crystallographica 34 (1978), S. 1027-1028 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electronic polarizabilities of cations have been obtained for the sodium D line (in Å 3): Mg2+ 0.1, Fe2+ 3.3, Zn2+ 5.4, Zr4+ 4.6. The polarizability of the O2- ion varies from one structure to another. It has been shown that calculation of electronic polarizability is possible only if an accurate structure refinement is available.
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  • 46
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    Acta crystallographica 34 (1978), S. 831-831 
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  • 47
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    Acta crystallographica 34 (1978), S. 832-832 
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  • 48
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    Acta crystallographica 34 (1978), S. 833-835 
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    Notes: The structure types of Rh7Mg44 and Mg6Pd are described by means of packing octahedra and tetrahedra. The host structure common to the two types is a cubic intergrowth of two different building units. One unit has the Mg atoms arranged as the anions in Keggin's ion (PW120403-), and the other is an octahedrally capped block of the pyrochlore structure.
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  • 49
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    Acta crystallographica 34 (1978), S. 901-905 
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    Notes: A method for finding probable Li positions in a given oxygen matrix in crystals is described. It is formally based upon bond strength-bond length discussions. The sums of bond strengths for simulated Li atoms are calculated and printed in three-dimensional maps. The method is tested on nine structures containing Li atoms. In five of these the Li sites are known from neutron diffraction studies, in two from X-ray powder diffraction data sets, and in the other two from X-ray single-crystal investigations. The calculated Li coordinates in all the tests are in fair agreement with the experimentally observed positions. The method is therefore likely to provide an auxiliary tool for determining Li sites in X-ray crystal structure studies.
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  • 50
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    Acta crystallographica 34 (1978), S. 905-908 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For rigid molecules which undergo large librations, the dynamic density and the dynamic molecular scattering factor are derived. The general case is treated where translations and librations of the molecule are coupled (no site symmetry). The dynamic molecular scattering factor is an integral which cannot generally be solved, and temperature factors generally do not appear. For the special case of statistically independent translations and librations, a temperature factor for the translations of the molecule is obtained. Moreover, temperature factors are obtained for density units which are spherically symmetric, since the motions of these density units can be described by translations only. The possible cases for which spherically symmetric density units can be assumed and, hence, temperature factors can be applied, are discussed.
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    Acta crystallographica 34 (1978), S. 936-939 
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    Notes: The presence of an antisymmetric component of the non-spherical atomic charge distribution results in a more general breakdown of Friedel's law in polyatomic noncentrosymmetric structures. That this is also true in the case of noncentrosymmetric structures of elements is demonstrated directly for the case of the trigonal structures of Se and Te.
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  • 52
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    Acta crystallographica 34 (1978), S. 955-959 
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    Notes: The unit vectors el, e2, e3 form a fixed orthogonal coordinate frame. The unit vectors el', e2', e3' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp [2πi(Σ3i,j = 1aijei.e'j)] is calculated. As an application the average of exp [2πi(h.x + k.y + l.z)] is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem.
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    Acta crystallographica 34 (1978), S. 994-999 
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    Notes: Form factors calculated from several theoretical models show that the Xα method is accurate to about 1%. With the latter scheme and the Watson-sphere model the atomic form factors for O2- and N3- are computed for varying sphere radii. To a first approximation this radial variation accounts for the different environments of such ions. Deviations of up to 25% in the scattering factors occur when compared with the results obtained from the wave functions of the corresponding neutral atom.
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    Acta crystallographica 34 (1978), S. 986-994 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The variance of X-ray intensities is W = Σ2 + (k - 1)S2 - ΣiQi|fi|4, where Σ is the sum of the squares of the moduli of the atomic scattering factors fi, S is the modulus of the sum of the squares of the atomic scattering factors, k is 1 for noncentrosymmetric crystals and 2 for centrosymmetric, Qi is an integer depending on the space group and Wyckoff position, and the summation is over the atoms of the asymmetric unit. Values of Qi for the general reflexions and general positions are tabulated for the line, plane and space groups; they tend to be moderately positive for the less symmetric space groups and large and negative for the more symmetric. Special reflexions and special positions are discussed briefly. Dispersion shows itself in the distinction between Σ and S and in the modulus signs in the final term.
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    Acta crystallographica 34 (1978), S. 1006-1013 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The average interference function ({\cal J}hkl(ΔS)) of a powder sample containing perfect crystals at a reciprocal distance ΔS from the peak is evaluated both for the case of identical parallelepiped crystals and for a Gaussian sample [probability of thickness d along a given crystal direction = C1 exp (-C2d2)]. In the latter case ({\cal J}hkl(ΔS)) decreases as 1/ΔS2 for large ΔS, by analogy with the Bernoullian model [Ailegra, Bassi & Meille (1978). Acta Cryst. A34, 652-655] although with a smaller amplitude, for a fixed integrated intensity and half-peak width. It is shown that the Gaussian interference function, or line profile, cannot be given by any real sample, at least if its crystals neither contain holes nor have concave surfaces. Number and weight probability distributions are calculated both for the Bernoullian and for the Gaussian crystal-size statistics. As expected from the calculated line profiles, the Bernoullian statistics correspond to a larger weight percentage of crystals smaller than the average.
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    Acta crystallographica 34 (1978), S. 832-832 
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    Acta crystallographica 34 (1978), S. 842-853 
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    Notes: An intermolecular force field for carboxylic acids has been derived by a least-squares fit of the parameters of non-bonded atom-atom potentials and a hydrogen-bond potential to experimental data. The latter include heats of dimerization and dimer structures of formic, acetic and propionic acid, and heats of sublimation and crystal structures of acetic, α and β-oxalic, α and β-fumaric and isophthalic acid. It was found that (exp - 6 - 1) atom-atom potentials and the Lippincott-Schroeder potential for the hydrogen bonds reproduce fairly well the experimental energies as well as the structures. The transferability of the potentials was studied with respect to the crystal structure of allene dicarboxylic acid and to the crystal structure and the lattice energy of formic acid, and was found to be good. A comparison is made with the results of other authors.
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    Acta crystallographica 34 (1978), S. 870-883 
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    Notes: A magic determinant is a Karle-Hauptman determinant in which the phases of reflexions forming the elements are expressed in magic-integer representation. By means of appropriate algorithms, which are described, magic determinants may be found, up to order 30, which have a high content of large E's. The value of the magic determinant depends on the values of the independent variables (usually two) in terms of which the magic-integer-represented phases are defined. Maxima are sought in a map of magic-determinant values and these give trial values for the constituent phases. These phases may be refined by maximizing one or more of the largest eigenvalues of the matrix of elements. Applications to five different structures are described and the usefulness and limitations of the magic-determinant concept are discussed. It is concluded that Karle-Hauptman determinants, chosen in the way described, provide a very discriminating figure of merit. However, the structure factors they contain usually provide a rather poor base for subsequent phase development and this limits the usefulness of the magic-determinant approach.
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    Acta crystallographica 34 (1978), S. 892-894 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper illustrates the potential of Karle-Hauptman determinants for the solution of the phase problem in a 'difficult' small structure. An outline of the procedure followed is given. Suggestions for the future are presented, together with a discussion of the results obtained.
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    Acta crystallographica 34 (1978), S. 931-935 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An improved method of crystallographic structure refinement, especially suitable for large molecules, is described, it is based on simultaneous minimization of a realistic potential-energy function and a crystallographic residual. The method has already proved its worth in the final stages of refinement of two structures; an application to crude wiremodel coordinates of a small protein is described and evaluated.
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    Acta crystallographica 34 (1978), S. 950-954 
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    Notes: The one-parameter model of Dunitz & White [Acta Cryst. (1973), A29, 93-94] for the analysis of torsional degrees of freedom within an otherwise rigid body has been applied to data for a number of representative compounds. The model gives results not significantly different from those of more elaborate models for librations about bonds, even when the r.m.s, amplitudes of these librations are as great as 24°. The limitations of this kind of analysis and some of the problems in applying it are discussed.
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    Acta crystallographica 34 (1978), S. 969-974 
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    Notes: A procedure is given for estimating the variance ratio σ21/σ211, of two models of a crystal structure where σ21 and σ211 are the variances of the weighted (|Fo| - |Fc|) distributions for models I and II, respectively, and |Fo| and |Fc| are the observed and calculated structure factors. The procedure provides a statistical test of the hypothesis that the above ratio is unity for a given pair of models and, thus, whether one of the models offers a significantly better description of the crystal structure. The method is applicable to crystallographic problems in which each of two or more structural models is expressed in terms of the same set of parameters. It has been applied to a number of atom-assignment problems, and the results are compared with those from Hamilton's R-factor ratio test.
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    Acta crystallographica 34 (1978), S. 1047-1047 
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    Acta crystallographica 34 (1978), S. 48-51 
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    Notes: By the use of convergent-beam and critical-voltage measurements it has become possible to measure the crystal potential to an accuracy of about 10-3. The possibility that the contribution from virtual inelastic scattering is greater than the errors in these experiments is examined and it is shown that only virtual scattering from single-electron excitations need be considered. Estimates are given for the Fourier coefficients of the virtual inelastic scattering potential for silicon, copper and germanium and these are compared with the errors in the critical-voltage experiments of Hewat & Humphreys [High Voltage Electron Microscopy (1974), edited by P. R. Swann, C. J. Humphreys & M. J. Goringe, pp. 52-56. London and New York: Academic Press]. It is concluded that the virtual inelastic scattering contribution is less than the experimental errors.
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    Acta crystallographica 34 (1978), S. 74-84 
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    Notes: The formation and growth of antiphase domains in lithium ferrite has been investigated through an analysis of the X-ray diffraction line broadening. Calculations of the parameter J'(0)/J(0) have been carried out by the method of Wilson & Zsoldos [Proc. R. Soc. London, (1966), A290, 508-514], for various boundary structure models with allowance being made for the presence of enantiomorphism. The experimental results indicate that the boundaries form predominantly on {110} planes, which is consistent with the principle of tetrahedral charge invariance. It has also been found that during the initial stages of growth the domain thickness distribution resembles a Gaussian curve, but as further growth occurs it takes on a truncated Cauchy-like character. The rate of this change is strongly correlated with the time of growth dependence of the mean domain thickness. Finally, an activation energy of 3.1 ± 0.8 eV was obtained for the growth process which is in reasonable agreement with the calculated value (2.53 eV).
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    Acta crystallographica 34 (1978), S. 112-116 
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    Notes: The calculation of dynamical elastic diffuse electron scattering from a crystal containing a point defect or dislocation may require prohibitively large amounts of computing time. Two approximations are described which greatly reduce the computer time required for these calculations, and so allow the simulation of electron-microscope images of defects at atomic resolution. The diffuse scattering expected from microdiffraction experiments can also be predicted in this way.
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    Acta crystallographica 34 (1978), S. 94-102 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Feynman path-integral formulation of quantum mechanics is used to investigate the theoretical problem of the propagation of high-energy electrons through thin crystalline specimens. The primary objective is to find a satisfactory scattering approximation that accurately describes the transmitted (elastically scattered) wave, and still retains a mathematically invertible relation between the transmitted wave function and the specimen structure. It is shown that the path-integral method leads naturally to an invertible, higher-order, phase-object approximation, in addition to the usual kinematic approximation and the usual phase-object approximation. The higher-order phase-object approximation in turn leads to the noninvertible, multislice approximation of Cowley & Moodie, which had previously been derived by those authors from a semi-classical, physical-optics point of view.
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    Acta crystallographica 34 (1978), S. 123-126 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The composition of In3Te4 has been established as a single-phase material. Single crystals of this material have been prepared and its structure has been identified as tetragonal with lattice parameters a0 = b0 = 6.173 and c0 = 12.438 Å. The stability of the structure has also been investigated.
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    Acta crystallographica 34 (1978), S. 137-138 
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    Notes: The lattice parameter of MoSCI was determined at different temperatures from 30 to 437°C with X-ray diffraction methods. The coefficient of thermal expansion of this cubic compound was determined from the above data. At 550°C it was found that the compound irreversibly transforms to α-MoO3, which belongs to the orthorhombic system.
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    Acta crystallographica 34 (1978), S. 139-140 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: If ionic radii are calculated so as to predict accurately mean interatomic distances, then the relationship between cell volume and the cube of the cation radius for a series of isotypic compounds is non-linear.
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    Acta crystallographica 34 (1978), S. 157-157 
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    Acta crystallographica 34 (1978), S. 140-142 
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    Notes: X-ray measurements of the lattice spacings in three Ag-Ge alloys in the temperature interval 30-595°C and in two Cu-Ge alloys in the temperature interval 25-611°C, in the solid-solution range, have been made with a Unicam 19 cm high-temperature camera. The measured lattice spacings have been found to increase non-linearly with temperature, this non-linearity being slightly enhanced for Cu-9.25 at.% Ge alloy. The dependence of the measured lattice spacings on temperature has been expressed in an analytical form (polynomial of second degree) from least-squares fitting of the data. The thermal expansion coefficient, α, for the alloys considered, in general, has been found to decrease linearly with increasing temperature (from ∼25 to ∼17 × 10-6°C-1), except for the greater germanium concentration (9.25 at.%) in copper solvent where the tendency is reversed.
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    Acta crystallographica 34 (1978), S. 159-160 
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    Acta crystallographica 34 (1978), S. 160-160 
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    Acta crystallographica 34 (1978), S. 165-170 
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    Notes: In this paper the possibility of applying powder diffraction patterns to determine polytypes and stacking sequences in disordered close-packed structures is discussed. It is shown that by using model structure analysis it is possible to establish some important features of the structure such as the presence of DS (Disordered Structure) and various simple polytypes.
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    Acta crystallographica 34 (1978), S. 268-274 
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    Notes: The crystal structure of RbH3(SeO3)2 has been determined in the low-temperature phase (space group P21) with neutron diffraction. The crystal undergoes an improper ferroelectric phase transition at 158 K and the unit cell is doubled below the transition temperature. This transition is induced by the condensation of a soft mode at the Brillouin zone boundary. Imposing the symmetry of the soft-mode eigenvector on the static displacements from the high-temperature positions (space group P212121) results in a reduction, by a factor of four, of the number of positional parameters required to describe the low-temperature structure. The crystal is constructed of two types of chains consisting of SeO3 groups connected by hydrogen bonds, and the order parameter for the transition is shown to be the rigid rotations of the SeO3 tetrahedra belonging to one type of chain. The atomic displacements necessary to produce the observed spontaneous polarization are shown to be too small to be observed in the present experiment, and the precise mechanism responsible for the spontaneous polarization remains unknown.
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    Acta crystallographica 34 (1978), S. 230-241 
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    Notes: Conditional probability distributions of the two-phase structure seminvariant φ12 = φh1kl1 - φh2kl2 in P21, given the values of one or more two-phase structure seminvariants, as well as appropriately chosen sets of structure factor magnitudes |E|, are derived. These distributions yield unique and reliable estimates, in the whole interval (-π,π), of the values of these seminvariants. In the case that a given structure seminvariant specifies the enantiomorph, the values of the remaining seminvariants are consistent with this choice of enantiomorph. In any event, the variance of any distribution of the kind described here is much smaller, in favorable cases, than that of a distribution which assumes as known magnitudes |E| alone, reflecting the fact that previously derived phase information severely limits the possible values of other phases.
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    Acta crystallographica 34 (1978), S. 275-282 
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    Notes: This paper is the first in a series concerned with a particular graph theoretical scheme for enumeration and derivation of structures of prescribed form. The problem spoken to by this work is that of finding a unique formal procedure for generating all distinct (i.e. non-isomorphic) graphs of a given number of vertices and prescribed valency. Here the scheme is outlined as applied to a search for regular trivalent graphs, some of which correspond to trivalent polyhedra. A systematic procedure for obtaining the number of equivalence classes of the adjacency matrices associated with trivalent graphs of n points is described. The procedure is of general applicability, though no proof of its correctness is offered. Instead, a number of examples are discussed, and its application is illustrated. The scheme is based on consideration of unique matrices associated with graphs which in turn are determined so that the corresponding binary code obtained by reading the rows of the matrix from left to right and from top to bottom represents the smallest possible binary code. Part of the scheme consists in finding all acceptable matrices, testing them for isomorphism, and selecting those which satisfy additional restrictions and ensure that the derived graph represents a structure of interest.
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    Acta crystallographica 34 (1978), S. 256-267 
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    Notes: The crystal structures of the dimeric pentahalides (MX5)2 have a close-packed arrangement of halogen atoms in which one fifth of the octahedral holes are occupied by metal atoms. From considerations of the geometrical possibilities of arranging the molecules and thereby resulting symmetry restrictions, the possible space groups and structures are elucidated with the aid of group-subgroup relationships. It is shown that only certain space groups can be achieved. Among the centrosymmetric space groups these include: 1. C2/m, C2/c and C{\bar 1} for hexagonal close packing when octahedral holes are occupied between layers A and B but not between B and A; 2. Pnma, Pnmn, Pnab, C2/m, P2/m, P21/m, P21/a and P{\bar 1} for h.c.p. when holes between all pairs of layers are occupied; 3. P21/m, P21/a and P{\bar 1} for the double hexagonal close packing; 4. I41/a, Bbmb, Fddd and the monoclinic and triclinic space groups for cubic close packing. The more important arrangements are illustrated and their expected cell dimensions are given. The results are compared with the known structures of the pentachlorides of Nb, Ta, Mo, W, U and Re, (NbBr5)2, β-(PaBr5)2, and also (WSCl4)2 and (WSBr4)2. It is deduced that the previously published structure of niobium pentaiodide is probably in error. Predictions are made for likely structures of (TaI5)2, α-(PaBr5)2, (PaI5)2 and (UBr5)2.
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    Acta crystallographica 34 (1978), S. 350-351 
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    Acta crystallographica 34 (1978), S. 351-351 
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    Acta crystallographica 34 (1978), S. 344-346 
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    Notes: Application of the matrix intensity equation of X-ray diffraction is discussed for the second problem of extrinsic faults in face-centred cubic crystals, discussed by Howard [Acta Cryst. (1977), A33, 29-32]. The second problem is generalized to the case that the probability with which inserted layers follow layers of the original crystal differs from that with which inserted layers follow previously inserted layers. The Q matrix for the case is obtained and the results of intensity calculation are shown.
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    Acta crystallographica 34 (1978), S. 349-349 
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    Acta crystallographica 34 (1978), S. 351-352 
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    Acta crystallographica 34 (1978), S. 362-367 
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    Notes: Plane-wave Pendellösung effects are shown to be effective and very sensitive for analyzing minute strains in silicon crystals with dimensions normally used for practical applications. In a triple-crystal silicon X-ray spectrometer with an angular beam divergence of less than 0.1" the Pendellösung effect is very pronounced for sample thicknesses up to 1.2 mm. Strain fields are shown for silicon crystals implanted with 60 keV phosphorus ions for doses down to 1013 ion cm-2 and the limit of resolution is one order of magnitude less.
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    Acta crystallographica 34 (1978), S. 353-361 
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    Notes: The advent of phase-determination computer programs like MULTAN has made the solution of many crystal structures a matter of routine. The next major step towards making the process completely automatic is to program the computer to recognize complete molecules and molecular fragments in E maps. Algorithms suitable for the machine interpretation of E maps are given. These include procedures for peak search, separation of peaks into bonded clusters, application of stereochemical criteria and comparison of the molecular fragments found with those expected. The algorithms are capable of giving alternative interpretations of the same map. Two methods of comparing molecular fragments found in E maps with the expected molecular structures are described. Both have been used successfully and examples of their use are presented. One of the methods can be programmed fairly easily in a completely general way and will be incorporated into MULTAN. The recognition of molecular fragments will allow the automatic use of a partial structure as a step in the determination of the complete structure.
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    Acta crystallographica 34 (1978), S. 432-441 
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    Notes: Using isomorphism properties of translation groups, an intrinsic definition of the classes of perfect objects belonging to n dimensional space, such as crystals, semicrystals, non-crystals and perfect gas, is given. Through the partition of space group G with respect to its (invariant) translation sub-group T, its point group is defined, an isomorph of the group of classes G/T. Examples are given, with symmorphic or non-symmorphic objects in spaces E2, E3, E4 and En. Moreover, the unsuitable expression 'Bravais lattice' should be changed into 'Bravais type of cell'.
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    Acta crystallographica 34 (1978), S. 378-384 
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    Notes: A proposal is made for a direct experimental method to determine the phases of crystallographic structure factors. The method is based on the observation of electron-microscope dark-field moiré patterns. The kinematical theory of electron diffraction is used in the presentation of the method. Compensation of dynamical effects and instrumental aberrations is briefly discussed.
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    Acta crystallographica 34 (1978), S. 384-388 
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    Notes: The structure of dichlorodurene in the ordered phase was determined from neutron diffraction data at 70 K with the help of intra- and intermolecular potential calculations already published [Messager & Sanquer (1974). Mol. Cryst. Liq. Cryst. 26, 373-380]. The space group is the same as at room temperature, P21/a, but the cell parameters are integer multiples of those at room temperature, and there are three molecules in the asymmetric unit, instead of half a molecule. The phase transition is of order-disorder type and the first-order nature of this transition is established by the observation of a weak hysteresis.
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    Acta crystallographica 34 (1978), S. 404-406 
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    Notes: Disposition of a monochromator crystal relative to the specimen crystal on a diffractometer, such that the respective diffraction planes are at 45°, makes knowledge of the actual value of the polarization ratio for the monochromator crystal unnecessary for the conversion of measured intensities to structure-factor values for the specimen crystal. This arrangement, therefore, avoids the uncertainty often associated with poor knowledge of the polarization ratio of monochromator crystals, and so can contribute to improved accuracy of measured structure factors.
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    Acta crystallographica 34 (1978), S. 414-421 
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    Notes: After usual properties of space subgroups have been described, the sufficient condition is given for a space group g to be any subgroup of a space group G: the translation vectors a, b, c of the conventional unit cell of g(o,a,b,c) must belong to the lattice of G and the 'generators' of equivalent general positions of g must be enclosed in the set of general positions of G. In order to verify this criterion, it is necessary to obtain the coordinates of general positions of g in the reference standard setting of G(O,A,B,C); it is necessary to know the coordinates of origin o and the components of vectors a, b, c in terms of the reference setting (O,A,B,C). Then, all the possibilities of a space group of standard symbol \cal s being any subgroup of a space group of standard symbol \cal l can be characterized. Classification of the standard settings of subgroups is established: different settings of the same subgroup and settings of conjugated subgroups.
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    Acta crystallographica 34 (1978), S. 551-553 
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    Notes: In practice, there are two methods of measuring the integrated intensity of a diffraction peak. Both can be optimized, that is, performed in such a way as to give the intensity, with a given accuracy, during a minimum measuring time. These optimizing processes are described along with a third, so-called absolute optimum, method. The three methods are compared and their relative merits discussed.
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    Acta crystallographica 34 (1978), S. 562-574 
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    Notes: The estimation of the one-phase structure seminvariants of first rank is carried out in any centrosymmetric or non-centrosymmetric space group. Representations theory [Giacovazzo (1977), Acta Cryst. A33, 933-944] is suitably associated to the joint probability distribution method: the diffraction magnitudes belonging to the first and second phasing shells of any seminvariant are exploited in order to give probabilistic estimates of the seminvariant cosines. Probabilistic formulae are also derived via the method of complementary invariants.
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    Acta crystallographica 34 (1978), S. 603-607 
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    Notes: The aromatic hydrocarbon antlianthrene (C22H12) has been imaged by high-resolution electron microscopy using minimal-exposure techniques. A simple photographic averaging technique has been applied to give structural information. The radiation sensitivity of this molecule is approximately 0.2 C cm-2 and it is suggested that smaller molecules of comparable sensitivity are capable of being imaged, the limitation being instrumental resolution rather than radiation sensitivity.
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    Acta crystallographica 34 (1978), S. 607-609 
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    Notes: Transmission electron micrographs resolving (100) lattice fringes of clinohumite revealed faults parallel to (100). A simplified model of humite minerals, which interprets them as layers of forsterite and brucite-sellaite, was used for analysis of the faults. These compositional faults produce one or two unit layers of humite and/or chondrodite interlayered between the regular sequence of clinohumite along a*. Thus, nonstoichiometric compositions of humite minerals can be explained as mixed layers.
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    Acta crystallographica 34 (1978), S. 547-550 
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    Notes: Complete tensor sets of piezoelectric, electro-optic, dielectric, elastic and thermoelastic properties were measured on hexagonal Cs2S2O6, LiClO4. 3H2O, LiClO4. 3D2O, and Ba(NO2)2. H2O. The space-group symmetry of Cs2S2O6 and Ba(NO2)2. H2O has been definitely established, by X-ray work in combination with the measurement of polar properties, to be P63mc and P61 (P65), respectively, contrary to earlier X-ray determinations. LiClO4. 3H2O and LiClO4. 3D2O possess almost identical physical properties, with the exception of density and density-dependent properties. The very small differences correspond to those observed in other hydrates and deuterates. Most components of the piezoelectric and electro-optic tensors do not exceed the effective values of other crystals already in technical use. However, an exceptionally strong longitudinal piezoelectric effect is observed in Cs2S2O6 (d333 = - 41 e.s.u, dyn-1, electromechanical coupling coefficient kt = 0.25), which together with other favourable acoustic and optical properties supports the application of this new material for acousto-optical devices in the high-frequency range.
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    Acta crystallographica 34 (1978), S. 556-561 
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    Notes: The structure of the partially ordered phase of TiO has been examined with a single crystal. While the space group is that first determined from powder X-ray diffraction and electron diffraction by Watanabe, Castle, Jostons & Malin [Acta Cryst. (1967). 23, 307-313], (B2/m), the average structure is somewhat different. There are waves of Ti and O ion vacancies every third (100) plane in the [010] direction of the monoclinic structure. The amplitude of the wave is twice as large for the Ti ion vacancies as for the O ion vacancies. There is no appreciable concentration of interstitial Ti ions in either the ordered phase or the disordered (cubic) phase. The ordering temperature Tc is 1026 (2)°C. The monoclinic angle is directly proportional to the square of the order parameter associated with vacancy ordering. A mean-field theory is developed that includes vacancy-vacancy and vacancy-electron interactions, and vacancy-strain coupling. This theory explains the main features of the order-disorder transition in this material.
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    Acta crystallographica 34 (1978), S. 578-582 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The conjugate gradient method allows the solution of least-squares equations A(u -- u0) = B without evaluating A-1. Storage limitations can thus be satisfied by approximating A by a sparse matrix which need not be block-diagonalized. Optimization of the method allows a satisfactory solution within 10-12 iteration steps for any sized matrix, enabling an economic use of conditional slack constraints.
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  • 99
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 648-651 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Standard density basis functions for hydrogen and the first-row atoms have been converted to K-shell and L- shell scattering factors. With the K shell fixed at two electrons, these scattering factors have been used for atomic-charge analysis of X-ray structure factors by the method of least squares. Results for cyanuric acid and uracil are given. The net charges for these cyclic amides are in reasonable agreement. It is recommended that scattering factors here be used for atomic-charge analysis of first-row atoms in routine structure refinements of chemically related molecular crystals.
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  • 100
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 480-480 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
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