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  • 1
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 7307-7314 
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A theoretical study of the vibrational relaxation of the adbond between a physisorbed molecule and a crystalline substrate is presented. The bond between the admolecule and the substrate is described as a one-dimensional Morse oscillator. Using standard perturbation theory, expressions for the relaxation of the vibrational adbond due to its interaction with the substrate lattice vibrations are derived. Both energy relaxation and pure dephasing are considered. A numerical evaluation of the resulting expressions for the relaxation constants is given for a Debye spectrum for the phonons and for a surface phonon spectrum. The relative importance of pure dephasing and energy relaxation in determining the absorption linewidth is derived as a function of the fundamental frequency of the active mode.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    s.l. : American Chemical Society
    Journal of the American Chemical Society 114 (1992), S. 1986-1989 
    ISSN: 1520-5126
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 5504-5511 
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The phonon relaxation of the vibrational adbond of an adsorbed molecule and a phonon-damped adbond irradiated by a laser are studied. In the first half of the paper, approximations are made within the Zwanzig projection operator formalism in order to arrive at a master equation for the reduced density operator of a small subsystem (the adbond) in contact with a reservoir (the phonons). The conditions of validity for the Born and Markov approximations are derived. It is shown that the master equation is only valid for times t(very-much-greater-than)τc, where τc is the characteristic time of the reservoir. These results are then applied to the phonon relaxation of the vibrational adbond of physisorbed molecules. It is shown that for CO adsorbed on Ni or Cu (a strongly bound physisorbed system) the Born and Markov approximations are not justified. For the weakly bound system Ar on W, numerical results show that these approximations can be made. Finally, an adbond interacting with both laser radiation and lattice vibrations is considered. This system can be regarded as a subsystem (the adbond) in contact with two reservoirs, where the conditions for validity of the Markov approximation is then seen to be more severe than when each reservoir is considered independently. For the phonons, these conditions can never be matched. However, for an initial state given by an adbond in equilibrium with the lattice vibrations, the conditions for validity of the approximations prove to be the same as for the phonons and the laser considered independently.
    Materialart: Digitale Medien
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  • 4
    ISSN: 1600-5767
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Geologie und Paläontologie , Physik
    Notizen: In the molecular structure of tetraferrocenyl-[3]-cumulene, (Fc)2C=C=C=C(Fc)2, four ferrocene molecules are connected via a linear bridge consisting of four carbon atoms. At room temperature, the crystal structure has space group P21/a (Z = 1) with a = 13.104 (5), b = 6.121 (2), c = 11.194 (4) Å, β = 114.922 (1)° and V = 814.3 (8) Å3. A phase transition during cooling was not observed from room temperature to 75 K. From high-resolution X-ray powder diffraction data, the structure of the room-temperature phase was solved by the method of simulated annealing and refined by the Rietveld method using rigid bodies and restraints. The crystal structure was found to be highly disordered with the molecules occupying two orientations with equal probability and a 50% occupancy of the carbon atoms in the cumulene bridge. The disorder could be modelled by stacking faults in ordered structures. In contrast to other compounds of this class, the ferrocenyl groups are in a syn rather than in an up–down conformation with respect to the cumulene bridge.
    Materialart: Digitale Medien
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  • 5
    ISSN: 1600-5740
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The compounds tetrakis(trimethylsilyl)methane C[Si(CH3)3]4 (TC) and tetrakis(trimethylsilyl)silane Si[Si(CH3)3]4 (TSi) have crystal structures with the molecules in a cubic closed-packed (c.c.p.) stacking. At room temperature both structures have space group Fm{\bar 3}m (Z = 4) with a = 13.5218 (1) Å, V = 2472.3 (1) Å3 for TSi, and a = 12.8902 (2) Å, V = 2141.8 (1) Å3 for TC. X-ray scattering data can be described by a molecule with approximately sixfold orientational disorder, ruling out a structure with free rotating molecules. Upon cooling, TSi exhibits a first-order phase transition at Tc = 225 K, as is characterized by a jump of the lattice parameter of Δa = 0.182 Å and by an exothermal maximum in differential scanning calorimetry (DSC) with ΔH = 11.7 kJ mol−1 and ΔS = 50.0 J mol−1 K−1. The structure of the low-temperature phase is refined against X-ray powder data measured at 200 K. It has space group P213 (Z = 4), a = 13.17158 (6) Å and V = 2285.15 (2) Å3. The molecules are found to be ordered as a result of steric interactions between neighboring molecules, as is shown by analyzing distances between atoms and by calculations of the lattice energy in dependence on the orientations of the molecules. TC has a phase transition at Tc1 = 268 K, with Δa1 = 0.065 Å, ΔH1 = 3.63 kJ mol−1 and ΔS1 = 13.0 J mol−1 K−1. A second first-order phase transition occurs at Tc2 = 225 K, characterized by Δa2 = 0.073 Å, ΔH2 = 6.9 kJ mol−1 and ΔS2 = 30.0 J mol−1 K−1. The phase transition at higher temperature has not been reported previously. New NMR experiments show a small anomaly in the temperature dependence of the peak positions in NMR to occur at Tc2. Rietveld refinements were performed for the low-temperature phase measured at T = 150 K [space group P213, lattice parameter a = 12.609 (3) Å], and for the intermediate phase measured at T = 260 K [space group Pa{\bar 3}, lattice parameter a = 12.7876 (1) Å]. The low-temperature phase of TC is formed isostructural to the low-temperature phase of TSi. In the intermediate phase the molecules exhibit a twofold orientational disorder.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 886-895 
    ISSN: 1600-5740
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: Crystalline dicaesium mercury tetrachloride (Cs2HgCl4) is isomorphous with \beta-K_2SO_4 (space group Pnma, Z = 4) in its normal phase at room temperature. On cooling a sequence of incommensurate and commensurate superstructures occurs, below T = 221 K with modulations parallel to a*, and below 184 K with modulations along c*. The commensurately modulated structures at T = 185 K with {\bf q}= {{1}\over{5}}\bf{a}^* and at T = 176 K with {\bf q} = {{1}\over{3}}\bf{c}^* were determined using X-ray scattering with synchrotron radiation. The structure at T = 185 K has superspace group Pnma(\alpha,0,0)0ss with \alpha = 0.2. Lattice parameters were determined as a = 5\times9.7729\kern2pt(1), b = 7.5276\kern2pt(4) and c = 13.3727\kern2pt(7) Å. Structure refinements converged to R = 0.050 (R = 0.042 for 939 main reflections and R = 0.220 for 307 satellites) for the section t = 0.05 of superspace. The fivefold supercell has space group Pn2_1a. The structure at T = 176 K has superspace group Pnma(0,0,\gamma)0s0 with \gamma = {{1}\over{3}}. Lattice parameters were determined as a = 9.789\kern2pt(3), b = 7.541 \kern2pt(3) and c = 3 \times 13.418\kern2pt(4) Å. Structure refinements converged to R = 0.067 (R = 0.048 for 2130 main reflections, and R = 0.135 for 2382 satellite reflections) for the section t = 0. The threefold supercell has space group P112_1/a. It is shown that the structures of both low-temperature phases can be characterized as different superstructures of the periodic room-temperature structure. The superstructure of the 5a-modulated phase is analysed in terms of displacements of the Cs atoms, and rotations and distortions of HgCl4 tetrahedral groups. In the 3c-modulated phase the distortions of the tetrahedra are relaxed, but they are replaced by translations of the tetrahedral groups in addition to rotations.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 310-316 
    ISSN: 1600-5740
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The pressure dependence of the crystal structure of cubic tetrakis(trimethylsilyl)methane C[Si(CH3)3]4 (TC) (P 〈 16.0 GPa, T = 298 K) is reported using high-resolution angle-dispersive X-ray powder diffraction. The compound has crystal structures with the molecules in a cubic-close-packed (c.c.p.) arrangement. It shows three phase transitions in the measured pressure range. At ambient conditions, TC has space group Fm{\bar 3}m (Z = 4) with a = 12.8902 (2) Å, V = 2141.8 (1) Å3 (phase I). Between 0 and 0.13 GPa TC exhibits a first-order phase transition into a structure with space group Pa{\bar 3} (phase II). A second first-order phase transition occurs between 0.2 and 0.28 GPa into a structure with space group P213 (phase III). Under non-hydrostatic pressure conditions (P 〉 10  GPa) a transformation is observed into a c.c.p. structure that is different from the face-centred-cubic structure at ambient conditions. A non-linear compression behaviour is observed, which could be described by a Vinet relation in the range 0.28–4.8 GPa. The extrapolated bulk modulus of the high-pressure phase III was determined to be K0 = 7.1 (8) GPa. The crystal structures in phase III are refined against X-ray powder data measured at several pressures between 0.49 and 4.8 GPa, and the molecules are found to be fully ordered. This is interpreted to result from steric interactions between neighbouring molecules, as shown by analysing the pressure dependence of intramolecular angles, torsion angles and intermolecular distances. Except for their cell dimensions, phases I, II and III are found to be isostructural to the corresponding phases at low temperatures.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 231-236 
    ISSN: 1600-5740
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The a0 × b0 × 2c0 twofold superstructure of dicaesium mercury tetrachloride, Cs2HgCl4, at T = 120 K has been determined by single-crystal X-ray diffraction using synchrotron radiation. Lattice parameters were found as a = 9.7105 (2), b = 7.4691 (1), c = 26.8992 (4) Å, and β = 90.368 (1)° with the supercell space group P21/c. Refinements on 1828 observed unique reflections converged to R = 0.053 (wR = 0.057) using anisotropic temperature factors for all atoms. This phase is the stable phase of Cs2HgCl4 below 163 K. A quantitative comparison is made of the distortions of the 2c0 superstructure with the undistorted phase that is stable at room temperature, and with the 3c0 and 5a0 superstructures that are stable at temperatures between 163 K and room temperature. The principal difference between the 2c0 superstructure and all other phases of Cs2HgCl4 is that the Cs cations are displaced away from the centers of their coordination polyhedra in the 2c0 superstructure. The structural basis for the driving force of the series of phase transitions in this compound is found in the variations of the environments of Cs atoms and in the variations of the distortions of the HgCl4 tetrahedra.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 248-251 
    ISSN: 1600-5724
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The Beevers–Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in n-dimensional space would lead to n nested loops over the n coordinates, respectively, and different computer code is required for each dimension. An algorithm is proposed based on the generalization of the Beevers–Lipson procedure towards transforms in n-dimensional space that contains the dimension as a variable and that results in a single piece of computer code for arbitrary dimensions. The computational complexity is found to scale as N\log(N), where N is the number of pixels in the map, and it is independent of the dimension of the transform. This procedure will find applications in the evaluation of Fourier maps of quasicrystals and other aperiodic crystals, and in the maximum-entropy method for aperiodic crystals.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 401-412 
    ISSN: 1600-5724
    Quelle: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Thema: Chemie und Pharmazie , Geologie und Paläontologie , Physik
    Notizen: The broken-bond model for the surface free energy of crystals is considered. The consequences are derived for the morphology of periodic crystals, quasicrystals, incommensurately modulated crystals and intergrowth compounds. It is found that low-index facets on periodic crystals and quasicrystals are the result of finding an optimized position along the vector normal to the surface of the surface plane. The same principle explains the normal facets on modulated crystals and intergrowth crystals. The so-called satellite facets are the result of surface pinning of the phase of the modulated wave. On intergrowth compounds, facets may be found that are stabilized by a combination of both mechanisms. It is shown that the most stable facets on intergrowth crystals are the normal facets that are common to the subsystems, independent of the details of the structure.
    Materialart: Digitale Medien
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