• E V Chelam

      Articles written in Proceedings – Section A

    • The normal vibrations in some typical cubic crystals

      E V Chelam

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      The normal modes of vibration of the simple cubic, body-centred and face-centred lattices as well as of the zincblende, diamond, rock-salt, flourspar and caesium chloride lattices have been derived by simple geometric methods on the basis of the fundamental ideas set out by Sir C. V. Raman in the introductory paper of the symposium. It is shown that the lattices mentioned have 5, 4, 4, 9, 8, 9, 14 and 11 distinct frequencies respectively.

    • Normal vibrations of crystal lattices: application of group theory

      E V Chelam

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      A group theoretical method to deal with the harmonic vibrations of a general crystalline lattice is indicated in this paper. Sir C. V. Raman’s theory of lattice vibrations3 is the basis of the work and it is indicated how the normal modes, frequencies, their degeneracies, etc., can be rigorously derived. Applications of this work to specific problems are given in another paper in this symposium.

    • Character tables for the atomic vibrations in some cubic crystals

      E V Chelam

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      In this paper, the character tables for groups associated with vectors defining normal modes are given for four cubic crystals based on a facecentred Bravais lattice,viz., rock-salt, diamond, zincblende and fluorite. The method of deriving normal modes from these tables, described in an earlier paper, is illustrated here.

    • The frequency spectrum of the diamond lattice

      E V Chelam

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      The eight frequencies in a diamond lattice are calculated with a suitable force field and explicit expressions are given for them. Sir C. V. Raman’s theory of superlattice vibrations is the basis of the investigation.

    • Elastic behaviour of matter under very high pressures - Uniform compression

      S Bhagavantam E V Chelam

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      In order to study the elastic behaviour of matter when subjected to very large pressures, such as occur for example in the interior of the earth, and to provide an explanation for phenomena like earthquakes, it is essential to be able to calculate the values of the elastic constants of a substance under a state of large initial stress in terms of the elastic constants of a natural or stress-free state. An attempt has been made in this paper to derive expressions for these quantities for a substance of cubic symmetry on the basis of non-linear theory of elasticity and including up to cubic powers of the strain components in the strain energy function. A simple method of deriving them directly from the energy function itself has been indicated for any general case and the same has been applied to the case of hydrostatic compression. The notion of an effective elastic energy—the energy require to effect an infinitesimal deformation over a state of finite strain—has been introduced, the coefficients in this expression being the effective elastic constants. A separation of this effective energy function into normal co-ordinates has been given for the particular case of cubic symmetry and it has been pointed out, that when any of such coefficients in this normal form becomes negative, elastic instability will set in, with associated release of energy.

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