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  • International Union of Crystallography (IUCr)  (1,175)
  • American Meteorological Society
  • 1995-1999
  • 1980-1984
  • 1975-1979  (1,921)
  • 1975  (1,921)
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  • 1995-1999
  • 1980-1984
  • 1975-1979  (1,921)
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  • 1
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 280-292 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The concepts embodied in the coincidence-site-lattice theory of grain boundaries are shown to be compatible with a large number of tensor quantities which have their origin in the continuum field theory of dislocations. More specifically such tensor quantities as distortion, grain-boundary dislocation density, and incompatibility have all been developed in terms of a general grain boundary for a continuum as well as for the discrete crystal. A generalized Burgers circuit about an arbitrary grain boundary is also shown to be a natural outcome of the present development.
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  • 2
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 386-387 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Calculations show that defects should occur in hexachlorobenzene crystals [typical atom (x, y, z)] consisting of a ½ vacancy, followed by n molecules along [010] with typical atom (x, ½ - y, z), terminated by a 3/2 vacancy. The energy of the defect is predicted as (12 ± 3) + (3 ± 2)n kJ mol-1, with ̃10-5 of the molecules in the crystal misoriented. X-ray diffuse scattering experiments may be interpreted to indicate that this is the defect that occurs, and that it has an energy of (12 ± 2) + (2.6 ± 0.8)n kJ mol-1.
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  • 3
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 388-389 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Fourier phase refinement for macromolecular crystal structures can be accomplished using electron density maps sampled at intervals of half the minimum interplanar spacing for which diffraction data have been measured in that direction. Order-of-magnitude economy in computation is thus gained as compared to use of customary sampling rates.
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  • 4
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 609-611 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The molecular refractivities of some corticosteroids C21 are calculated from the crystal refractivities. The latter are obtained from the measured principal refractive indices. The orientations of the principal molecular axes with regard to the steroid skeleton are given and the magnetic and optical anisotropies compared.
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  • 5
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 602-609 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A probabilistic theory of special quartets is described which is able to fix the sign of reflexions with even indices. The method proves suitable for removing a large percentage of the Σ1 formula failures.
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  • 6
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 612-619 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Knowledge of the absolute values of X-ray intensities is highly desirable for a quantitative interpretation of experimental electron densities. In the present work X-ray scale factors are determined by three experimental methods. In the first method, a small aperture is used to measure the direct X-ray beam and the crystal volume is determined by weighing. In the second method, a single-crystal plate large enough to intercept the entire direct beam is used, while the third technique is based on powder diffraction intensity measurements. Scale factors are measured for orthorhombic sulfur, oxalic acid, glycylglycine, hexamethylenetetramine, sodium azide, and ammonium tetroxalate, all of which have been the object of previous electron density distribution studies. Results from the three methods agree within experimental errors and it is concluded that scale factors can be measured with an accuracy of about 1%. Comparison of the experimental scale with the results of various least-squares refinements indicates that scale factors from conventional least-squares refinements contain a considerable bias. Scale factors from refinements with improved models are generally in better agreement with experimental values. The effect of a variation in scale factor on the experimental electron densities is discussed.
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  • 7
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 660-664 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Under irradiation by an intense electron beam a V6O13 crystal reacts with the carbon deposited on the surface during microscopic observation. The structural changes during the reaction were directly observed by means of lattice images, in which the array of VO6 octahedra was resolved. At the initial stage cavities smaller than 20 Å in diameter appear preferentially in the thin part of the crystal and some crystallographic shear planes are formed in their wall. The cavities with the heavily distorted surroundings are seen as white regions. Kinks in lattice fringes, indicating the occurrence of stacking faults, are simultaneously found in the matrix. At the advanced stage the VO2 phase and its twin component are produced. The mechanism of the transition of V6O13 to VO2 can be interpreted in terms of the cooperative movement of octahedra.
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  • 8
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 698-700 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple unconstrained steepest-descent procedure is described for the preliminary refinement of protein coordinates in real space. The method is illustrated by application to ribonuclease S.
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  • 9
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 704-704 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 10
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 705-708 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 11
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 32-38 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The behaviour of the Kikuchi lines parallel to the shadow edge, which are formed under diffraction conditions in the Bragg case, is experimentally studied for zincblende (ZnS), MgO and rock salt. A line of this group generally has an asymmetric intensity profile across it. Sometimes it shows contrast reversal from an excess appearance in the central range to a defect appearance in the side ranges along the line. These peculiarities become noticeable with the increase in the glancing angle of the incident beam with the crystal surface. It is pointed out that theoretically the form of the line term in the intensity formula for Kikuchi patterns in the Bragg case differs from that in the Laue case. The variation of the line profile, including the effect of contrast reversal, takes place by the change in the intensity formula, in the ratio of the band term to the line term, depending on the scattering vector appropriate to the inelastic electron scattering involved. By assuming approximate forms for the scattering factors for Kikuchi patterns, the observed results are qualitatively explained.
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  • 12
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 753-755 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It has been found by means of single-crystal X-ray diffractometry that the symmetry of the low-temperature phase of magnetite is rhombohedral, rather than orthorhombic as required by the commonly accepted theories of the transformation. The reason for the discrepancy between the observed structure and the uniaxial symmetry required to explain magnetic anisotropy measurements is found to lie in the discovery that cooling through the transition in the presence of a field causes the development of a superlattice of monoclinic symmetry and a twinned martensitic structure of pseudo-orthorhombic symmetry.
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  • 13
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 780-783 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Anharmonic effects are observed in a room-temperature neutron diffraction study of the intermetallic fluorite compound AuGa2. The analysis is performed on the basis of a single anharmonic vibrational parameter in addition to the harmonic vibrational parameters. It yields the values αAu = 3.08 (0.11) × 10-12 erg Å-2, αGa = 2.91 (0.08) × 10-12 erg Å-2 for the harmonic parameters and βGa = -- 2. 3 (1.2) × 10-12 erg Å-3 for the cubic anharmonic parameter. The Debye temperature is determined to be OM = 169 (3) K at 294 K. Neglect of the thermal diffuse scattering correction is found to introduce an error of ̃10% in the Debye-Waller factors obtained. Least-squares analyses using the Zachariasen and the Becker & Coppens extinction corrections are found to give equivalent results.
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 197-200 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Experimental determinations of the resolution function of a neutron time-of-flight diffractometer are compared with computations performed within and beyond the normal approximation.
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 813-817 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Direct methods are applied to the difference structure factors for a structure containing one or more heavy atoms in known positions. For those reflexions whose sign is determined by the heavy atoms, the known heavy-atom contribution is subtracted from the observed structure factor to obtain the magnitude and the sign of the light-atom contribution. The signs of the reflexions that do not have an appreciable heavy-atom contribution are found using the Σ2 sign relationship. For reflexions with an intermediate heavy-atom contribution the sign and magnitude ambiguity is also solved by the Σ2 formula. Thus it is possible to maximize the number of correct signs, and correct some of the amplitudes, before a difference Fourier map is calculated.
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 245-249 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The variance of diffractometer-collected diffraction intensities is discussed in terms of instrumental instability and uncertainties in the parameter used to bring the intensities to a common scale. It is shown that the inconsistent and/or divergent behavior of the reflections used as standards contributes in a major way to the uncertainty in the scaling parameter and can often account for the largest portion of the variance in excess of the Poisson contribution for reflections with large intensities.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 259-263 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recently derived expressions [Giacovazzo (1975). Acta Cryst. A31, 252-259] for the reliability of quartets have been tested. For the negative quartets (NQ's) the new expressions lead to an improvement compared with the empirical estimates of the NQ reliability used so far. However, the reliability of all quartets can be better estimated by means of the weights of the empirically derived strengthened quartet relation (SQR).
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 267-268 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The ten third-order elastic (TOE) constants of erbium have been calculated from a nearest-neighbour central-interaction model. The calculated TOE constants are used to evaluate the pressure derivatives of the second- older elastic (SOE) constants of erbium and are compared with the measured values. The TOE constants of erbium obtained on the central-force model agree well with those obtained from Keating's model for hexagonal metals.
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  • 19
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    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 31 (1975), S. 207-209 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The room-temperature elastic moduli, their temperature derivatives and the thermal expansion of KHSO4 have been measured. Both the elastic and the thermal properties exhibit a quasi-hexagonal symmetry, the crystalline a axis being the unique axis. On the other hand, the Grüneisen tensor is essentially isotropic. A qualitative correlation of these phenomena with the crystal structure is made.
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  • 21
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 215-220 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By the use of an SSD diffractometer and continuous X-rays, the energy dependences of Δf' and Δf” values of Ga have been studied on GaP with energy resolution of about several eV around the Ga K edge; the values of Δf” were determined by the measurement of the absorption coefficient, and then the values of Δf' have been obtained from the precisely measured ratio of Friedel-pair reflexions from a (111) single-crystal plate of polar GaP. Fine structures have been found in Δf” and therefore in Δf' corresponding to those of the absorption coefficient. The present work has shown that the measured values of Δf' more or less reasonably agree with the curves calculated from the dispersion relation.
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  • 22
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 234-235 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Expressions are derived for the set of structure factors, and for the polarization and Lorentz factors due to the multiple reflexion of X-rays.
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  • 23
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 236-240 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that it is reasonable to describe some structures such as γ brass and α- and β-Mn completely in terms of tetrahedral configurations of the atoms, even though constraints of the structural geometry do not uniquely prescribe the selected tetrahedra as they do for example in the Laves phases and the β-W structure. Such descriptions use a freedom of choice of tetrahedra in addition to the accepted distortion of tetrahedra in approximating to the non-attainable ideal of filling space with regular tetrahedra. An error parameter is developed which allows comparison of the average distortions of all of the tetrahedra for structures described in terms of tetrahedral configurations of the atoms. Comparison of the error parameters for the γ brasses Cu5Cd8 and Fe3Zn10 and for other structures such as α- and β-Mn where there is freedom of choice in the selection of tetrahedral configurations, with error parameters for other structures such as Cu2Mg and β-W where the tetrahedra are uniquely prescribed by the structural geometry, indicates that the first group of structures can reasonably be regarded as tetrahedral configurations of atoms, although slightly less effectively so than the Cu2Mg and β-W structures. Other γ brasses such as Cu5Zn8 and Cu9Al4 are found to be poorer examples of structures possessing overall tetrahedral configurations.
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  • 24
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 507-513 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The procedure for computing the resolution function of triple-axis spectrometers is reformulated to make allowance for the spatial configuration of the experimental set-up and for the curvature of the monochromator and analyser crystals. Simple formulae are given for computing the resolution function of conventional instruments as well as of spectrometers with focusing crystals.
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  • 25
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 523-525 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The origin of the anomalous peaks occurring in a neutron crystal spectrometer is explained by the use of reciprocal-space geometry. The anomalous peaks are due to Bragg reflexion in the sample of the incident neutrons with wavelengths different from the central value of the nominally monochromatic beam.
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  • 26
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 527-527 
    ISSN: 1600-5724
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  • 27
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 15-18 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is known that 13 among the 44 types of (Niggli) reduced cells correspond to centred monoclinic lattices. For these 13 types, the connexion is given between the reduced cell and a conventional cell. For centred lattices of monoclinic and orthorhombic symmetry, we describe the shape of the conventional cell for the different types of reduced cell. Errors are corrected in the section on Reduced Cells of the International Tables for X-ray Crystallography [Vol. I (1969), Birmingham: Kynoch Press].
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  • 28
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 42-49 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Diffraction patterns containing Pendellösung oscillations produced in different orders of diffraction by thin slices of perfect silicon crystals of different thicknesses have been recorded for both Bragg and Laue cases. The agreement of the curves obtained with those calculated from the dynamical theory is believed to be good enough to allow the derivation of values of the corresponding structure factors. For silicon 422 the value f0 = 6.81 ± 0.05 has been found.
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  • 29
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 59-63 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The contrast of 180° domains of PbTiO3 depends on temperature and is caused by differences in the intensity of the diffuse background. The thickness extinction fringes of 180° domains taken at different temperatures between room temperature and near the Curie temperature are qualitatively explained with the use of many-beam dynamical theory, in which different anomalous absorption factors are assumed for each case. The origin of the contrast is interpreted and discussed in terms of the difference in thermal diffuse scattering between the 180° domains.
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  • 30
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    Acta crystallographica 31 (1975), S. 80-83 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In anthrone (10H-anthracen-9-one) crystals there may be two distinct types of molecular orientational disorder. Firstly, whole stacks of molecules along [010] may, by association with vacancies, become orientationally disordered between positions related by a twofold screw axis in the crystal. Secondly, individual molecules may become disordered between orientations related by inversion through the molecular centre of mass. Calculations with previously developed Ising-like models (with an atom-atom intermolecular potential, the data for the low-temperature unit cell and the observation of a transition temperature at 357K) reveal that at 295K both types of disorder are present. This explains previous detailed X-ray diffuse-scattering data. Parts of these data give 16 ± 1, 36 ± 9 and 25 ± 2 Å for the observed range of the order in the a, b and c directions. The calculations predict 16 ± 0, 37 ± 12 and 24 ± 6 Å.
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  • 31
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    Acta crystallographica 31 (1975), S. 746-752 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Multibeam (001) electron-microscope lattice-image (N = 3,5) properties are studied when axial illumination is used. Numerical calculations were particularly applied to (001)-oriented gold foils observed with 1 MeV electrons. Conditions for obtaining images showing no artificial periodicity are determined. It is shown that in a particular range of thickness (40-60 Å for three-beam interference or 70-120 Å for five-beam interference) and with the proper defocusing distance high-contrast images would be obtained: the exact projected atomic positions are directly visible on these images. The influence of departure from exact symmetry conditions, and of large variation of the lattice parameter, are also studied. These calculations suggest that it would be possible to observe direct lattice images of metals and to study their defects with actual 1 MeV electron microscopes.
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  • 32
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 764-768 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structures of four long-period polytypes of SiC found in a sample of reaction-sintered material have been analyzed using transmission electron microscopy. Those structures which have been positively identified are 303R or [(33)16(32)]3, 180R or [(23)11(32)]3 and 222R or [(33)6(34) (33)4(34)]3. The fourth structure is tentatively identified as 150R or [(34)5(23)3]3. The lack of conclusive identification for this structure is due to structural irregularities throughout the very small size of this grain. The frequency of observing long-period structures in reaction-sintered SiC is quite high, especially when the grain size is small.
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  • 33
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 769-774 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By reference to intensity measurements made with an asymmetrically cut extended-face lithium fluoride crystal, attention is drawn to (a) the observation that the average of measurements at asymmetrical angles + a and -a is not always equal to the value at the symmetrical position, a = 0°, as implied by W. H. Bragg [Phil. Mag. (1914), 27, 881-899] and accepted as essentially correct by later experimentalists; and (b) the associated consequence that the conclusions of Hirsch and his colleagues concerning extended-face crystals arrived at ca. 1950 [e.g. Gay & Hirsch, Brit. J. Appl. Phys. (1951). 2, 218-222] are of general rather than specific significance. It is deduced that the standard formula for the absorption factor, Ac, for such crystals [International Tables for X-ray Crystallography (1967). Vol. II], should be modified to incorporate an additional component of the form exp { -μ't [cosec (θ + α) + cosec (θ - a)]}, where μ' is the effective absorption factor for the surface layer of thickness t and α is the angle between the surface and the Bragg plane studied. The formula for the integrated intensity is then given by {{E\omega}\over{I}} = {{Q}\over{2\mu}} (1 -cot θ. tan α). exp {- μ't[cosec (θ + α) + cosec (θ - α)]}, which reduces in the symmetrical case, α = 0°, to {{E\omega}\over{I}} = {{Q}\over{2\mu}} . exp ( - 2μ't cosec θ). The factor μ't can be determined experimentally by use of an appropriately prepared asymmetrically cut crystal or by selection of a reflexion plane at an angle to the surface used for measurement. The onus should be on the experimenter to establish the magnitude of the factor and hence whether its incorporation is mandatory. Its omission in application of this technique for the determination of structure factors may have significant effects on scale factors, particularly where absolute values are sought, and on derived temperature factors and extinction parameters.
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    Acta crystallographica 31 (1975), S. 804-810 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Symmetry rules are derived for relating the convergent-beam electron-diffraction pattern symmetries to the three-dimensional symmetry of the structure. These rules are applied to a study of 2M biotite. As a result the space group is determined as C2, or number 5 in International Tables for X-ray Crystallography, whereas it was previously held, in the absence of accurate data, to belong to C2/c or number 15. In addition, a method is described for uniquely determining the centrosymmetry of a crystal independently of space group, hence resolving the ambiguity between a centre of symmetry and a twofold axis present when approximations to dynamic electron scattering are used which take into accoufit only the symmetry of the projection.
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    Acta crystallographica 31 (1975), S. 810-813 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: NH4IO3 shows an abrupt contraction in the direction of spontaneous polarization at 82°C. This anomaly is accompanied by changes in the optical properties and phonon spectra, which were also studied at different pressures. On the basis of the lattice parameters and Raman spectra a probable mechanism is suggested for the phase transition.
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  • 36
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    Acta crystallographica 31 (1975), S. 823-824 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: PbI2 single crystals grown in gel and grown from vapour were studied by X-ray diffraction. The structure analysis of the type 2H with space group P{\bar 3}m1 has revealed that the z coordinate of the I ion is 0.268 and the thermal vibration of the Pb ion in its own layer is considerably smaller as compared with that perpendicular to the layer. From the dependence of the frequencies of types 2H and 12R[13]3 on temperature of crystal growth, it has been shown that type 2H is the most common type at room temperature and type 12R[13]3 the most common type at high temperatures. Observations on the 2H-12R transformation by annealing have revealed that this transformation is reversible.
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  • 37
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    Acta crystallographica 31 (1975), S. 820-822 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The lattice parameters of natural spinel, ferroan gahnite, magnesiochromite, and synthetic spinel at elevated temperatures have been determined. The results are: spinel at = 8.0870 + 35.24 × 10-6t + 45.73 × 10-9t2, 22 〈 t 〈 840°C; ferroan gahnite at = 8.1050 + 54.35 × 10-6t + 10.53 × 10-9t2, 22 〈 t 〈 845°C; magnesiochromite at = 8.2965 + 56.82 × 10-6t + 8.08 × 10-9t2, 22 〈 t 〈 823°C, synthetic spinel at = 8.0821 + 45.79 × 10-6t + 35.69 × 10-9t2, 26 〈 t 〈 800°C, where at is the lattice parameter in Å at t°C. Expressions for thermal expansions are derived. The replacement of magnesium cations by zinc and iron and of A12O3 by Cr2O3 in spinel decreases the mean thermal expansion in the range of temperatures covered, but increases the lattice parameters.
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  • 38
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    Acta crystallographica 31 (1975), S. 836-840 
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    Notes: The criterion for the validity of geometrical optics is quantitatively examined through a 'computer experiment' in the specific case of a crystal containing substantial deformations induced by a large thermal gradient. It is shown that the above-mentioned criterion is numerically correct. For larger deformations than those corresponding to the criterion the computed intensity shows that two wave fields appear where only one would normally have been expected, in good agreement with theoretical predictions. The intensity of the new wave field has been plotted as a function of deformation.
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  • 39
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    Acta crystallographica 31 (1975), S. 853-854 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple formula is derived which expresses the Debye temperature of a disordered multicomponent alloy with small atomic radius disparity in terms of the Debye temperatures of the pure components, the mole fractions of the components, and a set of undetermined parameters, each of which can be found from the Debye temperature for one composition of each possible binary alloy made from the components. The formula is an improvement on a similar formula for the binary case due to Mitra and Chattopadhyay because the physical significance of the undetermined parameters is more readily apparent. The influence of short-range order in the binary case is considered. Application is made to the Ag-Au-Pd, Cr-Fe, and Cu-Ni systems in order to test the formula.
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    Acta crystallographica 31 (1975), S. 526-527 
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    Acta crystallographica 31 (1975), S. 529-535 
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    Notes: A comparative study of the normalized and unnormalized Booth-type R indices is carried out in the structure completion stage corresponding to the following cases: (i) Crystals and models satisfying the requirements of the basic Wilson distributions and (ii) Crystals containing a few heavy atoms in the asymmetric unit (as well as a large number of light atoms) and belonging to triclinic, monoclinic and orthorhombic space groups. Indices based on intensity as well as on structure amplitudes are considered. In all cases the normalized index appears to be more powerful than the unnormalized one. Applications of the results to a few actual crystal structures confirm this.
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    Acta crystallographica 31 (1975), S. 543-550 
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    Notes: In this paper a translation function is derived for which there is a significant reduction in the intensity of the spurious maxima often experienced with the use of alternative methods. An analysis of partial structures indicates that the remaining atoms of a crystal structure may, in principle, be obtained directly from the translation function derivation by Fourier synthesis.
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    Acta crystallographica 31 (1975), S. 622-628 
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    Notes: This paper deals with transverse periodic fluctuations of atomic positions. The coherently scattered X-ray intensity is calculated for two types of modulating functions. 1. A rectangular wave: This type of modulation may be conceived for structures with domain-like antiparallel shifts of atomic positions (e.g. in antiferroelectics). 2. A triangular wave: Some type of micro-twinning can be described as a transverse triangular modulation of the structure. For these two types of lattice modulations the characteristic features of scattering patterns are discussed so as to determine the type of the modulating function and its parameters (wavelength, amplitude). These results are compared with those published by Korekawa [Theorie der Satellitenreflexe (1967). Habilitationschrift der Ludwig-Maximilian-Universität München] for sinusoidal type modulations.
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    Acta crystallographica 31 (1975), S. 704-704 
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    Notes: There exist other classes of ZEFG charge configurations than those defined by sets and subsets of vertices of centrosymmetric polyhedra of cubic and icosahedral symmetry [Knop, Palmer & Robinson. (1975). Acta Cryst. A31, 19-31]. A number of corrections required in the original paper are listed.
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    Acta crystallographica 31 (1975), S. 718-721 
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    Notes: Molecular models with magnetic multipoles, which were invented by the author for the purpose of simulating crystal structures, are revised. The models of the new type are made of Ba ferrite magnets and plastic pieces only, no Mn-Zn ferrite being used. The crystal structures of SiF4 and α-CF4, as well as those of UCI6 and WCI6 are represented by use of different species of molecular models.
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  • 46
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    Acta crystallographica 31 (1975), S. 731-737 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In order to establish a generalized form of an earlier derived algebraic relation between a structure factor, triple products and a single Patterson vector U, the joint probability distribution P(X0, X1, M) of Ek, Eh + k and cos 2π(h/2 + k). U with h fixed, is derived for space group P{\bar 1}. From this distribution the desired generalized equations are obtained. The sign probability formula for triple products is adapted to the case that cos 2π(h/2 + k). U is known. A numerical check on the expression for the conditional average (cos 2πh/2 + k). U||Ek| 〉 t, |Eh + k 〉 t )k, showed that for an artificial structure the set of signs of the structure factors obtained from this expression was better than that calculated from heavy-atom positions related by U.
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  • 47
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    Acta crystallographica 31 (1975), S. 743-746 
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    Notes: A procedure is described for the location of light atoms, particularly hydrogen, by means of a weighted difference synthesis, in which the weight is taken to be the scattering factor of the light atom which is sought. This convolution technique is illustrated in applications to the structures of an amine hydrochloride, C20H27N. HCI, and a complex borohydride, Mg(B6H9)2.2C4H8O.
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  • 48
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    Acta crystallographica 31 (1975), S. 136-141 
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    Notes: A quantitative knowledge of the refractivities and anisotropies of some organic molecules, aromatic and aliphatic, of different shapes and containing various electronic groupings was obtained. The studied aromatic compounds include three rings and one ring with different substituents while the aliphatic compounds contain six-membered rings, five-membered rings and open chains. The results show that strong magnetic anisotropy is always associated with strong optical anisotropy, and the optical anisotropy of the molecules divided by that of the benzene molecule is smaller than the corresponding value for magnetic anisotropy. Also the optical anisotropy in the case of aromatic compounds is markedly decreased by substitution.
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  • 49
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    Acta crystallographica 31 (1975), S. 149-152 
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    Notes: The values of the second, third and fourth-order moments of the normalized intensity z and the maximum probable values of two types of discrepancy index, namely RB and R2, are worked out for various types of pseudosymmetric structures considered by Rogers & Wilson [ Acta Cryst. (1953). 6, 439-449].
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    Acta crystallographica 31 (1975), S. 155-157 
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    Notes: The temperature dependence of the thermal expansion of KI and RbI at high temperatures is shown to be related to the concentration of thermally generated Schottky defects. the experimental value of the energy of formation of these defects for RbI has been estimated for the first time. The two halides are found to obey the 'law of corresponding states' established by Pathak & Vasavada [Acta Cryst. (1970). A26, 655-658].
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    Acta crystallographica 31 (1975), S. 158-159 
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    Notes: X-ray measurements of the lattice parameters have been made in four Cu-Ga alloys in the solid-solution range using a Unicam 19 cm high-temperature camera in the temperature interval of 30-514 °C. The measured lattice parameters have been found to increase non-linearly with the temperature and this variation has been expressed in an analytical form from least-squares fitting. The linear thermal expansion coefficients have been found to decrease with increasing temperature in these alloys with a tendency to attain a nearly constant value at higher solute concentrations, and the decrease is rather slow compared to that observed earlier with Ag-Ga alloys over the same range of temperature.
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    Acta crystallographica 31 (1975), S. 178-185 
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    Notes: Theoretical expressions relating six kinds of normalized R indices and the parameter σA(= σ1D) are derived and used to make a comparative study of the relative efficiency of these R indices in different crystallographic situations. It is found that the various R indices exhibit different properties in the various stages of structure analysis. In all stages the index based on intensity seems to be preferable to the corresponding index based on structure-factor magnitude. For structure completion and refinement of an incomplete model, the index BR1(I) seems to be the best. The indices R1(I) and R*1(I) are found to be best for the initial and final refinement stages respectively.
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    Acta crystallographica 31 (1975), S. 227-233 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: High-order covariance matrices are used to show that the maximal determinant rule and the regression equation can be applied successfully to the phase refinement and extension of protein structures. With structure factors calculated from the atomic model of insulin, the use of an order-400 covariance matrix leads to the structure phases with an average error ΔΦ of 15°. The method has also been applied to actual data of insulin for phase refinement and for phase extension from 2.8 to 2 Å.
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    Acta crystallographica 31 (1975), S. 391-392 
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    Notes: A new analytic approximation to atomic incoherent X-ray scattering intensities is proposed. Unlike other approximations in the literature, the present function has the correct asymptotic behaviour at both large and small values of s. Fits to the incoherent intensities calculated by Cromer are presented for all atoms from He through Am.
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    Acta crystallographica 31 (1975), S. 390-391 
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    Notes: Expressions are obtained for the variances and relative uncertainties of the molecular refractivities in the case of orthorhombic crystals. It is deduced that when the ratios of the gram molecular refractivities are nearly equal to the corresponding ratios of the squares of the direction cosines of one of the molecular principal axes, the relative molecular refractivity uncertainties along the other two molecular principal axes will be relatively large.
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    Acta crystallographica 31 (1975), S. 400-400 
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    Acta crystallographica 31 (1975), S. 407-416 
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    Notes: A method to predict all peaks of the rotation function corresponding to a given molecular crystal is formulated in a rigorous mathematical manner. The applicability of this method is shown both in the analysis of rotation function data and in testing the validity of model molecular crystals proposed on the basis of limited rotation function data. Possible models of crystalline bovine liver catalase are determined assuming that all peaks of the rotation function are contained in the set of peaks determined by Eventoff and Gurskaya. All peaks of the rotation function corresponding to a model of crystalline satellite tobacco necrosis virus (STNV) proposed by Klug and Akervall et al. are determined and tabulated. Experimental determination of all these peaks would be a final test of the validity of this generally accepted model of crystalline STNV.
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    Acta crystallographica 31 (1975), S. 570-574 
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    Notes: A simpler derivation of the equations of Schomaker & Trueblood [Acta Cryst. (1968), B24, 63-76] is given. It is shown that the ready interpretation of the meaningfulness of refinable parameters is best achieved by selecting the centre of action as origin and describing the motion with parameters defined relative to the principal axes of libration. A choice of 20 variables is made so that all meaningful constraints on the TLS model correspond to certain of the variables having zero value. It is shown that the five parameters that distinguish the TLS model from the TLX model do not alter the mean-square displacement of any atom. Neither do they alter the displacement of the mean from the position of maximum probability for any atom.
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    Acta crystallographica 31 (1975), S. 575-582 
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    Notes: The assumption that the phases calculated from a trial structure are indeed correct results in incorrect estimates of the variances of parameters. Modifications to least-squares equations and the evaluation of appropriate weighting schemes are discussed. It is shown that for a non-centrosymmetric structure a unique minimum is not to be expected, establishing a strong case for initial refinement of crystal structures with constrained refinement procedures. A method of obtaining an unbiased estimate of the variance - covariance matrix is given.
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    Acta crystallographica 31 (1975), S. 586-591 
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    Notes: A new method is described for applying fixed-shape, identical-molecule, or symmetry constraints to the least-squares refinement of groups of atoms by modifying the unconstrained coordinate shifts to satisfy the conditions of constraint after each refinement cycle. Application of the constraints requires negligible computation time compared to that for the usual refinement cycle. A new rational method is described for computing the translation and rotation of a group of atoms to give a best fit to a set of unconstrained coordinate shifts.
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    Acta crystallographica 31 (1975), S. 582-585 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Laue patterns of very thin single-crystal platelets of hexamethylbenzene at a temperature (80 K) below the cold-phase transition (116 K) have been recorded. In this colder phase (Ph. III), whose flat plate pattern is interpretable as a precession photograph because of the probable ordered fagmentation of the sample, the crystal symmetry appears to be hexagonal (or trigonal), as confirmed also by previous optical and spectroscopic observations. The X-ray diffraction spectrum of the powder taken at the same temperature gives 3.59 Å as the distance between the planes containing the molecular rings, and was indexed on the basis of a hexagonal cell with a = 31.5, c = 3.59 Å, containing 12 molecules (probable space group P6mm, with all molecules lying in special positions); the length of the basal axis is exactly four times that of the elementary mesh obtained from the hexagonal grid on which the single-crystal pattern lies.
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    Acta crystallographica 31 (1975), S. 19-31 
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    Notes: The general conditions are investigated under which an assembly of point charges will produce a zero electric-field gradient (ZEFG) at a reference point S0(0,0,0). It is shown that for equal charges it is necessary that they form a configuration of cubic or icosahedral symmetry about S0. Unequal charges must be located at the vertices of a centrosymmetric polyhedron of symmetry m3m, m3 or 53m in such a way that the sum of the charge values in a pair of charges related by the centre of symmetry of the polyhedron be the same for all the pairs. Configurations of this kind are self-dual (SD) with respect to interchange of vertices by inversion in the centre of symmetry of the polyhedron. Self-dual configurations containing two kinds of charges (SD2C) are listed for polyhedra of up to 20 vertices and enumerated for all the centrosymmetric cubic and icosahedral Archimedean polyhedra and their duals. The method of enumeration without construction is described. The conditions under which such discrete ZEFG configurations can be embedded in three-dimensional crystal structures to give ZEFG structures are also investigated and a number of examples of such embeddings are given. The potential usefulness of such structures as Mössbauer null matrices is briefly discussed.
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    Acta crystallographica 31 (1975), S. 142-145 
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    Notes: A method previously developed for high-precision orientation of low-index planes of perfect or nearly perfect crystals has been extended to planes with arbitrary indices. The extension has been accomplished by predicting the back-reflexion patterns of Laue spots due to characteristic X-rays and by identifying spots which should have equal intensity when the correct orientation is obtained. It is possible to orient the specimen crystal within 0.01° of the desired orientation in favourable cases. In cases where the equal-intensity criterion cannot be used the accuracy of the orientation using the predicted pattern is at least as good as that using the conventional Laue method. Furthermore there is no need to measure angular distances between the spots or the distance between the crystal and the film.
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    Acta crystallographica 31 (1975), S. 153-155 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Several serious errors which were included in a paper entitled Multiple diffraction of X-rays and the phase problem by R. Colella [Acta Cryst. (1974). A30, 413-423] are noted and discussed.
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    Acta crystallographica 31 (1975), S. 157-157 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Corrections to Sharma [Acta Cryst. (1974) A30, 299-300].
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    Acta crystallographica 31 (1975), S. 161-173 
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    Notes: The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaAlO3, PrAlO3) and for their ferroelectric properties (e.g. LiNbO3, PbZr/TiO3). In this paper, data scattered through the literature are correlated, with correction of some misleading mistakes of calculation. Geometrical descriptions are put in a form allowing comparisons. The structures, classified by their space groups, are described in terms of four structural parameters, the octahedron tilt ω, octahedron distortion d, and A- and B-cation displacements s and t, together with an elongation or flattening ζ of the octahedron, deducible with the help of ω from the interaxial angle αrh. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the R{\bar 3}c structures a correlation not previously noted in the literature is found between the tilt angle ω and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3c structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.
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    Acta crystallographica 31 (1975), S. 185-188 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Debye temperatures of potassium iodide and rubidium iodide have been determined by X-ray diffraction from room temperature up to about 800 K with methods due to Paskin [Acta Cryst. (1957). 10, 667-669] and Chipman [J. Appl. Phys. (1960). 31, 2012-2015]. The anharmonic contribution to the Debye θ up to about 650 K is shown to arise essentially from thermal expansion. The plot of the reduced thermal expansion α/αm/2 versus T/Aa2θ2 is a common curve. Here αm/2 is the value of α at T = ½ Tm, Tm being the melting point. A is the mean atomic weight and a is the lattice constant. The values of the anharmonic parameters γ0 in the potential energy function of Willis [Acta Cryst. (1969). A25, 277-300] are found to be -0.065 × 10-12 erg Å-4 for KI and -0.116 × 10-12 erg Å-4 for RbI.
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    Acta crystallographica 31 (1975), S. 88-95 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: For all space groups the groups of inner automorphisms are given. They are isomorphic with groups of motions, but fall into four sets according to their dimension. In the triclinic and monoclinic systems, however, the corresponding groups of all automorphisms cannot be represented by groups of motions. These groups of automorphisms therefore are only tabulated for the other cases. The relation between groups of automorphisms and Cheshire groups is discussed. By means of automorphisms sets of equivalent points are combined to "Konfigurationslagen'. For these complete tables are included.
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    Acta crystallographica 31 (1975), S. 84-88 
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    Notes: The theory of the internal strain, which has been verified experimentally for crystals with the diamond structure, is extended here to the zincblende structure. X-ray intensity measurements were taken on GaAs under a uniaxial stress along the [111] direction. It was found that this stress causes a slight change of the structure factor of the weak reflexion 006, from which the value ζ = 0.046 ± 0.002 for the bond-bending constant was estimated. This means that in GaAs the effect of the internal strain is very weak, so that the tetrahedral bond changes its length almost according to the macroscopic strain tensor.
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    Acta crystallographica 31 (1975), S. 95-100 
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    Notes: The influences of sample size and mosaic block size upon X-ray thermal diffuse scattering have been investigated. Surface and edge vibrational modes were incorporated into the Debye spectrum. Two additional terms, which depend on the surface/volume and edge-length/volume ratios, appear therefore in the expression for the scattered intensity. The TDS contributions of the volume and surface terms to the integrated Bragg intensity are calculated numerically.
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    Acta crystallographica 31 (1975), S. 292-299 
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    Notes: The coincidence-site-lattice theory of grain boundaries has been applied to simple two-phase boundaries. Symmetric and unsymmetric tilt boundaries, pure twist boundaries and unrotated and untwisted boundaries have all been considered. It has been shown that each type of boundary can be described in terms of a characteristic coincidence-site lattice. In addition, the dislocation content within the interphase boundaries has been defined in terms of Burgers circuits described with respect to the original crystal lattices in the new coincidence-site lattices.
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    Acta crystallographica 31 (1975), S. 318-322 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Within the framework of the research undertaken in the authors' laboratory, the magnetic anisotropy of some corticosteroids C21 has been studied. The diamagnetic molecular tensors are deduced from the measured crystal tensors by an original method. The orientation of the principal molecular axes with regard to the steroid skeleton is given.
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    Acta crystallographica 31 (1975), S. 327-333 
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    Notes: Two single-crystal energy-dispersive crystallographic methods (the fixed-crystal method and the rotating-crystal method) are described and investigated. Formulae for integrated intensities are derived for mosaic and perfect single crystals. Experimental results and a comparison between measured and calculated integrated intensities for a perfect germanium crystal are given. Special features and possible applications of the methods are discussed.
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    Acta crystallographica 31 (1975), S. 334-337 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A study of the Edgeworth expansion of a probability density function shows how an atom position may be refined so that it coincides with a position of maximum probability rather than the mean of the probability density function.
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    Acta crystallographica 31 (1975), S. 367-372 
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    Notes: A magic-integer approach, called the P-S set method is described. A primary (P) set of reflexions contains some which fix the origin and enantiomorph and others expressed symbolically in magic-integer form. Probable phases for a secondary (S) set of reflexions are derived, also in symbolic form, from single triple-phase relationships containing a pair of P reflexions. Relationships which link the combined P and S sets give rise to the terms of a Fourier map, the peaks of which indicate likely sets of phases for all the reflexions under consideration. These sets of phases are used as starting points for the computer program MULTAN. The process is completely automated and is illustrated by the solution of the structure of cephalotaxine, C18H21O4N, the space group of which is C2 with two molecules in the asymmetric unit.
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    Acta crystallographica 31 (1975), S. 388-388 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Comment is made on the paper by Hawthorne, F. C. [Acta Cryst. (1974). A30, 603-604].
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    Acta crystallographica 31 (1975), S. 395-396 
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    Notes: X-ray absorption factors A* for spherical samples were calculated in the range of the product of sphere radius R and linear absorption coefficient μ of 0 ≤ μR ≤ 2.5 and in the range of Bragg angle θ of 0° ≤ θ ≤ 90°. A new method that requires numerical integration over only one variable using high-accuracy values of A* recently calculated for cylinders was developed. A table of values of A* was tabulated. A full-range, curve-fitting procedure that is accurate to 0.05% also was developed for routine calculation of A*.
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    Acta crystallographica 31 (1975), S. 397-397 
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    Acta crystallographica 31 (1975), S. 399-400 
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    Acta crystallographica 31 (1975), S. 425-434 
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    Notes: It is shown that, in order to treat the problem of the propagation of an X-ray wave in a distorted crystal, the plane-wave assumption, which is one of the fundamental ingredients in the usual dynamical theory, should be removed. Both the incident and the crystal waves should be built as wave packets, i.e. continuous distributions of k vectors, characterized by their extensions in both reciprocal and direct spaces. The characteristic structure of the crystal wave packet for a perfect crystal, and the changes undergone by this structure as a result of the crystal distortions, are examined; the criterion for the validity of geometrical optics is thus reformulated.
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    Acta crystallographica 31 (1975), S. 442-445 
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    Notes: The two-dimensional version of the KKR eigenvalue equation is analysed in different limiting situations. and reduction due to symmetry is discussed. With the aid of the semiclassical approximation to the Bloch functions, it is shown that simple expressions are obtained for the complex eigenvalues responsible for absorption. A qualitative understanding of some of the basic features of pole patterns results from a consideration of the approximations to both wave functions and dispersion surface.
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    Acta crystallographica 31 (1975), S. 273-279 
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    Notes: The usual methods of collecting diffraction data using β-filtered X-rays lead to significant systematic errors in the low-angle data, especially when the shorter-wavelength radiations (e.g. Mo Kα and Ag Kα) are employed. These errors arise because of the structure introduced into the white-radiation background by the filter absorption edge. A technique is proposed for the correct removal of the structured white-radiation profile from low-angle data. Some experimental measures are recommended which will reduce the number of reflexions affected. The proposed procedures are simple and can be carried out 'by hand' or, preferably, incorporated in the data-reduction program. Given an accurate and easily applied technique for removing the white-radiation background, it is argued that in the majority of cases data collection with β-filtered radiation is to be preferred over other methods such as the use of monochromated radiation or balanced filters.
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    Acta crystallographica 31 (1975), S. 307-310 
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    Notes: Lattice images were computed with increasing incident-beam divergence with spherical aberration taken into account. The effect is as if the outer diffracted beams transmitted by the objective aperture do not contribute to the image, so that the resolution is effectively less than that expected from the aperture size. Images of Nb12O29, calculated with the inclusion of this effect, show improved agreement with experimental images.
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    Acta crystallographica 31 (1975), S. 340-344 
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    Notes: The dynamical theory of magnetic diffraction of neutrons is investigated within the two-wave approximation. In ferromagnets the dispersion surface Σ is of order 4: quadruple refraction and diffraction are found; in general the wave fields are not polarized. In antiferromagnets, Σ is in general made of two hyperboloids, each of them corresponding to a given polarization of the propagating neutron.
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    Acta crystallographica 31 (1975), S. 364-367 
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    Notes: The d spacing of the 355 reflexion in silicon has been compared with the d spacing of the 800 reflexion in germanium using pseudo non-dispersive multiple-beam X-ray diffractometry with Mo Ka1 radiation. This technique gives the ratio of the two lattice parameters without the need for a precise knowledge of the X-ray wavelength. Symmetric transmission geometry was used to eliminate the refractive index correction. The results were: {{d(800 Ge)}\over{d(355 Si)}} = 1.0002348 (± 0.0000006) at 22.5 °C and {{d(800 Ge)}\over{d(355 Si}} = 1.0002458 ( ± 0-0000016) at 25 °C. By using the known lattice parameter of silicon obtained by X-ray and optical interferometry it was found that the lattice parameter of germanium at 25 °C is 5.6579060 ± 0.0000092 Å.
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    Acta crystallographica 31 (1975), S. 375-380 
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    Notes: General expressions for the discrepancy indices BR1(IN) and BR(IN), which are needed to test the correctness of any type of incomplete model of a complex structure containing any number and species of atoms in the unit cell, are derived for the related and unrelated cases. Explicit expressions for these indices for crystals containing all atoms in general positions are also tabulated for the seven categories of space group in the triclinic, monoclinic and orthorhombic systems. Expressions needed for handling crystals containing atoms in both general and special positions and those needed for taking into account random errors of observation in the intensities are also derived.
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    Acta crystallographica 31 (1975), S. 694-696 
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    Notes: It is shown that if the eigenvalues of the TLS matrix C66 are all positive, then the trace of S must lie within an open interval, which is effectively determined. Further Scheringer's equation for the estimate of the trace of S is shown to have in this interval exactly one root which is simultaneously the point of the maximum of the determinant of the TLS matrix C66.
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    Acta crystallographica 31 (1975), S. 680-687 
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    Notes: It is assumed that a crystal structure in P1 is fixed and that the seven non-negative numbers R1, R2, R3, R4, R12, R23, R31 are also specified. The random variables (vectors) h, k, l, m are assumed to be uniformly and independently distributed in the regions of reciprocal space defined by |Eh| = R1, |Ek| =R2, |El| = R3, |Em| = R4, (1) |Eh + k| = R12, |Ek + l| =R23, |El + h| = R31, (2) and h + k + l + m = 0. (3) Then the structure invariant, (φ = φh + φk + φl + φm, as a function of the primitive random variables h, k, l, m, is itself a random variable, and its conditional probability distribution, given (1) and (2), is derived and compared with the conditional distribution when only (1) is given. The distribution leads to improved estimates for cos φ in terms of the seven magnitudes (1) and (2). The results secured here suggest a generalization which is described in terms of the 'neighborhood concept'; and a 'principle of nested neighborhoods' is formulated. This terminology permits, in turn, an analogy with interpolation formulas.
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    Acta crystallographica 31 (1975), S. 855-856 
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    Notes: The X-ray attenuation coefficient of carbon at λ(Cu Kα1) has been measured with a specimen of highly oriented pyrolytic graphite, tilted to average inhomogeneities and change the beam path length. The values determined are μ(Cu Kα1) = 9.246 (5) cm-1 and μ/Q (Cu Kα1) = 4.080 (2) cm2 g-1. For Cu K{\bar \alpha}, the derived value is 4.089 (2) cm2 g-1 and this differs significantly from the latest value, 4.219 cm2 g-1 given in Vol. IV of International Tables for X-ray Crystallography.
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    Acta crystallographica 31 (1975), S. 858-859 
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    Notes: The centred monoclinic lattices numbers 17 and 27 can be C or A lattices as well as I lattices.
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    Acta crystallographica 31 (1975), S. 857-858 
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    Notes: FeSiF6 6H2O shows extra reflexions inconsistent with the space group R{\bar 3}m. The same conclusion applies, for T〉 300K, to MgSiF6.6H2O whose structure is similar to that of MnSiF6.6H2O. These three compounds undergo similar phase transformations with decreasing temperature.
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    Acta crystallographica 31 (1975), S. 878-878 
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    Acta crystallographica 31 (1975), S. 878-879 
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    Acta crystallographica 31 (1975), S. 880-880 
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    Acta crystallographica 31 (1975), S. 628-634 
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    Notes: A probable crystallographic path for the thermal cycle of phase transformations, II-I-III-II, in KNO3 single crystals is proposed. It is based on the symmetry of the phases and a least-motion hypothesis that the 'shuffles' of the transformations (so remarkably like martensitic transformations in metals) are the minimum possible readjustments subject to accepted van der Waal distances between chemically non-bonded atoms. Twinning is adequately explained by the alternative paths provided by the symmetry of the parent phase. The observed disorientation of 2°9' in the c(II) axes of the end-phase twinned crystals is calculable by the well known Bowles-Mackenzie matrix method. The calculated value is now found to be 2.5°. Crystallographically an important possibility emerges: the structure of the higher-symmetry phase of a transformation may be predicted from only its unit-cell dimensions and space group if the crystal structure of the low-symmetry phase is known.
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    Acta crystallographica 31 (1975), S. 665-670 
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    Notes: Often a strong texture is found when metal thin films are evaporated in vacuum on amorphous substrates: the hkl dense planes have an average orientation parallel to the substrate. Then, in the hkl X-ray diffraction pattern, secondary fringes are observed on both sides of the Bragg central peak, although they do not appear on other Bragg lines. It is shown that such properties are consistent with lattice distortions and deformations peculiar to each crystal. When the sample consists of an epitaxic 'sandwich' stacking (i.e. two thin films with the same material and the same thickness separated by one or several foreign atomic layers) contrast and angular positions of the secondary fringes are modified. The geometrical interpretation suggested here explains the change in the diffraction pattern shape, and its evolution when foreign atoms are diffusing into the neighbouring films.
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    Acta crystallographica 31 (1975), S. 688-693 
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    Notes: A generalized formula for the integrated intensity of neutrons diffracted by a vibrating perfect crystal is derived on the basis of the lamella structure with the symbols of Zachariasen's general theory. The formula is introduced together with new experimental data for diffraction from a longitudinally vibrating quartz single crystal.
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    Notes: The c-axis oscillation photographs of platelet-shaped crystals exhibit curious disorder features on X-ray diffraction photographs. These disorders are shown to be shape-dependent and are not caused by any real disorder in the stacking of layers. Another type of disorder which appears on X-ray diffraction photographs of cadmium iodide polytypic crystals is the 'arcing' disorder. It is shown that in view of the paucity of experimental evidence, the 'arcing' cannot be understood on the basis of the occurrence of manifold tilt boundaries.
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    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 774-779 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The basic equation of dynamical diffraction for imperfect crystals, which has been derived previously by a general dynamical theory of diffraction, is rederived classically based on the Ewald–Laue–Bethe concept, thus completing the formulation of a 'scattering matrix' theory. It is shown in this classical derivation that a series of assumptions is required at each stage of the mathematical formulation to allow it to proceed further. These assumptions are then viewed in terms of the general dynamical theory of diffraction, and found unnecessary in the rigouous formulation. This classical formulation provides a conceptual relation between the traditional Ewald–Laue–Bethe dynamical theory and the general dynamical theory, one that has been derived with the aid of quantum-field theory.
    Type of Medium: Electronic Resource
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