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

Toupance, N.

doi:10.1002/pssb.2221400206

Cited by 9 publications

(3 citation statements)

References 12 publications

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“…Then, one needs an internal energy specified in terms of the strain tensor, q, and the specific entropy, s. The theory of lattice dynamics extended into the domain of finite strain, which had been previously developed [7,1,5] in terms of the thermodynamic variables q and T the absolute temperature, leads also to a fourth-order internal energy u expressed as cp is the static potential energy expanded to the fourth-order [l, 51 and u, is the thermal internal energy. Within the fourth-order anharmonic theory approximations [7] u is given by the expansion [8] Ckl, C$iM, CPiMN are the second-, third-, fourth-order elastic constants, Ck!…”

Section: Linear Adiabatic Compressibilities From the Fourth-order Anhmentioning

confidence: 99%

Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

Delannoy‐Coutris

Toupance

Belloy

1991

Physica Status Solidi (b)

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Expressions for the linear adiabatic compressibilities of an at least orthorhombic crystal and their pressure derivatives are derived in terms of the second-, third-, and fourth-order elastic constants within a finite-strain theory which includes thermal effects according to the quasi-harmonic approximation of lattice dynamics. The expressions are derived in terms of the Lagrangian strain tensor and the frame-indifferent analogue of the Eulerian strain tensor. Numerical applications are given for three hexagonal metals: cadmium, magnesium, and zinc, namely the temperature variations of the linear adiabatic compressib es and their pressure derivatives, including recent estimations of the combinations of fourth-order elastic constants appearing in the present work. When possible, the comparison with experimental data shows a rather good agreement with the compressibilities calculated within the present theory using the Green-Lagrange strain measure of the deformation. About the variations of the first pressure derivatives of the adiabatic compressibilities with temperature, the present work provides us with theoretical values in the lack of experimental data.Les coefficients lineaires de compressibilite adiabatique et leurs derivees par rapport a la pression sont exprimes, pour un cristal de symetrie au moins orthorhombique, en fonction des constantes elastiques des deuxiime, troisikme et quatrieme ordres dans le cadre d'une theorie des dkformations finies qui inclut les effects thermiques grice a la thtorie de la dynamique des reseaux cristallins developpee dans I'approximation quasi-harmonique. Deux tenseurs de deformation sont utilises: le tenseur de GreenLagrange et fe tenseur de deformation, invariant par changement de referentiel, analogue a u tenseur d'Almansi-Euler. Des applications numeriques sont donnees pour trois metaux hexagonaux: le cadmium, le magnesium et le zinc, a savoir les variations avec la temperature des coefficients lintaires de compressibilite adiabatique et de leurs derivees par rapport a la pression. Ces calculs utilisent de recentes estimations des combinaisons de constantes tlastiques du quatritme ordre qui figurent dans cette etude. Lorsque cela est possible, nos resultats sont compares aux valeurs experimentales, comparaison qui met en evidence un accord satisfaisant entre les compressibilites calculees d'apres la presente theorie avec le tenseur de deformation de Green-Lagrange et les valeurs mesurees experimentalement. En ce qui concerne les variations, avec la temperature, des dtrivees premieres par rapport a la pression des coefficients lineaires de compressibilite adiabatique, le present article permet de donner des valeurs theoriques en l'absence de resultats experimentaux.

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Section: Linear Adiabatic Compressibilities From the Fourth-order Anhmentioning

confidence: 99%

Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

Delannoy‐Coutris

Toupance

Belloy

1991

Physica Status Solidi (b)

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“…Moreover, it is well known that G! : ) and Hij$ are related to thermal effects and consequently to the temperature derivatives of the C$:)s at constant pressure [8,3]. Thus, for ijkl = 1111, 1122, 1133, 3333, 2323 one obtains by evaluation at initial state where al and a3 are the linear thermal expansion coefficients and a, is the volume coefficient of thermal expansion, with a, = 2 a l + a3 for the considered symmetry.…”

Section: Effective Adiabatic Elastic Moduli For Solids With a Princip...mentioning

confidence: 99%

“…to the rest configuration of the crystalline lattice [l]. Until now, the theoretical model used here has been developed only for materials of cubic symmetry with numerical applications for cubic crystals [2,3].…”

Section: Introductionmentioning

confidence: 99%

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

Delannoy‐Coutris¹,

Toupance²,

Belloy³

1990

J. Phys. D: Appl. Phys.

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The fourth-order anharmonic finite strain theory leads to a model for the temperature and pressure dependences of effective elastic moduli, for non-cubic crystals, involving the elastic constants up to the fourth-order. These relationships are used to give an estimation of some combinations of fourth-order elastic constants, using a mean deformation in the fourth-order term and fitting the experimental data at low temperatures. The fourth-order variations of the effective adiabatic elastic moduli with temperature at zero pressure can then be determined. A comparative study of the results with experimental data is given for three hexagonal metals-cadmium, magnesium and zinc-which shows a good agreement between theory and experiment over a large range of temperatures. This development uses both the Lagrangian and Eulerian strain measures previously introduced.

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Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

Barhoumi

2023

Silicon

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

Cited by 9 publications

References 12 publications

Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

Fourth‐Order Adiabatic Linear Compressibilities for Non‐Cubic Solids

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

Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

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