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  • 1
    Electronic Resource
    Electronic Resource
    A neutron diffraction study of anharmonic temperature factors in SrF2 (1974)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 30 (1974), S. 806-813 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Accurate integrated intensities for the Bragg reflexion of neutrons from two single crystals of SrF2 have been measured at temperatures between 295 and 1043 °K. Corrections for extinction and thermal diffuse scattering were applied and the experimental data were analysed in terms of a model which includes both harmonic and anharmonic components in the thermal vibrations of the atoms. Significant contributions from the third-order anharmonic term, βF, in the one-particle potential of the fluorine atoms, consistent with their tetrahedral site symmetry, were observed at all temperatures. At 773 °K significant anisotropic fourth-order components, δSr and δF, became apparent in the thermal vibration of both the strontium and the fluorine atoms. At this temperature βF was refined to - 3.45 ( ± 0.11) × 10-12 erg Å-3, with δSr = 1.30 ( ± 0.75) × 10-12 erg Å-4 and δF = 0.84 (± 0.29) × 10-12 erg Å-4. The positive signs of the parameters δSr and δF result from the influence of Coulombic forces on the atomic vibrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739474001902
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  • 2
    Electronic Resource
    Electronic Resource
    The temperature dependence of the Debye–Waller factor near a phase transition: CsPbCl3 (1982)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 38 (1982), S. 790-796 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: By fitting effective one-particle potentials to Bragg neutron diffraction intensities measured by Sakata, Harada, Cooper & Rouse [Acta Cryst. (1980), A36, 7-15] for the cubic perovskite caesium lead chloride, CsPbCl3, it has been established that, contrary to the results of Sakata et al., the effective one-particle potentials for the Cl ion are neither independent of temperature nor of a highly anharmonic form. To the resolution limit of the data, collected out to sin θ/λ = 0.58 Å-1, the one-particle probability density function of the Cl ion is singly peaked. It is proposed that the strong temperature dependence of the effective one-particle potentials, and the accompanying anomalous temperature behaviour observed for the mean-square displacements of the Cl and Cs ions above the anti-ferrodistortive phase transition temperature, result from soft-mode vibrations. The temperature dependence of the mean-square displacement in the presence of soft modes is derived and it is shown for the first time that a significant temperature-invariant component will be the main additional effect at temperatures well above the critical temperature. The Cl and Cs ions in CsPbCl3 obey this derived mean-square displacement relationship.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739482001612
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  • 3
    Electronic Resource
    Electronic Resource
    Anharmonic temperature factors: the limitations of perturbation theory expressions. Erratum (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 304-304 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The parts of Fig. 1 in Mackenzie & Mair [Acta Cryst. (1985). A41, 81-85] have been wrongly labelled, so that (a) to (d) and (e) to (h) run vertically. The correct labelling has parts (a) and (b) on the top line, (c) and (d) on the second line, (e) and (f) on the third line and (g) and (h) at the bottom. References to Scheringer (1984a, b) should read Scheringer (1985a, b).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000654
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  • 4
    Electronic Resource
    Electronic Resource
    The electron distribution of the hydroxide ion in lithium hydroxide (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 542-547 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Analysis of recently published X-ray and neutron diffraction data for LiOH reveals that there are pronounced non-spherical deformations of the electrondensity about the oxygen pseudo-atom. Comparison with a theoretical calculation of the electron density for the isolated hydroxide ion shows that these deformations are due to π-like bonding of the oxygen to the neighbouring hydrogen pseudo-atom. The observed features have shapes consistent with the non-spherical electron distribution of an isolated hydroxide ion undergoing rigid-body libration and translation. It is shown that an important effect of the rigid-body libration is a reversal in sign of the effective quadrupole component of the oxygen pseudo-atom electron density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001151
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  • 5
    Electronic Resource
    Electronic Resource
    Anharmonic temperature factors: the limitations of perturbation-theory expressions (1985)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 41 (1985), S. 81-85 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The error in the temperature factor arising from the use of anharmonic perturbation theory is investigated for a one-dimensional one-particle potential by comparison with an exact evaluation of the Fourier transform of the Boltzmann probability density. Results are presented for a range of values of cubic and quartic coefficients for temperature factors derived from moment or cumulant expansions about the harmonic probability density function. It is found that either expansion provides an adequate approximation to the anharmonic temperature factor for moderately small anharmonicity but that both expansions become increasingly Inadequate as the anharmonicity gets larger.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767385000149
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  • 6
    Electronic Resource
    Electronic Resource
    Computer simulation of Bragg and diffuse scattering intensities against temperature for a structural phase transition (1987)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 43 (1987), S. 690-694 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Molecular dynamics has been used to estimate the properties of a two-dimensional crystal exhibiting a second-order soft-mode phase transition. Using a vibrational potential for the crystal which is temperature independent, the essential features observed experimentally in the coherent scattering from analogous real systems are reproduced in the computer simulation. The potential consists of an effective one-particle component with multiple minima and a harmonic nearest-neighbour coupling component. It is emphasized that the coupling component is essential to reproduce correctly the qualitative features not only of the diffuse scattering, but also of the mean-square displacements as a function of temperature. The condition for appearance of a cusp at TC in the mean-square displacement versus temperature curve is discussed and the formation of superlattice peaks in the diffuse scattering is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0108767387098726
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  • 7
    Electronic Resource
    Electronic Resource
    Electron distribution and charge transfer in the ammonium ion (1978)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 34 (1978), S. 656-662 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A re-analysis of the single-crystal X-ray data of Adrian & Feil [Acta Cryst. (1969), A25, 438-444] for ammonium fluoride has shown that there is a transfer of negative charge from the 'surface' of the ammonium ion to the central nitrogen. In addition to charge transfer, models used in the analysis allow for non-rigid-body motion of the ammonium ion and asphericity in the hydrogen electron densities. This asphericitiy has been represented in two different ways, one involving a floated monopole and the other a polarized distribution centred on the neutron-determined position. Both models give comparable fits to the data and similar charge- transfer parameters are obtained, so that the floated-monopole model is considered adequate for obtaining properties of the total molecular electron distribution. However, the dipole model is to be preferred if information about the hydrogen pseudo-atom is desired. The present analysis is compared with previous ones employing structure factors derived from molecular wavefunctions for the ammonium ion. These previous analyses are less successful than might be expected and this is attributed to their over-simplified treatment of the ammonium ion as a rigid body and their neglect of crystal-field effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739478001400
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  • 8
    Electronic Resource
    Electronic Resource
    On the X-ray or neutron diffraction determination of atomic position parameters (1981)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 37 (1981), S. 264-266 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that, unless the atomic position parameters in a crystal are completely determined by symmetry, the position parameters corresponding to the minimum of the potential in the thermally strained lattice differ from those corresponding to thermodynamic equilibrium. By appropriate refinement of X-ray or neutron diffraction data, it is possible to obtain both sets of position parameters as well as the linear and higher-order coefficients of one-particle potentials expanded about the equilibrium positions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739481000582
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  • 9
    Electronic Resource
    Electronic Resource
    Anharmonic thermal vibrations in wurtzite structures (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 201-207 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The general form of the effective one-particle potential has been derived up to cubic terms for an atom undergoing anharmonic thermal vibration in a wurtzite-type crystal. The resulting potential suggests a mechanism for the primary pyroelectricity observed in these structures. The deviation of the structural parameters u in the various wurtzite structures from their predicted values, is shown to be closely related to the pyro-electric effect, and can also be attributed to anharmonicity. The effects of anharmonicity on the elastic scattering of X-rays and neutrons have been investigated. It is shown that the u parameter in the conventional expression for the Bragg intensities implicitly contains first-order anharmonic effects, but that a modified form of the intensity expression is necessary to account for higher-order anharmonic effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S056773947500040X
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  • 10
    Electronic Resource
    Electronic Resource
    The structure and Bijvoet ratios of cadmium selenide (1977)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 33 (1977), S. 355-359 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The structure of cadmium selenide has been determined from X-ray intensity data obtained with extended-face crystals. The wurtzite parameter u was found to be 0.37679 ± 0.00012. Comparison of the intensities of equivalent reflexions provided a test for the internal consistency of the measurements. Equivalent reflexions in two specimens differed on average by 1.4 and 0.6% from the mean measured intensity, attesting to the high internal consistency of measurements from extended-face crystals. Comparison of 36 structure factors derived from data obtained from both specimens showed their average deviation from the mean to be 0.9%. An attempted least-squares refinement of the dispersion corrections of both atoms from observed Bijvoet ratios failed, presumably on account of correlation. When the dispersion corrections of one atom were held constant, it did prove possible to refine the dispersion corrections of the other atom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739477000977
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