Electronic, quasiharmonic, and anharmonic entropies of transition metals

Abstract

For transition metals at temperatures to melting, the electronic entropy is calculated from linear muffin-tin orbital electronic densities of states (using both the atomic-sphere approximation as well as a full potential), the quasiharmonic entropy is calculated from neutron-scattering data, and the anharmonic entropy is then extracted from the measured entropy. The electronic entropy is large, and is strongly nonlinear in temperature, as a result of both the volume dependence and energy dependence of the electronic density of states. The anharmonic entropy is small and apparently negative for V, Nb, Ta, Pd, and Pt, but is large and positive for Cr, Mo, and W. For Ni, the anharmonic plus magnetic entropy is determined accurately, and the magnetic entropy is estimated. For Ti and Zr, the total lattice-dynamic entropy is accurately given by the quasiharmonic formula with temperature-dependent renormalized phonon frequencies, in both hcp and bcc phases.