Within the local pseudopotential model taken to second order, the metallic energy, U, is a sum of a volume dependent and a structure dependent term. Only the second term, expressed as a volume independent, effective ion–ion interaction, is usually retained for lattice dynamic calculations. Here we firstly evaluate the contribution from the volume dependence of U to the longitudinal elastic constants c11and c12 and the bulk modulus B for a variety of models. This contribution, Δbs, which is due to the volume dependence of the screening, was identified by Wallace, Brovman and Kagan, Pethick, and by Finnis but its magnitude is in dispute. We find Δbs is important and very model dependent, ranging from −10 to−50% of B in the alkali metals and Al (but is +50% in Pb for one model) depending on both the pseudopotential and screening employed. Secondly, the usual dynamical matrix is generalized to incorporate this volume dependence. The volume effects are important for long wave phonons only and for most practical purposes may be neglected otherwise. The volume contributions to the pressure and the deviation of the Cauchy relation are also evaluated suggesting that the observed deviation of the Cauchy relation does not provide a reliable estimate of Δbs.
Strain-dependent structure and Raman behaviours in the heavy-ion irradiated manganite at extreme low dose
