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1994 (1)
1993 (3)
1Author    S. Sh, Soulayman, C. Ch, Ch Marti, Ch, GuilpinRequires cookie*
 Title    Anharmonic Self-Consistent Theory of Crystals. I. A 1 d Quartic Crystal Model  
 Abstract    We apply the Unsymmetrized Self-Consistent-Field-Method (USCFM) to a linear infinite chain of identical atoms with a quartic pair interaction potential. We show that an exact solution of the USCFM can be found in terms of a single auxiliary function which is studied here in details. We use it to calculate the partition function, the energy and the free energy, the moments of the position, the corrections due to quantum effects and higher terms of the potential, the specific heat and the thermal expansion. An anharmonic approximative approach, based on the self-consistent potential of the used method, is developed also. We apply these two approaches to the study of the thermo-elastic properties of a one dimensional system (krypton). It is demonstrated that the approximate approach is very effective when dealing with pairwise potentials of positive second derivative. The Lennard-Jones potential is used in our calculations. 
  Reference    Z. Naturforsch. 48a, 1182—1192 (1993); received December 18 1992 
  Published    1993 
  Keywords    Linear chain, Anharmonicity, Thermodynamic properties, Inert gases 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-1182.pdf 
 Identifier    ZNA-1993-48a-1182 
 Volume    48 
2Author    Renzo Restori, Dieter SchwarzenbachRequires cookie*
 Title    X-Ray Diffraction Study of the Electron Density and Anharmonicity in K 2 PtCl 6  
 Abstract    X-ray diffraction data in heavy-atom compounds may be sensitive to anharmonic atomic displacements, since the large core electron densities result in appreciable scattering amplitudes at large reciprocal distances. Since bonding electron densities may also exhibit sharp features affecting high-order reflections, they may be difficult to distinguish from anharmonic effects. We have ana-lyzed an accurate room-temperature single-crystal X-ray data set of K 2 PtCl 6 using least-squares anharmonic displacement and charge density formalisms. The Hirshfeld charge density formalism, which has successfully been applied to many light-atom structures, fails to parametrize satisfactorily the data, whereas the electron densities at K and CI are easily accounted for by an anharmonic Gram-Charlier expansion to 4th order. Densities around Pt are parametrized only by a combination of anharmonicity and charge density formalisms. If economical parametrizations of the experimental data are preferred to more complicated ones, anharmonicity may be conjectured to play an impor-tant role while the main bonding feature consists of a preferential occupation of the 5d-orbitals of Pt with t 2g symmetry. 
  Reference    Z. Naturforsch. 48a, 12—20 (1993); received December 19 1991 
  Published    1993 
  Keywords    Charge density, Thermal motion, Anharmonicity, X-ray diffraction, d-orbitals 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0012.pdf 
 Identifier    ZNA-1993-48a-0012 
 Volume    48 
3Author    A. G. Tsarkov, V. G. TsirelsonRequires cookie*
 Title    The Identification of Phonon-Phonon Interactions in Anharmonic Crystals by X-Ray Diffraction Data  
 Abstract    The effect of anharmonic atomic vibrations on the elastic scattering of X-rays by a crystal is treated by time-independent perturbation theory. The complete expression for the anharmonic temperature factor (TF) in the high-temperature limit is presented for atoms in general positions. The phonon-phonon interactions in an anharmonic crystal may be identified with X-ray diffraction data by using various temperature and scattering vector q dependencies of different anharmonic contri-butions to the TF. The expression for the intensity of elastic scattering by an anharmonic crystal contains an additional factor -the anharmonic cross-term. This term has to be taken into account for obtaining the unbiased thermal parameters of fourth order in | q | from X-ray diffraction data. 
  Reference    Z. Naturforsch. 48a, 21—24 (1993); received November 8 1991 
  Published    1993 
  Keywords    Lattice vibrations, Anharmonicity, Phonon-phonon interactions, Temperature factor, X-ray diffraction 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0021.pdf 
 Identifier    ZNA-1993-48a-0021 
 Volume    48 
4Author    S. Sh, Soulayman, C. M. Ch, Ch Arti, Ch, GuilpinRequires cookie*
 Title    Anharmonic Self-Consistent Theory of Crystals. II. The 2d and 3d Quartic Crystal Models  
 Abstract    In this paper we apply the method developed in part I for describing the crystalline state of two and three dimensional inert gases. For strong anharm onicity of fourth order, the equations of state of these gases are obtained. This way we calculate the thermoelastic properties of two and three dimensional argon, krypton and xenon using the Lennard-Jones potential. The corrections to the Helmholtz free energy and thermodynamic properties due to quantum effects are considered. The results are compared with the available experimental data. 
  Reference    Z. Naturforsch. 49a, 663—670 (1994); received December 18 1993 
  Published    1994 
  Keywords    Inert gases, Anharmonicity, Thermodynamic properties, Two-and three-dimensional crystals 
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 TEI-XML for    default:Reihe_A/49/ZNA-1994-49a-0663.pdf 
 Identifier    ZNA-1994-49a-0663 
 Volume    49