Temperature dependence of the elastic constants in alkali metals

Abstract

The isothermal elastic constants C_ik(T) in alkali metals are calculated in the pseudopotential model previously described. The standard second approximation in the pseudopotential and the first one in the anharmonicity are used. An expression for C_ik(T) convenient for calculations is given in terms of the strain derivatives of the dynamical matrix. The results for the bulk modulus B(T) and shear constant C₄₄(T) agree well with experiment. The shear constants C'=¹/₂(C₁₁-C₁₂) decrease with increasing T more rapidly than in experiment. For Li this disagreement is large and may again indicate the inadequacy of the local pseudopotential model. For the other alkali metals the discrepancies are much smaller and may be connected, at least partly, with the higher-order anharmonic contributions. The volume dependence of the elastic constants at finite T, the temperature dependence of their pressure derivatives and the sensitivity of the results to the approximations for the dielectric function are also discussed.