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On the elastic properties of lattices

Epstein, Paul S. (1946) On the elastic properties of lattices. Physical Review, 70 (11-12). pp. 915-922. ISSN 0031-899X.

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The potential energy of a deformed lattice can be written in the form V=V0+V1+V2 where V0 is a constant (the energy of the undeformed lattice), V1 the part linear in the displacements of the lattice points from their normal positions, V2 the part quadratic in the displacements. The terms of higher order are neglected. In view of the requirement that the normal position of each lattice point be a position of equilibrium the linear part vanishes (V1=0) so that the energy is simply equal to V2 (apart from the constant V0). As the energy must be invariant with respect to rotations of the system, W. Voigt postulated the invariance of V2 and derived from this assumption the so-called Cauchy relations between the elastic coefficients. A closer analysis shows that this conclusion is open to objection. The term V2 represents the energy only because of the subsidiary condition V1=0 which, upon investigation, turns out to be not invariant with respect to rotations. Hence, V2 is not invariant either: a fact which removes the theoretical basis of the Cauchy relations.

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Additional Information:©1946 The American Physical Society. Received 13 August 1946.
Issue or Number:11-12
Record Number:CaltechAUTHORS:EPSpr46
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6375
Deposited By: Tony Diaz
Deposited On:05 Dec 2006
Last Modified:02 Oct 2019 23:32

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