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  • International Union of Crystallography (IUCr)  (4,538)
  • Annual Reviews
  • 1970-1974  (7,465)
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  • 1
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 24-34 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A direct method for the determination of polytype structures of SiC, ZnS and similar substances from X-ray data is described. It is based on the values of a Patterson-like function (the `Pattersonian') which only depends on the stacking of the translationally equivalent layers of the structure. The way of obtaining the Pattersonian function from the experimental intensities is described and an algorithm given by which the sequence of layers may be deduced. This sequence is conveniently characterized by the sequence of the digits of a binary number. The influence of experimental errors in the intensities on the possibilities of determining the real sequence is discussed.
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  • 2
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 1-18 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Seventeen sets of measurements of structure factors of D(+)-tartaric acid, within the range (sin θ)/λ 〈 0.5 Å−1, were provided by the participants in the International Union of Crystallography Single Crystal Intensity Measurement Project. Each participant used a different crystal, all being derived from a single crystallization batch. The results in the Project are representative of those from a wide variety of currently used diffractometers and techniques. The instruments included four-circle, normal-beam and equi-inclination diffractometers. Cu and Mo radiations were used – unfiltered, with single and balanced filters, and with crystal monochromators. The aims of the project were twofold: (a) to provide an estimate of the spread of F values associated with the range of variables involved in the project and (b) to locate, if possible, the sources of error. A number of agreement indices were used to measure the spread of F values both for equivalent reflections within any one experiment and for comparisons between experiments. In an attempt to allocate errors to certain plausible sources, an analysis-of-variance was applied to the weighted deviations of individual values of F from the set of mean values. The variables specified were intensity I, a θ angle factor d* and the Miller indices h,k,1. From the values of the agreement indices and the interaction curves from the analysis-of-variance, it was possible to recognize outlier sets that differ considerably from the mean and to isolate these, where necessary, before arriving at an estimate of the error spread of the main group. In this project, there is no one simple figure of merit which provides a ready assessment of the accuracy of measurement of structure factors. Rather, there are several ways of indicating the probable accuracy. One way is to present the spread of values of Rij(Σ(|Fi| − |Fj|)/Σ ½(|Fi| + |Fj|). This shows that two scaled experimental sets of structure factors, measured under circumstances similar to those of the project, will most probably differ by 6%, agree no better than 3%, and usually no worse than 10% except in cases of extreme systematic error where it may rise to 50% or more. From the analysis-of-variance, inferences are drawn concerning the concordance of results derived from the different types of diffractometer, on features of technique associated with the diffractometers and on other aspects, including 2 dependence, monochromaticity, count rates and extinction in the crystals. It is concluded that other sources of error may be present and that future projects should be designed to reveal these.
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  • 3
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 169-170 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 4
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 178-178 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 5
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 168-168 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 6
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 182-183 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 7
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 186-188 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 8
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 230-234 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Any crystal structure may be described in terms of a sublattice of points, each of which represents a certain fraction of the electron density. Multiplying this sublattice by a density function f(x) and applying a shift function s(x), which brings the atoms into the right positions, the correct crystal structure can be given in many different ways. It is shown that the shift function s(x) yields phase relations between the structure factors F(h), which may be evaluated directly, if the coefficients of the Fourier representation of s(x) converge rapidly. This behaviour is demonstrated for the case of a one-dimensional acentric model structure consisting of 50 atoms. Complete information on the structure may be obtained by routine methods with the aid of 5 given phases of the structure factor. This procedure may also be applied to three-dimensional structures, if the corresponding computer programs are available.
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  • 9
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 260-262 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The analysis in part I is generalized to any crystal containing rigid molecules which undergo anisotropic translational and librational motion about a site fixed by symmetry. The treatment is correct to terms in (ui2)2 and (ωi2)2, where (ui2) is the mean-square translational displacement of the molecule along the ith axis and (ωi2) is the mean-square angular libration about the same axis. The first-order treatment to terms in (ui2) and (ωi2) is shown to be equivalent to the rigid-body theory in current use.
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  • 10
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 289-292 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that the concept of the molecular centre of libration in the description of the average rigid-body thermal behaviour of molecules is a useful approximation. A restriction is made on the full theory, making the centre of libration model a constrained version of the complete model. The relationship between the models is discussed. Some examples are chosen to demonstrate the closeness of the approximation. These results show that for data reaching a reliability factor of no better than 7% an analysis using the full theory might yield a meaningless result. Some data of much higher accuracy does, however, show the need for the full theory.
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  • 11
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 293-294 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The number of independent non-vanishing constants required to describe the six known physical properties, involving a polar vector, has been determined by the character method of Bhagavantam & Suryanarayana for each one of the 58 double-coloured point groups.
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  • 12
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 295-295 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The lattice parameters of ammonium chloride have been measured at 31.5 and 54.0°C. The coefficient of linear expansion is found to be 58.5 × 10−6°C−1.
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  • 13
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 296-296 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 14
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 296-296 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 15
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 292-293 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The recent X-ray diffraction data front Mg2Si, obtained by Panke & Wölfel (Z. Kristallogr. (1969), 129, 9) show systematic differences in the structure factors from those predicted by a model which assumes harmonic thermal vibration of the atoms. These differences indicate an anharmonic component in the thermal vibration of the magnesium atoms, consistent with their tetrahedral site symmetry. An analysis of these data has therefore been carried out in terms of a model which includes anharmonic thermal vibration and a least-squares refinement gave a value of the anharmonicity parameter (βMg = − 2.39 × 10−12 erg.Å−3) which is similar in magnitude to those found for other systems with the fluorite structure.
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  • 16
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 311-314 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A diffraction theory is developed for the model of ordered zones embedded in an otherwise disordered binary alloy. Evaluation of the resulting lattice sums gives an equation for the diffuse scattering everywhere in reciprocal space except under the fundamental lines. From the experimental diffuse intensity one can calculate the relative volume of the ordered zones in the whole crystal, their mean sizes along each of the crystallographic axes, and the distribution of these sizes. A set of relations between the Warren short-range-order parameters αlmn and the size of the ordered zones is also obtained. Comparison with experimental αlmn given in the literature show that a 50 at.% CuAu alloy quenched from 500°C contains ordered zones in a disordered matrix. Similar results were obtained for a 50 at.% CuPt alloy held at 890°C or quenched from 930°C. In a Cu3Au alloy held at 450°C the calculations show the existence of ordered zones with a size of (3 × 3 × 3) unit cells, in accordance with the results of computer simulation work published in the literature.
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  • 17
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 327-336 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The counter method with a time basis has the disadvantage that it includes the systematic error resulting from the variation of the source. The counter method with a monitor counter gets rid of this systematic error but introduces a statistical error originating in the uncertainty of the flux received by the monitor counter. The author proposes a formula which is a compromise between the two methods and which partially retains the advantages of the two methods.
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  • 18
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 336-344 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An attempt is made to differentiate between the three previously proposed models of the structure of tetragonal BaTiO3. In the new model, the serious parameter-interaction problem was avoided by the use of both neutron and X-ray diffraction data collected from c-domain single crystals. The result of the refinement gave the displacement of the Ti atom from its cubic position as 0.0135 ± 0.0004 Å; the R value was 0.027 and 0.024 for the neutron and X-ray data respectively. The analysis also showed that the temperature parameters, B33, along the c axis are approximately independent of mass; B33 = 0.32 ± 0.03 Å2 from X-ray and 0.33 ± 0.04 Å2 from neutron diffraction. The average value obtained for the B11 temperature parameters, B11 = 0.50 Å2, is considerably higher than the B33 value, which thus clearly indicates the existence of low frequency optic modes at room temperature.
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  • 19
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 320-323 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Changes of particle size and strain during annealing of cold-worked aluminum powders have been determined by measuring X-ray line breadths. Aluminum powders ground under special conditions show a decrease in particle size as well as a reduction of strains within certain ranges of temperature. This is due to polygonization processes and allows conclusions to be drawn regarding the limits of coherent regions of X-ray diffraction. The X-ray measurements were supplemented by electron microscope studies.
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  • 20
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 324-327 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal packing of diketopiperazine may be predicted from the approximate molecular geometry and space group symmetry. The van der Waals and hydrogen bonding energies were computed as a function of three rotational degrees of freedom (space group P21/a and Z = 2). The Eulerian angles, relative to the deepest minimum, correspond to a good approximation to the real structure. The calculations were carried out using potential functions tested in some crystals and in the conformational analysis of synthetic and biological macromolecules. A potential function proposed by Stockmayer was chosen to describe the hydrogen bond formation. The rigid-body translations of the molecules in the crystal, known from an analysis of the anisotropic atomic thermal parameters, were qualitatively checked. For this purpose the van der Waals potential energy was computed by moving one chain of molecules and leaving the surrounding chains fixed. The good results obtained again confirm the validity of this method for the solution of the phase problem. It is hoped that this approach may be useful in crystal structure determinations of organic molecules of biological interest.
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  • 21
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 344-349 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The Christian–Gevers theory of X-ray diffraction from hexagonal close-packed crystals with deformation stacking faults is extended to include the effect of change in layer spacing at the faults. The results show that integral breadths as well as integrated intensities remain unaffected to a first approximation. The principal effect is to introduce peak shifts, the magnitude and direction of which depend on the reflexion.
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  • 22
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    Acta crystallographica 26 (1970), S. 354-358 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The elastic constants of certain single crystals may be obtained by the measurement of thermal diffuse X-ray scattering variation in regions close to reciprocal-lattice points. A method has been given which allows for second-order contributions to the total diffuse intensity by use of a least-squares procedure. The refinement was simplified by equating two functions, each depending on the elastic properties of the crystal, the nearby lattice point to the positions of observation and the direction along which the intensity variation is measured. For cubic crystals, there is an exact equality between appropriate powers of these functions for several important crystallographic directions, while for other directions some approximation results. The present paper includes a simple method of allowing for the deviation from equality in the latter cases.
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  • 23
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 363-364 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The lattice parameters of zinc telluride and mercury selenide were measured with a Unicam 19 cm high-temperature powder camera; the following equations represent the results: ZnTe, at = 6.1016 + 54.63 × 10−6t + 6.82 × 10−9t2 + 5.28 × 10−12t3; HgSe, at = 6.0854 + 28.61 × 10−6t + 4.93 × 10−9t2 + 3.74 × 10−12t3. The expressions for thermal expansion coefficients are also given.
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  • 24
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 26 (1970), S. 384-384 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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  • 25
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    Acta crystallographica 26 (1970), S. 443-446 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray diffuse scattering with an intensity distribution of one-dimensionally elongated shape in reciprocal space is observed for a single-crystal of AuCu3, which is in a transient state around the order-disorder transition point. The analysis is carried out on the basis of Wilson's model for the disordered structure of AuCu3. The probability that a unit cell at a given position is displaced by half the diagonal of the unit cell cube is derived as a function of the position of unit cell, and is found to be expressed by an exponential function.
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  • 26
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    Acta crystallographica 26 (1970), S. 376-377 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The coherent neutron scattering amplitude of rubidium has been remeasured using powders of RbCl, RbBr, and RbI. A consistent value, (0.68 5 ± 0.01) × 10−12 cm, was obtained, differing significantly from earlier measurements. The new value is believed to be more reliable. The bound coherent scattering cross section is 5.9 ± 0.2 barns.
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  • 27
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    Acta crystallographica 26 (1970), S. 379-379 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A corrected electron density expression is given for space groups P4122 (No. 91) and P4322 (No. 95).
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  • 28
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    Acta crystallographica 26 (1970), S. 405-408 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: From X-ray measurements at room and low temperatures it was found that the characteristic temperature Θ of the system Ag-Cd decreases by about 17°K in the concentration range from 0 to 30 at.% Cd. For the system Ag-Zn no systematic change of Θ with increasing concentration of Zn was observed.
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  • 29
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    Acta crystallographica 26 (1970), S. 470-472 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The advantages are discussed of using a ball model to determine the arrangement of lattice points in a given lattice plane and for determining the stacking properties of such planes. It is shown that the ball model can be considered as a simple analogue computer for solving the Diophantine equations involved. To date, such ball models have been used only for cubic and hexagonal crystals, but they can be constructed for many other structures.
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  • 30
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    Acta crystallographica 26 (1970), S. 463-470 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: One hundred and eighteen crystals of cadmium iodide have been investigated by X-ray diffraction methods to verify the disorder theory of polytypism in these crystals. The degree of one-dimensional disorder has been evaluated for eighty-two polytypes by intensity measurements on oscillation photographs. The frequency distribution curve of relative abundance of polytypes versus their degree of disorder shows two maxima, one for α1 ∼ 0.06 and the other for α2 ∼ 0.26. The results are in agreement with those obtained earlier by Jagodzinski in silicon carbide crystals and provide more information regarding the origin of polytypism in crystals. Fifty-three new polytypes of cadmium iodide, forty-four hexagonal and nine rhombohedral, have also been discovered during the investigation.
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  • 31
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    Acta crystallographica 26 (1970), S. 489-491 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The accuracy in X-ray diffraction intensities obtained by the use of an automatic IBM 1800-controlled SAAB film scanner is discussed. The random errors have been found to be around 4% of the intensities for most reflexions. By comparison with data obtained from a Joyce–Loebl microdensitometer it has been found that there are no serious systematic errors in the film-scanner data. Measurements from Weissenberg and precession films are discussed.
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  • 32
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    Acta crystallographica 26 (1970), S. 499-501 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new set of relations between structure factors corresponding to an isomorphous pair is established: inequalities, convolution equations, probabilities. These relations may enhance the power of direct methods for the determination of phases.
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  • 33
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    Acta crystallographica 26 (1970), S. 514-518 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
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    Notes: The atomic scattering factor of germanium has been obtained from measurements of the Pendellösung period in wedge-shaped single crystals with a three-crystal X-ray spectrometer. For the 220 reflexion the value is 23.78±0.35, in good agreement with the theoretical value of 23.76. Fine structure in the profile of the rocking curves has been observed in thickness regions close to Pendellösung minima.
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  • 34
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    Acta crystallographica 26 (1970), S. 522-527 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The description of n-dimensional space by a basis of (n + 1) vectors, ai (i = 1, . . . , n + 1), is discussed, with particular reference to the Miller–Bravais system of indexing hexagonal crystals. It is shown that if a hyperplane with normal h makes intercepts hi−1 on the ai and a vector u has components ui relative to the ai, then h. u = Σhiui without any further restrictions on the hi or ui. Furthermore, it is possible to find a basis a†i(i = 1, . . . , n + 1) for reciprocal space such that h = Σhia†i is always true and indeed there are n degrees of freedom available for choosing such a basis. Criteria which may lead to a unique choice of a†i are discussed.
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  • 35
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    Acta crystallographica 26 (1970), S. 535-542 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The high temperature X-ray diffraction study of the monoclinic tetragonal phase transition in ZrO2 showed that it is spread over a temperature range 930–1220°C. Anomalous intensity changes are observed in the pretransformation region 930–1100°C. Coexistence of phases through hybrid crystal formation in the region 1100–1220 °C and the mechanism of transition are discussed. The orientation relationship between the monoclinic (m) and the tetragonal (t) crystal structures consists in the parallelism of the (100)m plane to (110)t and of the bm axis to the ct axis. A drastic change in a small temperature range during the tetragonal–monoclinic transition is interpreted as a cooperative change in both short and long range interactions. The large thermal hysteresis is attributed to the difference in the mechanism of transition during heating and cooling.
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  • 36
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    Acta crystallographica 26 (1970), S. 460-461 
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  • 37
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    Acta crystallographica 26 (1970), S. 476-483 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The small angle X-ray scatter from crystalline polymers is evaluated by using a one-dimensional model where the density between crystal and amorphous phases changes linearly over a finite transition range t, and where the sizes of the crystal and amorphous regions fluctuate according to independent Gaussian distributions. The calculation is based on the general model formulated in part I. Approximate expressions are derived for the width and area of the diffraction peaks. The dependence on t occurs in the factor sin2 πst/(πst)2 which affects only the peak intensities. An analysis is made to find how the factor will modify theoretical interpretations based on experimental intensity measurements.
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  • 38
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    Acta crystallographica 27 (1971), S. 75-76 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The restriction of Ott's interval sequence in the polytypes of SiC to the numbers 2, 3 and 4 is related to the fact that 1 does not normally occur in the Zhdanov symbol.
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  • 39
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    Acta crystallographica 26 (1970), S. 647-654 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Takagi's equations of X-ray diffraction by an imperfect crystal are solved in the most general case by the method used in a previous paper in the particular case of a perfect crystal. It is shown that, for small strain gradients, the amplitude inside the crystal is the sum of two generalized wavefields obtained by convolution of the Hankel functions H10 and H20 with a `source distribution' depending on local deformations. This is in agreement with the results given by other authors (Kato, Penning, Malgrange). This corresponds to the approximation of geometrical optics for X-ray propagation in crystals. A quantitative criterion of validity for this approximation is given. When this criterion is not fulfilled in some part of the crystal, the generalized wavefields are diffracted. It is shown that this implies creation of new generalized wavefields. This provides a physical interpretation of the occurrence of this phenomenon in the vicinity of a dislocation line and properties of the contrast of images in X-ray topography.
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  • 40
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    Acta crystallographica 26 (1970), S. 543-558 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Problems in the collection and analysis of accurate diffraction data have been explored in a careful study of urea. Initial neutron measurements on non-spherical crystals show that little confidence can be placed in the values of extinction parameters derived for a non-spherical crystal of a hydrogenous material used in a neutron-diffraction experiment. It is also shown that multiple Bragg scattering is an important source of error. Uncertainties in the absorption and extinction corrections can be overcome by using a spherical crystal with μR ∼ 0.5. Corrections for the effects of multiple Bragg scattering were made by correlating complete sets of data measured at three different wavelengths. A number of models based on rigid-molecule vibrations and anharmonic interactions between atoms were used to treat the effects of thermal vibration. The best results were obtained from a refinement of the spherical-crystal data using general thermal parameters plus corrections for curvilinear motion, but a rigid-molecule treatment, with fewer vibrational parameters, was not much worse. Anharmonic effects did not seem to be appreciable. To look for possible `bonding features' in urea, difference syntheses computed from X-ray data and calculated X-ray structure factors based on the neutron results were plotted. It was not possible to remove the deep negative differences at the atomic positions by adjusting a scale factor and a thermal diffuse scattering correction, and it is probable that a real discrepancy exists between the observed and calculated structure factors.
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  • 41
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    Acta crystallographica 26 (1970), S. 574-574 
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  • 42
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    Acta crystallographica 26 (1970), S. 575-578 
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  • 43
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    Acta crystallographica 26 (1970), S. 691-692 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The range of validity of an approximation for the F distribution is investigated. The R factor ratio as used by crystallographers is calculated and compared with tabulated values. This is done for the range of degrees of freedom generally encountered in crystallographic problems.
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  • 44
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    Acta crystallographica 26 (1970), S. 692-694 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The rotation and translational parameters of a known molecular rigid group in an unknown crystal structure have been determined using reciprocal-space methods based on the Patterson function. Various refinements of the rotation function have been introduced in order to increase the speed and sensitivity of this method.
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  • 45
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    Acta crystallographica 26 (1970), S. 696-696 
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  • 46
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    Acta crystallographica 26 (1970), S. 599-603 
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    Notes: A practical and fast method for the determination of the layer sequence of high-order polytypes is described. Experimentally, the method involves only the determination of the relative order of reflexion intensities and does not employ actual intensity measurements. Auxiliary information, such as the percentage of hexagonality and the cyclicity of the polytype involved, considerably shortens the computer time needed. The method was used to identify a large number of ZnS polytypes and it is applicable to other polytypic material as well.
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  • 47
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    Acta crystallographica 26 (1970), S. 613-622 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The thermal diffuse scattering (TDS) contribution to X-ray Bragg peaks is discussed in terms of its two experimental components, the included and the background parts. The discussion is primarily directed toward situations where detailed elastic constant information and a large computer are not available. Graphs are displayed which, in the spherical average approximation, allow an accurate assessment of the influence of all the experimental variables on the TDS contribution. It is shown that, even in the general case where spherical averaging is a poor approximation, the included TDS varies linearly with length of scan for small scans. A technique for determining the constant of proportionality is suggested. Thus the included TDS may be evaluated even though the elastic constants are not known.
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  • 48
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    Acta crystallographica 26 (1970), S. 667-673 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Primary and secondary extinction are studied using the dynamical theory of X-rays diffracted by imperfect crystals. The transition from dynamical to kinematical scattering is explained in terms of fundamental processes in diffraction. Contrary to existing extinction theories, where the intensities diffracted dynamically by single coherent domains of a mosaic are combined using an ad hoc assumption of mosaic distributions, the present theory permits the dynamical amplitudes to change in response to disturbances of the dynamical interactions by imperfections. Neither the mosaic block model nor the statistical treatment of imperfections is used. The extinction of diffracted intensities is thereby treated as caused solely by inhomogeneous strains in a single coherent domain.
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  • 49
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    Acta crystallographica 27 (1971), S. 233-238 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An algorithm is presented for using equi-inclination Weissenberg and precession photographs to index an unknown triclinic cell to give a right-handed homogeneous vertex at the origin. Using such indexing, and known crystal parameters and camera settings, the geometry of reflexion is analysed to predict spot positions on both halves of equi-inclination Weissenberg photographs.
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    Acta crystallographica 27 (1971), S. 6-11 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is formulated for refining and/or extending a set of crystallographic phases by real-space convolution utilizing the fast Fourier-transform algorithm. The method is applied to extending a set of myoglobin phases and the results show that high-resolution structural information can be obtained from high-resolution intensities and low-resolution phases.
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  • 51
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    Notes: Three new polytypes of cadmium iodide, two rhombohedral 60R and 72R and one hexagonal 32H have been discovered. The detailed atomic structures of 60R and 72R have been worked out; these are [(22)3 1223]3 and [(22)4 1223]3. These structures indicate the existence of a structure series [(22)n 1223]3. The growth of the polytypes 60R and 72R has been discussed in terms of creation of periodic stacking faults in the basic structure. Evidences and arguments including electron microscope observations of dislocation dissociation have been presented to show that the proposed mechanism is the most likely one through which the above polytypes have resulted. Following Hirth & Lothe, theoretical stacking fault energies of the probable structures of the two polytypes have been calculated and it has been found that the stacking fault energies for the proposed structures are minimum. Based on this criterion the structure of 32H was deduced and was found to represent the correct atomic structure. It seems possible that the minimum stacking fault energy criterion may prove to be of value in general in determining the atomic structure of polytypes.
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    Acta crystallographica 27 (1971), S. 300-301 
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    Acta crystallographica 26 (1970), S. 674-678 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The correspondence of the thermal movement in crystals and the Bragg-reflexion intensity distributions is treated in terms of a theory developed for describing the effect of static mechanical distortions. The basic functions appearing in that theory are replaced here by the corresponding time averages. The dependence of the temperature factor on the crystal size is discussed. The effect that additional static mechanical distortions have on the temperature factor is also discussed. Moreover it appears from the given expressions that there is a broadening in the Bragg reflexions as a consequence of the crystal distortions due to thermal movement. In the kinematical approximation, the integral intensity of a Bragg reflexion is temperature independent. If the integral intensity decreases as the temperature increases this is either a dynamical effect or a consequence of a measurement that takes only into account the intensity in a limited region around the maximum of the Bragg reflexion. In line profile analysis, the thermal broadening effect can be separated from the mechanical distortion broadening effect by means of Stokes's method if a reference powder, of the same substance (in an undistorted constitution) as the powder subjected to analysis is used.
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  • 54
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    Acta crystallographica 27 (1971), S. 353-362 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: High-temperature diffraction experiments have been carried out on the NaCl: SrCl2 system, both in its poly- and monocrystalline form. These experiments have led us to the determination of the dilution enthalpy of the SrCl2 precipitates in the NaCl matrix (hD = 0.90 ± 0.05 eV). Brauer's method was used to calculate the distortion around one defect and Eshelby's model was used to evaluate the resulting change in the lattice parameter due to these perturbing centers. The concentrations of defects calculated from these models are in good agreement with those determined chemically. Small-angle X-ray scattering experiments were performed on the same crystals, with suitable thermal treatments, to follow the clustering of defects as a function of the annealing temperature. It is possible to maintain a large amount of nearly dispersed strontium in the lattice by quenching the crystals from high temperature. The point defects agglomerate by successive annealings from 100 to 300°C, forming clusters of increasing sizes. A discussion of the composition of those centers is included.
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  • 55
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    Acta crystallographica 27 (1971), S. 368-376 
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    Notes: An improvement is described in the automatic procedure for solving crystal structures incorporated in the computer program LSAM. The development of signs from an initial set containing symbols is carried only as far as is necessary to establish strong relationships between the symbols. The information so gained is used in a fresh beginning of the symbolic-addition process. Some failure of relationships between symbols is allowed to give a multisolution method. A phase-permutation computer program for non-centrosymmetric structures, MULTAN, incorporates a weighted tangent formula. This is of the form {\rm tan}\varphi_{\bf h} = {{\sum_{\bf h'}w_{\bf h'},w_{\bf h-h'}|E_{\bf h'}E_{\bf h-h'}| \sin (\varphi_{\bf h'} + \varphi_{\bf h-h'})}\over{\sum_{\bf h'}w_{\bf h'},w_{\bf h-h'}|E_{\bf h'}E_{\bf h-h'}| \cos (\varphi_{\bf h'} + \varphi_{\bf h-h'})}} = {{T_{\bf h}}\over{B_{\bf h}}} and w_{\bf h} = {\rm tanh}\{ \sigma_3\sigma_2^{-3/2}|E_{\bf h}|(T_{\bf h}^2 + B_{\bf h}^2)^{1/2}\}.All phases are accepted as soon as they are found with the associated weight. This gives a fourfold increase in speed in development of the complete phase set. An absolute figure of merit is described to indicate probably correct phase sets for multisolution methods.
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    Acta crystallographica 27 (1971), S. 398-398 
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    Acta crystallographica 27 (1971), S. 408-410 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A simple formulation is described which can be used to predict the line shape obtained in three-axis spectrometry. The method is shown to produce curves in good agreement with measured data.
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  • 58
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    Acta crystallographica 27 (1971), S. 140-147 
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    Notes: Measurements made on convergent-beam patterns from MgO taken near the [001] zone-axis at two fixed temperatures have been studied in detail. Two types of patterns, namely the symmetrical excitation of a single 200 reflexion and the simultaneous excitation of the 200, 020, 220, reflexions were studied, using up to 129 beams in the dynamical calculations. The absorption function, Vih exp (−BiS2), was found to be well defined at the zone axis, allowing separate determination of Vih and Bi. For the pattern for single excitation, Vi0 = 0.6 volt, Vih = 0.14 volt, Bi = B = 0.3, was determined at room temperature. In comparing the two types of pattern at high temperature an increase in Vih of between two and three times was found for the 3-reflexion pattern. This increase, and the more normal value found for the single excitation pattern, seems to accord with other experience that the dynamical increase in Vih, as predicted by Yoshioka and Kainuma, possibly occurs in the vicinity of a many-line intersection of the Kossel pattern but not at the zone axis.
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    Acta crystallographica 27 (1971), S. 148-157 
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    Notes: The nature of the scattering surfaces for thermal diffuse scattering (TDS) and the contribution of TDS to the intensity measured during a scan through a Bragg reflexion are considered for a model in which all phonons are assumed to have the same velocity in the crystal. For neutrons which are faster than this sound velocity the contribution is independent of the neutron velocity and can be calculated using the formulae derived for X-ray scattering. However, for neutrons which are slower than the sound velocity the contribution is a function of the neutron velocity and will be less than that given by the X-ray formulae. The behaviour of the TDS contribution as a function of the neutron velocity is considered for a type scan for which an analytical evaluation is possible and these considerations are extended to the conventional ω and θ−2θ types of scan. It is concluded that there is no discontinuity in the TDS contribution when the velocity of the neutrons is the same as that of the phonons, but that evaluation of a reliable correction is difficult for slower-than-sound neutrons for the conventional types of scan. These conclusions will also apply for a more realistic case for which the phonon velocities are not all identical.
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    Acta crystallographica 27 (1971), S. 157-165 
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    Notes: Normal probability plot analysis is applied to independent sets of crystallographic structure factor measurements (F) and the derived coordinates (p). Differences between corresponding pairs of structure factors (ΔF) in the two sets are examined in terms of their pooled standard deviations (σF) by plotting the ordered statistic δm = ΔF/σF against the expected normal distribution. Differences between pairs of coordinates (Δp) are similarly examined in a δp = Δp/σp half-normal probability plot. Both plots result in linear arrays of unit slope and zero intercept, for normal error distribution in the experiment and the model and correctly assigned standard deviations. Analysis of departures from this ideal, especially when both plots are considered together, provides detailed information of the kinds of error in δm and in δp. By inference, the kinds of error in F and σF as well as in p and σp can be deduced. The normal probability plot δR = |Fmeas| − |Fcalc|/σFmeas should ideally also be linear, with unit slope and zero intercept. Deviations from ideal provide considerably more information than the conventional R values. Analysis of δR in combination with δm plots allows further specification of the error distribution. Examples using these plots are given and discussed, based both on real and on simulated data.
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    Acta crystallographica 27 (1971), S. 187-188 
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    Notes: For those reflexions of which the sign is determined by a relatively small number of heavy atoms, the known heavy-atom contribution is subtracted from the observed structure factor to obtain the magnitude and the sign of the light-atom contribution. Thereafter the signs of the reflexions that do not have appreciable heavy atom contributions are found using the triple product sign relationship.
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    Acta crystallographica 27 (1971), S. 190-191 
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    Acta crystallographica 27 (1971), S. 202-206 
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    Notes: A general symbolic representation of the stacking faults in close-packed structures is given. It is based on n-layer symbols assigned to points in a three-dimensional space. Graphical symbols are introduced in order to represent undisturbed structures as well as stacking faults on a general basis.
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    Acta crystallographica 27 (1971), S. 198-201 
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    Notes: X-ray diffuse scattering from disordered alloys is the primary direct source of information concerning the Warren parameters which describe the existing state of order. However, the short range order diffuse intensity is obscured by other contributions to the diffraction pattern resulting from static atomic displacements from the average lattice, and from effects related to thermal motion. Described here is a method to separate the diffraction pattern into its various components so that each may be interpreted independently. No assumptions are made about the nature of the atomic displacements δ, except that they are sufficiently small, and that the diffraction vector k/2π is sufficiently small, that terms beyond the term quadratic in k . δ may be neglected in the series expansion of exp [ik . δ].
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    Acta crystallographica 27 (1971), S. 219-222 
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    Notes: A neutron diffraction study was made of the 222 reflection of germanium and silicon between the temperatures of 25 and 500 °C. Care was taken to reduce effects of simultaneous and higher order reflections. Extinction effects were considered, as nearly perfect crystals were employed in the study. Within the sensitivity of the experiment, no 222 neutron intensity was detected. The resulting upper limit placed on β, the cubic atomic potential constant, is roughly one half of a previously suggested value.
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    Acta crystallographica 27 (1971), S. 229-233 
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    Notes: Some potentials describing electrostatic interactions between oxygen and sodium, potassium, rubidium and caesium ions are tested in known organic crystal structures. The atomic and ionic coordinates may be predicted satisfactorily by locating the deepest minimum of the potential energy which depends on rotational and translational degrees of freedom.
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    Acta crystallographica 27 (1971), S. 238-243 
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    Notes: Measurement and theoretical estimate of the anharmonic non-quadratic contribution to the Debye–Waller factor for NaCl are reported. For the experiment the Mössbauer γ-ray diffraction technique was used to find the elastic diffracted intensity separated from the thermal diffuse scattering. The theoretical treatment makes use of the asymptotic form of the displacement correlation functions to give simple explicit expressions for the non-quadratic term. The role of the relevant lattice dynamical parameters is discussed. The deviation from the Gaussian form of the Debye–Waller factor is shown to be large enough to be observed, and the possibility of estimating the third-order anharmonic coupling constant from such a measurement is indicated.
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    Acta crystallographica 27 (1971), S. 256-259 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is proposed, for certain single crystals, of estimating the structure factor amplitudes corresponding to Bragg reflexions with strong to medium integrated intensities from measurements of the thermal diffuse X-ray scattering in regions of reciprocal space close to the appropriate lattice points. The values obtained conventionally from integrated Bragg intensities are often subject to considerable error due to extinction effects. The thermal diffuse scattering, being incoherently scattered and of a relatively weak intensity, would appear to be less likely to be affected by primary and secondary extinction. The structure factor amplitudes (or correction factors for those found from Bragg measurements) are obtained from the observed scattering data by a least-squares refinement method. Procedures are suggested for use where measurements are made on (i) a relative scale, (ii) an absolute scale, with respect to the direct beam intensity. The method is illustrated by application to some single-crystal data.
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  • 69
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    Acta crystallographica 27 (1971), S. 273-280 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The scattering amplitude of an X-ray interferometer is calculated using a general theory of X-ray diffraction. Analytic expressions are given for the intensities of diffracted beams in interferometry; these expressions include the effect of the positions of each crystal lattice in addition to ordinary dynamical effects. It is concluded that the fringes observed in X-ray interferometry of a lattice spacing are accounted for by an optical (Moiré) effect rather than by dynamical effects of X-ray diffraction.
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  • 70
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    Acta crystallographica 27 (1971), S. 280-284 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In the present article (i) a new formula for the single-crystal rocking curve for both the centrosymmetric and polar Bragg case is given; (ii) a geometrical construction is derived, whence many properties of the rocking curve are easily visualized; (iii) the different analytical expressions introduced by several authors are shown to be a consequence of different definitions of the variable `y'.
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  • 71
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    Acta crystallographica 27 (1971), S. 296-296 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Corrections to a previous paper [Acta Cryst. (1970). A26, 349] are given.
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  • 72
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    Acta crystallographica 27 (1971), S. 284-291 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron single-crystal analysis of complex protein structures requires the collection of intensity data on a large number of reflections. The use of time-of-flight analysis (in particular Fourier time-of-flight analysis employing phase detection) of diffraction data, offers a significant increase in the efficiency of the use of reactor neutrons. Such a method would facilitate the use of neutron diffraction in protein structure work. In this paper, we investigate the use of the Fourier chopper in single-crystal work. We examine the effect of various system parameters (frequency stability, flight path fluctuations, collimation, sample mosaic spread, inaccuracy in phase detection, and statistical counting errors) and determine general specifications for such an apparatus. None of these specifications appears to be beyond present day technology.
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  • 73
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    Acta crystallographica 27 (1971), S. 298-300 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A logical scheme is proposed for the ordering of general positions in International Tables for X-ray Crystallography.
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  • 74
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    Acta crystallographica 27 (1971), S. 296-298 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By comparing the crystal structure (investigated by means of X-ray diffraction) and the birefringence of disordered ZnS crystals it is shown that the birefringence Δn is proportional to the hexagonality σ, i.e. Δn = σ . ΔnWurt. The hexagonality σ is the part of hexagonal packing elements, ΔnWurt the birefringence of Wurtzite.
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  • 75
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    Acta crystallographica 27 (1971), S. 316-322 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: If the optical wave front is not normal to one of the principal axes of the indicatrix, diffraction of light in crystals, caused by ultrasound, is observed with maximum intensity when the incident beam is off the Bragg angle by an amount depending on double refraction. In a crystal plate of finite dimensions a standing ultrasonic wave also generates waves with propagation directions which are inclined to the normal of the plate, and interfere with the measurement of sound velocities by the improved Schaefer–Bergmann method. These difficulties are overcome by an appropriate choice of the angle of the incident light beam. Experiments with triclinic and trigonal crystals are reported. Formulae are derived for calculating the angles of incidence necessary for any measurements of sound velocities in crystals.
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  • 76
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    Acta crystallographica 27 (1971), S. 303-313 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Assuming a model based on permanent dipole-dipole, dispersion, induction and repulsion forces, the potential energy of a molecule in a nematic liquid crystal is derived as a function of its orientation. Analysis of the temperature variation of the degree of orientational order in p-azoxyanisole (PAA) and p-azoxyphenetole (PAP) indicates that the permanent dipole interactions are relatively unimportant. Making use of a mean field approximation, a statistical theory of long-range orientational order is developed and the thermodynamic properties of the ordered system are derived relative to those of the completely disordered one. Application of the theory to PAA and PAP shows conclusively that a certain degree of short-range orientational order is present in the liquid phase. Using just three parameters for each compound, viz. the two constants of the potential function and a numerical factor to allow for short range order, the following physical properties have been evaluated which are in quantitative agreement with the experimental data: the long-range orientational order parameter, specific heat and compressibility as functions of temperature in the liquid crystalline range, the latent heat and volume change at the nematic-isotropic transition point. The magnetic birefringence of the liquid phase affords an independent estimate of the short range order which supports the previous calculations.
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  • 77
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    Acta crystallographica 27 (1971), S. 341-347 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Limitations imposed by the geometry of Soller collimator systems on luminosity and resolution of neutron diffraction equipment are studied on the grounds of angular and spatial distribution of neutrons. Transmission functions for collimator systems of arbitrary complexity are derived. The influence of the mutual distances among the various components of the experimental set-up on the shape of transmission functions is given in evidence. Careful intensity measurements performed with well diversified arrangements of Soller collimators are in fair agreement with our theoretical results. The way to improve the performances of neutron diffraction equipment by a proper choice of all the geometrical parameters is shown.
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  • 78
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    Acta crystallographica 28 (1972), S. 33-35 
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    Notes: The presence of unoccupied space of sufficient cross section lying outside the van der Waals surfaces of the atoms in a crystal structure may mean that atoms have been omitted from the structure. A simple graphical method has been devised to display these voids. When such voids occur because of the omission of atoms from a trial structure, the significance of peaks in the difference map in the region of the void is enhanced. This makes it possible to detect and, within limits, to place poorly resolved atoms.
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  • 79
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    Acta crystallographica 28 (1972), S. 40-46 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A method is given for correcting the integral intensities of X-ray reflexions from platelets of single crystals or powders for secondary extinction and thermal diffuse scattering (TDS). The line profiles are calculated as folding integrals from theoretical functions considering the crystallite size distribution, the total absorption, and TDS. By means of variation of the unknown parameters (fraction of TDS to the overall intensity, mean crystallite size and their polydispersity, and absorption coefficient, secondary extinction included) the calculated function has to fit the measured line profile. A detailed description of this method according to Bradaczek and Hosemann is given after introducing some modifications such as collimation errors of the primary beam and anisotropy of the lattice vibrations. The method is applied to measured line profiles of NaCl and LiF single crystals.
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  • 80
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    Acta crystallographica 27 (1971), S. 699-699 
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  • 81
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    Acta crystallographica 28 (1972), S. 134-143 
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    Notes: By searching the 1.5 Å Patterson function of myoglobin (space group P21) with intragroup vector sets characteristic of the heme group and of the main chain of a 4- or 5-turn α-helix, it is shown that it is possible to determine the orientation of the heme, and the axial directions of the prominent helices A, B, E, G, and H. Additional searches performed with helices A, G, and H correctly reveal the true orientations about the helical axes. Translation searches with intergroup vectors, similarly yield the correct positions of the heme and helices A, G, and H relative to a 21 axis. The relative y coordinates (along 21) of the heme group and a helix can be unambiguously found by a search using vectors from the heme Fe atoms to the correctly oriented helix. Several image-seeking functions are explored by varying the selection and weighting of the search vectors. The best results are obtained with an image-seeking function defined as a weighted average over a selected subset of search vectors. The selection is made for each setting of the vector set, and is based on the value of the Patterson function at each search vector in relation to the distribution of values in the entire Patterson function.
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  • 82
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    Acta crystallographica 28 (1972), S. 143-151 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a recent paper (Werner, S. A. Acta Cryst. (1971). A27, 665) it was pointed out that the choice of scans in a neutron diffraction experiment should be based on the criterion that the diffracted beam enters the detector on its centerline for each angular setting of the crystal. The same criterion should be applied in X-ray diffraction. Since the spectral distribution of a source of X-rays and neutrons is quite different, conclusions regarding the optimum coupling between the detector and crystal motions are different in these two cases. In this paper, formulas are derived (within the framework of certain gaussian approximations) for the optimum scanning ratio g in equatorial plane X-ray diffraction experiments on single crystals. For the case when a monochromator is not used, g is independent of scattering angle 2θB for a large range of instrumental parameters and Bragg angles θB. It is found that a θ–2θ scan is essentially never advisable. An expression for g is derived for the case when a planar monochromator is used in symmetric Bragg reflection. The optimum scan is found to depend on the scattering angle, but not in such a marked way as in the neutron case. Coupling the detector and crystal motions in the manner suggested allows one to decrease the acceptance aperture to its minimum width, thus keeping the background due to thermal diffuse scattering (TDS) and incoherent scattering as low as possible.
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  • 83
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    Acta crystallographica 28 (1972), S. 84-88 
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    Notes: Non-bonded interatomic potential functions were altered to allow for the effects of vibration and anharmonicity by relating the mean displacement to the mean-square vibrational amplitude through the anharmonicity constant, K. Vibrational amplitudes were calculated in the harmonic approximation. The repulsive coefficient, B, of the potential was increased sufficiently to cause the minimum of the potential to shift by the amount of the displacement. The apparent lattice energy was then minimized in the usual manner. The method was checked against experiment by calculation of the lattice constants of noble gases at several temperatures, and of anthracene at two temperatures. The method differs from usual calculations of the Grüneisen type in that calculation of molecular-orientation change with temperature is possible. The anthracene molecular orientation was calculated at 95 and 290°K.
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  • 84
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    Acta crystallographica 28 (1972), S. 16-22 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Rocking curves for the 2nd to 7th order reflections of the systematic set from the (111) planes of a highly perfect silicon single crystal have been obtained in an ultra-high-vacuum reflection electron diffraction camera operated at 40 keV. These have been compared with the profiles computed with an n-beam dynamic high-energy electron diffraction theory adapted to the Bragg case at glancing incidence. It is shown that, for the 333 reflection, six nodes of the hhh row from {\bar 111} up to 444 are adequate to take into account the systematic multiple beam interference effects. The calculated widths are found to agree with the observed widths within the experimental error for all reflections. The peak reflectivities computed initially for a perfect semi-infinite crystal are systematically higher than the experimental values, by a factor of 7 for the 222 node, decreasing to near agreement for the 777 node. Possible reasons for such discrepancies are discussed. Neither inelastic scattering effects nor reasonable changes in the silicon lattice potential near the surface can bring the observed and calculated intensities into agreement. The discrepancy can be considerably reduced for all orders of reflection, however, when the non-flat nature of the surface is considered.
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  • 85
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    Acta crystallographica 28 (1972), S. 113-120 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The wave fields specified by the Laue-(Bragg)m cases are treated from the view points of the plane-wave and spherical-wave theory. The results are very similar to those in the Laue-Bragg case in Part I (Acta Cryst. (1972). A28, 102.). The diffraction phenomena for a finite polyhedral crystal and the experiment of Lehmann & Borrmann (Z. Kristallogr. (1967). 125, 234) are discussed from the view point of the spherical-wave theory.
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  • 86
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    Acta crystallographica 28 (1972), S. 30-33 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The coefficients of thermal expansion of LiF are determined at different temperatures using a diffractometer, Geiger counter, chart recorder and a specially designed furnace. Equations are obtained for the variation of lattice constants with temperature. The temperature dependence of the thermal expansion at high temperatures is shown to be related to the concentration of thermally generated Schottky defects. The energy of formation of Schottky pairs is found to be 2.42 eV. The Grüneisen constant γ is found to decrease with temperature. The mean frequency of the vibrational spectrum is found to decrease with temperature and the variation between 300 and 1000°K is about 13%.
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  • 87
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    Acta crystallographica 28 (1972), S. 353-354 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new precession retigraph is described which allows precession angles of up to 45°. It does not contain a universal-joint suspension, and it has a pure precession motion.
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  • 88
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    Acta crystallographica 28 (1972), S. 341-344 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An ambiguity arises in the study by powder neutron diffraction of compounds where the magnetic atoms lie on a uniaxial or cubic Bravais lattice, when the magnetic lines are indexed {{{h}\over{2}}kl} or {{{h}\over{2}}{{k}\over{2}}l}. Many multiaxial configurations, all having the same isotropic coupling energy, are compatible with a given set of lines. For a simple cubic lattice it is shown that every multiaxial configuration is indistinguishable, using powder intensities, from a particular uniaxial one, and that both have the same dipolar energy.
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  • 89
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    Acta crystallographica 28 (1972), S. 355-355 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Corrigenda are given for Acta Cryst. (1971). A27, 298.
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    Acta crystallographica 28 (1972), S. 344-353 
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    Notes: The surface structure of zinc single crystals subjected to a sublimation treatment has been studied by the techniques of optical metallography, optical goniometry and by Laue X-ray diffraction. Right cylinders with a 〈001〉 axis were enclosed, with titanium getter material, in Vycor tubes evacuated to 10−5 mm Hg and heated to temperatures in the vicinity of 370°C for periods of 100 to 200 hr. A thermal gradient existed in the evacuated chamber such that zinc was transported from one end of the tube to the other end. The sublimation process exposed macroscopically visible crystallographic planes in local regions of the crystals. The three-dimensional structure of the facet morphology has been determined. The exposed planes are of the type {10{\bar 1}0}, {40{\bar 4}1}, {30{\bar 3}1}, {30{\bar 3}2}, {10{\bar 1}1}, {40{\bar 4}5}, {20{\bar 2}3} and {10{\bar 1} 10}. The {0001} surfaces were relatively unaffected by the sublimation process. The facet structures appear to be related to some extent to the dislocation substructure and also to the Gibbs–Wulff surface energy construction for zinc.
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    Acta crystallographica 28 (1972), S. 225-225 
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    Acta crystallographica 28 (1972), S. 187-191 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Electron microscopy and diffraction evidence is presented for the existence of four new molybdenum oxides MonO3n−2, n = 19, 20, 21, and 22.
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    Acta crystallographica 28 (1972), S. 183-187 
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    Notes: For accurate measurements of lattice parameters of materials where symmetry differs only slightly from cubic, difficulties arise in the determination of single lines belonging to the lattice of Dower symmetry because of the overlapping profiles of the pseudocubic lines. In this contribution the profiles of single lines of lower symmetry are approximated by the Cauchy curve and the profiles of the pseudocubic lines are considered as superpositioning of these curves. The resolution of the profiles and the determination of the lattice parameters are performed by means of a computer fitting least-squares program. The conditions for solving the problem are discussed and the method is then applied to a pseudocubic perovskite.
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    Acta crystallographica 28 (1972), S. 201-207 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure of (+)-tartaric acid has been used as a test case to study the feasibility of absolute configuration determinations of compounds in which oxygenis the heaviest atom. Based on about 1100 Ni-filtered Cu Kα reflections (−7 ≤ k ≤ 7) measured on a Picker automatic diffractometer the (2R, 3R) and (2S,3S) configurations could be refined to R = 0.0228 and R = 0.0231 respectively. 94 selected enantiomer sensitive reflections gave R(2R, 3R) = 0.0336 and R(2S, 3S) = 0.0374 (Δf′′o = 0.032). Among the 38 most sensitive Bijvoet differences only one had the incorrect sign. A value of 0.041 (4) for Δf”o (Cu Kα) was derived from 36 observed Bijvoet differences. Similar measurements with Cr Kα radiation also permitted the unequivocal assignment of the correct absolute configuration; however, Cr Kα radiation was not found to offer any overall advantage over Cu Kα radiation. The cell dimensions used in this study are a = 7.7291 (5), b = 6.0069 (2), c = 6.2118 (3) Å, β = 100.147 (2)° (space group P21; Z = 2).
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    Acta crystallographica 28 (1972), S. 210-212 
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    Notes: A least-squares technique for direct refinement of the phases of structure-factors of crystals which obey the equations ahFh = \sum_{k}FkFh − k is described. It is shown by tests carried out under somewhat idealized conditions that the initial phases need not be of a completeness or accuracy sufficient to resolve the atoms of the structure. The technique may be able to provide a bridge in protein crystallography and structure determination generally between preliminary phasing techniques and final refinement of atom parameters.
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    Acta crystallographica 27 (1971), S. 634-647 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: X-ray Compton-Raman scattering is reviewed from an original point of view. The differential cross section for X-ray inelastic scattering from crystals is derived from first principles to explain the coexisting Compton and Raman scattering in solids. This derivation makes it possible to express the cross section in terms of the current correlation of electrons in a crystal. All the electrons, including the core electrons, are treated on an equal basis in this formulation. The relationship between the X-ray absorption spectrum and the inelastic scattering spectrum is discussed in detail. This formulation provides a theoretical justification to the importance of X-ray inelastic scattering experiments in connection with an experimental determination of the two-particle Green's function. In the Appendices the theoretical formulations are given in detail, which apply not only to the ordinary inelastic scattering process, but also to the processes involving Bragg diffraction.
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    Acta crystallographica 27 (1971), S. 665-669 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Neutron-diffraction experiments on single-crystal samples are generally carried out using either an ω-scan (crystal rotating, detector fixed) or a θ–2θ scan (detector coupled 2:1 to the crystal). In order for the center of the diffracted beam to enter the detector on its centerline at all angular settings of the crystal during the scan of a Bragg reflection, neither of these conventional scanning techniques is optimum. A formula is derived which gives the optimum coupling between the detector and the crystal motions, and it is suggested this mode of scanning should be implemented in performing neutron-diffraction experiments on single crystals.
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    Acta crystallographica 27 (1971), S. 670-675 
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    Notes: Theoretical expressions are presented for the Fourier coefficients, derived in terms of a linear `ideal paracrystalline' lattice defined by Hosemann. These coefficients are related to the `coordination statistic' of paracrystallites and their size distribution. The expressions have been used to review earlier Fourier transform analyses on `Marlex 50' polyethylene and various heat-treated samples of petroleum coke and it has been established that these substances have a homogeneous paracrystalline disorder. Up-to-date results of the X-ray diffraction line-profile analyses of various paracrystalline substances are summarized and discussed.
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    Acta crystallographica 27 (1971), S. 676-677 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The dynamical theories of X-ray and electron diffraction can be expressed in similar Schrödinger wave equation forms. The detailed correspondence between the two phenomena then becomes directly obvious.
    Type of Medium: Electronic Resource
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    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 28 (1972), S. 396-400 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Solutions of the convolution equation are given. A rigorous mathematical treatment shows that only one solution is consistent with the physical conditions. Application of these results to discrete examples has been carried out by means of an original deconvolution method, allowing isolation of the unique solution, and by a linear programming method. The results obtained are not satisfactory. This is because of the discrete nature of the problem and of the effect of errors in measurement. To obtain an acceptable solution it was necessary to introduce a weighting factor, as has been done in the LWL method.
    Type of Medium: Electronic Resource
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