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  • International Union of Crystallography (IUCr)
  • 1985-1989  (6,250)
  • 1
    Electronic Resource
    Electronic Resource
    A new approach to the measurement of X-ray structure amplitudes determined by the Pendellösung method (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 48-55 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Laue-case rocking curve from two thin crystals is known to exhibit fine structure which can be used to determine the corresponding structure amplitude Fh. Thus F444 and F777 have been measured for crystalline silicon to a standard deviation of 0.2%. F444 is in excellent agreement with published experimental values. There are no previous high-precision measurements of F777 in the literature. The values measured seem to indicate that the accepted theoretical dispersion corrections are somewhat too low. A highly stable monolithic thin-wafer silicon dittractometer of a novel design was employed. Using an energy-dispersive solid-state detector and the white spectrum of a tungsten X-ray tube, rocking curves from a number of planes of the hhh family could be recorded simultaneously, thus reducing measurement time considerably and minimizing the influence of some sources of systematic and random error. Least-squares computer fitting of the theoretical curve to the complete measured one is employed to determine the value of Fh from the data. A complete discussion of the method is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000083
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  • 2
    Electronic Resource
    Electronic Resource
    Exact random-walk models in crystallographic statistics. II. The bicentric distribution for the space group P\overline{1} (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 55-59 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An exact probability density function for the magnitude of the normalized structure factor |E| has been derived for the space group P\bar 1, taking account of the presence of one non-crystallographic center of symmetry. The function is based on the exact solution of the corresponding random-walk model and its expansion into a Fourier series. The above result is compared with simulated semi-cumulative distributions based on hypothetical structures and very good agreement is obtained for the equal-atom case, as well as for a heterogeneous asymmetric subunit containing fourteen carbon atoms and one uranium atom. The new exact bicentric probability density functions of |E|, for the space group P\bar 1, reduce to the well known asymptotic expressions that are valid for equal-atom structures and a large number of atoms in the asymmetric unit of the space group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000095
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  • 3
    Electronic Resource
    Electronic Resource
    The estimation of average molecular dimensions. 2. Hypothesis testing with weighted and unweighted means (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 85-89 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The average value (μ) of a molecular dimension may be estimated by a weighted (\bar xw) or unweighted (\bar xu) mean. Computer simulations show that \bar xu can be used in hypothesis tests, since the distribution of (\bar xu - μ)/σ(\bar xu) is closely approximated by Student's t distribution. In contrast, hypothesis tests based on the weighted mean are inexact and potentially misleading.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000150
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  • 4
    Electronic Resource
    Electronic Resource
    Modern crystallography. Vol. III. Crystal growth by A. A. Chernov (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 112-112 
    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/S0108767385000216
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  • 5
    Electronic Resource
    Electronic Resource
    Local density approximations in quantum chemistry and solid state physics edited by J. P. Dahl and J. Avery (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 112-112 
    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/S010876738500023X
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  • 6
    Electronic Resource
    Electronic Resource
    Simulation of multiple diffraction (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 128-133 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The multiple diffraction of X-rays and neutrons is discussed on the basis of the kinematical theory; a program for the simulation of ψ scanning and λ scanning is developed, where the influence of the wavelength width of incident beams on the Ewald construction is properly taken into account. The effect of higher-order diffraction (n-beam interaction, n 〉 3) is treated as the sum of those of (n-2) pairs of relevant double diffractions (three-beam interactions). Applications are made for some examples for which experimental data are available; it is shown that the results are in very good agreement with experiment. This suggests that the kinematical approach is appropriate. The simulation is useful in planning ψ-scanning experiments for precise structure determination and for examining experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000265
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  • 7
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    Electronic Resource
    On the classical interpretation of thermal probability ellipsoids and the Debye–Waller factor (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 156-157 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In many standard text books on crystallography, the Gaussian expression for the Debye-Waller factor is derived from a classical point of view. The physical model normally used is too simple in that it is incompatible with the concept of probability ellipsoids used to depict atomic thermal motion. A classical derivation of the Debye-Waller factor expression is given that corrects some misconceptions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000307
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  • 8
    Electronic Resource
    Electronic Resource
    X-ray diffraction lenses with spherical focusing (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 17-25 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray spherical-wave focusing in multibeam dynamical diffraction by a biaxially bent single crystal has been considered. In contrast to cylindrical lenses already studied in the two-beam case, which presented a line focus, here wave packets focusing in two directions into a single point are dealt with. The conditions for focusing of the trajectories of the X-ray Bloch waves are established and the algorithm for the determination of the parameters of corresponding X-ray optical systems is described. Possible sets of parameters are calculated. The X-ray wave field distribution in a crystal is simulated numerically. The calculated topographs confirm the existence of the focusing effect.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000034
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  • 9
    Electronic Resource
    Electronic Resource
    The extension and refinement of the 1.9 Å spacing isomorphous phases to 1.5 Å spacing in 2Zn insulin by determinantal methods (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 3-17 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new mathematical description of phase relationships which connects different approaches, both in reciprocal and direct space, is formulated. It leads to the development of a novel algorithm for phase extension and refinement based on a probability function for atomic presence. This function, calculated from the elements of the Karle-Hauptman inverse matrix, is used in an iterative procedure. Various tests have been performed on an idealized set of calculated structure factors for an insulin model structure. The method has been applied to experimental data, Fobs, and the isomorphous phases for 2Zn insulin. An assessment of the quality of the phase refinement and calculation has been made by comparison with the crystallographically refined phases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000022
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  • 10
    Electronic Resource
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    Multilayer thin films as polarizing monochromators for neutrons (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 41-48 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent progress in the development of polarizing multilayer thin-film monochromators for neutrons is reported. In particular, multilayers consisting of thin films of Fe and Ge with bilayer thicknesses of the order of 50 Å have been made with high peak reflectives and polarizing efficiencies. The results of measurements of multibilayer reflectivity and polarizing efficiency are compared with other neutron polarizers. A picture of the microscopic structure of the individual Fe and Ge films has also been obtained. Finally, practical applications of polarizing multibilayers are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000071
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  • 11
    Electronic Resource
    Electronic Resource
    Tensorial classification of non-magnetic ferroic crystals: tensors of rank N≤4 (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 89-90 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The tensorial classification of all non-magnetic ferroic crystals is given for all possible macroscopic tensorial properties of rank N ≤ 4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000162
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  • 12
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    Electronic Resource
    Positron solid-state physics edited by W. Brandt and A. Dupasquier (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 110-110 
    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/S0108767385000186
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  • 13
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    Electronic Resource
    The structure of matter: from the blue sky to liquid crystals by A. Guinier (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 112-112 
    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/S0108767385000228
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  • 14
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    Electronic Resource
    Round-off errors in inter-experimental comparisons (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 122-128 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two independent determinations of the same structure may be compared by means of statistical techniques such as normal probability plots and χ2 hypothesis tests. Computer simulations show that errors may arise in the application of these techniques if rounded estimates of structural parameters and their e.s.d.s are used in the calculations. Round-off errors are particularly serious in goodness-of-fit hypothesis tests, since they increase the probability of making type I errors, i.e. falsely rejecting the null hypothesis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000253
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  • 15
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    Maximum entropy theory (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 113-122 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A maximum entropy method (MEM) map of electron density is obtained by maximizing S = -Σ p log p subject to whatever data are available. MEM is derived as the only reconstruction technique that is consistent with simple and general requirements. The method is very widely applicable, but, in this paper, attention is focused on the problem of producing electron density maps in crystallography. The entropy formula can also be derived by analogy with a thermodynamic system of quanta, but it is shown that this model can be misleading, and can break down in practice. MEM applied to a different problem related to quantum fluctuations in the thermodynamic model is shown to lead to formulae equivalent to the maximum determinant method. It is argued that direct MEM will produce superior maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000241
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  • 16
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    The 'best' unit cell for monoclinic structures consistent with b axis unique and cell choice 1 ofInternational Tables for Crystallography (1983) (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 142-151 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Diagrams with the c/a ratio as ordinate and cos (180° - β) as abscissa are given, which allow one to find out how a given monoclinic unit cell can be transformed so that a and c are the shortest translation vectors compatible with the symmetry of the space group in a setting corresponding to the standard space-group symbol given in International Tables for Crystallography [Vol. A. (1983). Dordrecht: Reidel] [denoted as IT(1983)], which means b axis unique and cell choice 1 where applicable. The diagrams contain the transformation matrices and indicate whether the origin of the transformed cell has to be shifted in order to obtain a structure description with the Wyckoff positions listed in IT (1983). A 'best' monoclinic unit cell consistent with cell choice 1 is one of the requirements for a standardized description of crystal-structure data according to Parthé & Gelato [Acta Cryst. (1984), A40, 169-183].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000289
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  • 17
    Electronic Resource
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    Image processing in high-resolution electron microscopy using the direct method.I.Phase extension (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 163-165 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure to combine the information from an electron micrograph (EM) and the corresponding electron diffraction (ED) pattern is proposed. Here the ED data will be used to obtain a set of amplitudes of the structure factors, while the EM will be used to obtain a set of starting phases assuming the weak-phase-object approximation. A direct method is then used to extend the phase information from a resolution of about 2 to 1 Å. The efficiency of the procedure has been verified by the test calculation on the model structure of copper perchlorophthalocyanine.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000320
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  • 18
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    Electron density in KCl and LiF crystals in the self-consistent local-density-functional approximation (LDA) (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 175-177 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The γ-ray single-crystal structure factors of Schmidt, Colella & Yoder-Short [Acta Cryst. (1985), A41, 171-175] for the 'isoelectronic' salt KCl are shown to be in excellent agreement with the values computed by us using the method of augmented spherical waves in the LDA approximation. Small differences exist for the 600 and 400 reflections whose structure factors indicate some 'asphericity' in the valence charge density - an effect not included in the theoretical calculation. The corresponding data by the same authors for the ('non-isoelectronic') salt LiF are also in good agreement with the LDA theoretical values available in the literature. A discrepancy remains, instead, between the γ-ray structure factors for 'isoelectronic' NaF by Yoder & Colella [Phys. Rev. B. (1982), 25, 2545-2549] and the LDA theoretical values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000356
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  • 19
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    Intensities, structure factors and their variances (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 189-195 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Hypothetical variances are checked and improved and observations are tested for normal and independent distribution by means of χ2 distributions. For the conversion of σ2I into σ2F and of I into F the quantity X(I) = sign (I) [I]1/2 instead of F = pI1/2 (p = Lorentz correction etc.) is considered. With the probability density function f(I) for I the variance of F is: σ2F = p2 \Biggl \{ {\int_{-\infty}^{+\infty}} X^{2}(I) f(I) {\rm d}I - \Biggl [ {\int_{-\infty}^{+\infty}}X(I)f(I) {\rm d}I \Biggr ]^{2}\Biggr \}. This formula is also valid if the observed intensity is zero or negative. Unexpectedly, the approximate σ'F = pσI/(2I1/2) are in most cases smaller than the correct ones. The simple formula F = pI1/2 yields F that in the mean are too low. The correction formula valid for all ratios I/σ1 is Fcorr = p(2I1/2 - A), where I is the observed intensity and A the second integral in the above formula for σF2. Since the expressions σF2 and Fcorr are known, there is no other reason to discard weak intensities than the fact that this saves computing time. Examples are given and the normal probability plot is applied.
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    URL: http://dx.doi.org/10.1107/S0108767385000381
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  • 20
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    Theory of structural transformations in solids by A. G. Khachaturyan (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), 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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    URL: http://dx.doi.org/10.1107/S0108767385000447
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  • 21
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    The dynamic theory of X-ray diffraction by the one-dimensional ideal superlattice. I. Diffraction by the arbitrary superlattice (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 212-217 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The theory of X-ray two-beam dynamic diffraction by the one-dimensional ideal superlattice (SL) in the Laue and Bragg cases is developed. The reflection and transmission amplitudes of the SL are expressed by those for one period of the SL. General expressions revealing the behavior of the diffraction pattern, irrespective of the particular model, are obtained. A detailed analysis is carried out for the most important case: z0 〈〈 \bar \Lambda (z0 and \bar \Lambda being the SL period and the mean extinction length of the crystal, respectively).
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    URL: http://dx.doi.org/10.1107/S0108767385000484
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  • 22
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    Statistical mechanics approach to the structure determination of a crystal (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 268-273 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The previously formulated new approach to the structure analysis of a crystal based on the profound analogy between the problem of determination of thermodynamic equilibrium in statistical mechanics and the optimization problem for a function of many variables [Khachaturyan, Semenovskaya & Vainshtein (1979). Soy. Phys. Crystallogr. 24, 519-524; (1981). Acta Cryst. A37, 742-754] is developed. In this approach, a crystal structure is determined by the equilibrium low-temperature state of a model non-ideal gas composed of the atoms within a crystal unit cell, the unit cell and the R factor being regarded as a vessel and an interatomic interaction Hamiltonian, respectively. In contrast to the above cited papers, the low-temperature equilibrium state is found by means of the Monte Carlo sampling scheme usually utilized in statistical mechanics applications. The main advantage of such a treatment is that the system reaches the equilibrium state avoiding all 'traps', metastable (local) minima of the free energy, and thus provides automatic determination of the crystal structure. The method is successfully tested on the known L-proline structure containing 32 non-hydrogen atoms per unit cell. The proposed statistical mechanics approach can also be applied with minor modifications to optimization problems in the multi-dimensional space of many variables.
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    URL: http://dx.doi.org/10.1107/S0108767385000563
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  • 23
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    Effect of heavy atoms on the two-phase structure seminvariant φh + φk in P\overline{1} (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 209-212 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A crystal structure in P\bar 1 consisting of P heavy atoms and Q light atoms in the unit cell is considered, and the random variable vectors h and k, subject to well defined restrictions, are uniformly and independently distributed in reciprocal space. The linear combination of two phases ψ = φh+ φk is a structure seminvariant if and only if h + k = 0 (mod ω) where ω = (2, 2, 2). Eh and Ek are the two normalized structure factors associated with phases φh and φk and EPh and EPk are the contributions of the heavy atoms respectively. The first neighborhood of ψ consists of the four magnitudes |Eh|, |Ek|, |E(h + k)/2|, |E(h - k)/2|- The conditional probability distribution of ψ, given the four magnitudes |Eh|, |Ek|, |E(h + k)/2|, |E(h - k)/2| and the known contributions EPh, EPk from the heavy atoms, is derived to the approximation of 1/N. In favorable cases, i.e. when phase indications from the four-magnitude neighborhood of the seminvariant and the heavy-atom contributions coincide, a reliable estimate for ψ is obtained. The result obtained is applied to the structure of a derivative of β-lactam and its usefulness is demonstrated.
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    URL: http://dx.doi.org/10.1107/S0108767385000472
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  • 24
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    Solving the phase problem in fiber diffraction. Application to tobacco mosaic virus at 3.6 Å resolution (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 252-262 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The diffracting particles that give rise to a fiber diffraction pattern are randomly oriented about the fiber axis and, in consequence, the diffraction pattern is cylindrically averaged. The phase problem in fiber diffraction is not only to determine the phase in the usual crystallographic sense, but to overcome the loss of information from this averaging. This has been done by a multi-dimensional analog of protein crystallographic isomorphous replacement, combined with the use of information from the fine splitting of layer lines that occurs when a helical structure repeats approximately, but not exactly, in a given number of turns. The phases thus determined have been refined by a solvent-flattening procedure. They have been further refined by assuming the separation of cylindrically averaged Bessel-order terms (from multi-dimensional isomorphous replacement at an early stage and from a model at a later stage) and applying conventional isomorphous replacement (two-dimensional isomorphous replacement) to determine the phases of the terms. Cycles of model building and two-dimensional isomorphous replacement were found in the case of tobacco mosaic virus to improve greatly the quality of the electron density map, and enabled an atomic model of the virus to be built based on a highly interpretable map at 3.6 Å resolution with five Bessel orders (terms overlapping because of cylindrical averaging) separated.
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    URL: http://dx.doi.org/10.1107/S010876738500054X
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  • 25
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    Anharmonic temperature factors: the limitations of perturbation theory expressions. Erratum (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 304-304 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The parts of Fig. 1 in Mackenzie & Mair [Acta Cryst. (1985). A41, 81-85] have been wrongly labelled, so that (a) to (d) and (e) to (h) run vertically. The correct labelling has parts (a) and (b) on the top line, (c) and (d) on the second line, (e) and (f) on the third line and (g) and (h) at the bottom. References to Scheringer (1984a, b) should read Scheringer (1985a, b).
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    Transferability of nonbonded Cl...Cl potential energy function to crystalline chlorine (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 296-301 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal structure of molecular chlorine could not be accurately predicted using a transferred nonbonded Cl...Cl potential function that was found satisfactory for prediction of perchlorohydrocarbon crystal structures. Additional consideration of quadrupole-quadrupole interaction did not resolve this problem. One possible solution, which has been explored in the literature, was to define a new, nontransferable, Cl...Cl potential function specifically tailored to molecular chlorine. Such a specialized Cl...Cl function required additional adjustable parameters that defined an anisotropic nonbonded energy function for chlorine. A second possible approach, explored here, transferred the perchlorohydrocarbon Cl...Cl potential function to molecular chlorine. This simple isotropic nonbonded energy function was then supplemented by a partial intermolecular bonding force constant, which was applied to the short contacts present in this structure type. The resulting empirical model described the crystal structure of molecular chlorine within threshold accuracy.
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    Electro-optical and magneto-optical properties of liquid crystals by L. M. Blinov (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 304-304 
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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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    Lattice-dynamical calculation of second-order thermal diffuse scattering in molecular crystals (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 316-320 
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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 procedure has been developed to calculate second-order thermal diffuse scattering (TDS) intensity for molecular crystals from lattice-dynamical calculations with an atom-atom potential in the Born-von Kármán formalism. It is applied to monoclinic phenothiazine and different contributions to second-order TDS intensity, acoustic-acoustic, acoustic-optic and optic-optic, are compared. Calculations are also performed in the long-wave approximation allowing for dispersion (LWD) and correction factors of Bragg intensities due to TDS contribution in the LWD approximation are, generally but not always, lower than lattice-dynamical ones; the ratio between LWD and 'exact' factors ranges from 0.4 to 1.4 for reflections considered.
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    Interpretation of dynamical diffuse scattering of fast electrons in rutile (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 320-327 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An Einstein model for thermal diffuse scattering is extended to a fully dynamical n-beam Bloch-wave treatment, where explicit account is taken of the scattering site symmetry from individual atoms. Dynamical effects in this model are related to orientation-dependent fluctuations in current density on localized scattering centres within the crystal, yielding excess or deficit Kikuchi bands. Calculated diffuse scattering distributions are compared with experimental observations from rutile (TiO2). The predicted diffuse distribution for scattering from oxygen sites correlates reasonably well with experiment, implying a relatively weak contribution for (localized) thermal diffuse scattering of fast electrons from titanium sites.
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    The use of structural information in the estimation of crystal-structure phase invariants (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 583-586 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Recent developments in translation-function methods have secured a priori estimates of the imaginary component of molecular transform products, which are here shown to permit improved estimates of crystal- structure phase invariants when the orientations, but not the positions, of conformationally known structural fragments are available. Trial calculations indicate that the values of the triple-phase invariants computed from the phases of the oriented molecular transform products are indistinguishable from values of these invariants computed with the various oriented molecular structures at their true locations in the unit cell, provided that the fragments comprise half or more of the contents of the asymmetric unit. The Σ1 phases calculated for such structures are equal to the phases produced by the various properly positioned fragments of the partial structure. These results imply that a unique direct-methods solution to determine the positions of the fragments is virtually guaranteed for partial structures of this size or larger. The accuracy of the computed triple invariants for smaller fragments, comprising about one quarter or less of the contents of the asymmetric unit, remains sufficiently better than the corresponding ab initio direct-methods estimates, and should provide a more reliable basis for determining the positions of the fragments by multi-solution procedures. Computed phase-invariant procedures should possess an important advantage over translation-function methods in applications which involve multiple fragments of known orientation.
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    Lattice complexes and limiting complexes versus orbit types and non-characteristic orbits: a comparative discussion (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 421-426 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The concept of lattice complexes is compared with the concept of orbit types, and the correspondences and differences are worked out in some detail. For this, it turned out to be necessary to distinguish whether a set of symmetrically equivalent points is regarded as attached to or as detached from its generating space group. The terms 'crystallographic orbit' and 'point configuration' used as synonyms so far are applied here to discriminate between these distinct meanings. On this basis, the terminology within both concepts is redefined stressing the aspect of equivalence classes. After that, the relations between non-characteristic orbits and limiting complexes are carefully discussed for the first time.
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    X-ray particle-size broadening (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 6-13 
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    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.
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    The diffraction pattern of projected structures (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 36-43 
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    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.
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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 
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    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.
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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 
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    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.
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    Journal of materials Research (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
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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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 
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    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].
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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 
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    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.
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    Translation functions: the minimization of structure-independent spurious maxima (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 578-582 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is described whereby the magnitudes of the structure-independent spurious maxima produced by translation syntheses are minimized. The new method has the advantage that it is applicable to all space groups. Structure-dependent spurious maxima are not as markedly reduced by the new method, but may be confidently suppressed by means of previously described procedures. Translation syntheses for which both sources of spurious maxima have been treated generally possess fewer strong peaks and flatter backgrounds. Trial calculations for test fragments comprising about half of the contents of the asymmetric unit typically produce a single solution vector which may be enhanced to ten times the magnitude of the next largest maxima. The usefulness of these procedures appears to diminish rapidly once the size of the search fragment is reduced to less than a quarter of the contents of the asymmetric unit. The solution vector may not be the largest maxima produced by these smaller fragments, but the translation maps will possess far fewer sizable spurious maxima to be confused with the solution vector than maps which have not been treated to reduce these spurious maxima.
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    Note on the use of reciprocal-space translation functions for planar-molecule problem structures (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 586-588 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Correlation functions in reciprocal space are applied to 'problem' structures consisting of approximately planar molecules stacked in layers. The relative position of two molecular fragments is determined by a two-dimensional translation function. With three-or four-dimensional translation searches two independent fragments can be positioned relative to one another and, simultaneously, relative to a symmetry element.
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    Thermal diffuse scattering within a Bragg peak (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 598-603 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The dynamical theory of X-ray-phonon interactions for one-phonon processes is applied to find the thermal diffuse scattering for incident radiation within the angular region of a Bragg peak. In this region contributions must be included from phonons that do not obey the traditional selection rule of connecting points on the two-beam dispersion surface. The general result is evaluated explicitly for the Ge 220 symmetric reflection. The thermal diffuse scattering distribution in output angle is strongly suppressed in the central region, and shows peaks close to the edges of this region as well as at the direction of specular reflection. The suppression of the interaction, and the appearance of the pseudospecular peak, can be traced to the large primary extinction for both the incident and outgoing beams in this region, in addition to the boundary condition that the phonon-excited signal be entirely internally generated. Both effects also combine to eliminate the traditionally expected divergence of thermal diffuse scattering at the Bragg peak.
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    On periodic and non-periodic space fillings of Em obtained by projection. Erratum (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 619-619 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Errors in the paper by Kramer & Ned [Acta Cryst. (1984), A40, 580-587] are corrected. p. 585, § 7, first paragraph, last sentence should read: The enumeration of the dodecahedral faces is taken from Kramer (1982), except for an interchange of faces 1 and 6, and leads to Table 1. p. 585, Table 4, column 'Class representative', third row should read: g3, g23. p. 585, Proposition 7.1, first equation should read: = D1' = m-1 \Biggl [ \matrix { D_{1} \, 0 \cr 0 a, D_{2}} \Biggr ] m, D1 = D[311]i, D2 = D[311]ω.
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    Methods and applications in crystallographic computing edited by S. R. Hall and T. Ashida (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 621-622 
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    Crystals. Growth, properties and applications. Vol. 10 edited by H. C. Freyhardt (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 623-623 
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    Physical properties of crystals: their representation by tensors and matrices by J. F. Nye (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 624-624 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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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 
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    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.
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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 
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    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.
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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 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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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 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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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 
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    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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    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 
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    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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    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 
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    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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    New methods for deriving joint probability distributions of structure factors. I (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 613-617 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: With new probabilities, based on the Patterson function, for the 'atomic' random variables x1,..., xN in P\bar 1, it is shown that an improved estimate can be obtained for the sign of the seminvariant E2h in P\bar 1. Two probability measures are considered. A method is also given for the case of a known Patterson vector of the form 2r1, giving an estimate for the sign of any structure factor Eh by using its first neighborhood.
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    Compilation of Temperature Factors for Elements and Binary Compounds (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 620-620 
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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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    Dislocations in solids. Vol 6. Applications and recent advances edited by F. R. N. Nabarro (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 623-623 
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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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    Die Farbe von Mineralen und ihre Aussagefähigkeit für die Kristallchemie by K. Langer (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 623-623 
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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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    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 
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    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.).
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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 
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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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    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 
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    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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    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 
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    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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    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 
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    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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    Positional parameters obtained with anharmonic temperature factors (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 356-362 
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    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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    Green's tensor for a cubic crystal (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 202-203 
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    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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    Secondary extinction in an anisotropic crystal (1986)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 42 (1986), S. 464-469 
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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Comparison of the X-ray atomic form factors for crystalline and free-atom lithium (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 195-197 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray atomic form factors, f, have been calculated for crystalline and free-atom lithium using the same Gaussian-orbital basis and the same exchange-correlation potential in the local density approximation by the self-consistent linear combination of Gaussian orbitals (LCGO) method. The difference between f calculated for an Li crystal and f for free Li atoms is less than 0.8%, which is rather small. For free Li atoms the values of f deviate from those obtained by Hartree-Fock calculations by 1.5 to 3% for sin θ/λ 〈 1.2 Å-1.
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    A procedure for the automatic choice of dynamical coordinates for semirigid molecules (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 198-201 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A fully automatic procedure for the generation of constraint-conserving coordinates especially suited for the lattice dynamics of molecular crystals has been developed. Molecules with arbitrary constraints from rigid, semirigid to completely flexible may be treated. The procedure generates a mapping from new dynamical coordinates {ζp} to Cartesian atomic displacements. The new coordinates are defined by this mapping. It is accurate up to second order in ζp, thus allowing for the inclusion of force-constant contributions due to curved paths of atoms whose displacements are subject to some constraints. The procedure has been implemented in a lattice dynamics program currently under development. Exemplifying calculations on an oxalic acid molecule with several sets of constraints are presented.
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    Superspace-group description of short-period commensurately modulated crystals (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 202-207 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The symmetry of superstructures is described by an ordinary three-dimensional space group, based on a unit cell which is a multiple of the basic structure unit cell. Alternatively, superstructures can be looked upon as commensurately modulated structures. Then, the structure is described by its basic structure plus some distortion wave. In this paper the application to superstructures of superspace groups, originally devised to describe the symmetry of incommensurately modulated structures, is discussed. The Bravais classes of superspace groups for commensurately modulated structures are derived. A comparison is made between the superspace group and the ordinary three-dimensional space-group description for commensurately modulated structures. With the help of the structure of Ag0.35TiS2, the consequences for the interpretation of the diffraction pattern are discussed. Also, the nature and number of the independent parameters in the superspace-group approach are compared with the description of the structure by an ordinary space group.
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    Reciprocity in electron energy-loss spectra from non-centrosymmetric crystals (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 208-211 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The energy losses of fast electrons propagating through a thin crystal show a strong effect associated with the interference term between Bloch-wave eigenstates. Reversing the direction of the electrons gives the same spectrum, and reciprocity is observed in the interference term between eigenstates in inelastic electron scattering. The reciprocity principle may be used to advantage to observe for GaAs a very large difference in the characteristic energy-loss spectra for pairs of experimental arrangements related by a mirror operation around the polar (111) planes. This provides a sensitive way of determining the polarity of a crystal based on simple two-beam arguments, and may also be used to obtain direct structure-factor phase information.
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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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    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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    Crystallography, geometry and physics in higher dimensions. III. Geometrical symbols for the 227 crystallographic point groups in four-dimensional space (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 294-304 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A geometrical 'WPV' notation for crystallographic point symmetry groups (PSG) in four-dimensional space is proposed. This simple notation generalizes the Hermann-Mauguin notation and makes it possible to retrieve the PSG elements easily. Tables classifying all elements of each PSG for systems 1 to 28 are presented. For higher systems, from 29 up to 33 inclusive, the results of the work are not reported owing to the space required, but they are at the disposal of the reader upon request.
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    A new method of deriving and cataloguing simple and multiple antisymmetry Gl3 space groups (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 326-337 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Antisymmetric characteristics of 230 (Fedorov) G3 space groups are constructed. By application of a partial cataloguing method based on a newly defined term of antisymmetric characteristic type, a partial catalogue of simple and multiple antisymmetry Mm type space groups and numbers of these groups are obtained.
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    Extinction in the framework of transfer equations for general-type crystals (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 304-316 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An improvement of the classical theory of extinction in mosaic crystals is made by starting from the energy transfer equations valid for a general-type crystal according to Zachariasen's [Acta Cryst. (1967), 23, 558-564] classification. Within the assumption that only the integrated intensity of the diffraction peak is needed, the equations are first simplified and then solved. The result obtained for the extinction factor is similar to that of Becker & Coppens [Acta Cryst. (1974), A30, 129-147], but two new parameters appear if the crystal is not of type I. One of them, determining the peculiarity of the transfer equations, gives differences in the extinction factor not greater than 8%. The other, representing the ratio of the kinematical cross-section strengths along the diffracted and incident beams, gives differences up to 50%. For crystals of ellipsoidal shape, empirical formulae appropriate for structure refinement programs are proposed.
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    X-ray diffraction by a low-angle twist boundary perpendicular to crystal surface. II. Plane-wave image profiles (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 322-326 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The formulae for the structure factor of a dislocation superlattice, obtained in paper I, are analyzed in a variety of situations. The plane-wave image profiles of a twist boundary perpendicular to the crystal surface are plotted for various values of the satellite order l and (hb), where h is the diffraction vector and b is the Burgers vector. The kinematic profiles are in qualitative agreement with the superstructure factor of the dislocation superlattice. Because of extinction, the dynamical profiles appreciably differ from the kinematic ones. The X-ray channelling through the twist boundary is demonstrated.
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    X-ray diffraction by a low-angle twist boundary perpendicular to crystal surface. I. Superstructure factor of screw dislocation superlattice (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 316-321 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The X-ray two-wave diffraction on a dislocation wall perpendicular to a crystal surface, consisting of periodically arranged dislocations (low-angle twist boundary), is considered in the case when the dislocation superlattice period is much less than the crystal extinction length. The formula obtained for the reflected intensity is of the same form as that for an ideal crystal with a modified crystal structure factor. The superstructure factor of a dislocation superlattice is calculated. The recurrence relations are produced which enable a superstructure factor to be calculated for a satellite of any order and magnitude hb (h is the diffraction vector, b is the Burgers vector).
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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 
    Details
    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 
    Details
    ISSN: 1600-5724
    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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    Diffusion in crystalline solids edited by G. E. Murch (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 159-159 
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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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    Creep of crystals by J.-P. Poirier (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 159-160 
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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 of holors. (A generalisation of tensors) by P. Moon and D. E. Spencer (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 160-160 
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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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    Crystallographic computing 3: Data collection, structure determination, proteins, and databases edited by G. M. Sheldrick, C. Krüger and R. Goddard (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 160-160 
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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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    Advances in X-ray analysis. Vol. 27 edited by J. B. Cohen, J. C. Russ, D. E. Leyden, C. S. Barrett and P. K. Predicki (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 160-160 
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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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    Dynamical properties of solids edited by G. K. Horton and A. A. Maradudin (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 160-160 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    Polycrystalline semiconductors: physical properties and applications edited by G. Harbeke (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 160-160 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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    A treatment of the coplanar three-beam Si[000,440,404] diffraction (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 161-167 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The peak of the spectral line Ni Kα2 was measured by the double-crystal spectrometer in the arrangement (Si 440 sym., +Si 440 sym.). It is possible to adjust the Si crystal so that the conditions for coplanar three-beam Si[000, 440, 404] diffraction are satisfied for the wavelength of the incident radiation λ ̃0.166288 nm involved in the Ni Kα2 peak. When the second Si crystal was adjusted to this three-beam diffraction position an anomalous change of the measured dependence was found. A very simple model of the experiment was suggested and the necessary calculation completing the paper of Graeff & Bonse [Z. Phys. B, (1977), 27, 19-32] was performed to explain qualitatively the anomalous change.
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    Random elastic deformation (RED) – an alternative model for extinction treatment in real crystals (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 167-173 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A modification of the Hamilton-Zachariasen theory of extinction in imperfect crystals is reported. Unlike the generally adopted Darwin mosaic model the crystal is supposed to consist of elastically deformed domains so that individual reflection events can be treated within the quasiclassical approach developed by the author in an earlier study [Acta Cryst. (1984), A40, 120-126]. In this way a modified expression for the scattering cross section, taking into account multiple wave interference, is introduced into the energy transport equations. Under the assumption of a constant magnitude of the strain gradient and of spherical isotropy of its orientation distribution, generally valid results formally compatible with the standard solution of Becker & Coppens [Acta Cryst. (1974), A30, 129-147] are obtained. A significant achievement is the physically correct description of the primary extinction effect.
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    The phases of forbidden reflections (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 173-179 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The invariant phases of large numbers of germanium triplets, consisting of one forbidden and two permitted reflections, have been determined experimentally. The forbidden reflections include members of the forms {200}, {222}, {420} and {442}. Phase effects in triplets containing members of the ultra-weak (forbidden) {622} and {640} were detected but were too weak to provide reliable phase indications. The phases of all triplets which include a forbidden reflection and the {\bar 3}{\bar 1}{\bar 1} reflection are observed to be negative. The phases of individual forbidden reflections, whose indices are described as summing to (4n - 2), are equal to (-1)n. The imaginary part of the dispersion correction to the atomic form factors is relatively large (0.89 for Cu Kα1 radiation): it makes significant contributions to the structure factors and the phases of the vanishingly weak forbidden reflections.
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    Sayre's equation is a Chernov bound to maximum entropy (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 428-430 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Sayre's equation is fundamental to a large part of classical direct methods. In this paper, it is shown that this equation can be derived via an integral bound to the entropy integral. While positivity is implicit in this derivation, atomicity is not used.
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    X-ray study of planar defects in highly oriented pyrolytic graphite (HOPG) (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 418-425 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A detailed X-ray study of HOPG reveals extensive wings on the 00.l Bragg reflections whose width in a scan normal to 00.l is comparable to the mosaic spread. These wings, which are absent in single-crystal profiles, are attributed to rotational or twist (T) defects between perfect substacks of pyrolyzed graphite. Along 11.l, the twists destroy coherence and produce an effective 'particle-size' broadening. The average substack size, or spacing between T defects, is estimated through profile fitting to be about 110 Å. The lateral extent of T defects is comparable to a mosaic-block size.
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    Superimposing several sets of atomic coordinates (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 426-428 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A procedure is described which determines the best rotations to superimpose M rigid n-point objects, such that the weighted sum of mutual squared deviations is minimized. Apart from providing an easy and rigorous way for the least-squares superposition of any number of similar structures, this procedure can also be used to obtain a set of mean atomic positions for a substructural fragment that is contained in different structures with slight deviations from its mean geometry or to symmetrize distorted structures.
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    Are (TSeT)2I crystals homochiral or microtwinned? (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 430-431 
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    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple experimental test is described for deciding whether a crystal with a chiral space group is built from homochiral or heterochiral domains; this test is applied to (TSeT)2I {TSeT= tetraselenotetracene (naphthaceno[5,6-cd, 11,12- c' d']bis[1,2 ]diselenole )}.
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