Lattice-dynamical calculations for Chevrel-phase superconductors

Born-von Kármán (BvK) lattice-dynamical calculations were performed for the rhombohedral Chevrelphase superconductors such as Pb${\mathrm{Mo}}_6$ ${\mathrm{S}}_8$. The dynamical matrix was obtained using Lennard-Jones (LJ) potentials, which describe interactions between Mo-Mo, Mo-S, S-S, and Pb-S pairs of atoms. The parameters for these potentials were adjusted using the comparison of the moments of the phonon spectrum $F\left(\omega \right)$ with their values obtained from heat-capacity data. Dispersion curves along the threefold axis show a splitting of the three Pb-atom-dominated modes into a low-lying transverse doublet and a longitudinal singlet. These branches hybridize with the acoustic branches. $F\left(\omega \right)$ is calculated for binary and ternary Chevrelphase sulfides and selenides by making appropriate mass changes. Moments and site-dependent projections of $F\left(\omega \right)$ are calculated and their associated Debye temperatures are tabulated. Torsional character is found for certain modes in agreement with previous identifications made using the molecular-crystal model. The heat capacity, entropy, inelastic neutron-scattering spectra, Mössbauer recoil-free fraction for ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, anharmonicity, the apparent $T^2$ resistivity below 40 K for sputtered films, and the form of the superconducting tunneling spectrum ${\alpha }^{2}F$ are discussed. The applicability of the BvK approach using LJ potentials indicates that short-range interactions are important. Hence, the previously introduced molecular-crystal model is a reasonable, though not rigorous, simplification of the lattice dynamics of this important class of superconductors.