On the determination of the volume dependence of Grüneisen parameters in cubic and non-cubic solids

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The fourth-order anharmonic finite-strain theory leads to a model for the volume dependence of the Griineisen parameter and simultaneously to a Mie-Griineisen equation of state. These relations are used t o derive the fourth-order expressions for the thermal expansion coefficient of cubic crystals. A comparative study of theresults with experimental data is given for the temperature dependence of the linear thermal expansion coefficient a of aluminum, copper, germanium, and silicon. It is shown that the theory agrees with experiment even better since the Gruneisen coefficient can be reasonably assumed to be temperature independent. Finally, an estimation of the variation of the thermal expansion coefficient with volumetric compression is given for aluminum, copper, germanium, and silicon using both, the Lagrangian and Eulerian strain measures.L'extension au domaine des deformations finies de la theorie non linertire du quatribme ordre conduit & exprimer les variations en fonction du volume du parametre de Griineisen ainsi qu'nne Bquation d'btat dn type de Mie-Griineisen. Ces relations sont utilisBes ici pour obtenir I'expression au quatrieme ordre du coefficient de dilatation thermique, a , en fonction de la temperature et du volume specifique pour les solides it sgmetrie cubique. Des applications numbriques sont donnees pour I'aluminium, le cuivre, le germanium e t le silicium. En ce qui concerne les variations de a avec la temperature, I'accord entre thCorie e t expbrience s'avbre d'csutant meilleur que les variations du parametre d e Griineisen avec la temperature restent faibles. La variation de cx avec le titux de compression volumique a Bgalement Ct6 calculee pour les quatre m6taux prBcitCs en utilisant successivement deux mesures, lagrangienne e t eulkrienne, de la dkformation.

“…With our model for the Griineisen parameters [3], it is also possible to consider the case of solids of non-cubic symmetry. The problem is under study, especially for crys-…”

Section: Resultsmentioning

confidence: 99%

“…According to this formulation, we have also derived the volume dependence of the Gruneisen parameters in cubic and non-cubic solids resulting from the fourth-order anharmonic theory of lattice dynamics [3]. This formulation was found to be unambiguous for predicting the variation of the Griineisen coefficients with volume.…”

Section: Introductionmentioning

confidence: 99%

Fourth‐Order Thermal Expansion for Cubic Solids. Application to Aluminum, Copper, Germanium, and Silicon

Delannoy‐Coutris¹,

Perrin

1986

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“…If the pressure P is given, (6) determine the variations of (Cz:ii)s with temperature when the temperature variations of the strain parameters E i j ( 6 ) are known. For this purpose, we shall use the fourth-order quasi-harmonic equation of state [4] which gives the mechanical behaviour of a hyperelastic medium under hydrostatic pressure P when its free energy Y/ is given by (4).…”

Section: !mentioning

confidence: 99%

“…We have used here the fourth-order anharmonic theory discussed by Delannoy and Perrin [4, 51. According t o this formulation, these authors have previously studied the volume dependence of the Griineisen perameter [6], the melting curves a t high pressure [7], and also calculated some combinations of the fourth-order elastic constants for Cu and Ag [4]. A brief review of this theory is presented in Section2.…”

Section: Introductionmentioning

confidence: 99%

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

Toupance

1987

The extension of the finite strain expansion of the Mie-Griineisen equation (taking into account the elastic constants in the reference configuration up to the fourth-order) is used to derive the temperature dependence of the volumetric compression and of the second-order elastic adiabatic moduli of cubic solids. Numerical results are given for germanium and silicon and compared to experimental data. FinalIy, the second pressure derivative of these constants is estimated a t zero pressure and 300 K.L'extension au domaine des dkformations finies du modele d'kquation d'ktat de Mie-Gruneisen (prenant en compte les constantes klastiques dans la configuration de rkfkrence jusqu'au quatrikme ordre inclus) permet d'obtenir les variations, en fonction de la tempkrature, du taux de compression volumique et des modules klastiques adiabatiques du second ordre pour les solides de symktrie cubique. Des applications numkriques sont donnkes pour le germanium et le silicium et comparkes aux mesures expkrimentales. Finalement, nous donnons une estimation des dkrivkes secondes des modules effectifs par rapport B la pression, B pression nulle et 300 K.

Equation d'état et structure de bandes d'énergie de l'argent métallique

Perrot

1980

occasion de son 758meanniversaire La mkthode lin6aris6e des ,,orbitales muffin-tin'' (LMTO) est appliqu6e au calcul auto-cohbrent de la structure Blectronique de 1'Argent mbtallique. La pression est calcul6e en fonction de la densit6, dans une gamme allant de la densit6 normale eo h 5e0. L'accord avec les rbsultats de mesuree statiques, jusqa'8 170 kbar, est bon; il en est de m6me avec l'isotherme 0 K d6duite de mesures dynamiques, jusqu'8 1,3 Mbar environ. Les modifications de la strdcture de bandes d'6nergie sous pression sont ensuite discutbes.The linearized "muffin-tin orbitals" method (LMTO) is used to calculate the self-consistent electronic structure of metallic silver. The variation of pressure as a function of density is computed in the range eo (normal density) to 5e0. The agreement with experimental static data, in the range 0 to 170 kbar, is good. For higher pressures up to 1.3 Mbar, the zero-temperature isotherm deduced from shock-wave measurements and the calculated values compare well too. The modifications of the energy band structure under pressure are then discussed.