J. Phys. IV France 129 (2005) 45-49
DOI: 10.1051/jp4:2005129010

The generalized Cauchy relation as an universal property of the amorphous state

J.K. Krüger^{1, 2}, U. Müller^{1, 2}, R. Bactavatchalou^{1, 2}, J. Mainka^{1, 2}, Ch. Gilow^{1, 2}, W. Possart^{1, 2}, A. Tschöpe^{1, 3}, P. Alnot^{1, 4}, D. Rouxel^{1, 4}, R. Sanctuary^{1, 5} and B. Wetzel<sup>6

1</sup>  Laboratoire Européen de Recherche Universitaire : Saarland-Lorraine
²  Fachrichtung 7.2, Experimentalphysik, Universität des Saarlandes, Bau 38, 66041 Saarbrücken, Germany
³  Technische Physik - Gebäude 43B, Universität des Saarlandes, Postfach 15 11 50, 66041 Saarbrücken, Germany
⁴  Laboratoire de Physique des Milieux Ionisés et Applications, CNRS-UMR 7040, Université Henri Poincaré, 54506 Nancy I, France
⁵  Laboratoire de Physique des Matériaux, Université du Luxembourg-Limpertsberg, 1511 Luxembourg
⁶  Institut für Verbundwerkstoffe, TU Kaiserslautern, 67663 Kaiserslautern, Germany

Abstract
From the structural point of view a simple Cauchy relation is not expected to hold for isotropic materials. Such a Cauchy relation would imply the reduction of independent elastic stiffness constants for the isotropic state from two to one. However, high frequency elastic data of glasses and viscous liquids show a linear transformation between the shear and the longitudinal elastic stiffness which is called a generalized Cauchy relation. It seems, that the parameters of the linear transformation are related to the global and local symmetry and/or order. Brillouin investigations on the elastic stiffness coefficients of a consolidated nano-crystalline material (CeO₂) and of DGEBA/SiO₂ nano-composites are used in order to elucidated the role of the discrepancy between local and global symmetry and/or order.

© EDP Sciences 2005