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  • International Union of Crystallography (IUCr)
  • 1980-1984  (2,527)
  • 1984  (1,211)
  • 1980  (1,316)
  • 1
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 1-7 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Short-range order parameters were obtained for a single crystal of 62Ni3Fe quenched from above Tc. These are the first absolute measurements of diffuse elastic neutron scattering complete enough to separate the effects of local order and atomic displacements (up to quadratic terms) and indicate that neutrons are ideally suited for such studies. The results are compared to those obtained with X-rays. The short-range order intensity of Ni3Fe is similar in shape to that for Cu3Au but in this alloy it is due to the plate-like nature of ordered domains, not the antiphase domain boundaries which are present in such regions in Cu3Au.
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  • 2
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 54-57 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray investigations of Eu2+-rich precipitates in NaCl single crystals have revealed the presence of two phases. Phase A of chemical formula EuCl2 with a CaF2-type structure and lattice parameter a = 6.969 (2) Å preserves strictly the orientation of the matrix lattice. Phase B with the lattice parameter a = 7.47 (1) Å and tentative formula EuCl2.2NaCl, containing Eu2+ ions and charge-compensating cation vacancies, is localized at subgrain boundaries and is thermally less stable than phase A.
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  • 3
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 68-74 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The present paper deals with the finding and the estimation of negative quartets. The use of symmetry is also discussed and the results obtained for four structures of increasing size are reported. Conditional probability distributions using magnitudes contained in the second representation of the quartets provides improved estimates of their phases.
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  • 4
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 116-122 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The concept of disorientation, previously used for studying the statistical distribution of the relative orientation of identical cubic crystals, is defined in this work for any two lattices. Using the proposed definition, an algorithm is presented, allowing all the known relative orientations between the two lattices to be conveniently classed. As an example, a unified classification of the numerous mutual orientations of the Al and CuAl2 crystals is suggested. The unit quaternion method used by Grimmer [Acta Cryst. (1974), A30, 685-688] for identical cubic lattices is here proved efficient for discussing the pair axis/angle disorientations in more complicated cases: cubic 1/cubic 2; tetragonal 1/tetragonal 2; hexagonal 1/hexagonal 2; cubic/tetragonal; cubic/orthorhombic and cubic/hexagonal. The general expressions of equivalent quaternions are given for any point group of lattice 1 or lattice 2.
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  • 5
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 122-126 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The controversial space-group problem of spinel, MgAl2O4, whether it is Fd3m or F{\bar 4}3m, was studied by electron diffraction. It was confirmed that the appearance of 'forbidden reflections' such as {200} was caused by the double reflection process of reflections with high indices on the non-zero-order Laue zone. Consequently, the space group of spinel is Fd3m, and the assignment of the space group to F{\bar 4}3m is ruled out. The change of space group from F{\bar 4}3m to Fd3m associated with a phase transition, proposed by Mishra & Thomas [Acta Cryst. (1977), A33, 678], can also be explained by double diffraction: the magnitudes of primary reflections with high indices rapidly decrease due to the increase of the Debye-Waller factors at elevated temperatures.
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  • 6
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 143-146 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is pointed out that there is some uncertainty as to the correct behaviour of the integrated reflectivity as a function of the degree of asymmetry for the scattering of X-rays from imperfect crystals in the extremely asymmetric Bragg case. Numerical calculations based on the Takagi-Taupin equations are exemplified and indicate that the integrated reflectivity for such crystals tends asymptotically to the perfect-crystal result in the asymmetric limits, the perfect-crystal result, in turn, tends to the kinematical value at these limits, as has been shown previously. In addition, comments are offered on the relevance of the present work to the study of highly imperfect crystals by section topography, and in particular to the study of the near-surface grain-boundary structure of crystals.
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  • 7
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 147-148 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The mean Debye-Waller parameter {\bar {\it B}}of TlCl has been determined by double- as well as triple-axis neutron diffraction for a powder sample. Thermal diffuse scattering (TDS) corrections have also been made to the intensity of the diffraction peaks obtained by these techniques. TDS was found negligible in the triple-axis diffraction pattern as expected. The {\bar {\it B}} values thus found are 3.08 ± 0.43 and 3.07 ± 0.22 Å2, respectively, for double- and triple-axis methods. These values are in good agreement with those found by recent X- ray diffraction measurements.
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  • 8
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 157-158 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 9
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 171-177 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Based on the new energy-transfer equations [Kato (1976). Acta Cryst. A32, 458-466; Kato (1979). Acta Cryst. A35, 9-16] the integrated intensities (II) are calculated. Since the energy-transfer equations have physical meanings different from the traditional ones originally given by Darwin [Philos. Mag. (1922), 43, 800-824] and extended by Hamilton [Acta Cryst. (1957), 10, 629-634], the method of calculating (II) must be modified, particularly in the case of a wide incident beam. Since the modified method does not include the angular integration, it is much simpler than the traditional method. Thus, the analytically rigorous expressions of (II) can be obtained for parallel-sided crystals including absorption, and for any diffraction conditions.
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  • 10
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 190-193 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: High-resolution electron microscopy can be used to differentiate between two structural models of long-period ordered alloys. These models differ in the nature of the disorder as seen in the stacking irregularities which can have planar boundaries as exemplified by Ag3Mg or wavy boundaries as in AuCu II. In the composition range 22-27 at.% Mg, Ag3Mg is built up with a regular arrangement of two kinds of structural layers, 1 or 2 L12 cells in thickness. Some stacking disorder exists, but this alloy can be locally described using a space-group notation and has the character of being an infinitely adaptative structure. High-resolution images have been used to show the perfect planarity of the boundaries in Ag3Mg, thus demonstrating the way in which disorder is accommodated in this alloy.
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  • 11
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 333-333 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 12
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 334-334 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 13
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 344-350 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Retention of known geometry, with regard to mean atomic positions, has proved useful in the refinement of macromolecules. In structures with a paucity of diffraction data and large displacements of the atoms from their mean positions, it is also of value to restrain the thermal factors to be consistent with known stereochemistry. This paper presents a technique for accomplishing this by restraining the variances of the interatomic distributions (which are functions of the mean atomic positions and the thermal parameters) to suitably small values. This procedure allows meaningful anisotropic refinement of macromolecules to be carried out with low-resolution diffraction data. Anisotropic thermal parameters obtained in this way should prove useful in understanding the dynamics of the biological functions of macromolecules.
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 353-356 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: From careful measurement and indexing of the powder diffraction patterns obtained for pure dicalcium silicate, unit-cell parameter vs temperature plots have been obtained covering the β and α' dicalcium silicate phases. It is found that these phases are all closely related, the temperature variations, for example, being gradual from 293 K (the β phase) and more discontinuous between 993 and 1043 K corresponding to the β = α'L transition. Our conclusions lead to a simplified dicalcium silicate transformation scheme which requires that there is no phase differentiation within the β-phase regime.
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 372-378 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The ordered domain structure present in the α-phase Cu-Al alloys investigated by Epperson, Ffirnrohr & Ortiz [Acta Cryst. (1978), A34, 667-681] is determined by an extension of the computer method developed recently by Epperson [J. Appl. Cryst. (1979), 12, 351-356] for analyzing a Gehlen-Cohen type simulated structure for a binary, f.c.c., locally ordered alloy in terms of nearest-neighbor atomic configurations. The dominant ordered feature of the more concentrated of these alloys is the existence of randomly dispersed Boric-Sparks tetrahedra; that is, four nearest-neighbor Al atoms arranged tetrahedrally about a Cu atom. The majority of these tetrahedra are isolated; however, as many as three or four are occasionally found to be joined in fragments of a Cu3Au-type antiphase-shift structure. This extended ordered structure also incorporates the Cu3Au-type ring configuration, another principal characteristic structural feature of these Cu-Al alloys. As a typical example, a Cu-14.76 at.% Al alloy quenched from 923 K and annealed for 1580 h at 423 K was found to contain 87 such locally ordered regions in an 8000-atom model. Of these 'domains', 74 were isolated tetrahedra and the remainder consisted of pairs of tetrahedra joined such that their central atoms were mutual second-nearest neighbors. For this alloy and heat treatment, the locally ordered regions of this type amount to about 14 volume % of the microstructure and contain 32% of the Al in the alloy. The average (spherical) domain size is only 3.4 Å. Not only are the locally ordered regions very small, but there are also perceptible imperfections in the packing sequence.
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 470-475 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of using quartets and quintets in the direct-methods program MULTAN is described with several successful applications.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 330-330 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 331-332 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 19
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 334-334 
    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 36 (1980), S. 496-496 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Agarwal [Acta Cryst. (1978), A34, 791-809], equation (61) should read: c3 = 2Cm1 Cm2. All information is given in the Abstract.
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  • 21
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 499-500 
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  • 22
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 502-502 
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  • 23
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 520-530 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Above the 1300 K transition and in the defect fluorite phase, there is diffuse X-ray scattering which is similar for both Ca- and Y-stabilized zirconias. This is largely due to ionic displacements from the average structure, principally oxygen ions displaced locally in (100) directions. It has been proposed that some of this scattering is due to fine precipitates of ZrCa4O9 or ZrY4O9. The quantitative analysis of this diffuse scattering reported here does indeed indicate some similarities to this phase; in particular the stabilizing ions form rods in the ({\bar 3}{\bar 3}2) directions similar to those in the precipitate. However, in this compound the stabilizing ion is a second neighbor to an oxygen-ion vacancy, whereas the present results indicate that these tend to be first neighbors. This is the first direct evidence for this association in these materials. This probably occurs to reduce local distortions and to provide local charge balance. It is concluded that the diffuse intensity is from locally ordered regions, not precipitates.
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  • 24
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 573-578 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Some algorithms have been derived to calculate the expected values of one-phase seminvariants of first rank in space groups up to orthorhombic by a probabilistic approach [Giacovazzo (1978). Acta Cryst. A34, 562-576]. The method has been tested on several known structures. The results show how the method can secure a very reliable estimate for a limited number of one-phase seminvariants which can be used from the initial stages of phase determination. In addition, the estimated values can be used as a good figure of merit to select the correct K2 solution in a multisolution procedure.
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  • 25
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 600-604 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Extinction effects in white-beam X-ray and neutron diffraction are considered following the formulation developed for monochromatic-beam diffraction by Becker & Coppens [Acta Cryst. (1974), A30, 129-147]. In white-beam diffraction, a small deviation of the wavelength from the Bragg condition Δλ is a variable which represents the line profile of the diffraction peaks, so that by using the new parameter Δλ the theory is converted to one in white-beam diffraction. It is shown that for a convex crystal, primary extinction yp agrees with the results calculated already for monochromatic diffraction. The same relation is shown to hold in secondary extinction ys. It is concluded that extinction theory derived for monochromatic diffraction is applicable without any modification in white-beam diffraction.
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  • 26
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    Acta crystallographica 36 (1980), S. 620-624 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The minimum-variance weighting scheme for calculating the weighted mean of a quality for the following unusual case is analysed. The quantity is derived from the product of two independent quantities for each of the which a set of data is available. All the products between the two sets of data are taken into consideration. The application to measurements of the polarization state of X-radiation is outlined.
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  • 27
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    Acta crystallographica 36 (1980), S. 653-656 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Direct methods are applied to difference-structure factors for a structure containing one or more heavy atoms at known special or pseudo-special positions, such that the heavy atoms do not contribute to several reflection parity groups. Phases of reflections in these parity groups, represented by symbols, are analysed by the sign-correction method. Phases as well as amplitudes of the difference-structure factors are refined by the general DIRDIF procedure as described previously.
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  • 28
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    Acta crystallographica 36 (1980), S. 74-82 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A phase relationship involving triplet and quartet contributions is given. It is able to take account of the correlation between triplet and quartet relations. The information exploited by the formula is discussed and compared with that exploited by phase relationships arising from the properties of the Fourier transform of periodic positive functions. In particular, the information contained in a Karle-Hauptman determinant of low order is briefly considered.
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  • 29
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    Acta crystallographica 36 (1980), S. 57-67 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two approximations that are commonly used to describe the scattering of high-energy electrons are the first Born approximation (kinematic approximation) and the closely related 'weak phase-object' approximation. The quantitative domains of validity for the use of these two scattering approximations for structural analysis of organic crystals are evaluated numerically in terms of resolution, crystal thickness and incident electron energy. The resulting calculations show how progressively important dynamical scattering effects lead to an increasingly large contribution to the R value in a structure factor analysis. Alternatively, the results show that an increasing dissimilarity is produced between the structure inferred from electron microscope images and the correct structure. The results also show that the actual images (and the structure inferred from the images) remain qualitatively similar to the projected Coulomb potential, even though dynamical scattering effects may lead to a large quantitative dissimilarity relative to the correct structure.
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  • 30
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    Acta crystallographica 36 (1980), S. 96-103 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure of sodium chloride has been studied by gas-phase electron diffraction using photographic plates designed for high-temperature work [Kakumoto, Ino, Kodera & Kakinoki (1977). J. Appl. Cryst. 10, 100-103]. The molecular structure at about 1130 K has been determined by an analysis based on the new complex scattering factors for Na+ and Cl- calculated recently by the present authors. The radial distribution function shows the existence of a considerable amount of dimer molecules in the vapor. The structures of the monomer and dimer have been analyzed by a least-squares method assuming that the dimer is of a planar diamond shape: for monomer ra(Na--Cl) = 2.392 ± 0.028, for dimer ra(Na-Cl) = 2.515 ± 0.017, ra(Cl-Cl) = 3.893 ± 0.021 Å, ∠ClNaCl = 101.4 ± 0.8°. The present study indicates that the Na--Cl distance of the dimer is longer than that of the monomer and the determined structure parameters differ appreciably from existing theoretical predictions.
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  • 31
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    Acta crystallographica 36 (1980), S. 741-746 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Notes: The cation distribution of the compounds (Fe0,5Ta0,5)O2 and (Fe0,45Nb0,53)O2 has been redetermined by the combined use of neutron and X-ray powder diffraction. Analysis of the powder patterns showed that the compounds are isostructural, their structure being of the rutile-type AO2. The cations are statistically distributed. There exists no partial ordering, neither of Fe and Ta nor of Fe and Nb. Neutron diffraction patterns taken at 4.2 K showed only one magnetic reflection, which is strongly broadened. The magnetic structure of (Fe0.5Ta0.5)O2 is of MnF2-type, whereas (Fe0.45Nb0.53)O2 orders in the BEY-structure. Profile analysis of these broadened reflections was carried out with the convolution integral of a Gaussian with a Lorentzian function, from which correlation lengths could be derived.
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  • 32
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    Acta crystallographica 36 (1980), S. 156-156 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Abstract by Modlin & Rodgers [Acta Cryst. (1978), A34, S4, 381] was submitted without the knowledge of the present author, who was not aware of its content. Only preliminary discussions and work on certain aspects of a research programme had taken place at the time that the Abstract was submitted. The conclusions claimed in the last sentence had not been arrived at.
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    Acta crystallographica 36 (1980), S. 155-156 
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    Notes: The scattering factors of the 1s22s22p6 core for K+ and Cl- have been calculated from analytical wave functions and also with one-term Gaussian representations. These scattering factors, together with the experimental structure factors, have been used to obtain, by difference Fourier inversion, the valence-electron charge distributions of KCl in the [100], [110] and [111] directions. By comparison, a very simple one-term Gaussian representation has been shown to yield reliable results.
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  • 34
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    Acta crystallographica 36 (1980), S. 157-157 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Bertaut & Dulac [Acta Cryst. (1972), 28, 580-588], for clerical reasons an error has crept in so that the numerical moment values of y and z components of Cr1 are to be interchanged. One should read in the Abstract and in relation (8.9): Sz(Cr1) = -0.73 (instead of -0.45); sy(Cr1) = 0.45 (instead of + 0.73).
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    Acta crystallographica 36 (1980), S. 819-826 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: All geometric units in crystal structures of space groups P{\bar 4}3m, I{\bar 4}3m, Pn3m, F{\bar 4}3m and Fd3m possess point group {\bar 4}3m. These units may be vacant, or may contain one or more atoms. In units containing more atoms than one, the atoms form one or a collection of these polyhedra: tetrahedron, truncated tetrahedron, octahedron, cuboctahedron or truncated octahedron; the last two may be distorted. Therefore, a formula that lists the consecutive polyhedra starting from the center of the unit can be used for the tabulation of these crystal structures. Only structures of Cu2O type are known in Pn3m and typical structures of the other four space groups are tabulated.
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  • 36
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    Acta crystallographica 36 (1980), S. 830-830 
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    Notes: The equivalence relationships for general planes (or reflexions) in Laue class {\bar 3}1m are different from those for Laue class {\bar 3}m1. Table 3.5.1 of International Tables for X-ray Crystallography [(1969). Vol. I. Birmingham: Kynoch Press] makes no allowance for these differences. The necessary corrections are given.
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  • 37
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    Acta crystallographica 36 (1980), S. 834-834 
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    Acta crystallographica 36 (1980), S. 835-836 
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    Acta crystallographica 36 (1980), S. 836-836 
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    Acta crystallographica 36 (1980), S. 851-856 
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    Notes: New twin domains of thickness of the order of a few micrometres can be created in KClO3 crystals by applying a small uniaxial stress. The observed domain structure can be explained by postulating a hypothetical prototype phase of symmetry 4/mmm. The magnitude of spontaneous strain, σs, for the room-temperature monoclinic phase, computed on the basis of the postulated tetragonal prototype, has an exceptionally large value of 0.257. Further, σs varies linearly as the square root of temperature, implying a mean-field-like behaviour. However, presumably because of the very large spontaneous strain, attempts to move the domain walls back and forth by applying uniaxial stress (at room temperature) have not yet been successful, and the question asked in the title may be a matter of definition.
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  • 41
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    Acta crystallographica 36 (1980), S. 198-205 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A systematic theoretical analysis is made of the kinds of structural irregularity which occur in biological systems. The theoretical problems investigated were: (1) the precise meaning of the term 'paracrystal' when applied to biological systems such as tropomyosin tactoids, collagen fibrils, keratin and the myelin sheath of nerve; (2) the relationship between the paracrystal and liquid-theory descriptions of disorder which have recently been applied to the structure of collagen fibrils; (3) how structural irregularity affects the diffraction patterns (X-ray, neutron and electron) which are commonly used to investigate the structure of these systems experimentally. The conclusions are: (I) paracrystalline disorder of the first kind refers to a spatially disordered crystal but for biological systems it would generally be impracticable to distinguish this from thermal disorder; (2) paracrystalline disorder of the second kind provides a conceptually clumsy method for describing liquid-like systems; (3) paracrystal models are not strictly valid for finite systems; (4) modern liquid theory, as applied, for example, to the structure of the collagen fibrils, provides an elegant and economical alternative to paracrystal theory for disorder of the second kind; (5) the presence of peaks in diffraction patterns from biological systems does not necessarily imply that the system has very much regularity, i.e. it is not evidence for the existence of a lattice.
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  • 42
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    Acta crystallographica 36 (1980), S. 228-237 
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    Notes: Ternary oxides AMO2, A2MO3 and A5MO6 with monovalent A and tri-, tetra- or hepta-valent M metals can exhibit order/disorder transitions with about 20 superstructures of the NaC1 lattice. Some structures can be related to AM, A2M and A5M alloys with a larger distortion of the lattice due to stronger interactions between metal atoms. In ternary oxides about 30 short-range order configurations are selected for the first, second and third shell of metal atoms in applying Pauling's electrovalence rule. Stable configurations are characterized by the strength of Coulomb interactions and by a high point symmetry of the M atoms. Mainly disordered ternary oxides can vary stoichiometrically with a frequent occurrence of vacancies or with partial occupation of tetrahedral interstices by A atoms.
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  • 43
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    Acta crystallographica 36 (1980), S. 259-265 
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    Notes: A statistical distribution of ions M in lattices or partial lattices ∞[A1 - xMxLm] of mixed crystals being assumed, the probability functions PJ(V)(x) for single coordination polyhedra MLn (j = 1), pairs (j = 2) and larger clusters of MLn groups (j 〉 2) in 1D (v = 2) and v-connected 2D systems (v = 3, 4, 6) are calculated. On raising the connecting number v, increasing cluster probabilities are distinctly shifted to lower concentrations x of the foreign ion M. For a relation between the numerical values P(x) and experimental results, the mixed-crystal series (BaF)2[Zn1 - xCuxF4] of a four-connected 2D structure is given as an illustrative example.
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    Acta crystallographica 36 (1980), S. 282-287 
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    Notes: Oriented specimens of biomembranes give distinct X-ray diffraction patterns of circular symmetry along the equatorial plane. In order to interpret such a diffraction pattern, properties of the radial autocorrelation function were examined in detail in conjunction with electron-density distribution and applied. The radial autocorrelation function, which is the Fourier-Bessel transform of an intensity function with circular symmetry, is the radial projection of a two- dimensional autocorrelation function and can be interpreted in terms of Fourier components of electron-density projection along the membrane normal. Some useful information is obtainable on the structure of the scatterer: (i) the approximate size of the X-ray scatterer; (ii) judgement of crystalline or non-crystalline arrangement of molecules; (iii) the existence of a regular arrangement of the electron-density fluctuations in a projection along the membrane normal; (iv) the rotational symmetry element existing in the scatterer if any.
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    Acta crystallographica 36 (1980), S. 299-303 
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    Notes: The pressure dependence of the lattice parameters of PdZn having an L10-type structure has been measured up to 24 GPa (240 kbar) with a diamond-anvil-type cell and sodium chloride as an internal-pressure marker. The axial ratio c/a, which was originally 0.814 (1) [between the two extreme values 1.00 and 0.707 (= 1/ \sqrt{2}) for this type of structure], does not decrease but increases with increasing pressure and after reaching 0.822 at 10 GPa it remains almost constant on further compression. The equation of state has been derived for the L10-type structure assuming pairwise interactions between like atoms and between unlike atoms and comparison is made between the calculated and observed compression curves of the a and c axes. The anisotropy in the lattice compressibility leads to a considerably larger interatomic potential for the unlike atom pair than for the like atom pair.
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    Acta crystallographica 36 (1980), S. 442-450 
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    Notes: Formulas are derived extending several semi-empirical absorption-correction methods to diffractometers operating in Weissenberg geometries, with particular attention paid to flat-cone geometry. These formulas are useful for a variety of instruments using both area and linear position-sensitive detectors. While a complete data set can sometimes be corrected using a single absorption reflection, it was found that the best corrections are usually obtained by considering two absorption reflections rather than one. A discussion of the optimum choice of absorption correction when a crystal has at least a twofold symmetry axis is presented. The accuracy of the methods and the limits of applicability have been examined by computer simulations.
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    Acta crystallographica 36 (1980), S. 436-442 
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    Notes: Both real and imaginary components of the anomalous X-ray scattering were measured by single-crystal diffraction experiments with synchrotron radiation at wavelengths through the region of the three L absorption edges of cesium, the first such experiment for any element at the L edges. Near the L3 edge f' varies between -26.7 and -13.9 and f" between 4.0 and 16.1 electrons in a wavelength interval of 0.008 Å. Similar but smaller changes occur near the L2 edge, and still smaller ones at L1. Fine structure in the f" curve corresponds to that observed in an absorption curve and also, by a dispersion relation, to fine structure in the f' curve. These effects offer promise as a substitute for isomorphous replacement for solving the phase problem for macromolecular crystal structure. Similar experiments with cobalt near the K edge give f' values in agreement with measurements by other workers for nickel and copper by different methods at corresponding wavelengths; the lowest value observed is f' = -7.5 electrons.
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    Acta crystallographica 36 (1980), S. 1065-1070 
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    Notes: A systematic investigation of the effect of phase errors of different types on E maps is presented. Both random and systematic errors have been considered with distributions depending in different ways on the resolution of the data. Considerably large random errors can be tolerated without great loss of structural information in the E maps, while smaller systematic errors have greater destructive effects. These effects are explained by the introduction and analysis of a phase-error function.
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    Acta crystallographica 36 (1980), S. 1072-1088 
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    Acta crystallographica 36 (1980), S. 1093-1093 
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    Acta crystallographica 36 (1980), S. 1094-1094 
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    Acta crystallographica 36 (1980), S. 904-915 
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    Notes: Based on accurate X-ray diffraction intensity data collected from spherically shaped single crystals, net atomic charges and electron density distributions have been studied for MnO, Mn2SiO4, Mg2Si2O6, LiAlSi2O6 and CaMgSi2O6. Examination of various procedures for determining atomic charges in a given structure has led to the conclusion that the following approach appears to be most reliable. (1) For cations: the number of electrons in the sphere of radius ER, effective distribution radius, which is defined according to the characteristics of radial distribution functions or difference-Fourier maps, is calculated. (2) For oxygen atoms: with the cation charges fixed at the values obtained from the above procedure and the total charge of the crystal constrained to be neutral, oxygen charges are estimated from least-squares refinements using atomic scattering factors. The final charges of atoms examined are less ionic than the corresponding formal ones: those of Li, O, Mg, Al, Si, Ca and Mn are respectively + 0.7 (1), -1.1 to -1.5, + 1.4 (1) to + 1.8, + 2.4(1), + 2.2 (1) to + 2.6, + 1.4 (2) and + 1.2 (1) to + 1.6 e. Residual electron densities between Si and O have been clearly observed in difference-Fourier maps after charge refinements for crystals of LiAlSi2O6, CaMgSi2O6 and Mg2Si2O6.
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    Acta crystallographica 36 (1980), S. 937-944 
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    Notes: Beu, Musil & Whitney [Acta Cryst. (1962), 15, 1292-1301; Acta Cryst. (1963), 16, 1241-1242] proposed a maximum-likelihood method of estimating the lattice parameters of cubic, tetragonal and hexagonal crystals, and a method of testing the hypothesis that systematic errors had been satisfactorily accounted for. The use of maximum likelihood is unnecessary, and open to some objection. The argument is therefore rewritten in the more familiar least-squares form, and is generalized to cover the remaining crystal systems. Only if systematic errors are absent is it legitimate to estimate standard deviations of parameters from the differences of observed and calculated Bragg angles. With minor modifications the results are applicable to structural parameters also.
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    Acta crystallographica 36 (1980), S. 945-946 
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    Notes: If dispersive atoms are present the structure factor of a centrosymmetric crystal is not purely real, and the probability distribution of the modulus of the structure factor becomes P(F)dF = ( 2F/μ) exp (-ΣF2/μ2)I0(SF2/μ2)dF, where Io is the modified Bessel function of zero order, Σ is the sum of the squares of the moduli of the atomic scattering factors, S is the modulus of the sum of their squares, and μ is (Σ2 - S2)1/2. For a non-centrosymmetric crystal the form of the distribution is not altered, but Σ must be defined as in the preceding sentence.
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    Acta crystallographica 36 (1980), S. 975-978 
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    Notes: The comparison of molecular structures is facilitated by a combination of graphical and numerical techniques. Conversion to a molecular reference frame makes the linear relationships between the molecules or fragments easily visualized, and can be used to produce diagrams clearly displaying the molecular similarities and differences.
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    Acta crystallographica 36 (1980), S. 1002-1013 
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    Notes: The results of experiments in which an anomalous form of the Pendellösung fringes has been discovered together with a classical one are presented. The general theory of X-ray spherical-wave diffraction has been constructed taking into account the change of phase relationships for radiation propagating in vacuum. An explanation of the observed experimental results and classification of possible manifestations of the Pendellösung effect are given. New data concerning the previously discovered phenomenon of focusing are presented.
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    Acta crystallographica 36 (1980), S. 989-996 
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    Notes: The results of an investigation of the polarization coefficient of X-ray radiation diffracted in real crystals are given. The form of the angular dependence of the polarization coefficient in the range of the Bragg reflection is found to be qualitatively different in the cases of primary and secondary extinction. It allows the unambiguous identification of the type of extinction in the crystal. On the basis of the experimental data analysis of the polarization coefficients for silicon and germanium crystals with different dislocation densities, it is shown that the mosaic model of a crystal is suitable for describing X-ray scattering in real crystals if the dislocation density is higher than 104 mm-2 and in practice only primary extinction is present in mosaic crystals. An expression is given for the primary extinction factor for the mosaic crystal, obtained on the basis of the solution of the Takagi-Taupin equations for finite crystals. This expression was used for the analysis of the LiF and NaF structure factors measured by different authors. The effective size which was obtained for the domains appeared to be physically reasonable and to be directly connected with the value of the dislocation density in the crystal.
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    Acta crystallographica 36 (1980), S. 1025-1030 
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    Notes: Pendellösung intensity beats of white radiation diffracted from parallel-sided single-crystal wafers of silicon were measured by a solid-state detector. After a few corrections, the extremum positions in the beat were measured to evaluate the atomic scattering factors for various reflections. The scattering factor shows a dependence on wavelength, λ, which can be interpreted by the anomalous dispersion term, f', as calculated by Cromer [Acta Cryst. (1965), 18, 17-23]. The obtained values of the atomic scattering factor expressed as linear functions of wavelength are listed with those at λ = 0.5594 Å for comparison with the data so far obtained with Ag Kα1 and wedge crystals. The values for 111 and 220 reflections in the present experiment, 10.59 and 8.40, were almost the same as Tanemura & Kato's [Acta Cryst. (1972), A28, 69-80], 10.664 and 8.463, respectively.
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    Acta crystallographica 36 (1980), S. 1050-1057 
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    Notes: The direct-analysis formalism of Kurki-Suonio [e.g. Isr. J. Chem. (1977). 16, Nos. 2-3, 115-123, 132-136] is modified to apply to the calculation of nuclear distributional moments 〈xλyμzv〉, which are linear combinations of the multipole moments 〈rkylmp〉. They are integrated from the radical coefficients of the corresponding multipole terms through Gaussian and difference series procedures. An application to the thermal neutron diffraction structure factors of Merisalo & Larsen [Acta Cryst. (1977). A33, 351-354] on zinc indicates that the moment 〈x2〉 agrees with the anharmonic result of Merisalo & Larsen 〈z2〉 does not show discrepancy with the value based on harmonic assumption. The existence of the third-order component in the nuclear smearing function and, due to this, anharmonicity of thermal motion is well established, but the magnitude of 〈x3〉 is not accurately defined on the basis of the present data. The ratios of the fourth and second moments do not reveal deviation from harmonic thermal smearing.
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    Acta crystallographica 36 (1980), S. 1071-1071 
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    Notes: Corrections are given to §§ 4.3 and 4.4 of International Tables for X-ray Crystallography [Vol. I (1969), Birmingham: Kynoch Press].
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    Acta crystallographica 36 (1980), S. 1090-1091 
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    Acta crystallographica 36 (1980), S. 1091-1091 
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    Acta crystallographica 36 (1980), S. 1095-1095 
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    Acta crystallographica 36 (1980), S. 1096-1096 
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    Acta crystallographica 36 (1980), S. 641-653 
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    Notes: Within certain good approximations the probability distribution function (p.d.f.) used to describe mosaic-block orientation in secondary-extinction models is exactly analogous to the p.d.f. for atomic thermal motion in the harmonic approximation. Use is made of this relationship to explain carefully, with the aid of several diagrams, certain distinctions and relationships common to both p.d.f.'s - which if not properly understood can lead (and have led) to some important confusions. For example, if the three-dimensional p.d.f. is Gaussian, surfaces of constant probability density are ellipsoidal (e.g. the thermal-vibration ellipsoid); but the scattering process 'sees' this p.d.f. as a one-dimensional projection, the half-width of which lies on a fourth-order surface (shaped, for example, like a peanut shell). For extinction it is shown explicitly that the form of this projected one-dimensional function is independent of experimental conditions (e.g. collimation), and that an earlier form [Coppens & Hamilton (1970), Acta Cryst. A26, 417-425], still commonly used and tested, is always incorrect. Apart from the intentional restriction of the detailed analysis of secondary extinction to type I extinction (in which mosaic-block orientation is the dominant effect), the approximations adopted are shown to have a wide range of validity. The (unusual) conditions under which the approximations may be sufficiently invalid to produce detectable effects are examined qualitatively in relation to the possibility of experimental investigations.
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    Acta crystallographica 36 (1980), S. 697-704 
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    Notes: A numerical method is developed for calculating the thermal diffuse scattering (TDS) correction from phonon inelastic scattering in a neutron diffraction pattern measured by the time-of-flight method. The correction is evaluated for a nickel powder spectrum at room temperature. It is shown to be more important than had been suggested previously. It gives rise to a reduction of the apparent Debye-Waller factor by about 10%. It may also lead to the appearance of the higher-order Debye-Waller factor previously ascribed to anharmonicity.
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    Acta crystallographica 36 (1980), S. 732-734 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple method is given for deriving the triclinic-cell parameters from three general reflections by vertical or horizontal measurements on upper-level films.
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 739-740 
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 740-740 
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 796-800 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Derivative lattices are related to one another by transformation matrices having rational elements. A simple algorithm for finding these matrices consists in testing if the scalar products of the vectors defining two arbitrary primitive cells of two lattices can be exactly or approximately related by equations with rational coefficients. A rational relationship indicates that two or more lattices have a number of geometrical features in common such as common superlattices, sublattices, etc. The algorithm can, therefore, be applied to a variety of crystallographic problems such as the study of twinning, the indexing of powder patterns, single-crystal diffractometry and the critical evaluation of crystal data. Five examples are discussed in detail.
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  • 71
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    Acta crystallographica 36 (1980), S. 916-921 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A neutron diffraction study of Debye-Waller factors has been performed on ThC and ThC0.77 powder samples at 4 and 250 K on the high-resolution diffractometers D1A and D1B of HFR (Grenoble); 25 diffraction lines were resolved and analysed with wavelength λ = 1.21 Å on D 1A, and 22 lines with λ = 1.28 Å on D1B. In the case of ThC, it is shown that the results (BTh = 0.07 ± 0.05 Å2 and BC = 0.40 ± 0.08 Å2 at 4 K; BTh = 0.32 ± 0.08 Å2 and BC = 0.68 ± 0.08 Å2 at 250 K) are mainly due to the thermal vibrations. For ThC0.77, we find BTh = 0.23 ± 0.03 Å2 and BC = 0.47 ± 0.05 Å2 at 4 K, and BTh = 0.48 ± 0.04 Å2 and BC = 0.69 ± 0.05 Å2 at 250 K. The enhancements of the Debye-Waller factors compared to the stoichiometric case are attributed to the static distortions induced by the presence of 23% vacancies in the carbon sublattice. The mean-square static displacements of thorium and carbon atoms are found to be about 1% of the lattice parameter \sqrt{\langle \Delta x^{2}\rangle _{\rm Th} = 0.08 ± 0.03 Å and \sqrt{\langle \Delta x^{2}\rangle _{\rm c}\simeq _{\rm Th} 0.05 ± 0.03 Å.
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    Acta crystallographica 36 (1980), S. 966-974 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It has been observed that the reflectivity of the (110) planes of a quartz lamina can be increased by submitting it to a static or alternating electric field. Measurements have been performed on 2.5 and 6 mm thick plates using a curved-crystal spectrometer with DuMond geometry. Photon energies were in the range 50 to 300 keV. Under the proper conditions, the increase in reflectivity is accompanied by negligible loss in resolution. The effects are explained by the occurrence of a quasi-mosaicity.
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  • 73
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 36 (1980), S. 996-1001 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Small-angle scattering experiments of horse-spleen ferritin solutions have been performed at various wavelengths near the K absorption edge of iron, using synchrotron radiation from the storage ring DORIS. The anomalous dispersion of the atomic form factor f as described by f' and if” has been monitored by the dependence of the radius of gyration R and the absorption coefficient μ respectively. There is a 4% increase of R at the absorption edge. The relative full half width of this peak of 0.0016 corresponding to 1 1 eV of the energy scale reflects the drastic variation of f' by 7 electrons. The predictable relation between R and has been verified by the Kramers-Kronig relation. As small-angle scattering is primarily influenced by f', best advantage from anomalous dispersion in small-angle scattering can be taken by measurements very near the absorption edges.
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    Acta crystallographica 36 (1980), S. 1017-1025 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The theory of representations has been used to obtain probabilistic estimates of the two-phase variants and seminvariants for the non-centrosymmetric space groups up to orthorhombic. Some practical applications show that the phase estimations can be useful in direct procedures, mostly for those crystal structures in which the enantiomorph definition is difficult.
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  • 75
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    Acta crystallographica 36 (1980), S. 1041-1043 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In MX2-type structures atoms are always in a sandwich form with an M atom surrounded by two X atoms. The orientation of the M atom is always determined by the two X atoms, e.g. an M atom with γ orientation will always have two X atoms in A and B (or B and A) orientations around it. Therefore, by representing both X atoms by one M atom, the calculation can be reduced to one third of the original since the summation in the structure-factor calculation over all atoms will reduce to the summation over M atoms only. How this can be done is examined in the paper.
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  • 76
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    Acta crystallographica 40 (1984), S. 88-88 
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    Acta crystallographica 40 (1984), S. 167-167 
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    Acta crystallographica 40 (1984), S. 297-305 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A realistic molecular dynamics calculation for naphthalene is presented and a comparison is made between the simulation and the crystallographic data. The molecular dynamics sample consists of 4096 molecules arranged in a volume with cyclic boundary conditions, each molecule being associated with one processing element of the ICL DAP computer. The potential functions used are the same as those used for lattice dynamics, and are developed from atom- atom 6-exp functions. A comparison with a lattice dynamical result establishes the correctness of the program. Temperature is introduced in the usual molecular dynamics way, resulting in a true modelling of anharmonic behaviour. The calculation proceeds at zero pressure throughout, yielding the temperature variation of the crystalline unit cell, the mean molecular orientation and the rigid-body thermal vibration tensors T and L. These are compared with the recently reported results measured by neutron scattering from powder samples and analysed through constrained refinements. The variation of unit-cell volume with temperature is particularly close to the experimental result, though discrepancies begin to be significant in measurements involving the orientational behaviour of the molecules.
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    Acta crystallographica 40 (1984), S. 309-310 
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    Acta crystallographica 40 (1984), S. 309-309 
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    Acta crystallographica 40 (1984), S. 308-309 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The incorrect assignment of atom type leads not only to incorrect thermal parameters but in unfavourable circumstances, such as having a limited data set or through overweighting low-order reflections, to incorrect bond distances.
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    Acta crystallographica 40 (1984), S. 310-310 
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    Acta crystallographica 40 (1984), S. 312-312 
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    Acta crystallographica 40 (1984), S. 340-346 
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    Notes: An a posteriori method of the determination of a correct set of structure-factor phases based on a comparison between the trial and theoretical distribution functions of semivariants, using the χ2 test, makes possible the full utilization of a priori structure information contained in the phase relationships. It is expected that the application of this method should raise the efficiency of existing direct methods.
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    Acta crystallographica 40 (1984), S. 42-50 
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    Notes: Three-periodic nets are connected graphs which permit embeddings having a threefold periodicity. To many crystal structures such nets can be meaningfully assigned and used to express the topology of the structures. It is shown that such a net can be fully characterized by a finite graph in which the edges are labelled in a suitable way. The reversal of the process of assigning a labelled finite graph to a given net can be used to generate nets of real and hypothetical crystal structures in a systematic fashion.
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    Acta crystallographica 40 (1984), S. 116-120 
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    Notes: The internal strain parameter (or the bond-bending parameter) of zinc-blende-structure materials can be obtained from the stress dependence of the intensity of weak reflections in uniaxially stressed crystals. The theory, including dispersion and temperature effects, is presented and applied to the reanalysis of earlier work on gallium arsenide. The results are inconsistent, leaving the bond-bending parameter of this material unknown.
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    Acta crystallographica 40 (1984), S. 502-507 
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    Notes: In this paper is described the realization of an idea due to J. W. M. Dumond who, almost 50 years ago, suggested that Bragg diffraction peaks might be made narrower by multiple reflection [Dumond (1937). Phys. Rev. 52, 872-883]. The optical elements which result belong to a family of harmonic free monochromators, X-ray and neutron polarizers whose properties make feasible many new Bragg diffraction optical systems.
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    Acta crystallographica 40 (1984), S. 264-269 
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    Notes: The hydrous lanthanide oxides comprise a complicated series of both crystalline and amorphous compounds. The amorphous short-range-order (SRO) phase of hydrous erbium oxide is the subject of this work. A thorough discussion of the instrumental arrangement and electronic counting chain for the X-radiation diffraction data collection is included. The scattering profiles for hydrous erbium oxide are shown and details of the ensuing data correction procedures are given. A radial distribution analysis of the calculated interference function, Si(S), was performed. SRO interatomic distances and the first-shell coordination number are reported. The mean Er-O bond distance is found to be 2.36 Å and the erbium metal is nine coordinated. Comparison of the experimental radial distribution curve to ones calculated from crystalline systems lend credibility to the experimentally determined distances.
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    Acta crystallographica 40 (1984), S. 269-277 
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    Notes: A procedure is suggested for the refinement of a set of protein phases and for its extension to a higher resolution, which is a development of the approach of Agarwal & Isaacs [Proc. Natl Acad. Sci. USA, (1977), 74, 2835-2839]. A new set of phases is obtained by combining the starting phases with those calculated from a stereochemically non-conditioned coarse 'atomic' model which is automatically constructed and subjected to a least-squares refinement in reciprocal space. The method has been tested with actinidin data generated from atomic coordinates. Starting from the phases calculated to 3 Å resolution and the amplitudes calculated to 2 Å resolution a new set of phases was obtained with a mean error of 31° for 12 713 non-centrosymmetric reflections in the range to 2 Å. The refinement of the phases to 3 Å, resolution for γ-crystallin IIIb from calf lens and its extension to 2.7 Å resolution resulted in a noticeable improvement in the electron density map.
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    Acta crystallographica 40 (1984), S. 283-291 
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    Notes: The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendellösung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented.
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    Acta crystallographica 40 (1984), S. 313-313 
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    Acta crystallographica 40 (1984), S. 338-340 
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    Notes: The aim of the phase determination is formulated as a minimization of a function of estimated errors in the phases. It is concluded that a good phase-determining procedure in direct methods has to fulfil the following requirements. 1. The probability distributions of seminvariants used should contain the maximal amount of a priori structure information. 2. The whole information contained in probability distributions should be employed. 3. The choice of the starting set and the set of phase relations used should minimize Σ|FH|2 var φH. The procedures that are able to fulfil these requirements are described in the following papers [Hašek (1984). Acta Cryst. A40, 340-346, 346-350, 350-352].
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    Acta crystallographica 40 (1984), S. 331-337 
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    Notes: The interpretation of physical properties of incommensurate modulated crystals leads to the use of their point groups and their total character tables in their superspaces. Examples are chosen of point groups of holohedries of the two hypercubic crystal systems - primitive and body-centred- in four-dimensional space. A geometrical presentation is given of the point group - including its character table - of the primitive hypercubic crystal system, as it is useful for the prediction and simplification of tensorial physical properties of the corresponding crystals. Through geometrical considerations, the exceptional splitting of the hypercubic family of \bb E4 into two crystal systems is easily proved. Finally, the two different relations - according to the parity of n - existing between the point group of the primitive hypercube of \bb En and its subgroup of rotations are explained.
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    Acta crystallographica 40 (1984), S. 350-352 
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    Notes: The proposed method of determination of a correct set of phases is based on a comparison between the trial and theoretical distributions of seminvariants using the Kolmogorov test. If the Kolmogorov test is restricted to a single region of magnitudes where only a small variance around the mean seminvariant value is expected, then the test is reduced to a simple rule. The smaller the number of seminvariants differing significantly from the expected mean value, the more probable the set of phases. In this simple form the Kolmogorov test has been used since the very beginnings of direct methods. In spite of the fact that the method seems to be less efficient than the distribution fitting using the x2 test [Hašek (1984). Acta Cryst. A40, its simplicity and low claim on computing time enables one to survey a large number of trial sets and so to increase the power of the method based on a combination of the Kolmogorov test with the x2 test, or with the low-order distribution moment test.
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    Acta crystallographica 40 (1984), S. 364-366 
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    Notes: A comparison of the two methods available for the calculation of exact values of pseudorotation parameters P, τm, i.e. the Fourier-series (FS) method [Rao, Westhof & Sundaralingam (1981). Acta Cryst. A37, 421-425] and the least-squares (LS) method [Jaskólski (1983). J. Chem. Educ. 60, 980-981] reveals that they yield identical values for τm and P. The variances σ2(τm) and σ2(P) calculated by these methods are, however, different since they have different interpretations.
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    Acta crystallographica 40 (1984), S. 355-363 
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    Notes: By its two-dimensional nature, the Δω, Δ2θ intensity distribution of a Bragg X-ray reflexion has greater angular resolution and greater information content than the corresponding one-dimensional Δω reflexion profile. It allows for the measurement of integrated intensity, exactly and equally truncated, over the full range of θ. Also, it is potentially correctable point by point for extinction and simultaneous diffraction. Consequently, it has inherent capabilities for the estimation of structure-factor values with improved accuracy. To realize this potential, it is necessary to identify and appreciate the various factors which, convoluted together, determine the 2D distribution. Among these factors, important ones are the crystal mosaic/fragment distribution, μ, the X-ray source emission distribution and the wavelength distribution. By first treating the situation for a hypothetical point source, the relation of the reflectivity (or 'level of interaction') with the μ distribution is highlighted. Extension to a real source indicates the probable need for deconvolution in practical cases to extract meaningful estimates of the μ distribution and hence the reflectivity distribution, the most significant measured quantity for accurate structure-factor evaluation. The 2D distribution is discussed in relation to single (H) scattering, multiple (H.{\bar H}) scattering (extinction) and simultaneous (H. K) scattering.
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    Acta crystallographica 40 (1984), S. 374-379 
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    Notes: On the basis of a common characteristic observed in previously derived formulas for the evaluation of triplet phase invariants from either isomorphous replacement data or anomalous dispersion data, it has been found possible to combine mathematical expressions, certain differences of magnitudes, arising in the analysis of the two techniques to form a myriad of new mixed formulas. The common characteristic is that the various types of differences of magnitudes that are involved in the formulas are all definable in terms of the heavy-atom structure. The formulas involve the mixing of terms arising from several isomorphous derivatives or from a combination of such terms with various types of terms arising in anomalous dispersion or the mixing of various terms arising in anomalous dispersion alone. The evaluation of the triplet phase invariants is facilitated by the use of a simple rule, called the General Rule, that is generally applicable to the case of one predominant type of anomalous scatterer. In the case of more than one predominant type of anomalous scatterer, a slightly more complicated calculation is required and is described. Test calculations show that a very large number of invariants may be evaluated by these means with reliabilities that are potentially high, but depend, of course, on the reliability of the experimental data. A benefit from having the large variety of formulas is that triplet phase invariants can be evaluated at many points throughout the range -π to π and their reliability is enhanced because much information is obtained from only the largest differences of magnitudes.
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    Acta crystallographica 40 (1984), S. 394-398 
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    Notes: Using a double crystal diffractometer with an additional crystal between the two crystals used as X-ray-optical polarizer and analyzer the phase relation between mutually perpendicularly polarized wave fields is examined in the Bragg case. The additional crystal is a (110)-surface oriented silicon crystal adjusted for the symmetric 220 Cu Kα1 Bragg case. In the case of coherent excitation of both σ- and π-polarized wave fields in the silicon crystal it is experimentally shown that a unique phase relation exists. In a further experiment it is demonstrated that in the case of incoherent excitation the rocking curve is the sum of the σ- and π-polarized intensities without any phase relation. Owing to the different half width of these two curves, step-shaped flanks of the rocking curve are found at excitation with unpolarized radiation.
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    Acta crystallographica 40 (1984), S. 445-450 
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    Notes: Multiple Laue rocking curves of perfect crystals show a narrow central peak with a width of some 10-3s arc and an additional oscillatory structure. The finite structure of these curves is analyzed for two- and three-crystal Laue arrangements. These profiles can be used for precise determinations of structure factors and for an extension of small-angle scattering experiments to the extreme small-angle regime where large objects and long-range particle correlations become visible. An extremely high angular resolution can be achieved without significant reduction of the intensity, owing to a decoupling of the angular resolution from angular width of the beam. The analytically calculated rocking curves are compared to numerical results and to experimental results and show good agreement with both.
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    Acta crystallographica 40 (1984), S. 459-465 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Diffraction experiments with resonant γ-radiation were performed on a single crystal of silicon at room temperature. The high energy resolution of the Mössbauer effect was used to separate elastically and inelastically scattered radiation. A special experimental setup is described, which in addition allows the determination of the total thermal diffuse scattered intensity. Inelastically scattered radiation was observed in the whole investigated angular range. In the vicinity of Bragg reflections the ratio of the integrated intensities of inelastically to elastically scattered radiation was in very good agreement with the results of calculations using different computer programs based on first-order thermal diffuse scattering theory for a wide range of chosen scan lengths. The measured ratios of the elastically scattered radiation of different Bragg reflections were used to determine the temperature factor B.
    Type of Medium: Electronic Resource
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