• V Ramamurthy

      Articles written in Pramana – Journal of Physics

    • The electron-ion interactions in metals

      V Ramamurthy

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      The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating it by a sphere, by making use of simple coordinate axes transformations and lattice symmetry in the case of f.c.c. and b.c.c. structures. It is shown that there are several alternative ways of expressing the interference factor,S(q) and the different expressions given by Sharan and others and Bross and Bohn are just two of these equivalent expressions. By comparing these expressions in the symmetry directions with those obtained under spherical approximation their apparent differences are discussed.

    • The electron-ion interactions in tetragonal metals

      V Ramamurthy

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      The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating it by a sphere or an ellipsoid, by making use of simple co-ordinate axes transformations and lattice symmetry in the case of fct and bct structures. It is shown that there are several alternative ways of expressing the interference factor,S(q), one of which was obtained by Sharan and others in the case of indium. By comparing these expressions with the latter, with those of corresponding cubic structures as well as with those obtained under spherical approximation respectively, the crystallographic equivalence and stability of tetragonal structures as well as the validity of Wigner-Seitz approximation are discussed.

    • Lattice dynamical study of body-centred tetragonal indium

      V Ramamurthy S B Rajendraprasad

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      The phonon dispersion curves, phonon frequency distribution function as well as the lattice specific heat of body-centred tetragonal indium have been deduced using a lattice dynamical model which includes central, angular and volume forces. Six elastic constants, four zone boundary frequencies and an equilibrium condition were used in the evaluation of the force constants. It is shown that this model is elastically consistent and satisfies the symmetry requirements of the lattice, the phonon frequencies of indium deduced from it are in very good agreement with the experimental values of Reichardt and Smith and the theoretical values of Garrett and Swihart, and theθD values compare well with the experimental values over a wide temperature range. The apparent discrepancies in the phonon dispersion curves and theθD-T curves obtained from deficient models, importance of umklapp processes and the significance of angular forces in the lattice dynamical models are discussed.

    • Lattice dynamical study of alkali metals: An unified approach based on CGW model

      V Ramamurthy M Satishkumar

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      The phonon dispersion relations for lithium, sodium, potassium, rubidium and cesium along the principal symmetry directions as well as their lattice specific heats have been deduced using Clark, Gazis and Wallis angular force model. This model which conforms to the translational symmetry of the lattice, reproduces the observed crossover in lithium along [ζ00] direction at ζ = 0·49, without producing any crossovers in other alkali metals. Besides, the theoretical dispersion curves of all alkali metals are in excellent agreement with the corresponding experimental or homologous dispersion relations and theirϑD values compare well with the experimental values over a wide temperature range. It is shown that the strength of electron-ion interactions plays a significant role in the success of any unified lattice dynamical study of alkali metals while the three-body interactions of thecgw model do not. The importance of umklapp processes, failure of the earlier models to produce a crossover and the experimentalϑD-T curve in lithium as well as the apparent variation in the nature and range of atomic interactions of alkali metals are discussed.

    • Electron-ion interactions in close packed metals

      V Ramamurthy

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      The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron by making use of simple co-ordinate axes transformations and lattice symmetry in the case of hcp and ccp structures. It is shown that the expressions for the interference factor,S(q,t) of hcp structure are complex while those of ccp structure are real, even when both atomic arrangements are referred to the same orthorhombic co-ordinate axes, and in each case, lattice atom contributions could be distinguished from basis atom contributions toS(q,t). By comparing these expressions with each other as well as with those obtained by approximating their atomic polyhedra by an ellipsoid of equivalent volume, apparent differences between interference factors of hcp and ccp structures, validity of Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-ion interactions contribute to the different modes of vibration in a hexagonal lattice are discussed.

    • Three-body interactions, rotational invariance and the elastic consistency of lattice dynamical models for face-centred tetragonal indium

      V Ramamurthy S B Rajendraprasad

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      The origin of the elastic inconsistency ofdaf, mas andgtf models for non-cubic solids and the failure of their force constants to comply with all the rotational invariance conditions are analysed by resolving the atomic displacements of face-centred tetragonal indium along three mutually perpendicular directions. It is shown that a lattice dynamical model suffers from these deficiencies as a consequence of its neglect of three-body interactions as well as the mixed neighbour interactions associated with the angular forces, while thecgw model which incorporates both these interactions is elastically consistent and its potential energy rotationally invariant. The degree of equivalence that exists among the force constants ofdaf, mas, gtf andcgw models, the distortions introduced by the elastic inconsistency into the phonon dispersion curves of fct indium as well as the consequences of imposing the rotational invariance conditions on the force constants of a lattice dynamical model are discussed.

    • Electron-phonon interactions in bct white tin

      V Ramamurthy

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      The electron-phonon interactions are evaluated exactly over the actual shape of the atomic polyhedron as well as the lattice polyhedron of diatomic white tin by making use of simple coordinate axes transformations and crystal symmetry. It is shown that the expressions for the interference factor,S(q, t) of the atomic polyhedron are complex while those for the lattice polyhedron are real and the reciprocal lattice vectors derived from the former do not correspond to those derived either from the latter or from x-ray structure factors. By comparing these expressions with each other as well as with those obtained by approximating these polyhedra by an ellipsoid of equivalent volume, apparent differences between the interference factors of atomic and lattice polyhedra, consequent ambiguity regarding the shape and size of the first Brillouin zone of white tin, validity of the Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-phonon interactions contribute to acoustical and optical modes of vibration are discussed.

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