A first principles study of coupled substitution in galena

Coupled substitution is an important mechanism responsible for Ag enrichment in galena. Studies show that the concentration of Ag in galena tends to equal the sum of the concentrations of Sb and Bi (Foord et al., 1988). The thermodynamic mixing properties of the binary solid solution: Pb2S2–AgSbS2(gal), Pb2S2–AgBiS2(gal), and Pb2S2–AgAsS2(gal) have been investigated using quantum-mechanical and Monte-Carlo simulations (where gal. indicates phases constrained to the galena structure). Quantum-mechanical methods were used to account for electron transfer between the substituting species. Total energies for different substitution configurations were used in Monte-Carlo calculations to derive the excess enthalpy of mixing (ΔHmix), entropy of mixing (ΔSmix), and free energy of mixing (ΔGmix) at temperatures ranging from 200 °C to 1300 °C. ΔGmix was used to calculate phase diagrams that can be compared with experimental results. Electron transfer between Ag and either Sb, Bi, or As is shown to affect cation ordering in these systems. Quantum-mechanical simulations allow for the visualization of specific orbitals that are predominantly responsible for this electron transfer. Intermediates of the Pb2S2–AgBiS2 solid solution tend to order into alternating Ag-rich and Pb/Bi-rich layers parallel to [111]. Phase diagrams were determined for each solid solution series and an Ag solubility limit of 6.0 mol% of AgSbS2 (at 350 °C) was determined to be in reasonable agreement with experiments showing a value of ~ 5.5 mol% AgSbS2.