Where the Grüneisen parameter is now represented by a second-rank tensor, γ ij, and c ijkl T is Where γ is the average Grüneisen parameter, κ the isothermal compressibility, c V the specific heat at This approach leads to the Grüneisen relation that relates the thermal expansion coefficients and the elastic constants: The anharmonicity is most conveniently accounted for by means of the so-called `quasiharmonic approximation', assuming the lattice vibration frequencies to be independent of temperature but dependent on volume. The thermal expansion of a solid is a consequence of the anharmonicity of interatomic forces. ![]() The volume thermal expansion, β, relates the relative variation of volume Δ V/ V to Δ T: The deformation is described by the strain tensor u ij and the coefficient of thermalĮxpansion is represented by a rank 2 tensor, α ij, given by: In the first order approximation it is given by: ![]() (Δℓ/ℓ) of the length ℓ of a bar to the temperature variation Δ T. The linear coefficient of thermal expansion, α, relates the relative variation The coefficient of thermal expansion relates the deformation that takes place when the temperature T of a solid is varied by the temperature variation Δ T.
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