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  • 1
    Electronic Resource
    Electronic Resource
    The influence of crystal and sample symmetries on the orientation distribution function of the crystallites in polycrystalline materials (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 889-899 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the most general case the orientation distribution of crystals in a polycrystalline sample is to be described by a function of orthogonal transformations which splits up into two functions of rotations corresponding to right- and left-handed crystals. The properties of these functions are influenced by crystal and sample symmetry. The rotational subgroup of crystal symmetry leads to symmetry relations which may be written in the form of selection rules. Elements of the second kind of the crystal symmetry give rise to a determinability condition, according to which the texture function may be split into a part \tilde{f}(g) which can be determined from polycrystal diffraction experiments and a part \tilde{\tilde{f}}(g) which cannot. The determinability condition may take on three different forms according to whether the crystal symmetry contains a centre of inversion, a mirror plane or a \bar 4 inversion axis. In the case of normal scattering the Laue symmetry is to be considered instead of the true crystal symmetry. The sample symmetry is to be described by a black-white or Shubnikov group containing four kinds of elements which give rise to four kinds of symmetry conditions in the function f(g). The sample symmetry may be a conventional one consisting of one-to-one relationships between crystal orientations. It may, however, also be a non-conventional one defined by an integral relation between an infinite number of crystal orientations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739481001915
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  • 2
    Electronic Resource
    Electronic Resource
    Symmetries in texture analysis (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 59-67 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that a comprehensive symmetry description in polycrystalline bodies needs black-white point groups rather than the usual (one-colour) groups that are sufficient for single crystals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000101
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  • 3
    Electronic Resource
    Electronic Resource
    A generalized library program for texture calculations with even and odd coefficients (1982)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 15 (1982), S. 122-125 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A previously published library program [Wagner, Esling & Baro (1977). Texture Cryst. Solids, 2, 225–241] allowed the creation and storage of the set of numerical values necessary for three-dimensional texture analysis, with the even ranks in the spherical harmonics expansion. To take into account the recent developments in texture analysis, a more general version of this program is proposed, including, besides the calculation for even ranks, its extension to the odd ones. In addition, the formulae and the general analytical expressions, valid whatever the rank l, are given for the set of the calculated constants and functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889882011558
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  • 4
    Electronic Resource
    Electronic Resource
    An effective algorithm for calculation of the Clebsch–Gordan coefficients (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 26 (1993), S. 302-304 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: An algorithm to calculate the numerical values of the Clebsch–Gordan (C–G) coefficients is described. It uses a well elaborated recursive procedure yielding significantly high computation efficiency and accuracy. A 60-line Fortran program that implements the algorithm can be applied to the calculation of various symmetry-adapted C–G coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889892011749
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  • 5
    Electronic Resource
    Electronic Resource
    Evalution of volume fractions of fiber-type texture components (1994)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 27 (1994), S. 358-361 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A method of evaluating the volume fractions of fiber-type texture components in tube-like regions around selected fiber axes is described. The application of the method is illustrated on a rapidly solidified and annealed Fe–6.5mass%Si alloy ribbon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889893010714
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  • 6
    Electronic Resource
    Electronic Resource
    Determination of a Mean Orientation from a Cloud of Orientations. Application to Electron Back-Scattering Pattern Measurements (1996)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 29 (1996), S. 662-666 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The purpose of this work was to determine the orientations of grains in polycrystals using electron back-scattering patterns (EBSP). In order to lower the degree of statistical uncertainty, the orientation of the same grain was measured several times. The orientation of the corresponding grain was assumed to be the mean of the orientations measured. From a theoretical point of view, the way to calculate a mean orientation from several orientations was solved on the basis of the properties of quaternions. The accuracy of the measurements, including the mean and maximum deviation of the orientations established, could be evaluated. The orientation of α plates of Ti-64 products was determined and it was possible to show that the metallurgical state of the parent β phase prior to the β–α phase transformation is likely to influence the orientation spread of the variants inherited from the same β grain, belonging to the same orientation family.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889896006693
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  • 7
    Electronic Resource
    Electronic Resource
    A non-linear positive method to reconstruct the parent textures from the inherited textures in phase transformation (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 206-212 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The orientation distribution function (ODF) of the parent phase is reconstructed from the inherited ODF of the transformed phase, provided that the lattice symmetry of the parent phase is higher than that of the inherited one and that the orientation relation between both phases is known. In the cases of experimental errors or variant selections, the positivity of the ODF of the parent phase is ensured by assuming that it is of quadratic form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889899014879
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  • 8
    Electronic Resource
    Electronic Resource
    The role of the inversion centre in texture analysis (1980)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 13 (1980), S. 544-554 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Polycrystalline samples of non-centrosymmetrical enantiomorphic materials may be considered as two-phase materials consisting of a right-handed and a left-handed phase, each of which has its own texture. Centrosymmetrical crystals may be considered as right- or left-handed at the same time. If the right- and left-handed nature of the crystals is fully to be taken into account then the statistical sample symmetry is correctly to be described by black–white point groups rather than by the ordinary ones. If the sample symmetry does not belong to one of the `grey' groups then the series expansion of the texture functions contains terms of odd order which are blotted out in polycrystal diffraction experiments by virtue of the inversion centre in the crystal symmetry or by Friedel's law. In certain cases it seems possible, however, to obtain an approximation to the odd part by making use of the non-negativity condition in the zero ranges of the texture function. Many important physical properties are centrosymmetric (even if the crystals themselves are not). In these cases the odd part of the texture function does not enter into the expression relating the polycrystal property to the corresponding one of the single crystals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889880012757
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  • 9
    Electronic Resource
    Electronic Resource
    Volume fractions of texture components in polycrystalline materials (1993)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 26 (1993), S. 422-425 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The orientation distribution of crystallites has until now been interpreted by a small number of texture components. In the frame of the harmonic formalism, an analytical method for the accurate determination of the volume fractions of peak-type components in restricted regions is developed without recourse to additional assumptions. Its validity and feasibility are demonstrated through two numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889892013396
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  • 10
    Electronic Resource
    Electronic Resource
    Determination of the odd part of the texture function by anomalous scattering (1981)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 14 (1981), S. 253-255 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The texture function f(g) of a polycrystalline material may be split into two parts \tilde{f}(g) and \tilde{f}(g), where the first one contains the terms of even order l in the series expansion, whereas the second one consists of the odd-order terms. In the case of centrosymmetric crystals, or by virtue of Friedel's law in noncentrosymmetric crystals, the contribution of {\approx}\atop{f} to experimental pole figures is identically zero. Hence it is impossible to determine {\approx}\atop{f} from pole figures obtained by `normal' polycrystal diffraction experiments. It is suggested therefore that anomalous scattering of X-rays or neutrons should be used to determine {\approx}\atop{f} from pole figure measurements directly and the corresponding formulae are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889881009308
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