Electronic-structure calculations, photoelectron spectra, optical spectra, and Mössbauer parameters for the pyritesMS2(M=Fe,Co,Ni,Cu,Zn)

Abstract

Electronic-structure calculations on the basis of a self-consistent charge, linear combination of atomic orbitals band-structure method have been performed for the pyrites Fe${\mathrm{S}}_2$, Co${\mathrm{S}}_2$, Ni${\mathrm{S}}_2$, Cu${\mathrm{S}}_2$, and Zn${\mathrm{S}}_2$. Photoelectron spectra, optical spectra, and Mössbauer parameters are evaluated and are found to compare well with experimental data. Molecular-orbital cluster calculations have been performed to derive local properties (Mössbauer parameters) only, which are compared with band-structure and experimental results. Clusters which include ${\mathrm{S}}_2$ anion pairs, i.e., ${\left[M{\left({\mathrm{S}}_2\right)}_6\right]}^{10-}$, yield reasonable results, while for the smaller clusters ${\left[M{\mathrm{S}}_6\right]}^{4-}$, even convergence could not be achieved. Our further investigation includes (i) the pressure dependence of $\Delta E_Q$ and $\delta$ in Fe${\mathrm{S}}_2$; (ii) the concentration dependence of $\Delta E_Q$ in the solid solutions ${\mathrm{Fe}}_x{\mathrm{Co}}_{1-x}{\mathrm{S}}_2$ ($x=0.01,0.25,0.5,0.75\mathrm{}$); (iii) the sign of the nuclear-quadrupole coupling constant $e^2\mathrm{qQ}$, which was found to be negative except for Zn${\mathrm{S}}_2$; (iv) the various contributions to the electric-field gradient (EFG) tensor (in Fe${\mathrm{S}}_2$ the main contribution arises from the valence shell, and proceeding from Fe${\mathrm{S}}_2$ to Zn${\mathrm{S}}_2$ in the pyrite series, the valence contribution continuously decreases, and in the $d^{10}$ system Zn${\mathrm{S}}_2$ only a small and positive lattice EFG is left); (v) the interpretation of the independence of the Mössbauer line intensity ratio from the single-crystal orientation with respect to the $\gamma$ beam on the basis of our calculated EFG tensor.