Lattice-dynamical calculations for Chevrel-phase superconductors

Born-von K\'arm\'an (BvK) lattice-dynamical calculations were performed for the rhombohedral Chevrelphase superconductors such as PbMo₆{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(ω) 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(ω) is calculated for binary and ternary Chevrelphase sulfides and selenides by making appropriate mass changes. Moments and site-dependent projections of F(ω) 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, M\"ossbauer recoil-free fraction for ¹¹⁹Sn, anharmonicity, the apparent T² resistivity below 40 K for sputtered films, and the form of the superconducting tunneling spectrum α²F 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.