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  • International Union of Crystallography (IUCr)
  • 2015-2019
  • 1980-1984  (1,211)
  • 1984  (1,211)
  • 101
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 485-485 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 102
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 251-254 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Application of the Rayleigh criterion for the limit of resolution of a simple lens with axial illumination leads to the value 0.61λ. In two-dimensional electron density maps based on X-ray data, the limit of resolution has been considered to be 0.61 dmin, the counterpart of the optical case, and in three-dimensional maps 0.715 dmin. It is shown here that point atoms separated by these distances are not resolved in two- and three-dimensional electron density maps. Such maps are amplitude functions rather than intensity functions as in the optical case. Application of the Rayleigh criterion to the three-dimensional amplitude function for point atoms leads to a value of 0.917 dmin, for the limit of resolution in three-dimensional electron density maps. This result is confirmed by superposing both analytic and numeric functions for point atoms and numeric functions for real atoms with B = 0 and 10 Å2. Finally, some implications of diffraction effects in X-ray structure analysis are considered.
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  • 103
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 485-486 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
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  • 104
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 225-228 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Results of the experimental study of X-ray diffraction under specular reflection conditions are presented. The experimental arrangement which permits the measurement of the intensity of a specularly reflected diffracted wave with respect to its exit angle to the crystal surface is described. Experimental confirmation of the theory [Afanas'ev & Melkonyan (1983). Acta Cryst. A39, 207-210] has been obtained for silicon crystals. The angular distributions of the specularly reflected and diffuse intensities have also been studied. The experiments showed the diffuse scattering to be primarily scattering at the back edge of the sample.
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  • 105
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 306-307 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In a comment [van de Waal (1981). Acta Cryst. A37, 762-764] on a paper by D. E. Williams [Acta Cryst. (1980), A36, 715-723] on the conformation of small clusters of benzene molecules, it was understood that Williams's results had been obtained from the application of an aufbau algorithm. Subsequently, it was made clear by Williams (private communication) that his results were actually derived from the reversed procedure. In the present note a comparison is made between the two approaches.
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  • 106
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 314-323 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An enantiomorph-dependent probability distribution is derived by integrating the joint probability distribution of two related triple-product phases with respect to one of the variables over the range 0 to π. The result, which is correct up to and including terms of order N-1, can be written as a Von Mises distribution, of which the mode can be anywhere between - ½π and + ½π. Application of the results to the X-ray data of a P1 structure, which could not be solved by conventional direct methods, is discussed. It is shown that resolving the enantiomorph ambiguity by means of the new formula leads to a successful structure determination, provided some alterations are made in the usual tangent-formula algorithm. From the derived distribution function a new figure of merit (ENFOM) is also determined which indicates whether a given set of phases for the largest normalized structure factors corresponds to an E map dominated by only one enantiomorph, or to an E map in which both enantiomorphs are present. For the test structure, ENFOM correctly classifies the different phase sets obtained in a multi-solution approach.
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  • 107
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 532-538 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A computational model of a crystal consists of a description of the crystal structure, expressions for calculating the energy of the model in terms of this structure, and a way of minimizing this calculated energy with respect to the structural variables. External forces such as hydrostatic pressure, normal and shearing stresses, or electric fields can be simulated by adding a term to the energy which describes the external energy of the force-producing device. Minimizing the total energy produces a structure distorted by the external force. From the calculated distortion it is possible to obtain the complete elastic tensor and the dielectric and piezoelectric constants of the crystal. Some phase changes can be simulated, and it should be possible to induce ferroelastic or ferroelectric transitions in the model. The effect of these forces on the orientation and conformation of molecules in the crystal can also be computed.
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  • 108
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    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 40 (1984), S. 548-558 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Theoretical expressions for the measurability of Bijvoet differences have been derived for triclinic, monoclinic and orthorhombic crystals containing p (= 1 or 2) anomalous scatterers and many normal scatterers per asymmetric unit. Results for the many- atom cases (i.e. P = MN and MC cases) in space group P1 are also obtained. The theory takes into consideration the effect of data truncation due to unobserved reflections. The measurability values for the various cases are given in the form of compact tables as functions of the relevant parameters k and σ21. The theoretical results are also used to discuss briefly the following aspects. (i) The effect of k and σ21 on the measurability. (ii) Measurability to be expected in the heavy-atom derivatives of proteins with Cu Kα radiation. (iii) A comparison of the measurabilities in Sm derivatives of a protein for Cu Kα and for a wavelength (λ = 1.8448 Å) at which the anomalous scattering effect has been observed to be the largest. It is also found that in the case of the heavy-atom derivatives of proteins measurability is strongly influenced by variation in σ21.
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  • 109
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    Acta crystallographica 40 (1984), S. 404-410 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A Hermann-Mauguin type notation is devised for the 227 four-dimensional (geometric) crystal classes, and appropriate conventions are proposed for each of the 23 crystal families.
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  • 110
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    Acta crystallographica 40 (1984), S. 410-445 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A revision of the classical statistical methods of phase determination is presented which widens their theoretical foundations and consolidates their practical implementation, thus bringing about a major increase of their power. In a brief introductory survey (§ 1), the basic concepts and mathematical techniques of direct methods are analysed. Closer scrutiny (§ 2) reveals that severe inadequacies still impair the effectiveness of these methods. The asymptotic character of the series used to approximate joint distributions of structure factors demands that great caution be exercised to guarantee their accuracy, and this requirement can only be fulfilled if they are used within a multisolution algorithm in which the prior distribution of atoms is constantly updated so as to incorporate at every stage all the phase information assumed to that point. Further limitations follow from the traditional practice of approximating joint distributions by products of marginal distributions of single invariants. A scheme for simultaneously overcoming both difficulties is then proposed. The pivotal element of this scheme is a device, based on Jaynes's maximum-entropy principle, for exploiting the prior knowledge of some structure factors in the construction of the joint distributions of others conditional to that knowledge. Jaynes's maximum-entropy formalism is presented and systematically applied to the construction of the requisite non-uniform prior distributions of atoms in § 3. The problem of effectively approximating conditional distributions of very large numbers of structure factors is solved in § 4 by a novel technique of 'maximum-entropy inversion' of Karle-Hauptman matrices, and the result obtained is shown to generalize the most sophisticated probabilistic formulae hitherto obtained. This procedure is proved in § 5 to coincide with an enhancement of the standard method of asymptotic expansions by means of Daniels's saddlepoint approximation. Its relationship to determinantal methods is investigated in § 6. A numerical algorithm for implementing these ideas is presented in § 7, together with an application to data from the small protein Crambin, and a unified strategy for its use ab initio is described and discussed in § 8. It is concluded that the phase-determination strategy proposed here will expedite the realization of the full potential of probabilistic direct methods, and is likely to bring macromolecular structures within their reach.
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  • 111
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    Acta crystallographica 40 (1984), S. 617-619 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Darwin derived a system of difference equations which relate the incident and reflected amplitudes of X-rays in a crystal in Bragg diffraction. These equations are recast in matrix form. Using a well known result from optical multilayer theory, an exact analytic solution of these difference equations is obtained for a crystal of an arbitrary number of atomic planes. In the limiting case of a semi-infinite crystal, and with the appropriate approximations, Darwin's expression for the reflectivity of a crystal in Bragg diffraction is obtained.
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  • 112
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    Acta crystallographica 40 (1984), S. 631-635 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two-colour two-dimensional crystals may be considered as heightened projections of (2 +1)- dimensional semi-crystals. In these semi-crystals, the structure spreads on both sides of a plane; the positions are repeated by a translation lattice parallel to the plane; there is no crystal-lattice repetition in the third dimension. It is possible to classify the two-colour two-dimensional crystals as follows: (1) One-colour crystals, which are the projections of the semi-crystals whose equivalent positions are all situated on the same side of the plane for a given set. (2) Two-colour crystals based on ordinary lattices, which are the projections of the semi-crystals possessing equivalent positions situated on both sides of the plane; but this plane is neither a reflection nor a glide plane of the semi-crystals. (3) Two-colour crystals based on coloured lattices, which are also the projections of the semi-crystals possessing equivalent positions on both sides of the plane; this plane is a glide plane of the semi-crystals. (4) Grey crystals, which are the projections of the semi-crystals with equivalent positions on both sides of the plane; this plane is a reflection plane of the semi-crystals. The sets of equivalent positions of the coloured groups are easily obtained from the sets of equivalent positions of the symmetry groups of the semi-crystal by a method due to Wood [Bell Syst. Tech. J. (1964), 43, 541-559; Bell Teleph. Syst. Tech. Publ. (1964), Monogr. No. 4680].
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  • 113
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    Acta crystallographica 40 (1984), S. 646-651 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The probabilistic theory of the three-phase structure invariant for a triplet of isomorphous structures is worked out. In particular, when diffraction data are available for a native protein and two derivatives, the conditional distributions of the three-phase structure invariants, given the nine magnitudes in their first neighbourhoods, are derived for the special case that the heavy atoms of the two derivatives are located in different positions in the unit cell. The distributions have the form P(Ω) = (1/K) exp (A cos Ω), where the parameters K and A are functions of the nine magnitudes in the first neighborhood. In the favorable case that the variance of a distribution happens to be small, a reliable estimate, 0 or π, of the invariant is obtained. An example shows that these distributions, which employ simultaneously the diffraction data from a triple of isomorphous structures, yield more accurate estimates for the three-phase structure invariants than are obtainable from earlier distributions, which employ diffraction data from only a pair of isomorphous structures [Hauptman (1982). Acta. Cryst. A38, 289-294]. Unique origin and enantiomorph specification in direct-methods applications to all three structures is an advantage of the present approach.
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  • 114
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    Acta crystallographica 40 (1984), S. 660-662 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The η refinement of Rogers [Acta Cryst. (1981), A37, 734-741] has been applied to a wide range of noncentrosymmetric structures containing medium to strong anomalous scatterers; it has been shown to be an effective and robust method. The use of the general term 'absolute structure' (to signify a structure successfully distinguished from its inverse by, for example, analysis of anomalous scattering effects) is recommended.
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  • 115
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    Acta crystallographica 40 (1984), S. 668-675 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: An extension of existing structure-factor formalisms for anharmonic thermal motion in crystals and the corresponding one-particle potentials is presented and applied to ordered and disordered structures. A generalized probability density function (joint p.d.f.) is introduced and it is first shown that anharmonic temperature factors ('thermal motion') and split positions ('disorder') are mathematically equivalent in describing electron or nuclear densities. When probability densities are interpreted in terms of an effective one-particle potential, however, ordered and disordered structures show different behaviour. For ordered structures the effective one-particle potentials are found to be almost independent of temperature; for disordered structures one obtains a temperature-dependent pseudo potential. The different temperature dependence can be used to distinguish between order and disorder. Pseudo potentials are calculated for several types of disorder and compared with potentials derived from X-ray or neutron diffraction experiments.
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  • 116
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    Acta crystallographica 40 (1984), S. 675-679 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The optical coherence approach has been used for computing the reflection curves of crystals with spherical precipitates in the Bragg case and the curves were compared with those obtained from the usual kinematical theory. It has been shown that the asymmetry of the curves depends on the sign of the volume change caused by defects. Near their maximum the shape of the curves is not dependent on the type of deformation field of the precipitates and it depends on the properties of the perfect crystal. In comparison with the kinematical theory it has been demonstrated that the difference between the results of the dynamical theory and those of the kinematical theory are significant only near the maximum of the reflection curves.
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  • 117
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    Acta crystallographica 40 (1984), S. 684-688 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The [222] n-beam pattern of germanium has been recorded using Cu Kα1 radiation and newly developed instrumentation. The asymmetric unit of the pattern contains 17 interaction maxima. At least one invariant triplet phase may be derived from each maximum. Two of the latter are considered unsuitable for phase determination owing to overlap with adjacent peaks. The phases of the remaining 15 were determined. Relevant experimental data are presented and from these the validity of the authors' phase assignments can be readily checked. Techniques for indexing n-beam patterns and for improving the visibility of triplet phase interactions are discussed. It is shown that procedures for improving the visibility of n-beam interactions do not necessarily lead to increased visibility of phase indications.
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  • 118
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    Acta crystallographica 40 (1984), S. 703-704 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Crystal movement, detected during data collection, requires the orientation matrix to be modified, so that reflection positions can be correctly predicted. If the unit cell is assumed to remain unchanged, the necessary modification is a small rotation of the matrix, viz premultiplication by an orthogonal matrix. This rotation is easily calculated from the observed positions of two or more centred reflections, by the application of quaternion algebra.
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  • 119
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    Acta crystallographica 40 (1984), S. 708-712 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Two fast methods of superposing two sets of atomic coordinates by least-squares refinement are described and related to two earlier fast methods. A Newton method is applied to rotations of a 3 x 3 outer product matrix used previously by Ferro & Hermans [Acta Cryst. (1977), A33, 345-347] and by McLachlan [Acta Cryst. (1972), A28, 656-657]. Three of the methods work better if one molecule has its inertial matrix aligned with xyz. A Newton-Gauss method that rotates the coordinates can converge rapidly after a rough orientation using three strategic atoms. The average superposition takes about 0.003 s on a Cyber 175 with the best method, rotations about the xyz axes in turn. Experience with reliability is reported for large residuals.
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  • 120
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    Acta crystallographica 40 (1984), S. 713-716 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: When Fourier syntheses are calculated using phase information from both isomorphous replacement and the refined model it is usual to combine the information for each reflection by multiplying the two probability distributions together. It is well known that phase information from a model contains 'bias' towards that model; it is also true that such bias will be diluted by the process of phase combination. A method is proposed of tailoring the amplitude coefficients individually to correct for the likely residual bias in the combined phase.
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  • 121
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    Acta crystallographica 40 (1984), S. 721-721 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Tables 13 and 17 of the paper by Tanaka, Sekii & Nagasawa [Acta Cryst. (1983), A39, 825-837] are not perfect. The correct tables are given.
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  • 122
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    Acta crystallographica 40 (1984), S. 538-544 
    ISSN: 1600-5724
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The exact intensity formula of the h-line profile from small crystallites has been obtained as the orientational average of the diffraction intensity of the h plane given by Ino & Minami [Acta Cryst. (1979), A35, 163-170]. While the formula is expressed as a triple integral including a sine Fourier integral, it can be expressed asymptotically with respect to the crystal size according to the theorem of asymptotic expansion of a Fourier integral. Hence the profile can be estimated by the sum of terms of single-integral type. The first term is of the same type as Wilson's formula but it has been shown that second and third terms improve considerably the accuracy of the asymptotic estimation especially for a very small crystal. The h-line profile can be successfully calculated for quite a small crystal of any shape and any crystal system by the asymptotic formula, which can be computed as easily as Wilson's formula.
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  • 123
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    Acta crystallographica 40 (1984), S. 544-548 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Integrated direct methods- isomorphous probability distributions [Hauptman (1982). Acta Cryst. A38, 289-294] are interpreted in terms of the familiar parameters of the isomorphous replacement method, the diffraction ratio and the differences in the diffraction intensities of a native protein and its heavy-atom derivative. The analysis shows that the reliability of the phase estimates is a function of the degree of heavy-atom substitution in the derivative. It clearly pinpoints the most favorable conditions for retrieving phase information from the intensity data of an isomorphous pair of structures. Finally, it provides a means to determine a priori the overall reliability of the phase estimates and to design the calculations accordingly.
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  • 124
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    Acta crystallographica 40 (1984), S. 663-668 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A survey of 102 structures flagged with 'absolute configuration' in the Cambridge Crystallographic Data Centre files for 1982 reveals many unsatisfactory features in the original publications. These are associated with data collection (lack of Friedel opposites and of absorption corrections), misinterpretation of the term 'absolute configuration' (claimed for achiral molecules and space groups), methods used to determine absolute configuration (over-optimistic interpretation of discriminatory tests) and presentation of results (little experimental detail, no prominent statement that an absolute configuration was assigned, no clear description of the methods used). Some confusion arises because of unintentional flagging of absolute configurations determined by solely chemical means.
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  • 125
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    Acta crystallographica 40 (1984), S. 728-728 
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    Acta crystallographica 40 (1984), S. 728-728 
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    Acta crystallographica 40 (1984), S. 728-728 
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    Acta crystallographica 40 (1984), S. 728-728 
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  • 129
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    Acta crystallographica 40 (1984), S. 87-87 
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    Acta crystallographica 40 (1984), S. 88-88 
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  • 131
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    Acta crystallographica 40 (1984), S. 103-107 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Attention is drawn to a hitherto-neglected instrumental consideration in Bragg scattering. It requires a new sin θ factor to be included in expressions for Bragg reflectivity. The factor, which arises out of a consideration of mosaic spread is also relevant to scattering from a perfect single crystal. The scattering process is examined within a framework of neutron triple-axis spectrometry and implications of the effect for normalization of the instrumental resolution function in that connection are examined in detail.
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    Acta crystallographica 40 (1984), S. 89-95 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The previous theory of X-ray diffraction in crystals with anisotropic X-ray susceptibility [Dmitrienko (1983). Acta Cryst. A39, 29-35] is applied to cubic crystals. Such a theory is needed if the X-ray wavelengths are near the absorption edges because in this case the X-ray susceptibility may be anisotropic. The most general form of the spatially dependent tensor of X-ray susceptibility is obtained for all cubic space groups. This tensor is anisotropic at any point of a unit cell except those with cubic point symmetry (being averaged over a unit cell the tensor becomes isotropic providing the macro- scopic isotropy of cubic crystals). From the tensor of susceptibility the structure amplitudes and new extinction rules are derived for the glide-plane and screw-axis forbidden reflections (such reflections are forbidden if the susceptibility is isotropic). For example, the hhh forbidden reflections remain extinguished even if the anisotropy is taken into account. Further restrictions on the structure amplitudes of forbidden reflections are obtained with the natural assumption that the anisotropy of susceptibility is localized at the special atomic positions. The tensor form of the structure amplitudes of nonforbidden reflections is also discussed. The general methods are illustrated by their application to the A15 structure (space group Pm{\bar 3}n).
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    Acta crystallographica 40 (1984), S. 163-164 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The roles of prior information, event space and choice of constraint functions in information-theoretic approaches to the crystallographic inversion problem are discussed, with a view to relating recent articles on the inversion problem. In particular, the important distinction between the general expression for the entropy of a probability distribution function and specific derived forms for entropy involving, for example, mean values of the corresponding random variables, is pointed out and illustrated.
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    Acta crystallographica 40 (1984), S. 50-57 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Some very large biological macromolecules, such as viruses, exhibit a high degree of non-crystallographic symmetry. A method is described to refine crystallographically such large structures using a combination of molecular averaging in real space, automatic real-space refitting and interactive refitting using computer graphics. The method has been successfully applied to a small plant virus, satellite tobacco necrosis virus, containing 11 700 amino acids in the crystallographic asymmetric unit. The starting model for the refinement was built with 3.7 Å phases. These have been refined and the resolution extended to 2.5 Å.
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    Acta crystallographica 40 (1984), S. 88-88 
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    Acta crystallographica 40 (1984), S. 24-31 
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    Notes: The flipping ratios for polarized neutron scattering from the first six reflections in Ni have been measured on a series of samples of varying thickness and perfection and at a number of wavelengths. The results were corrected for secondary extinction on a point-by-point basis, using the measured absolute reflectivities, and multiple scattering was detected using conservation of neutrons. No adjustable parameters were used, and all data, except those from a rather perfect specimen which showed both primary and secondary extinction, agree to within the experimental accuracy after extinction correction. A diffuse scattering process with spin dependence was also detected, and the flipping ratios corrected for this. The corrected values differ somewhat from the values given by Mook [Phys. Rev. (1966), 14B, 495-501].
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    Acta crystallographica 40 (1984), S. 16-23 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A new method for the treatment of secondary extinction in polarized neutron diffraction data has been developed. As in previous models, the Zachariasen solutions to the Darwin intensity transfer equations are used, but in this case the extinction corrections are made on a point-by-point basis across the rocking curve and the corrections are determined by the absolute reflectivity at each point. There are no adjustable parameters (other than background). Measurement of the reflectivity also provides a simple test for multiple scattering, since the sum of diffracted and transmitted intensities should equal the direct-beam intensity, corrected for absorption, if no multiple scattering is present. The present method should give more reliable results than parametrized models where the correlation between the extinction and other parameters, such as the scale factor and temperature factors, are important.
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  • 138
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    Acta crystallographica 40 (1984), S. 68-85 
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    Acta crystallographica 40 (1984), S. 88-88 
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  • 140
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    Acta crystallographica 40 (1984), S. 113-115 
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    Notes: Stress-optical constants (q11 - q12), (q11 - q13) and q44 of mixed alum [(NH4) 1 - xKxAl(SO4)2.12H2O] crystals have been determined employing a modified form of Filon's spectrometer method in the wavelength range 4800-6200 Å. Corresponding strain-optical constants (P11--P12), (P11--P13) and P44 are derived from these using elastic constant data. It is observed that at a given wavelength all the constants vary regularly, though nonlinearly, with the composition of crystals. The deviation from linearity is found to be largest around equimolar concentrations.
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  • 141
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    Acta crystallographica 40 (1984), S. 120-126 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The propagation of neutron waves in a deformed crystal is considered from the point of view of quantum mechanics. Instead of solving the Takagi-Taupin equations the probability of transitions, induced by the variation of the interaction potential, between quantum states corresponding to the two sheets of the dispersion surface is calculated. In this way transmission and reflection coefficients for an incident plane wave are obtained after a simple analytical calculation for a wide class of crystal deformations. The predictions of this theory are found to be in agreement with direct solutions of the Takagi-Taupin equations as well as with the experimental results.
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  • 142
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    Acta crystallographica 40 (1984), S. 169-183 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper describes a proposal for a standardized presentation of inorganic crystal-structure data with the aim to recognize identical or nearly identical structures from the similarity of the numerical values of the atom coordinates.
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    Acta crystallographica 40 (1984), S. 200-213 
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: This paper investigates changes of the bicrystal symmetry caused by rigid-body relaxation. Analytical expressions are derived for the determination of the symmetry of a bicrystal, or, more generally, of a binary composite, corresponding to a particular relative displacement of its components. Such displacements can change the point and/or space symmetry of the composite either by compressing symmetry operations or by transforming symmorphic symmetry operations to their nonsymmorphic counterparts, or vice versa. In the latter case the relative displacements have a well defined magnitude and direction and it is shown that the composite space groups associated with these displacements correspond to a new type of subgroups of space groups. These subgroups, although having the same unit cell as the original space group, are similar to the klassengleiche subgroups in the sense that the descent in symmetry has affected the translations in the unit cell of the original group. Furthermore, it is pointed out that the reduction of symmetry due to relative displacements is accomplished by a multiplicity of crystallographically equivalent ways and that their number and interrelation depends on the space symmetry of the original composite.
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    Acta crystallographica 40 (1984), S. 213-221 
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    Notes: A group-theoretical method is presented that enables the derivation of the symmetry of any composite created by the superposition of two identical point groups. The invariant points of the two components are considered in coincidence and the composite symmetry is expressed as the intersection of two sets of symmetry operations. The first set contains the symmetry operations common in the components when their mutual disposition is taken into account, whereas in the second set belong the additional symmetry operations relating the two equivalent components. The existence of such symmetrizing operations is revealed particularly clearly by using the framework of two-coloured symmetry. Analytical expressions for the operations of each set are derived in terms of the mutual orientation of the two components and theorems are given for the determination of the composite point symmetry when the components are rotated relative to each other along a direction passing through their origin. The application of the methodology is demonstrated by considering particular examples and a table of all possible composite symmetry groups associated with superpositions of the 32 crystallographic point groups is given.
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    Acta crystallographica 40 (1984), S. 221-225 
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    Notes: Lists of 8- and 12-fold two-coloured groups consistent with zero- and one-dimensional periodic objects are given. These groups are derived as extensions of the corresponding crystallographic two-coloured groups and are of particular interest because they are the only non-crystallographic groups obtained by the appropriate superposition of crystallographic point or rod groups.
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  • 146
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    Acta crystallographica 40 (1984), S. 487-487 
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    Acta crystallographica 40 (1984), S. 305-306 
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    Notes: The conditional joint probability distribution of the phase φ = φh + φ-h given |F+|, |F-| is used in order to suggest coefficients for a Patterson synthesis for the determination of the positions of anomalous scatterers. A theoretical comparison with Rossmann's approach [Rossmann, M. G. (1981). Acta Cryst. 14, 383-388] is made.
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    Acta crystallographica 40 (1984), S. 515-522 
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    Notes: The creation of new wavefields in deformed crystals, a phenomenon widely recognized as responsible for some contrast features in X-ray topography, has been demonstrated analytically for the first time only very recently [Balibar, Chukhovskii & Malgrange (1983). Acta Cryst. A39, 387-399] in the case of a constant strain gradient. In the present paper it is shown by means of computer experiments (i.e. by solving Takagi's equations numerically) that the most important results of the theoretical approach can be readily extended to variable strain gradients. In particular, the conjecture is verified that the creation takes place only in the region of maximum curvature of the wavefield trajectory. Its relative intensity is shown to be equal to exp (-2π/|α0|), α0 being proportional to the value of the strain gradient in that region. The utility of these results is demonstrated in a refined interpretation of the dislocation contrast in plane-wave reflection topography.
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  • 149
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    Acta crystallographica 40 (1984), S. 522-526 
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    Notes: A simple construction procedure is given for convergent-beam electron diffraction (CBED) pattern matrices as symmetry elements in diffraction space coordinates. These are constructed from a limited set of point-group elements, namely those belonging to the layer groups of Alexander & Hermann [Z. Kristallogr. (1929), 70, 328-345]. As a result a transformation is found between crystal and diffraction space in which the three-dimensional crystal symmetries transform into four-dimensional intensity distributions. Equivalent anti-symmetric matrices which operate on amplitudes rather than intensities are found for non-symmorphic space-group elements.
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  • 150
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    Acta crystallographica 40 (1984), S. 323-330 
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    Notes: Physical phenomena such as incommensurate phases or diffraction enhancement of symmetry are interpreted by using symmetry groups in four, five or six dimensions. This first paper concerns the point-symmetry operations (PSO) in these Euclidean superspaces. Elementary, non-elementary, degenerate and non-degenerate PSOs are defined and their geometrical supports and geometrical symbols are specified. A geometrical description is thus given of nineteen types of PSO which are either the crystallographic rotations of the four-dimensional space or the crystallographic rotations and improper rotations of the five-dimensional space or the improper crystallographic rotations of the six-dimensional space. These PSOs are elements of crystallographic point groups of these spaces and the physical application to polar point groups is given.
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    Acta crystallographica 40 (1984), S. 312-312 
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    Acta crystallographica 40 (1984), S. 310-312 
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    Acta crystallographica 40 (1984), S. 567-571 
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    Notes: Hexagonal space groups, i.e. those with an hP lattice, are classified from the geometric-unit viewpoint by considering hexagonal crystal structures as combinations and permutations of some basic hexagonal prisms. Geometric units are the Dirichlet domains of the Wyckoff positions with the highest point-group symmetry in the space group. In this classification, there are six types of hexagonal space groups. Type h1 consists of two independent geometric units of the same symmetry per crystallographic cell; in type h2, the two units are identical, but differently oriented. Type h3 has six independent geometric units, again of the same point-group symmetry, but the six units can be made up of three pairs, each consisting of two identical units, thus giving rise to type h4. There are subclasses in types hl and h3. Centers of geometric units in hl(a) and h3(a) are uniquely defined by intersections of point-group symmetry elements, whereas those in h1(b) and h3(b) are not because the space groups in these subtypes are hemimorphic. Therefore, the two units along the polar axis may be combined as one. Type h5 consists of three units, each turned 120° from its neighbors owing to the screw axis 31, 32, 62 and 64. Similarly, type h6 has six units due to screw axes 61 and 65, and adjacent units are 60° apart. Rhombohedral space groups show two types of patterns: type r1 has two independent, and type r2 two identical, units. The h.c.p. and related structures are used to demonstrate the application of geometric units to crystal-structure descriptions.
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    Acta crystallographica 40 (1984), S. 488-488 
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    Acta crystallographica 40 (1984), S. 488-488 
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    Acta crystallographica 40 (1984), S. 495-498 
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    Notes: The error treatment given by Blow & Crick [Acta Cryst. (1959). 12, 794-802] in the isomorphous replacement method can be readily introduced into direct methods when they are used to handle the single isomorphous replacement (SIR) or the one-wavelength anomalous scattering (OAS) data. The 'best phase relationship' is defined similarly to the 'best Fourier'. Expressions of the 'best phase' and the 'figure of merit' for individual reflection have been derived for the SIR or OAS case. These enable initial signs to be obtained for a set of ΔφH without knowing the sign of any one ΔφH in advance. Finally, a weighting scheme is proposed for the refinement of signs and magnitudes of ΔφH.
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    Acta crystallographica 40 (1984), S. 507-514 
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    Notes: It has been commonly admitted that the theories of X-ray propagation in distorted crystals based on the principles of geometrical optics [Penning & Polder (1961). Philips Res. Rep. 16, 419-440; Kato (1963). J. Phys. Soc. Jpn, 18, 1785-1791; Kato (1964). J. Phys. Soc. Jpn, 19, 67-71, 971-985] were applicable only in the transmission (Laue) case. It is demonstrated in this paper that they can be applied more generally in all cases where beams can be defined, i.e. also in the Bragg case outside the total reflection range. Simple formulae for the case of a constant strain gradient in symmetric Bragg geometry are derived from a general formulation of the basic equation of geometrical theory using a new universal parameter a. They are verified by solving Takagi's equations numerically. The results are visualized by means of an original method of ray tracing directly from Takagi's equations.
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    Acta crystallographica 40 (1984), S. 486-487 
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    Acta crystallographica 40 (1984), S. 486-486 
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    Acta crystallographica 40 (1984), S. 610-616 
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    Notes: An index subgroup of strong main reflexions and cosets of weak reflexions are typical features of crystal structures with systematic rational dependence of the atom coordinates exhibiting a pseudotranslational symmetry. The mean squares of these normalized structure-factor sets which deviate significantly from unity are interpreted in terms of correlation coefficients of the atom coordinates. An asymptotic form of the von Mises distribution of a structure factor phase is derived which allows for rational dependence and makes explicit use of the |\bar E|2 values of the different structure-factor sets. The formula provides a basis for the use of phase relationships of the type 'weak-strong-weak' proposed in the recent literature. The limits of the method are estimated. In particular, symmetry and homometry problems in superstructures are more complex than in usual cases and their careful consideration is essential for the success of procedures intending an automatic solution.
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    Acta crystallographica 40 (1984), S. 620-624 
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    Notes: Spin-only magnetic form factors and X-ray form factors for Mn, Mn+, Co, Co2+, Ni and Ni2+ are calculated using configuration interaction wavefunctions. The magnetic form factors for Co2+ are used in the analysis of polarized neutron diffraction data for Cs3CoCl5, to give spin populations. The inclusion of correlation functions in the wavefunction leads to changes in Hartree-Fock form factors of transition metal atoms, which maximize at K/4π ̃0.4 Å-1, where they amount to approximately 5% of the form factor at that value of K.
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    Acta crystallographica 40 (1984), S. 635-642 
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    Notes: The 80 space groups of infinitely extended layers are identified as the defining groups for transmission electron diffraction symmetries obtained from lamellar crystals. These layer groups are retabulated using a notation which characterizes the symmetries of convergent-beam diffraction patterns. The new tabulation provides a means for determining the three-dimensional space group of a particular structure from one or more convergent-beam zone-axis patterns. This is a two-stage process, involving determination of a layer-group corresponding to a principal zone-axis pattern, followed by identification, where necessary, of the appropriate class-equivalent subgroup. For this final identification, the three-dimensional extinction conditions, determined from an alternative set of convergent-beam zone-axis patterns, are required. In terms of standard group symbols [e.g. Vainshtein (1981). Modern Crystallography I. Berlin: Springer], the one-way interrelation between patterns and space groups G32 → G33 (space group analysis) is given. The inverse problem, equally accessible from group theory, of providing the interrelation G33 → G32 (pattern symmetry prediction) is left for separate tabulation.
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    Acta crystallographica 40 (1984), S. 651-660 
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    Notes: Probability density functions that are exact solutions to classical random-walk problems have been adapted to represent distributions of the magnitude of the normalized structure factor, for the space groups P\bar and P1. The functions are given by readily summable Fourier and Fourier-Bessel series, and account explicitly for the atomic composition of the asymmetric unit. These new probability density functions have been extensively tested by comparison with simulated histograms of |E|, for a wide range of atomic compositions. The most heterogeneous compositions examined are C14U and C29U, for P\bar 1 and P1, respectively. Very good agreement between the simulated and theoretical distributions has been obtained in all these tests, over the entire (useful) range 0 〈 |E| 〈 3. A distribution of |E| values, recalculated from published data on a triclinic platinum complex with chloroorganic ligands, has also been compared with the new probability functions and excellent agreement with the (expected) P\bar 1 theoretical distribution has been obtained. The discrepancy between the recalculated distribution and the P1 theoretical rules out the latter space group both by visual comparison and quantitative discrepancy criteria. It is concluded that probability density functions are definitely preferable to moments in attempting to resolve a space-group ambiguity. Measures of discrepancy to be used in such statistical tests are proposed and discussed in some detail.
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    Acta crystallographica 40 (1984), S. 679-684 
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    Notes: Any crystal whose point group is a subgroup of index p of its lattice symmetry (merohedral crystals, p = 2, 4 or 8) can be referred to p non-equivalent possible settings of the cordinate axes. These possible settings are tabulated, for all 44 oriented point groups and for each setting s, as the triplet of indices hsksls, into which the original hkl transforms, together with the relevant transformation operation. At least one such set of suitable observed structure factors should be published with every structure description for merohedral crystals so that the chosen setting can be identified. A list of the types of reflections unsuitable for orientation purposes is given. A unique orientation of the coordinate axes could be reached experimentally, without structural knowledge, by attributing to the largest Iobs, indices hkl in a specified asymmetric domain of the point-group symmetry of the lattice. The table also serves as a complete collection of possible twin laws in twinning by merohedry; each transformed symbol hsksls represents the reflection which, on the diffraction pattern of the twin, contributes its intensity to that of hkl.
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    Acta crystallographica 40 (1984), S. 688-695 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By integrating joint probability distributions of two related invariant phases with respect to one of the variables over the range 0 to π, enantiomorph-dependent phase indications may be obtained. In the present paper the full potential of such a strategy is described. For probability distributions correct up to and including terms of order N-1, all cases of interest appear to consist of combinations of two invariants with one or two structure factors in common. For each case the joint probability distribution of the phases of such a pair of invariants, given a number of suitable structure-factor amplitudes, is derived. Subsequently, all these distribution functions are integrated from 0 to π with respect to one or other variable, thus exploring the full range of enantiomorph-dependent distributions. The resulting expressions are grouped together according to whether the chosen enantiomorph definer is a triplet, quartet, quintet or higher-order invariant, thereby facilitating their future implementation in direct-methods procedures.
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  • 166
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    Acta crystallographica 40 (1984), S. 705-708 
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    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Entropy maximization is an alternative to least-squares or squares minimization for the relative scaling of intersecting data sets. The iterative calculations converge rapidly, even for difficult cases, and the scaling is truly relative in contrast-to that of other widely used methods.
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  • 167
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    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Results obtained from four X-ray and five neutron data sets collected under a project sponsored by the Commission on Charge, Spin and Momentum Densities are analyzed by comparison of thermal parameters, positional parameters and X - N electron density maps. Three sets of theoretical calculations are also included in the comparison. Though several chemically significant features are reproduced in all the experimental density maps, differences in detail occur which caution against overinterpretation of the maps. Large differences between vibrational tensor elements Uij are observed which can often not be corrected by the scaling of all temperature parameters in a set. Positional parameters are reproducible to precisions of 0.001 Å or better. The biggest discrepancies between theoretical and experimental deformation density maps occurs in the lone-pair regions where peaks are higher in the theoretical maps. However, this comparison may be affected by inadequacies in the thermal-motion formalism which must be invoked before experimental and theoretical maps can be compared in a quantitative way.
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  • 168
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    Applied crystallography online 17 (1984), S. 140-146 
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    Topics: Geosciences , Physics
    Notes: One of the main sources of error when studying weakly absorbing materials using an X-ray diffractometer with Bragg–Brentano focusing geometry is specimen transparency. Its undesired effects (peak displacement and loss of intensity in the medium angular range) can be avoided by using a slab-like specimen in symmetrical transmission, in which case the type of diffractometer is more or less immaterial except that a non-focusing diffractometer offers a series of advantages, e.g. a very simple lining-up procedure and the possibility of using rod-like specimens. Such a diffractometer with a flat monochromator in the primary beam is described and both the equatorial aberration and the axial aberration are discussed.
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  • 169
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    Applied crystallography online 17 (1984), S. 189-195 
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    Topics: Geosciences , Physics
    Notes: The optimum parameters and properties of a new type of neutron monochromator based on elastically bent silicon single crystals are theoretically evaluated. The use of a fully asymmetrical geometry permits the achievement of rocking-curve widths exceeding 20' in the incident beam. The associated effect of the reflected-beam widening is compensated for by the second crystal in the parallel (1,−1) setting in opposite geometry. Reflectivity calculations indicate that this double-crystal system might be compared with the best single-crystal mosaic monochromators. Besides the easy control of the effective mosaicity and the corresponding integrated reflectivity by variation of the bending radius, a further advantage of this system is its simultaneous action as a neutron filter improving the ratio of the thermal neutron signal to the background.
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  • 170
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    Applied crystallography online 17 (1984), S. 206-207 
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    Topics: Geosciences , Physics
    Notes: The usual powder diffraction technique needs about one hour for the registration of a pattern with either a Guinier camera or a powder diffractometer. This is a long time compared to the time of most chemical reactions and phase transitions. Quite recently the recording time has been reduced by using position-sensitive detectors and rotating-anode X-ray sources, but the registration time is still about one minute. With a Guinier diffractometer in front of a synchrotron-radiation source a time resolution of 300 μs can be achieved.
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  • 171
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    Applied crystallography online 17 (1984), S. 196-205 
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    Notes: The study of the physical properties of the superlattices (Ga 1− xAlxAs)n1(GaAs)n2/GaAs(001) requires the knowledge of their structural parameters n1, n2 and x and of their crystalline state. X-ray diffraction enables the existence of such artificial superstructures, obtained by molecular-beam epitaxy, to be revealed and their characteristic parameters to be determined. Two experimental techniques are used: a standard powder goniometer and a double-crystal diffractometer. The diffraction diagrams directly yield the superperiod and the average Al concentration in the superlattice. The value of x is determined by refinement between observed and calculated structure factors. The results are even more accurate when the number of observed satellite peaks for a given periodicity is greater; this number depends at the same time on the Al composition x, the n1/n2 ratio, the periodicity and its dispersion and the shape of the interfaces. This method is illustrated by a few examples with superlattice periods varying from 51 to 397 Å. The consequence on the X-ray diagrams of various defects (dispersion in n1 and n2, superperiod gradient, Al diffusion) is discussed.
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  • 172
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    Applied crystallography online 17 (1984), S. 257-264 
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    Topics: Geosciences , Physics
    Notes: With a compact arrangement using single-crystal collimator and analyzer (silicon 220 reflection) of channel-cut type, angle-resolved scattering (ARS) curves of X-rays (Cu Kα1) for optically flat mirrors have been measured at various glancing angles, ω, of X-rays to the mirror surface with an angular resolution of 4′′. Weak scattered intensity (10−3–10−5 of the specularly reflected beam) is observed over an angular range of a few hundred arc s below and above the direction of specular reflection. When ω is close to the critical angle for total reflection, the scattered intensity at the low-angle tail of ARS curves is higher than that at the high-angle tail. This asymmetric tail profile of ARS curves is explained by simply superposing intensities of specularly reflected beams from surface elements inclined to each other.
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  • 173
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    Applied crystallography online 17 (1984), S. 307-314 
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    Topics: Geosciences , Physics
    Notes: The many-beam dynamical theory of moiré fringes of Gevers [Phys. Status Solidi (1963). 3, 2289–2297] has been applied to the parallel moiré case and the results have been verified on epitaxically grown Sn/SnTe specimens showing the sensitivity of moiré patterns to the presence of systematic reflections. The Fourier analysis of the calculated intensity profiles showed that each additional diffracted beam gives rise to a new term in the Fourier series so that the profile can be sinusoidal only in the two-beam approximation. The same result has been obtained recently by Pardo, Pariset & Renard [Phys. Status Solidi A. (1981). 64, 283–295], who applied a slightly different theoretical approach to Sb/Bi specimens. It is shown that the corrections to scattering factors for temperature effects are not important since they do not affect the general character of the moiré profiles. Some experiments were performed showing the dependence of the moiré pattern on the number of beams that are transmitted through the objective aperture. The effect of the gradual thinning of one layer on the moiré pattern could be reproduced by computer simulation.
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  • 174
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    Applied crystallography online 17 (1984), S. 328-330 
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    Topics: Geosciences , Physics
    Notes: Vapor-phase ZnS crystals were grown under strict stabilization of temperature and pressure. Many crystals containing wide polytypic regions were found. Hollow tubes were observed, almost exclusively in the wide regions; the regions with no hollow tubes consist of a large number of very narrow faulted sub-regions. It is suggested that the creation of Shockley partials is associated with the strain in the vicinity of the growth screw dislocations. Those regions where the core of the dislocation is hollow are unstrained and the Shockley partials, moving in from neighboring regions, can climb unimpeded along the helicoidal basal planes, transforming them into the various observed polytypes.
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  • 175
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    Applied crystallography online 17 (1984), S. 334-336 
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    Topics: Geosciences , Physics
    Notes: Enhancements in the auto-indexing procedure for cell determination improve its power and reliability. A proper selection of three basis reflections for construction of an initial subcell is essential. A standard cell-reduction procedure applied to the subcell, and the calculation of appropriate limits for the direct-lattice-vector generation integers, make a comprehensive coverage of the direct space efficient and effective. Refinement of the generated lattice vectors against all the available reflection data makes assignment of the correct unit cell easier and more reliable. Generation of some additional long vectors is recommended in special cases.
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  • 176
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    Applied crystallography online 17 (1984), S. 337-343 
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    Topics: Geosciences , Physics
    Notes: A high-resolution small-angle X-ray scattering camera has been built, which has the following features. (i) The point collimation optics employed allows the scattering cross section of the sample to be directly measured without corrections for desmearing. (ii) A small-angle resolution better than 0.5 mrad is achieved with a camera length of 1.6 m. (iii) A high photon flux of 0.9 photons μs−1 is obtained on the sample with the rotating-anode X-ray generator operated at 40 kV–30 mA. (iv) Incident X-rays are monochromated by a bent quartz crystal, which makes the determination of the incident X-ray intensity simple and unambiguous. (v) By rotation of the position-sensitive proportional counter around the direct beam, anisotropic scattering patterns can be observed without adjusting the sample. Details of the design and performance are presented with some applications.
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    Applied crystallography online 17 (1984), S. 363-363 
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    Notes: The new compound 7HgI2.Fe(C5H5)2 was prepared by the reaction of solid tetragonal mercuric iodide with ferrocene vapours at 423 K. The product is a dark green powder, stable in air, and decomposes at 463 K. The cubic unit-cell parameters (298 K) are: a = 20.12(2) Å, V = 8157.3 Å3, Z = 8, Mr = 3366.8, Dx = 5.49 Mg m−3; extinctions indicate a face-centered space group. X-ray (Cu Kα radiation) powder diffraction data (50 lines) are reported. The compound has interesting electrical properties. The JCPDS Diffraction File No. for 7HgI2.Fe(C5H5)2 is 35-2000.
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    Applied crystallography online 17 (1984), S. 364-366 
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    Notes: A program is presented that solves crystal structures completely using advanced Fourier methods starting from a small known fraction (about 8%) of the structure. The program uses a statistical test based on the R2 factor to check the correctness of the model obtained so far. The results obtained with four test structures are given.
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    Applied crystallography online 17 (1984), S. 369-369 
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    Applied crystallography online 17 (1984), S. 366-368 
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    Notes: The well known molecular drawing program, PLUTO78, has been made more widely available in the UK by mounting it on the minicomputers of the Joint Academic Network (JANET) wide-area network. Enhancements include interaction, faster plotting, use of colour and simulated half tone, easy access to centrally maintained high-quality-output devices, and the provision of comprehensive documentation in the form of on-line help and a user manual.
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    Applied crystallography online 17 (1984), S. 369-370 
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    Applied crystallography online 17 (1984), S. 370-370 
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    Applied crystallography online 17 (1984), S. 464-469 
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    Notes: The possibility of combining time-of-flight powder neutron-diffraction patterns collected at different scattering angles is examined, with a view to increasing data-collection rates by the use of a large total solid angle and by including multiple frame overlaps. The basic design features of the required diffractometer are enumerated and a test experiment, using a spectrometer possessing basic characteristics pertinent to the proposed diffractometer, is used to evaluate these assertions.
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    Applied crystallography online 17 (1984), S. 476-480 
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    Notes: The system Na decyl sulfate/water/decanol/Na sulfate, which forms a nematic NL lyomesophase with planar micelles at 298 K, changes to a CG phase at 295 K on cooling. Phase CG studied by X-ray diffraction has a lamellar structure with repetition distance 31.4 Å. Comparison of observed and calculated intensities from a step-function model defines the CG phase as a coagel where anhydrous lamellar aggregates of extended tilted bilayers are dispersed in water. This result gives support to the model of aggregates of micelles in the NL phase previously proposed.
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    Applied crystallography online 17 (1984), S. 470-475 
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    Notes: A new curved linear position-sensitive detector has been developed and used in a computer-controlled high-speed data collection system with Weissenberg geometry for X-ray crystallography. This detector system enables one to see the entire Weissenberg diagram on a CRT display monitor in real time. A comparison between refinement results of the room-temperature phase of LiRbSO4 by this system and a conventional four-circle diffractometer showed that the atomic coordinates almost agree within the experimental errors. A new phenomenon was found with this system: LiRbSO4 changes into the twin state under external electric field at room temperature.
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    Applied crystallography online 17 (1984), S. 486-486 
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    Applied crystallography online 17 (1984), S. 1-6 
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    Notes: A technique for the measurement of diffuse X-ray scattering by a combination of an energy-dispersive detector and a source of white X-rays is described by taking the instrumental resolution into account. A high-power X-ray generator was used to generate white X-rays. The short-range-order (SRO) diffuse scattering from Au4Mn alloy was measured and the Warren–Cowley SRO parameters of this alloy were determined up to the 50th shell. The results are in good agreement with those obtained by the angle-dispersive technique. Possible application of this method with the use of X-rays from a synchrotron radiation source is presented.
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    Applied crystallography online 17 (1984), S. 7-12 
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    Notes: The vertical intensity distributions of X-rays from a synchrotron source are measured by powder diffraction. The components polarized in the orbital plane and perpendicular to this plane are separated by measuring a reflection 90° to the vertical and horizontal planes, respectively. The measurements are made at three wavelengths between 0.65λc and λc, where λc is the characteristic wavelength. In each case, the degree of linear polarization reaches a maximum of 90% at the center of the beam. The results agree closely with calculations which use machine optical parameters.
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    Applied crystallography online 17 (1984), S. 18-21 
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    Notes: The proposed method is aimed at the analysis of phase distribution in thin surface layers comparable to the penetration depth of X-rays. The phase distribution is modelled mathematically and the parameters of the distribution are evaluated from diffraction data taken for various peaks and with various radiations. The method was applied to the analysis of austenite distribution in cathodically charged stainless steel.
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    Applied crystallography online 17 (1984), S. 13-17 
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    Notes: It is shown by a diffraction technique that 2-naphthalenethiol (C10H8S) undergoes a first-order phase transition which occurs at 313 ± 0.5 K. The low-temperature form III is ordered whereas the high-temperature one I is disordered and may be kept as metastable far below 313 K. Thermal expansion studies, performed on the stable form III and on both metastable and stable forms I, indicate that: form III exhibits a pronounced `pretransitional' effect; discontinuities of the lattice constants occur at the III →I transition; the lattice-constant thermal-expansion curves of form I do not show any inflexion at the metastable to stable transition; in every case a large thermal expansion anisotropy is observed. Curiously, the compacity of the ordered low-temperature form is lower than that of the disordered high-temperature form. The JCPDS Diffraction File No. of the low-temperature form III is 34–1990.
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    Applied crystallography online 17 (1984), S. 22-26 
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    Notes: Several procedures for Fourier analysis of single diffraction peaks for microstrains and mosaic sizes are compared. A simple new method works well, especially when the size distribution is broad, and/or when the strains vary in an unusual manner.
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    Applied crystallography online 17 (1984), S. 27-32 
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    Notes: A convenient approximation has been obtained for the intensity of the small-angle X-ray or neutron scattering from an assembly of independently scattering spherical particles with constant density when the radius-distribution function is a Gaussian with a full width at half maximum which is not greater than 1.7 times the most probable radius. The approximation expresses the intensity in terms of elementary functions. Criteria are given for setting a bound on the error in the approximation.
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    Applied crystallography online 17 (1984), S. 33-38 
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    Notes: The energy-dispersive X-ray diffraction method has been used to measure integrated Bragg intensities from TaDx single crystals as a function of D concentration and scattering vector. The observed attenuation can be described in terms of a thermal and a static Debye–Waller factor (DWF). From the static DWF, for small scattering vectors, the displacements u1 = 0.095 (5) Å of the four Ta atoms closest to the D atom are obtained and, for large scattering vectors, the change of the mean-square thermal displacement of these atoms Δv21 = −[5.5 (3)] × 10–4 Å2.
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    Applied crystallography online 17 (1984), S. 39-39 
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    Notes: The rare-earth n-butyrate dihydrates Ln(C4H7O2)3.2H2O (where Ln = Nd, Tb, Ho, Er, Tm, Yb or Y) were synthesized and the structural parameters determined employing X-ray powder diffraction techniques. The salts are isomorphous and possess monoclinic symmetry with space group P21/m and contain four molecules per unit cell. Nd(CH3CH2CH2COO)3.2H2O: a = 12.69 (6), b = 14.34 (6), c = 10.31 (4) Å, β = 97.06 (36)°, V = 1862 Å3, Dm = 1.655, Dx = 1.575 Mg m−3; Tb(CH3CH2CH2COO)3.2H2O: a = 12.74 (2), b = 14.22 (4), c = 10.34 (3) Å, β = 98.02 (16)°, V = 1856 Å3, Dm = 1.666, Dx = 1.633 Mg m−3; Y(CH3CH2CH2COO)3.2H2O: a = 12.68 (2), b = 14.08 (4), c = 10.28 (2) Å, β = 98.57 (16)°, V = 1814 Å3, Dm = 1.423, Dx = 1.414 Mg m−3; Ho(CH3CH2CH2COO)3.2H2O: a = 12.62 (2), b = 14.00 (3), c = 10.22 (2) Å, β = 98.09 (13)°, V = 1789 Å3, Dm = 1.727, Dx = 1.716 Mg m−3; Er(CH3CH2CH2COO)3.2H2O: a = 12.60 (2), b = 14.02 (2), c = 10.19 (1) Å, β = 98.71 (13)°, V = 1780 Å3, Dm = 1.707, Dx = 1.733 Mg m−3; Tm(CH3CH2CH2COO)3.2H2O: a = 12.61 (2), b = 13.96 (2), c = 10.21 (2) Å, β = 98.30 (16)°, V = 1779 Å3, Dm = 1.714, Dx = 1.741 Mg m−3; Yb(CH3CH2CH2COO)3.2H2O: a = 12.64 (1), b = 13.92 (1), c = 10.19 (1) Å, β = 98.32 (10)°, V = 1773 Å3, Dm = 1.745, Dx = 1.762 Mg m−3. The JCPDS Diffraction File No. for Er(CH3CH2CH2COO)3.2H2O is 34-1991.
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    Applied crystallography online 17 (1984), S. 39-42 
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    Notes: A computer program for unambiguous and consistent indexing of a series of single-crystal diffraction patterns is discussed which allows determination of the unit triangle and therefore tilting of the specimen into any special orientation even if no Kikuchi patterns can be observed.
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    Applied crystallography online 17 (1984), S. 42-46 
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    Notes: A new direct-methods computer program, MITHRIL, is described. Written in a neutral subset of Fortran IV, it is built around a heavily modified MULTAN80 system. It incorporates many recent theoretical developments in direct methods including the use of quartet and quintet invariants, a new method for estimating triplets, YZARC and MAGEX, and random-phase tangent refinement. It can be run as a menu-driven interactive real-time package or in the more conventional batch mode. Several levels of user-program interaction are provided.
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    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 17 (1984), S. 47-54 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: For the application of Rietveld profile analysis to neutron powder diffraction data a precise knowledge of the peak profile, in both shape and position, is required. The method now in use employs a Gaussian-shaped profile with a semi-empirical asymmetry correction for low-angle peaks. The integrated intensity is taken to be proportional to the classical Lorentz factor calculated for the X-ray case. In this paper an exact expression is given for the peak profile based upon the geometrical dimensions of the diffractometer. It is shown that the asymmetry of observed peaks is well reproduced by this expression. The angular displacement of the experimental profile with respect to the nominal Bragg angle value is larger than expected. Values for the correction to the classical Lorentz factor for the integrated intensity are given. The exact peak profile expression has been incorporated into a Rietveld profile analysis refinement program.
    Type of Medium: Electronic Resource
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  • 198
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 17 (1984), S. 55-60 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: The use of the Rietveld full-profile refinement technique to estimate cation distributions is exemplified by a neutron powder diffraction study of the farringtonite-type solid solution γ-(Zn0.70Fe0.30)3(PO4)2, with five- and six-coordinated cation sites. A review of similar studies (neutron or Guinier–Hägg X-ray data) of phases with the farringtonite, sarcopside, Ni2P4O12 or olivine structure is given. The accuracy is discussed in terms of KD distribution coefficients and metal–oxygen distances. Some investigations of olivines based on X-ray single-crystal data are reviewed for comparison.
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  • 199
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 17 (1984), S. 61-76 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: X-ray diffraction experiments on amorphous Fe40Ni40P20 were performed in association with a detailed study of the accuracy, limitations and reproducibility of experimental radial distribution functions (RDF's). A novel counting strategy is presented, and the merits of conducting two diffraction experiments in different geometries as a test for internal consistency are argued. Experimental methods and data-processing techniques are treated in detail. The results indicate that the RDF can be determined virtually with pre-selected accuracy. The positions of the co-ordination shells for Fe40Ni40P20 show a remarkable periodicity.
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  • 200
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 17 (1984), S. 77-84 
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: In the solvent contrast variation technique, the structure factor is a linear function of contrast, and the intensity is therefore a parabolic function of contrast. A method has been developed which scales together data measured at different contrasts on different samples. Once the data are scaled, structure-factor amplitudes or intensities for any other contrast can be obtained by inter- (or extra-)polation. The magnitude of the relative phase change between contrast, an important piece of phasing information in single-crystal studies, can be determined.
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