Über Gitterschwingungen in Molekülkristallen

Hahn, H.; Biem, W.

doi:10.1002/pssb.19630031018

Cited by 40 publications

(11 citation statements)

References 2 publications

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“…In the case of 2D adsorbed molecular systems similar structures were observed experimentally [11]. The alternating orientation ordering differs from the parallel equilibrium ordering of molecules chosen in [6][7][8].…”

Section: Introductionmentioning

confidence: 51%

“…Some approximations are necessary to simplify the system's description because of complexity even for a 1D molecular chain. For linear models such approximations use a force matrix (harmonic expansion near the equilibrium position) instead of parameters of interaction, or use a given parallel ordering of molecules [5] (p. 428), [6][7][8]. In nonlinear consideration such approximations are a model potential and 1D rotation [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…1D and 2D models are a necessary stage of investigation of dynamics and thermodynamics of more complex systems: crystals, nonlinear dynamics of atomic and molecular lattices [1][2][3][4]. 1D chain models are applied to the description of linear lattice dynamics and thermodynamics of molecular cryocrystals [5,6], with generalization into 3D systems [5,7,8], to nonlinear dynamics [9] and to thermoconductivity [10]. Real objects, to which 1D and 2D models can be applied, are adsorbed structures [11,12] or crystals with lowdimensional motives [13].…”

Section: Introductionmentioning

confidence: 99%

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Orientational vibrations of 2D molecular layers with quadrupolar interaction

Lykah

Syrkin

2007

Physica Status Solidi (b)

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Molecular layers with rotational degrees of freedom and quadrupolar interaction between linear molecules are investigated theoretically. Rotation of the molecules in the plane of an adsorbing surface is considered; centers of gravity of the molecules are pinned to sites of a rectangular lattice. The energy of the system contains an additional parameter ρ (ratio of the lattice constants of a 2D system), in comparison with the 1D case. It is found that alternating orientation of the adsorbed molecules along both sides of the rectangular unit cell corresponds to the minimum of the energy. Equations of rotational movement are derived for linear oscillations of molecules near the equilibrium positions in a 2D lattice. Dispersion relations are obtained and analyzed. The Brillouin zone cannot be divided as in the 1D case after unit-cell doubling. The parameter ( ) B k , which describes the topology of the dispersion surfaces, is introduced. It is shown that both branches of the spectrum have optical behavior. The gaps and bandwidths are found as functions of ρ . The method of calculation of the density of states (DOS) for translational oscillations of a 2D rectangular lattice with one atom per unit cell is generalized for rotational oscillations of a 2D twosublattice molecular lattice. The diagram describing three regions with different analytical properties of the DOS which correspond to different topologies of the isofrequency lines is introduced. This diagram is a portrait in the plane of the parameters B and ρ . The DOS is found in terms of complete elliptic integrals of the first kind.

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Section: Introductionmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orientational vibrations of 2D molecular layers with quadrupolar interaction

Lykah

Syrkin

2007

Physica Status Solidi (b)

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“…Thus the DFT approach of interpreting the continuous extended diffuse scattering domains is not totally alien to the usual lattice dynamical approach. More recent theories on lattice dynamics of molecular crystals have been given by Sandor (1962), Cochran & Pawley (1964), and Hahn & Biem (1963). Of these, Cochran & Pawley's theory seems to be more detailed and can be employed more readily for numerical calculations.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

Diffuse X-ray scattering from crystals of hexaamminecobalt(III) nitrate

Gowda¹,

Banerjee²,

Fletcher³

1970

Acta Cryst Sect A

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Crystals of hexamminecobalt(III) nitrate are found not to be cubic like those of the thiocyanatopentammine derivative but to be tetragonal and of space group symmetry P42nm. The unit-cell parameters are a = b = 21.66, c = 33"32 + 0"05 A. The most prominent feature of the difference in response to X-rays of these and similar crystals is the heavy diffuse scattering produced by the hexamminecobalt(III) nitrate. By means of a series of cylindrical Laue photographs, taken with monochromatic cobalt (Co Ke) radiation, covering a quadrant of reciprocal space at regular intervals of 5 ° about the tetragonal axis, the diffuse domains in the reciprocal lattice are explored and information obtained on the nature and direction of propagation of the thermal waves in the crystal. An interesting feature of the crystal dynamics of hexamminecobalt(III) nitrate is that the only effects observed as a result of independent motion of large structural units are those of transverse waves. There are no noticeable similar effects ascribable to longitudinal waves. Thus information is obtained on the behaviour, shape and orientation of the structural units [Co(NH3)613 + and (NO3)-.

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“…The intermolecular force-constants, expressed in terms of the interatomic force constants, were given by Hahn & Biem (1963),~Yenkataraman & Sahni (1970, DPP, and Scheringer (1973). Here, we use the matrix representation of our earlier paper.…”

Section: Derivation Of the Self-termsmentioning

confidence: 99%

Self-terms of intermolecular force constants

Scheringer¹

1974

Acta Cryst Sect A

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The self-terms of the intermolecular force constants are derived by employing the condition of translation invariance. The self-terms thus obtained ensure that the dynamical matrices of the crystal are always Hermitian. The role of the condition of rotation invariance is discussed. The expressions for the self-terms differ in part from those published by Dolling, Pawley & Powell [Proc. Roy. Soc. (1973). A333, 363-384]. The conditions under which the self-terms of these authors are identical with the present ones are discussed.

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Über Gitterschwingungen in Molekülkristallen

Cited by 40 publications

References 2 publications

Orientational vibrations of 2D molecular layers with quadrupolar interaction

Orientational vibrations of 2D molecular layers with quadrupolar interaction

Diffuse X-ray scattering from crystals of hexaamminecobalt(III) nitrate

Self-terms of intermolecular force constants

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