Theoretical study of shear-modulus instabilities in the alkali metals under hydrostatic pressure

The elastic stability of the bce and fee alkali metals is studied theoretically over wide ranges of hydrostatic pressure P. A pseudopotential model is employed to compute the variations of the bulk moduli kappa and shear moduli mu and mu', as well as the differences between the Gibbs energies of the two structures. Stability is assessed according to the criteria of Hill and Milstein, i.e., kappa(P) > 0, mu (P) > 0, and mu'(P) > 0. In compression, the stability ranges of both phases are controlled primarily by the shear modulus mu, and high pressure bcc-->fcc transitions in K, Rb, and Cs are found to be associated with the vanishing of this modulus. The ''interplay'' between the ranges of elastic stability and thermodynamic phase equilibrium (at 0 K) is also studied.