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  • International Union of Crystallography (IUCr)
  • Annual Reviews
  • 2005-2009
  • 1985-1989  (2,162)
  • 1980-1984
  • 1986  (2,162)
Collection
Publisher
Years
  • 2005-2009
  • 1985-1989  (2,162)
  • 1980-1984
Year
  • 1
    Electronic Resource
    Electronic Resource
    X-ray particle-size broadening (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 6-13 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray diffraction profiles and Fourier coefficients are given for particles distributed according to experimentally verified size distributions. Calculations are based upon the log normal distribution of sphere diameters and intercept lengths in addition to a normal distribution of column heights. It is found that the diffraction profile is not sensitive to the fine details of the distribution but rather the mean column height and the column-height variation coefficient. Errors in particle-size determinations will result from an improper choice of the variation coefficient. Two simplified models are given that describe the diffraction profiles for a large range of variation coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099981
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  • 2
    Electronic Resource
    Electronic Resource
    The diffraction pattern of projected structures (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 36-43 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method for calculating the properties of structures obtained by projection is developed and applied to a three-dimensional generalization of the Penrose tiling. The diffraction pattern is shown in general to consist of a dense set of delta-function peaks. For the Penrose model the pattern in addition has the symmetry of the icosahedron.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099932
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  • 3
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    The determination of absolute structure. III. An ambiguity table for the non-centrosymmetric crystal classes (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 57-57 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The general term 'determination of absolute structure' is more precisely defined for each non-centrosymmetric crystal class.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099890
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  • 4
    Electronic Resource
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    Two-dimensional space groups with sevenfold symmetry (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 55-56 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Fivefold and sevenfold symmetry operations are, of course, incompatible with repetition by a lattice but, with the appearance of structures involving curved sheets, they and other non-crystallographic operations must now be taken into consideration as possibilities of non-Euclidean crystallography develop. Here are described the symmetry groups which might be called 732 and 73m and which may be found in two-dimensional manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099907
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  • 5
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    Journal of materials Research (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 80-80 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099853
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  • 6
    Electronic Resource
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    Measurement and correction of secondary extinction in CaF2 by means of synchrotron X-ray diffraction data (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 106-110 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The analysis of the full-width at half-maximum (FWHM) of X-ray diffraction profiles measured with monochromatic synchrotron radiation enables the evaluation of the mosaic spread of the sample. This method presupposes the high collimation of synchrotron radiation (FWHM ̃20” of arc). As an example the results from a CaF2 crystal sphere (90 μm diameter) are presented. The reflections strongly affected by extinction show a significantly greater FWHM, thereby indicating at once the need for an extinction correction. A mosaic spread of 75(3)” of arc was determined from the FWHM of all reflections recorded in the step-scan mode, which was used to correct the secondary extinction and to estimate the radius R of the mosaic blocks [R = 4 (1) μm].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099798
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  • 7
    Electronic Resource
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    Asymptotic Bragg diffraction. Single-crystal surface-adjoining-layer structure analysis (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 116-122 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The angular dependence of the X-ray pure-diffraction intensity I(θ) has been measured in Ge and Si single crystals (surface covered with natural oxide films) by means of triple-crystal diffractometry. Measurements were extended to specimen-crystal angular deviations from the Bragg angle of up to 500 Bragg-peak half- widths. The I(θ) data at such large deviation angles are informative of both static and dynamic Debye-Waller-factor variation over crystal depth, the achievable spatial resolution turning out to be of the order of 1 nm. The high spatial resolution of the asymptotic Bragg diffraction made it necessary to consider in theory the layer-to-layer variation of both the scattering characteristics (Debye-Waller factor) and the interplanar spacings. A theoretical treatment of the problem is presented. Reconstructed Debye-Waller factors for the first four atomic planes, counting from the crystal-oxide boundary, are 0.3, 0.4, 0.7, 0.7 and 0.6, 0.6, 0.9, 1 for Ge and Si, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099762
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  • 8
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    Statistical geometry. IV. Maximum-entropy-based extension of multiple isomorphously phased X-ray data to 4 Å resolution for α-lactalbumin (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 197-202 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The simplest level of the statistical geometric (SG) or maximum-entropy (ME) approach to X-ray structure refinement is applied to the task of trying to extend the resolution of electron-density maps for a small protein (α-lactalbumin). The refinement was started from X-ray structure factor data to 4 Å resolution, which had been phased by multiple isomorphous replacement (MIR), and it was found that, even at this simple level, the ME-based approach yields a significant improvement in the maps and gives encouragement to the more general applications of these methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099531
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  • 9
    Electronic Resource
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    Statistical inference and crystallite size distributions (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 30-35 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An information theory approach is devised in order to obtain crystallite size distributions from X-ray line broadening. The method is shown to be superior to those based on Fourier expansions, as illustrated by numerical examples and a realistic situation. The powder model of Warren and Averbach is considered, in which the sample is thought of as a 'column-like' structure of unit cells perpendicular to the diffraction plane. Errors in excess of 100% arise as a result of truncating the diffraction peak. It is shown that, with the present approach, the corresponding figure is reduced to 5%, which confirms the power of information theory, and makes this method especially convenient in those cases in which there are large overlaps between the tails of two diffraction peaks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099944
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  • 10
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    Crystal structure analysis: a primer by J. P. Glusker and K. N. Trueblood (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 206-207 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099452
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  • 11
    Electronic Resource
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    Electronic and atomic collisions edited by M. J. Coggiola, D. L. Huestis and R. P. Saxon (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 208-208 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099427
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  • 12
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    The use of non-local constraints in maximum-entropy electron density reconstruction (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 212-223 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Different expressions of the maximum-entropy estimates of the electron density function, corresponding to different prior information are obtained. They show that no general-purpose configurational entropy of density maps exists. Some universal properties of the modellings are discussed. In particular, the meaning of super-resolution is clarified. The information of lower and upper bounds of the electron density is not in general strong enough to produce atomic maps. Atomicity is then introduced as non-local constraints and applied to the problem of phase extension using experimental data and low-resolution model phases. In all cases, the knowledge of phases up to 3.5-3 Å and observed moduli up to 1.5-1 Å allows an estimate of the electron density of roughly the same quality as the 1 Å map obtained from a Fourier summation to be produced.
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    URL: http://dx.doi.org/10.1107/S0108767386099397
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  • 13
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    Triplet phase invariants from single isomorphous replacement or one-wavelength anomalous dispersion data, given heavy-atom information (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 246-253 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Certain general algebraic formulas for computing triplet phase invariants become accessible when structural information is available concerning the replacement atoms in isomorphous replacement or the predominant type of anomalously scattering atoms in one-wavelength anomalous dispersion experiments. The formulas of interest are presented and subjected to a number of test calculations to obtain insight into their accuracy and to determine the effects of errors in the data. The formulas are simple to calculate and some possible strategies for their use are discussed.
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    URL: http://dx.doi.org/10.1107/S010876738609935X
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  • 14
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    The electron distribution in silicon. A comparison between experiment and theory (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 271-281 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Deformation and valence-electron densities in silicon are derived via Fourier summation and multipole refinement of highly accurate measurements of X-ray structure factors. These results provide a new perspective for the comparison between theory and experiment. The model electron density derived from experiment is in quantitative agreement with recent solid-state calculations, but not with earlier experimental results reported by Yang & Coppens [Solid State Commun. (1974), 15, 1555-1559].
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    URL: http://dx.doi.org/10.1107/S0108767386099312
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  • 15
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    Fluorescence X en incidence rasante: application au trace des profils d'implantation (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 304-309 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: When the incident angle α of an X-ray beam (λ ∼ 1 Å) on a surface is increased, the penetration depth changes from 30 Å (α = 0.1°) to 10 μm (α ∼ 1°). The X-ray fluorescence observed is sensitive to the chemical composition of the irradiated layer. If the composition changes with the depth z (for example in the case of ionic implantation), the spectrum depends on α and the variation with α of the X-ray emission intensity of one of the elements is related to its concentration profile c(z). It is shown that c(z) can be determined with a layered-medium approximation. The profile thus obtained is in good agreement with that obtained by the destructive and heavy secondary ionic emission (SIMS) method. The same mathematical treatment can be used, from X-ray measurements, in order to determine other profiles (amorphization etc.).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767386099208
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  • 16
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    Neils Bohr centennial conferences, 1985: Recent developments in quantum field theory edited by J. Ambjørn, B. J. Durhuus and J. L. Petersen (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 136-136 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108767386099671
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  • 17
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    The determination of the orientation of anthracene molecules in the unit cell by a refractivity method (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 137-139 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The monoclinic anthracene crystal is used as an example to demonstrate the feasibility of optimizing the orientation of molecules in the unit cell by matching calculated and experimental refractivity ellipsoids using a simplex algorithm. The calculated refractivity ellipsoid is determined by use of an empirical formula using bond directional polarizabilities. Optimization of the molecular orientations to provide the best fit to the experimental ellipsoid starting from several assumed orientations results in fits for which the maximum deviation from the experimental molecular orientation was no more than 10°. The method can be applied to other monoclinic molecular crystals directly and could be extended to other crystal systems with anisotropic optical properties.
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    URL: http://dx.doi.org/10.1107/S0108767386099634
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  • 18
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    Single-crystal structure of rapidly cooled alloys with icosahedral symmetry. I. experimental analysis (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 156-164 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Crystallographic analysis is applied to a set of electron diffraction patterns taken from a rapidly cooled Al-Mn alloy to construct reciprocal-lattice patterns in agreement with the observed icosahedral results. The analysis leads to a proposed atomic scale model which is derived from two sets of experimental modulations, each of which has six independent modulation vectors. The underlying structure has a lattice, the unit cell of which involves 32 atomic sites with the required symmetry properties. The appearance of the experimental electron diffraction patterns is explained either by the coherent arrangement of this lattice with an irrational sublattice or by an independent set of modulations. The relationship of this structure to three-dimensional nonperiodic Penrose tilings is explored.
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    URL: http://dx.doi.org/10.1107/S0108767386099609
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  • 19
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    The role of the crystal rotation axis in experimental three- and four-beam phase determination (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 178-184 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The geometry of four-beam diffraction and procedures for generating it systematically are described. These utilize relatively simple Renninger-type experimental arrangements. The four reciprocal-lattice points involved in each four-beam interaction are located at the comers of rectangles or symmetrical trapezoids in reciprocal space. One of the sides, or a diagonal, of each such quadrilateral serves as the axis of the azimuthal rotation of the crystal. Experiments designed to compare the relative merits of different types of rotation axes have been carried out. It is found that axes of twofold (or higher) symmetry provide advantages over alternate arrangements for experimental phase determination. Four-beam interactions are then generated systematically and in greater abundance than in all other n-beam interactions combined (n 〉 2). Such interactions usually provide stronger phase indications than comparable three-beam interactions. The experiments also showed that, although the phase of an 'invariant' quartet is clearly invariant to the choice of unit-cell origin, it is not necessarily invariant to a change of rotation axis from one two-fold axis to another.
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    URL: http://dx.doi.org/10.1107/S0108767386099579
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  • 20
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    Positional parameters obtained with anharmonic temperature factors (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 356-362 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Comparisons of distances between the positions obtained from harmonic and anharmonic refinements lead to the conclusion that the positional parameters may have different physical meanings for the two cases. The mean positions are obtained if the temperature factor (t.f.) has no first-order terms in the reciprocal-lattice vector Q (harmonic t.f., Fourier transforms of the Gram-Charlier series); if there are first-order terms in Q, other positions will be obtained whose meaning needs to be established. The advantages associated with the mean positions are described, and the disadvantages associated with other positions are illustrated with an example from the literature. A procedure is described in which the physical meaning (if there is any) of a non-mean position can be established and the mean position calculated. The problem of parameter bias is analyzed and numerical results are discussed for three structures. Provided the anharmonic model produces a significantly better fit to the experimental data, it is concluded that better estimates of the mean positions are obtained with anharmonic than with harmonic t.f.'s
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    URL: http://dx.doi.org/10.1107/S0108767386099117
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  • 21
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    Green's tensor for a cubic crystal (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 202-203 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The equilibrium equations of classical elasticity for a cubic crystal are solved and Green's tensor for elastic displacements is derived.
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  • 22
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    Secondary extinction in an anisotropic crystal (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 464-469 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The formalism for secondary extinction developed by Kato [Acta Cryst. (1976), A32, 453-457, 458-466] is extended to apply to a crystal with anisotropic strain. If an anisotropic correlation for the lattice phase factors is assumed, the formalism can be developed in the same way as for an isotropic crystal. If the geometric average of the correlation lengths of the phase factors is sufficiently smaller than the extinction distance, the ensemble averages of the intensity fields satisfy a set of energy-transfer equations of the same form as in an isotropic crystal. The distribution function of the deviation angle from the exact Bragg condition for the misorientation model of a crystal is given using the notation introduced by Coppens & Hamilton [Acta Cryst. (1970), A26, 71-83].
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  • 23
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    Direct measurements of the complex X-ray atomic scattering factors for elements by X-ray interferometry at the Daresbury Synchrotron Radiation Source (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 456-464 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A scanning X-ray interferometer system [Hart & Siddons (1981). Proc. R. Soc. London Ser. A, 376, 465-482] has been rebuilt for operation at the SERC Daresbury Synchrotron Radiation Source (SRS). The SRS permits an increase in energy resolution by one decade and simultaneously an intensity gain of one thousand times, though in practice the solid-state detector employed limited the peak intensity utilized so that experiments which hitherto demanded one month of counting time are now performed at higher spectral resolution in 2-4 h. Absolute measurements are reported of f' and f” for the K edges of most elements between 34Se and 26Fe and for L edges of 79Au and 74W over energy ranges of about ± 2 keV near absorption edges and scans with better than 1 eV energy resolution of X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectra near the edges. Over wide energy ranges the results are compared with the most recent calculations of Cromer & Liberman [Acta Cryst. (1981), A37, 267-268], which are now easily available to workers in the field.
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  • 24
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    X-ray birefringence and forbidden reflections in sodium bromate (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 478-481 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Reflections forbidden by a screw-axis rule are observed in sodium bromate with synchrotron radiation near the bromine K absorption edge, where X-ray birefringence occurs. The intensities vary with azimuthal angle according to theoretical predictions and indicate a larger magnitude for the birefringence than did earlier experiments. This technique is a method of selective diffraction in which atoms of a single element in a single chemical state contribute to the signal, and it can reveal their positions with precision.
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    URL: http://dx.doi.org/10.1107/S0108767386098859
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  • 25
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    The intensity fringes of three coupled waves in crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 191-197 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two different kinds of interaction between three waves D0, Dh and Dg in a perfect crystal are investigated in the case of Laue scattering using the Takagi-Taupin equations. Polarization effects (coupling between {\hat \sigma} and {\hat \pi} waves) are neglected, and it is assumed that the incoming vacuum wave D0(e) has a small wave-front area whose spatial extension is simulated by a point source on the crystal surface. The solutions of the diffraction equations thus constitute the boundary-value Green functions for the wave fields. In the first case it is assumed that Dg is only indirectly coupled to D0. In the second case energy is allowed to be exchanged between D0 and Dh and between D0 and Dg, but no Dh-Dg interaction is present. In both of these situations the field amplitudes are given by expressions that contain simple products of zeroth- and first-order Bessel functions. It is suggested that the intensity pattern can be observed directly. The transition to an incoming plane wave is outlined, and it is also demonstrated that the hyperbolic intensity fringes generated by two spherical waves can be deduced from the derived expressions.
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  • 26
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    International Union of Crystallography announces the Ewald Prize (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 204-204 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Translation funcions: the minimization of structure-independent spurious maxima erratum (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 204-204 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Langs [Acta Cryst. (1985), A41, 578-582], the expression Ah(AkAl)k|Gh(GkGl)k] appearing in the text on pages 580 and 582 should include a cosine term and be written as Ah(AkAl)k| Gh( GkGl cos Φh.k)k|.
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    The structure of surfaces edited by M. A. Van Hove (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 205-206 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Ferroelectrics and related materials edited by G. A. Smolenskii (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 207-208 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Determination of the velocity of sound in crystals by time-of-flight neutron diffraction (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 514-525 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a neutron Laue (time-of-flight) experiment, the nature of the thermal diffuse scattering by elastic waves depends on the ratio β, of the sound velocity in the crystal to the neutron velocity. For slower-than-sound neutrons, there is a certain range of β for which a 'wavelength window' appears in the incident beam; TDS is forbidden for all wavelengths lying within this window. The window is best observed in back scattering, and for a scattering angle close to 180° the centre of the window coincides with the Bragg wavelength. At the edges of the window, the TDS intensity rises abruptly to two sharp peaks, one due to phonon emission and the other to phonon absorption. The sound velocity is derived by measuring the time of flight of either peak. The method is illustrated by applying it to pyrolytic graphite, which was examined using the neutron spallation source ISIS.
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    A new approach to multibeam X-ray diffraction using perturbation theory of scattering (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 525-533 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Perturbations to conventional two beam X-ray diffraction arising from multibeam scattering effects have been studied theoretically. A simple analytical expression for the diffracted wave field and intensity near a multiple excitation is derived by using the perturbation theory of scattering of electromagnetic waves. Although it cannot be applied to the center of a multibeam diffraction peak, it does show explicitly the asymmetry effect observed in experiments and its phase dependence in the neighborhood of the multibeam point. A numerical calculation for the \bar 11\bar 1 Umweganregung peak on the almost-forbidden 442 reflection of silicon gives excellent agreement with experimental data and exact n-beam computer calculations based on conventional dynamical theory. From the analytical expression, a simple rule is derived for phase determination in centrosymmetric crystals. A general 'pseudo-four- beam' case where no asymmetry effect exists is also discussed as another example of the applications.
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    Space-group analyses of thin precipitates by different convergent-beam electron diffraction procedures (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 368-380 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Convergent-beam electron diffraction point- and space-group analyses were performed on thin γ' precipitate plates, which had been extracted from an A1-15 wt% Ag alloy aged for either 30 or 120 min at 623 K. Although the space groups of precipitates in both samples were determined to be P63/mmc, it is shown that different results can be obtained, depending on the method of convergent-beam electron diffraction analysis that is employed. Comparative analyses using a pure α-titanium standard demonstrate that the limited thickness of the plate-shaped precipitates is responsible for the variable results, suggesting a preferred method for point- and space-group determination of thin particles.
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    IMPAS–A simple structure determination procedure based on intermolecular Patterson vectors (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 380-386 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A computer method for interpreting Patterson functions of crystals belonging to space groups of higher symmetry than P1 is described. A table of all Patterson peaks in the entire cell is initially searched for vectors between symmetry-related atoms. Such 'generalized Harker vectors' are identified not only by known symmetry-fixed components, but also by statistical criteria based on a systematic search for pairs of vectors which relate additional atoms to the pair involved in the generalized Harker vector. Subsequent searches, using the same basic principle, are carried out to find additional atoms. Pairs of vectors, whose components add up to the previously established Harker vector, indicate newly found atom positions after appropriate transformations into crystal space. The correctness of these atom positions can be further tested by applying all symmetry operations of the space group in question and looking for a complete set of related vectors. In contrast to many other Patterson search methods no information about known molecular fragments is requested. Also described are four structures which were solved with the IMPAS procedure following unsuccessful attempts to solve them by direct methods.
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    Dynamical diffraction calculations for RHEED and REM (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 545-552 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The multislice formulation of the many-beam dynamical diffraction theory has been applied to the Bragg case of electron diffraction for the extended surface of a perfect crystal and also for a crystal surface with a surface step. The wavefunctions within and outside the crystal have been calculated and used to derive the standing-wave pattern in the top atomic layers of the crystal, the intensities of the reflection high-energy electron diffraction (RHEED) pattern and the contrast of the reflection electron microscopy (REM) image. Calculations made for the diffraction of 19, 40 and 80 keV electrons from (111) surfaces of Pt and Au demonstrate the channeling of electrons under the conditions of surface resonance, the perturbation of the standing-wave field in the crystal by a one-atom-high surface step and the REM contrast for a through-focus series of images of a surface step. The method is applicable to models including surface relaxations and reconstructions and any kind of local defect of the surface or of the bulk crystal.
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    X-ray diffraction of multilayers and superlattices (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 539-545 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recursion formulae for calculating the reflected amplitude ratio of multilayers and superlattices have been derived from the Takagi-Taupin differential equations, which describe the dynamical diffraction of X-rays in deformed crystals. Calculated rocking curves of complicated layered structures, such as non-ideal superlattices on perfect crystals, are shown to be in good agreement with observed diffraction profiles. The kinematical theory can save computing time only in the case of an ideal superlattice, for which a geometric series can be used, but the reflectivity must be below 10% so that multiple reflections can be neglected. For a perfect crystal of arbitrary thickness the absorption at the center of the dynamical reflection is found to be proportional to the square root of the reflectivity. Sputter-deposited periodic multilayers of tungsten and carbon can be considered as an artificial crystal, for which dynamical X-ray diffraction calculations give results very similar to those of a macroscopic optical description in terms of the complex index of refraction and Fresnel reflection coefficients.
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    An analytical function for absorption correction (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 19-23 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new analytical function is proposed for absorption correction. It is expressed by surface harmonics with polar angles that specify the primary and secondary beam directions. This function has an advantage over Fourier expansion because it is rotationally invariant. Two empirical, methods are used to determine the expansion coefficients. One uses the intensity deviations of equivalent reflections, and the other uses the calculated intensities at the stage of structure refinement. The utility of the analytical function is demonstrated with a model and with actual data.
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    Union Sponsorship and Financial Support for International Meetings (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 80-80 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Nondiagonal momentum density of Si by coherent inelastic X-ray scattering (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 86-98 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: When the coherent superimposition of two (nearly) plane waves is used as the initial photon state of an inelastic X-ray scattering experiment on solids (coherent Compton scattering), information can be obtained about the projection of nondiagonal elements of the one-particle density matrix in momentum space on the scattering vector q, provided the requirements of the impulse approximation are fulfilled. The double differential scattering cross section for this new scattering phenomenon is derived and then subjected to impulse approximation. It is further demonstrated that the standing wave pattern, which on passing the Bragg reflection range is sweeping the atomic sites, yields an appropriate approach to the desired initial photon state for coherent Compton scattering. Experimental coherent Compton spectra from 111 and 220 Bragg reflections are used to extract the corresponding projections of nondiagonal elements of the density matrix. Possible experimental improvements are discussed.
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    Program construction for macromolecule atomic model refinement based on the fast Fourier transform and fast differentiation algorithms; erratum (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 57-57 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In Lunin & Urzhumtsev [Acta Cryst. (1985), A41, 327-333] references to Lifshitz (Agarwal, 1981) on pages 327 and 329 should be amended to Lifchitz (Agarwal, 1981).
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    Commission on Journals. Author Grievance Procedure (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 407-407 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Lattice complexes and limiting complexes versus orbit types and non-characteristic orbits: a comparative discussion. Erratum (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 406-406 
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    Notes: In the paper by Koch & Fischer [Acta Cryst. (1985), A41, 421-426] the words 'or more' are missing on p. 423 (left column, sixth line from bottom). The sentence should read: Then the point configurations of the intersection form another lattice complex or, in very exceptional cases, two or more other lattice complexes (for a proof see Koch, 1974).
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    An atlas of hyperstereograms of the four-dimensional crystal classes by E. J. W. Whittaker (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 407-407 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    L'ordre et le désordre dans les matériaux edited by F. Reynard, N. Clément and J. J. Conderc (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 408-408 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Medium-energy ion reflection from solids by E. S. Mashkova and V. A. Molchanov (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 408-408 
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    Appointments in the IUCr Office (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 288-288 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Numerical vector representation of physical properties of crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 293-296 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Notes: The idea of a numerical vector representation (NVR) of a physical property of a crystal, introduced in a previous paper [Fumi & Ripamonti (1980). Acta Cryst. A36, 535-551], is a convenient way to account for its rotational invariance properties. The main advantages of the NVR are the possibility of dealing with single invariance relations independently from the others and the direct display of the simplest features of the invariance relations (vanishing of components, equalities or proportionalities among components, independence of components and 'form invariance' with respect to interchange of components). The NVR also provides a direct-expansion method of the set of tensor components of a crystal property in terms of a minimal subset. A simple rule is reported for obtaining a NVR of any given tensorial set (i.e. a set of given rank and rotational and permutational symmetry) in the axial rotational groups. The use of the NVR in establishing general results such as isomorphisms between tensorial sets is also illustrated. Finally, a few examples are reported of NVR's for high-rank tensorial sets in axial rotational groups (specifically the second-order piezoelectric tensor, the second-order Pockels elastooptic tensor and the fourth-order elastic tensor).
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    Novel application of anomalous (resonance) X-ray scattering for structural characterization of disordered materials by Y. Waseda (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 135-135 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Surface crystallography: an introduction to low energy electron diffraction by L. J. Clarke (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 135-136 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Comparison of vector search and feedback methods for finding heavy-atom sites in isomorphous derivatives (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 325-334 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Heavy-atom sites in an isomorphous replacement derivative are usually found by inspection of a difference Patterson map. A systematic search procedure is necessary in the presence of high non-crystallographic symmetry as in a crystalline virus. A reciprocal-space equivalent of the Patterson search procedure has been developed. Furthermore, it is shown that the Patterson search is closely analogous to the usual 'feedback' tests applied in checking a proposed site. The separation of self and cross vectors in the Patterson map is shown to have its equivalent in reciprocal space. The procedure was used to identify the heavy-atom sites and the particle position in crystals of a human common cold virus.
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    Group analysis of octahedral librations involved in phonon-induced displacive phase transitions in perovskite-related ABX4 compounds (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 318-325 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The group-theoretical analysis of phase transitions in perovskite-related ABX4 compounds using the framework of Landau's theory for second-order transitions is outlined. It is assumed that the only symmetry-reducing distortions during these transitions will be the tilting of rigid BX6 octahedra as a consequence of the softening of a particular librational phonon mode. The analysis is applied to phase-transition sequences in CsFeF4, CsVF4, RbFeF4, RbVF4, RbAlF4 and TlAlF4 and compared with available experimental results. For many transitions the prediction of such a second-order transition is borne out by the experiments, which justifies the hypothesis of rigid tilting octahedra. General conclusions about the character of this type of transition are drawn and the allowed transition sequences are examined in terms of the diffraction features (i.e. diffraction typologies) of the involved phases.
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    The intercomparison of Bragg X-ray reflections from a small single crystal – zero-wavelength-dispersion profile measurement (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 435-441 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In conventional one-dimensional profile measurement procedures, either by diffractometry ('counter' profile) or by photography ('film' profile), intercomparison of Bragg reflections from a small single crystal, c, in a given experiment is rendered difficult, or impossible, by their wide variation in size with θc. Using synthetic I(Δω, Δ2θ) distributions, obtained by convolution of four components, the mosaic spread of the specimen crystal μ, the emissivity distribution of the source, σ, its wavelength distribution, λ, and the detector aperture, δ, analysis shows how the 'counter' and 'film' profiles change with scan mode. In particular, it is shown that the 'film' profile obtained using an ω/2θ (s = 2) scan mode does not involve wavelength dispersion, so that the profile distribution can yield information about μ for each reflection and therefore about small differences in mosaic spread (and hence reflectivity) between reflections. Possible means of obtaining this profile using film or counter procedures are outlined.
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    On the theory of six-beam X-ray spherical-wave diffraction (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 441-449 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A general formula is obtained for the intensity distribution in the film behind a single crystal in the case of spherical-wave X-ray multiple diffraction. The theory takes into account the phase shift of the waves not only inside the crystal but also in the vacuum before and after the crystal along the wave path source-crystal-film of length L. The topographic images are calculated in the case of (220/242/044/\bar 244/\bar 202) six-beam diffraction of Cu Kα radiation in a germanium crystal of thickness 0.2 mm for different values of L. The enhancement of the anomalous transmission effect is weakly displayed on the topographs because of strong scattering of the radiation inside the crystal. The intensity distribution depends on L. The possibility is shown of focusing X-rays to a considerable extent.
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    Modified two-beam description of X-ray fields and intensities near a three-beam diffraction point. Second-order solution (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 449-456 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The previously developed first-order modification of two-beam diffraction near a third reciprocal-lattice point [Juretschke (1984). Acta Cryst. A40, 379-389] is extended to second order. To this order a modified two-beam description is still retainable, and the normal modes persist in their original polarization, but now with respect to two-beam asymptotes rotated and with a Bragg angle altered relative to the original two-beam case. Integrated intensities are evaluated for modified strong and weak primary two-beam symmetric Bragg reflections, in the Bragg-Bragg and Bragg-Laue configurations, and some implications of the results are discussed.
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    Structure and statistics in crystallography edited by A. J. C. Wilson (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 206-206 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    X-ray crystallography by E. M. Uygur (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 136-136 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Semiclassical descriptions of atomic and nuclear collisions edited by J. Bang and J. De Boer (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 136-136 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Improved Fourier coefficients for maps using phases from partial structures with errors (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 140-149 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Unrefined or partially refined models of macromolecules are generally incomplete and typically have large coordinate errors. It is shown that phase probability equations appropriate for a perfect partial structure lead to inaccurate estimates of phase probabilities in such cases. Therefore, it is necessary to use equations that have been derived allowing for errors in the partial structure. A method is given to estimate the parameter σA in these phase probability expressions from the observed and calculated structure factor amplitudes. From the variation of σA with resolution, one can estimate the mean coordinate error for the model. Electron density maps calculated using partial structure phases are biased towards the partial structure. When there are coordinate errors, a new expression for the non-centric Fourier coefficients [(2m|FN| - D|FcP|) exp(iαcP)] is required to suppress this model bias. Judged by correlation coefficients comparing electron density maps with the correct and the partial structure maps, the Fourier coefficients derived here are superior to others currently in use.
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    Single-crystal structure of rapidly cooled alloys with icosahedral symmetry. II. Theoretical analysis - internal modulations (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 164-172 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The icosahedral cubic cell, derived in the first of this set of two papers, is further developed. Rules for the occupancy of atomic sites are derived based on periodic modulations over the reference lattice. The form of the derived structure, which involves partial Fibonacci sequence stacking, suggests that the true structure is the limit of a superposition of successively larger periodic sequences. The structure factor for the limiting (nonperiodic) structure is derived and some physical insights into the application of almost periodic functions to icosahedral phase Al-Mn are given.
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    Accurate measurement of the Si structure factor by the Pendellösung method (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 469-478 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The X-ray structure factor of Si was measured for 30 net planes from the thickness dependence of the integrated intensity on the λ scale. In ten low-order planes, the accuracy level was estimated to be 0.05% in the probable error. Therefore, the deviation from the standard model of Hartree-Fock isolated atoms under harmonic oscillation could be determined with high precision. In the remaining net planes, the accuracy level was 0.1%. Dawson's rule (that even and higher-order reflections should be normal) was well satisfied for eight net planes higher than 660. Against this background, some Fg values of odd and middle-order planes deviate from the standard model. In the difference Fourier map, not only the bonding charge and the charge deficit in the anti-bonding region but also a slight excess near the atomic position were recognized.
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    On the wavelength dependence of the reflectivity of one-dimensionally distorted crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 481-483 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Scaling properties of the integrated reflectivity of non-absorbing perfect or ideally imperfect crystals as a function of wavelength, in the symmetrical Laue and Bragg cases, are shown to be valid for distorted crystals where the gradient of the lattice phase factor is perpendicular to the crystal surfaces. This result is obtained by an analysis of the Taupin-Takagi equations. Some previous experiments (test of a proposal for extinction-free measurements of FM/FN in polarized neutron scattering by magnetic crystals, and neutron diffraction from curved and non-curved crystals) are discussed from this point of view.
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    Some remarks on the Laue–Laue interferometer (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 289-292 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The two-crystal Laue arrangement has been utilized as a tool for diffraction focusing, as a spectrometer with rocking curves showing an extremely narrow central peak and as a LL interferometer. For these applications different approaches have been used independently, which are brought together in a description using spherical waves, plane waves and ray optics. It is shown that the frequently used ray optics fails in the focal region of the interferometer. The theory may be applied to neutron or (absorbing) X-ray interferometry.
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    The chemical physics of solvation. Part A: Theory of solvation edited by R. R. Dogonadze, E. Kalman, A. A. Kornyshev and J. Ulstrup (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 208-208 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    An examination of the relationship of the Δω,Δ2Θ intensity distribution to crystal substructure (mosaic distribution) and shape (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 223-230 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The basic Δω, Δ2θ technique for examining single-crystal Bragg reflections [Mathieson (1982). Acta Cryst. A38, 378-387] has recently been improved [Mathieson & Stevenson (1984). Aust. J. Phys. 37; 657-665], by using a simple experimental modification which reduces the source component to a minor (angular) role, thereby making the extraction (deconvolution) of the remaining components more accurate. The application of this new technique in the determination of reflectivity (rocking) curves for imperfect crystals has been demonstrated [Mathieson & Stevenson (1985). Acta Cryst. A41, 290-296]. In the present case, the examination of individual reflections from a small single crystal of CuInSe2 reveals that the improved technique is capable (i) of identifying, by its locus extension in Δω, Δ2θ space, diffraction from one side of the specimen crystal to the other (in the diffraction plane), even for a crystal of average dimension 0̃.06 mm, and (ii) of estimating the reflectivity curve for different parts of the crystal. A series of model eases is discussed, to clarify the interpretation of observed two-dimensional intensity distributions. While considered here in relation to a small crystal, this technique is applicable to extended-plate crystals (in transmission mode) by a selected-area procedure.
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    On absolute scaling in protein crystallography using sums of low-resolution intensities and Wilson statistics at low resolution (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 230-240 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method of absolute scaling of diffraction data is proposed, based on the calculation of the sum of the intensity diffracted at low resolution (Bragg d spacing 〉 15 Å). This sum is proportional to the mean-square deviation of the scattering-length density in the unit cell, and this property is used to determine the scale factor. The method is applied to the case of neutron diffraction using contrast variation experiments with biological molecules, and it is used to check the validity of some assumptions concerning the system under study, such as the global rate of H/D exchange or the uniformity of scattering-length density in the molecules. The use of this method requires an asymptotic correction of the sum of intensity. This correction is based on Porod's law, whose application to diffraction experiments is discussed, in particular for contrast variation experiments. An analysis of the spherical average of the diffracted intensity as a function of the scattering vector, compared to isotropic solution scattering, allows the conditions of applicability of Wilson statistics to be specified at low and medium resolution, i.e. the random statistical model underlying the Wilson statistics in this scattering range to be defined.
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    Exact joint distribution of Eh, Ek and Eh+k, and the probability for the positive sign of the triple product in the space group P\overline{1} (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 240-246 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A recently formulated method of deriving exact Fourier-series representations of joint probability density functions (p.d.f.'s) of several normalized structure factors is applied to the derivation of an exact expression for the conditional probability that the sign of the triple product EhEkEh + k is positive. The relevant joint and conditional probabilities are derived for the space group P\bar 1. The Fourier coefficients of the p.d.f. are given by rapidly convergent series of Bessel functions, and the convergence properties of the Fourier summations are also found to be favourable. The exact conditional probability is compared with the currently employed approximate one, well known as the hyperbolic tangent formula, for several hypothetical structures. The examples illustrate the effects of the number of atoms in the unit cell, the magnitude of the E values and the atomic composition on the exact and approximate probabilities. It is found, in agreement with previous studies, that the hyperbolic tangent formula may indeed significantly underestimate the probability when the number of equal atoms is small and the E values are only moderately large, and when the structure contains outstandingly heavy atoms. The opposite behaviour, i.e. the approximate probability overestimating the exact one, was not observed in the present calculations. For large values of the triple product in equal-atom and heterogeneous models, the agreement between the approximate and exact probabilities is usually good.
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    Crystallography of quasi-crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 261-271 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The symmetry of quasi-crystals, a class of materials that has recently aroused interest, is discussed. It is shown that a quasi-crystal is a special case of an incommensurate crystal phase and that it can be described by a space group in more than three dimensions. A number of relevant three-dimensional quasi-crystals is discussed, in particular dihedral and icosahedral structures. The symmetry considerations are also applied to the two-dimensional Penrose patterns.
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    Structure Reports (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 288-288 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    'Peakiness' test functions (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 297-299 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A number of common functions have been tested to determine their efficiency in refining structures using the criteria of 'peakiness' and non-negativity of the electron density distribution. It is concluded that the best function to maximize, generally, is ∫ ρ3dv, although, in special cases, a higher power of ρ may be better. When there is a heavy atom in the structure the method is much less sensitive to the particular function used so long as it involves powers of ρ greater than ρ2.
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    Diffraction d'un faisceau de rayons X en incidence très rasante (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 299-303 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The penetration depth τ of an X-ray beam (λ ∼ 1 Å) incident on a surface with an angle α decreases rapidly when α goes below αc, the critical angle of total reflexion. It is shown experimentally that at the same time the Bragg peaks have a stick-like shape perpendicular to the sample surface. The variation of the depth τ as a function of α has been determined by measuring the length of the stick. The variation of the Bragg intensity and the position of the peak as well as the depth are calculated precisely using the simple Fresnel formulae.
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    A new joint probability distribution for the triplet phase sum. Inclusion of higher-order terms (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 309-317 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new joint probability distribution of three normalized structure factors is derived for the case of N equal atoms in the space group P1. The distribution appears in a series expansion. Convergence of the series is obtained by inclusion of higher-order terms up to order N-5, although with the exception of terms up to order N-1/2 the distribution does not contain all possible terms. Test results show improved estimates of the absolute value of the triplet phase sum when compared with the Cochran distribution. In particular, the systematic errors are reduced appreciably.
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    On integrating the techniques of direct methods with anomalous dispersion. I. The theoretical basis. Corringenda (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 134-134 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In equation (2.7) of Hauptman [Acta Cryst. (1982), A38, 632-641] 2θjH should be replaced by 2δjH. On the seventh line of equation (3.34), CHCKCL - CHSKSL should be replaced by CHCKCL + CHSKSL. On the sixth line of equation (3.51), replace R_{\bar 1}R_{\bar 2}R_{\bar 3} cos ζ2 by R_{\bar 1}R2R_{\bar 3} cos ζ2. On the line immediately following equation (3.54), ωjB_{\bar j} should be replaced by ωj, B_{\bar j}.
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    Automated calculation of coordinate transformations for the superposition of protein structures (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 172-178 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A computer program is described that performs a superposition of two protein structures. The program calculates a coordinate transformation that minimizes the root-mean-square deviation between atoms representing homologous structure in the two proteins. All atoms of the main chain and those atoms of side chains that bear common labels contribute to the calculation of the transformation. Required input by the user is either a small set of integers representing the sequence numbers of spatially equivalent residues in the two proteins and/or the initial and terminal residues of homologous elements of secondary structure. After using the starting set of homologies to calculate an initial transformation, the program discards the user input and then determines the full set of homologous residues by application of simple criteria. The superposition that results is the point of departure of a search for alternative transformations that represent superpositions of merit. The computation time for the superposition of two structures of 150 residues is approximately 20 s on a VAX 11/780 and rises linearly with the size of the problem. Thus, the program is inexpensive in computer time and applicable to even the largest of macromolecules whose three-dimensional structures are known.
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    Neutron diffraction from single-crystal silicon: the dependence of the thermal diffuse scattering on the velocity of sound (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 188-191 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is well known [Willis (1970). Acta Cryst. A26, 396-401] from the theory of one-phonon scattering of thermal neutrons by a crystal that the nature of the thermal diffuse scattering (TDS) near the Bragg peak depends on whether the neutron velocity is greater than or is less than the sound velocity in the crystal. For faster-than-sound neutrons the TDS rises to a peak coinciding with the Bragg peak, whereas for slower-than-sound neutrons the TDS tends to give a flat background across the Bragg reflection. These theoretical predictions are supported by experiments using pulsed neutron diffraction from single crystals of perfect silicon. In particular, the integrated TDS across a reflection undergoes a pronounced fall when the neutron velocity drops below the velocity of sound.
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    X-ray diffraction profiles described by refined analytical functions (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 14-19 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The line profiles from a sample containing small spherical particles, non-uniform strain and instrumental broadening can be described exactly by using error functions with complex arguments. Consequently, the development by Houska & Smith [J. Appl. Phys. (1981). 52, 748-754] has been revised in terms of these functions. This calculation has been extended, by the use of error functions with complex arguments, to include a more general distribution of particle size or column heights than that obtained from a single sphere. The latter extension is applied to profiles obtained from a partially stabilized zirconia wear debris. It is found, in this example, that a column-height variation coefficient that is greater than that from a single sphere gives a somewhat better fit of the experimental line profiles. We find that if the single-sphere model is used to fit the profiles the particle size and root-mean-square strain differ by about 12 and 5% respectively.
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    Correction of some formulas of Agarwal's fast Fourier transform least-squares algorithm (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 204-204 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The formulas (34), (37) and (38) of Agarwal [Acta Cryst. (1978). A34, 791-809] should be changed to: TeXTeXTeX
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    International tables for crystallography: Brief teaching edition of Volume A: Space group symmetry edited by T. Hahn (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 205-205 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Ferroelectric space groups (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 44-47 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The 440 ferroelectric space groups, viz the Heesch-Shubnikov (magnetic) space groups, which are symmetry groups of ferroelectric electric-dipole arrangements in crystals, are derived and tabulated. By considering automorphisms induced by the automorphisms of the discrete space-time group, we show that although ferroelectric, ferromagnetic and ferrocurrent point groups all number 31, the number of ferroelectric space groups differs from 275, which is that of both ferromagnetic and ferrocurrent space groups.
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    Temperature effect of X-ray diffraction intensities for a perfect crystal across the absorption edge: Laue case (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 113-116 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By using a Ge perfect crystal, the 422 X-ray reflection intensities have been measured across the Ge K absorption edge in the Laue case. A conspicuous temperature dependence has been observed in the ratio of the integrated diffraction intensities below and above the absorption edge, which is peculiar to an absorbing perfect crystal. This temperature dependence is much larger in the Laue case than in the Bragg case.
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    Fourier versus Hermite representations of probability distributions (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 81-83 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Finite Fourier approximations fitted by use of orthogonality properties are identical with Fourier approximations fitted by least squares, but finite Gram-Charlier or Edgeworth (Hermite) approximations fitted by the two methods differ. This may give a partial explanation of the better performance of Fourier expressions for the probability distributions of structure factors. An alternative Hermite (Myller-Lebedeff) expansion exists, for which the orthogonality and the least-squares coefficients are identical, but they are not readily evaluated.
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    Compound identification and characterization using lattice-formula matching techniques (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 101-105 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A lattice-formula matching technique has been developed to be used in conjunction with the NBS Crystal Data File [(1982), National Bureau of Standards, Gaithersburg, MD] for the identification and characterization of crystalline materials. This technique is reliable, efficient and highly selective. In the first step of the identification/characterization procedure, a unit cell defining the lattice is determined. The cell is reduced and derivative supercells and subcells are calculated. These cells are then checked against the NBS Crystal Data File in which all lattices have been represented by standard reduced cells. By routinely calculating derivative supercells and subcells and matching against the file of known compounds, it is possible to find related materials and/or to make an identification in spite of certain types of errors made by the experimentalists (e.g. missing rows of spots on diffraction photographs or the diffractometer etc.). Finally, the identification obtained by lattice matching is verified using known chemical data. Practical experience and an analysis of the data in the NBS Crystal Data File have proved that the lattice-formula combination is highly characteristic of a crystalline material. Since the method is subject to precise mathematical techniques, the entire procedure can be highly automated. Both the unit-cell determination and the identification/characterization procedure can be carried out in the same instrument. A Fortran program and the NBS Crystal Data File are available.
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    Space and time inversion in physical crystallography (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 122-127 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Conventional (point) symmetry, antisymmetry, magnetic and complete symmetry are used for the description of specific features of space, time and some crystallographic phenomena. The Onsager principle is extended to phenomena described by second-rank axial tensors. As a result it is seen that the symmetric part of such a tensor changes the sign on time reversal. The actions of two operations - time reversal R and time inversion T (T = \bar 1, 'spatial inversion') - are compared. It is shown that the equations of crystal physics derived by Voigt are in agreement with the Onsager principle.
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    Note on 3D (3,4)-connected nets (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 133-134 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Three new 3D (3, 4)-connected nets are described belonging to the special family of nets in which each 3-connected point is connected to three 4-connected points and each 4-connected point is connected to four 3-connected points.
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    The so-called correction of Bragg's law (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 411-413 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The traditional 'correction of Bragg's law' is discussed for any value of the refractive index of the diffracting medium. The finite angular range of reflection, as given by the dynamical theory of interference, is symmetrical about the corrected Bragg glancing angle only if absorption can be neglected. In this case the centroid of the reflected intensity is given by the corrected Bragg law. When absorption has to be taken into account or when, besides the surface-reflected ray, other strong diffracted rays occur inside the crystal, the simple corrected law is not sufficient. For spectroscopic work of precision equal to that achieved for visible light a careful analysis of the incident X-ray appears necessary concerning its collimation (angular width) and polarization. Furthermore, the setting of the diffracting crystal has to be investigated in order to avoid unwanted simultaneous reflections. The ideal would be to combine a recording of the actual reflection curve with the high-precision absolute measurement of the glancing angle that serves as zero for the reflection curve. This requires novel instrumentation.
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    The dynamical diffraction of X-ray spherical waves in two perfect crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 426-435 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The general theory of X-ray spherical-wave diffraction in two, either identical or different in nature, spatially separated perfect crystals is developed. The theory takes into account the phase shift of the waves both inside the crystals and in vacuum before, between and after the crystals. The nonmonochromaticity of radiation, the source dimension and the placing of a slit before the first crystal are considered. The results of theoretical calculation and an experimental study of the interference fringes and focusing the radiation are presented. A good agreement between the experimental and theoretical data is obtained for values of the experimental parameters that affect focusing.
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    Angular dependence of the absorption-induced nodal plane shifts of X-ray stationary waves (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 414-426 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The classical equations of dynamical theory in the Bragg case are rederived in a way which is valid even in the presence of absorption where every quantity used is complex. The properties of the phase and the amplitude of the diffracted wave are discussed in detail. It is shown that for non-centrosymmetric crystals the position of the nodes at the centre of the reflection domain is strongly absorption dependent. The limit of the phase of the ratio of the diffracted to the incident amplitude far from the reflection domain is calculated to be equal to φh + π and φh, below and above the reflection domain, respectively, where φh is the phase of the structure factor calculated taking into account anomalous dispersion and the imaginary part of the form factor. It is therefore absorption dependent and so is the position of the nodes of stationary waves which is never invariant with the angular position of the crystal, even outside the total reflection domain. The example of a non-centrosymmetric crystal, GaAs, opposite reflections, 111 and {\bar 1}{\bar 1}{\bar 1}, and of wavelengths close to the absorption edges of gallium and arsenic is used to illustrate the results. It shows that the absorption-induced shifts of the nodal planes are in general directed towards the surface of the crystal, independently of the sense of the diffraction vector. The variation of the penetration depth within the total reflection is interpreted in the non-absorbing case by means of a new surface which completes the dispersion surface within the Bragg gap.
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    The Ewald energies of complex crystals: the 'biochlorites' (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 340-344 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Calculation of the electrostatic Ewald energies of complex crystals requires much time. For such crystals, two methods, suggested by the methods of Ewald and Bertaut, are proposed to obtain rapid convergence of the series: the 'multi-radii method' and the 'overlapping method'. These methods are applied to the 'biochlorites', complex crystals formed by mixing biotite and chlorite layers. The Ewald energy of 1-1 biochlorite (1 biotite layer-1 chlorite layer) with a value of 181.6 MJ mol-1 (eight tetrahedral cations T per molecule) is found to be approximately equal to the sum of the energies of biotite: 74.6 MJ mol-1 (four T per molecule) and chlorite: 107 MJ mol-1 (four T per molecule). The energy of mixing (of biotite and chlorite layers) is thus nearly equal to 0, which is an indication of the possible stability of biochlorites.
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    Experimental observation of the Borrmann pyramid – the Borrmann fan for four-beam transmission of X-rays (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 348-352 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The polyhedron which confines the Poynting vectors of N-beam transmissions in crystal space is referred to as the Borrmann pyramid. The observation of this Borrmann pyramid is realized from the diffraction images of the four-beam, (000)(220)(2\bar 20)(400), transmission case of silicon single crystals for Mo Kα. The directions of the Poynting vectors for the eight modes of wave propagation involved and the diffraction images are calculated. These calculations confirm the experimental observations. The variation of the direction of the Poynting vector for each mode is also reported.
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    The effect of measured vs conventional polarization factors in structure refinements (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 184-188 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The polarization ratio K is measured for LiF (200) and graphite (00.2) monochromators at different X-ray wavelengths. In each case the kinematical value cos2 2θM is a poor approximation, and the actual value of K may exceed the dynamical limit cos 2θM. An explanation is offered in terms of a model that includes secondary extinction. The effects of an incorrect value of K are studied by refining the model for a ruby standard crystal. The positional parameters are not affected, but the scale, extinction and thermal parameters change. The effects are, however, smaller than the ones observed in the structural parameters due to termination of the data set at lower sin θ/λ values.
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    Unique solutions for the SIR and SAS phase problems and the use of partial structural information in phase refinement (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 362-368 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Algebraic formulae are presented which permit a unique phased solution for diffraction data measured from a single isomorphous pair of crystals. Trial calculations performed on an SIR (single isomorphous replacement) data set from an 84-atom structure demonstrate that complete phasing can be achieved from a single chirally positioned replacement atom representing less than one percent of the total scattering power of the derivative structure. Similar phase refinements employing error-free SIR data for 2Zn pig insulin are less remarkable, and converge to an average phase error of 50°. The phase convergence of the formulae can be markedly improved if estimates of the cosine invariants from the SIR data are available [Hauptman (1982). Acta Cryst. A38, 289-294; Fortier, Moore & Fraser (1985). Acta Cryst. A41, 571-577]. The precision of these cosine estimates was found not to be critical; modular estimates of +1 or -1 were sufficient to allow the SIR phase refinement of the insulin structure to converge to an average phase error of 6°, which compares favorably with the value of 3° produced if the cosine invariants were known precisely. The derived formulae are also shown to be applicable to single-crystal analyses which utilize one-wavelength anomalous dispersion or partial structural fragments to initiate phasing. Test examples indicate that tangent-formula recycling procedures based on the derived formulae compare favorably with the traditional tangent-formula methods to exploit partial structure information.
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    Order–disorder phase transition in stage-2 Agx TiS2 (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 399-402 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Based on the phenomenological Landau-Lifshitz theory of phase transitions it is shown that the order-disorder transition observed around 200 K in the intercalated silver atoms between TiS2 sandwiches for a stage-2 AgxTiS2 (x ̃1/6) system belongs to the three-state Potts universality class. The corresponding critical exponents can be measured experimentally using synchrotron radiation.
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    Graphic representation and nomenclature of the four-dimensional crystal classes. IV. Irrational crypto-rotation planes of non-crystallographic orders (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 387-398 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystallographic symmetry operations in four dimensions that have orders 5, 8, 10 and 12 can be formulated as double rotations of these orders instead of in the ways that have been used previously. The crystallographic character of the operations is compatible with the non-crystallographic orders of their constituent crypto-rotation planes because these lie in crystallographically irrational orientations. The orientations of these planes are derived in terms of the usual crystallographic axes and are illustrated by means of hyperstereograms. The analysis is used to throw further light on the nature, on the enantiomorphy, and on the degrees of freedom of the symmetry operations, but the irrational orientations lead to substantial disadvantages in such a formulation of the symmetry operations for both the graphical and the symbolic representations of the four-dimensional crystal classes.
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    A full-symmetry translation function: the influence of model misorientation (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 402-404 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A translation function is described which takes into account the full space-group symmetry. It can be easily computed by means of a standard Fourier program with modified coefficients and seems to be applicable if search-model orientation errors are less than 5°. This function has been tested on three structures.
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    First-order asymmetry in the Renninger interaction of a strong reflection with weak beams (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 405-406 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Application of perturbation theory to the modification of a strong two-beam reflection near a three-beam point involving a weak secondary reflection shows that in perfect crystals the first-order asymmetry with azimuthal angle of the integrated intensity in a Renninger scan is caused primarily by changes in absorption. The intensity is always enhanced when the third reciprocal-lattice point is outside the Ewald sphere, and thus this asymmetry does not contain any phase information.
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    Commission on Journals. Atomic labelling (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 407-407 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Theory and computation of optical rotatory power in inorganic crystals (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 560-569 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The classical polarizability theory of optical activity in crystals is elaborated and a method of calculating rotatory power from crystal structure data is described. By varying the polarizabilities of the atoms within reasonable limits, optical rotatory powers are computed for crystals of α-quartz, AlPO4, cinnabar, Bi12SiO20, Bi12GeO20, α-LiIO3, NaClO3 and NaBrO3. In general, the agreement between theory and experiment is excellent. As expected, considerable variability in polarizabilities is required in different structures in order to obtain satisfactory fits to the observed refractive indices and rotatory powers. The orientations of anisotropic polarizability ellipsoids derived in the course of the calculation are compared with those suggested earlier by Glazer & Stadnicka [J. Appl. Cryst. (1986), 19, 108-122].
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    Convergent-beam reflection high-energy electron diffraction (RHEED) observations from an Si(111) surface (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 569-577 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Conditions for the intensity enhancement of a Bragg reflection are investigated through convergent-beam (CB) reflection electron diffraction experiments. This intensity enhancement is of great interest for reflection electron microscopy of surfaces. Comparison of CB reflection diffraction patterns with CB transmission diffraction patterns shows a very similar enhancement which can be explained by Bloch waves. The observed surface diffraction parabolae are closely related to Kikuchi envelopes. The intensity enhancement can be interpreted as a channelling phenomenon.
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    Extremely skew X-ray diffraction (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 585-587 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Skew reflections are becoming more and more important in X-ray surface diffraction. A geometrical discussion of the whole dispersion surface in extremely skew cases gives the angular ranges of incidence and emergence in which the condition of X-ray diffraction is fulfilled. The main intensity comes from the incidence range given by |χ0 - χh|1/2 〈 θi 〈 |χ0 + χh|1/2, where χ0 and χh are the Fourier coefficients of dielectric susceptibility of the crystal. Furthermore, the exit angle of the diffracted beam is of the order of the critical angle of specular total reflection.
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    Prices of Acta Crystallographica and Journal of Applied Crystallography (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 587-588 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Nuclear Structure 1985 edited by R. Broglie, G. Hagemann and B. Herskind (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 136-136 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Solid state physics by J. S. Blakemore (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 136-136 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    URL: http://dx.doi.org/10.1107/S0108767386099646
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