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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
    Experimental determination of the instrumental transparency function of texture goniometers (2000)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 33 (2000), S. 1162-1174 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The instrumental transparency functions of five commercially available texture goniometers were measured experimentally with six monocrystalline samples cut in different orientations from a large highly perfect silicon crystal with a rocking curve of less than 0.01°. Transparency functions were measured in steps of 0.02 to 0.2° in the pole-figure angles α, β. The window size Δα depends on the Bragg angle θ in the form 1/sinθ; the window size Δω is constant for each goniometer. The dominant instrumental parameter determining the long axis Δα of the pole-figure window is the axial width of the detector entrance slit. This parameter is smallest for area detectors (smaller by more than an order of magnitude compared with conventional scintillation detectors as well as one-dimensional position-sensitive detectors). The main features of the pole-figure window and their dependence on the instrumental parameters can be deduced fairly well from a simple geometrical model. The particular shapes of the transparency functions of the studied goniometers are markedly different. Particularly, they are not very well represented by Gauss functions. The two-dimensional transparency function can be fairly well characterized by its α and β profiles. The normalized profiles are virtually independent of the goniometer angles 2θ and α. The increasing size of the pole-figure window with decreasing θ puts a lower limit on the Bragg angle below which pole-figure measurement ceases to be meaningful.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889800007251
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  • 4
    Electronic Resource
    Electronic Resource
    Diffraction contrast in X-ray radiographic images of octahedrite meteorites (2001)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 34 (2001), S. 566-572 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Slices of ∼12 mm thickness cut out of an octahedritic iron–nickel meteorite of the Gibeon shower were investigated by conventional X-ray transmission radiography. When the direction of the incident X-ray beam is parallel to one or two of the four habit planes of the kamacite lamellae, black–white contrast lines are observed in the radiographs. These lines are attributed to Bragg reflection, at lattice planes parallel to the lamellae planes, of a narrow band of wavelengths filtered out of the incident white spectrum by absorption in the sample.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889801009529
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  • 5
    Electronic Resource
    Electronic Resource
    The development of the rolling texture in copper measured by neutron diffraction (1971)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 4 (1971), S. 303-310 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Three-dimensional orientation distribution functions of the crystallites in copper sheets, cold rolled to different degrees of reduction, have been determined using neutron diffraction pole figures. The main features of the textures may be represented by the orientation `tube' already described in prior publications. Two ranges of rolling reduction can be distinguished, a lower one (30 to 50%) and a higher one (70 to 95%) the texture changes of which correspond to those calculated after the Taylor theory. In an intermediate range (50 to 70%) a different deformation mechanism occurs which leads to an intermediate (001) [110] texture component. It is supposed that anisotropic hardening may have occurred in this range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889871007027
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  • 6
    Electronic Resource
    Electronic Resource
    The texture transition in α-brasses determined by neutron diffraction (1972)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 5 (1972), S. 27-40 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: Three-dimensional orientation distribution functions were calculated from (111), (200), (220) and (311) pole figures for α-copper–zinc alloys in the concentration range from 0 to about 30% zinc. The pole figures were measured by neutron diffraction. The main feature of the texture transition is a continuous shortening or cut off of the tube of preferred orientations present in the copper texture beginning with the end orientation (̃\bar 112) [1\bar 11]. This orientation has nearly completely disappeared at about 5% zinc. Simultaneously its twin orientation (011) [100] appears. A second feature is the continuous decrease of maximum density of all texture components over the whole concentration range. The results support Wassermann's theory of mechanical twinning as the reason for the texture transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889872008684
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    The iterative series-expansion method for quantitative texture analysis. I. General outline (1989)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 22 (1989), S. 439-447 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The orientation distribution function (ODF) of the crystallites of polycrystalline materials can be calculated from experimentally measured pole density distribution functions (pole figures). This procedure, called pole-figure inversion, can be achieved by the series-expansion method (harmonic method). As a consequence of the (hkl)−({\bar h}{\bar k} {\bar l}) superposition, the solution is mathematically not unique. Rather it contains a range of possible solutions (kernel) which is only limited by the positivity condition of the distribution function. The complete distribution function f(g) can be split into two parts \tilde{f}(g) and \tilde{\tilde f}(g) expressed by even- and odd-order terms of the series expansions. For the calculation of the even part \tilde{f}(g), the positivity condition for all pole figures contributes essentially to an `economic' calculation of this part, whereas, for the odd part, the positivity condition of the ODF is the essential basis. Both of these positivity conditions can be easily incorporated in the series-expansion method by using several iterative cycles. This method proves to be particularly versatile since it makes use of the orthogonality and positivity at the same time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889889005261
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  • 9
    Electronic Resource
    Electronic Resource
    Orientation distribution, elastic and plastic anisotropy in stabilized steel sheet (1969)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 2 (1969), S. 116-128 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The texture of commercially produced stabilized steel in the temper rolled condition has been represented by a three-dimensional orientation distribution, defined by a set of coefficients of a series of generalized spherical harmonics. The coefficients have been used to calculate the elastic and plastic properties in the plane of the sheet and comparison is made between the predicted and experimental values. Errors in the experimental determination of pole figures have been analysed and estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889869006704
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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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