Etude théorique du comportement avec la température des modules élastiques des solides à symétrie cubique

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Etude théorique du comportement avec la température des modules élastiques des solides à symétrie cubiqueM. Delannoy-Coutris, G. Perrin To cite this version:M. Delannoy-Coutris, G. Perrin. Etude théorique du comportement avec la température des modules élastiques des solides à symétrie cubique.Résumé. -L'extension au domaine des déformations finies et aux solides de symétrie non cubique du modèle d'équation d'état de Mie-Grüneisen permet d'obtenir une expression de l'énergie libre, fonction de la déformation et de la température, faisant apparaître les constantes élastiques jusqu'au quatrième ordre inclus. Utilisant cette expression, nous formons des équations qui conduisent à la détermination des déformations thermiques et à l'étude des modules élastiques à basse température. En application, nous donnons (et comparons aux mesures expérimentales) les variations des modules élastiques adiabatiques C11, C12, C44 en fonction de la température, de 0 à 300 K, pour deux solides cubiques : l'aluminium et le cuivre, ainsi qu'une estimation des dérivées secondes des modules effectifs par rapport à la pression, à pression nulle et température ambiante.Abstract 2014 With the extension of the finite strain expansion of the Mie-Grüneisen equation to the case of noncubic crystals, we get an expression for the free energy taking into account the elastic constants up to the fourthorder. Hence, equations giving the strain parameters and the elastic moduli versus temperature are derived. Numerical results are given (and compared to experimental data) for the temperature variation (from 0 to 300 K) of the elastic adiabatic moduli C11, C12, C44 of two cubic solids : aluminum and copper. Finally, the second pressure derivatives of these moduli are estimated at zero pressure and 300 K.

Temperature dependence of the elastic constants for solids of cubic symmetry.Application to Germanium and Silicon

“…By operating on (10) with ( a / a Q , (az/aP2)e, and (a/a6), in appropriate combinations and by evaluating a t initial state, one derives the following system of three linear equations [5] :…”

“…By operating on (10) with ( a / a Q , (az/aP2)e, and (a/a6), in appropriate combinations and by evaluating a t initial state, one derives the following system of three linear equations [5] : All the quantities appearing in (18c) can be evaluated from available experimental data 191. Unfortunately, the second pressure derivatives of the effective elastic moduli (C",ff), are not available a t present time.…”

“…Unfortunately, the second pressure derivatives of the effective elastic moduli (C",ff), are not available a t present time. Then, the other constants will beevaluated by iteration [ 5 ] . First, we assume that ?…”

Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

“…Fourth order with E, ---fourth order with e; ones [20] (i.e. C g and CftLqL in (6)) so that every experimental error in the determination of the SOEC and the TOEC leads to a large inaccuracy in calculating 2; or xi.…”

Temperature dependence of elastic moduli for non-cubic solids: application to cadmium, magnesium and zinc

“…It is well known that the effective elastic moduli, which describe the mechanical behaviour of a hyperelastic medium subjected to an additional infinitesimal deformation that is superimposed upon a state of hydrostatic compression, are related to the thermodynamic elastic constants, defined as the strain derivatives of the free energy. Therefore in previous papers [ 1,2], we have developed a quasi-harmonic finite-strain model for the free energy of cubic and non-cubic crystals that involves the elastic constants up to the fourth order. As the free energy is required to be frameindifferent, this development can be carried out in terms of any Lagrangian strain tensor expressing the deformation from the unstrained reference state which has been identified…”