Iron and Sulfur Isotope Factors of Pyrite: Data from Experimental Mössbauer Spectroscopy and Heat Capacity

Mössbauer spectra of pyrite (FeS₂) are measured within a temperature range of 90–295 K. The isomer shift is described by the Debye model with a Mössbauer temperature θ_M = 551.4 K. These results are used to calculate the kinetic energy of thermal vibrations of the iron sublattice of pyrite and the iron β-factor for pyrite: 10³\({\text{ln}}{{\beta }_{{^{{{\text{57}}}}{\text{Fe}}{{{\text{/}}}^{{{\text{54}}}}}{\text{Fe}}}}}\) = (1.2665 ± 0.0391)x – (0.4584 ± 0.0283) × 10^–2x² + (0.2581 ± 0.0239) × 10^–4x³; x = 10⁶/T ² (K^–2). The calculated iron β-factor in pyrite is in good agreement with results of ab initio calculations, ⁵⁷Fe nuclear inelastic X-ray resonant scattering in synchrotron experiments, and direct isotope exchange experiments between pyrite and Fe²⁺ dissolved in water. The heat capacity of pyrite is measured within a temperature range of 79–300 K and is described using the Thirring expansion. Based on this expansion, the kinetic energy of thermal vibrations of the total crystalline lattice of pyrite is calculated. The kinetic energy of the thermal vibrations of the sulfur sublattice in pyrite is found by subtracting the kinetic energy of the iron sublattice from the total kinetic energy of pyrite crystalline lattice. The temperature dependence of ³⁴S/³²S β-factor for pyrite, which was calculated from the kinetic energy of the sulfur sublattice, is 10³\({\text{ln}}{{\beta }_{{^{{{\text{34}}}}{\text{Fe}}{{{\text{/}}}^{{{\text{32}}}}}{\text{Fe}}}}}\) = (1.7532 ± 0.0623) x – (1.0470 ± 0.0752) × 10^–2x² + (1.0424 ± 0.1126) × 10^–4x³; x = 10⁶/T² (K^–2). This value of the ³⁴S/³²S β-factor is in good agreement with the ab initio calculations and with results of isotope-exchange experiments in the pyrite–sphalerite–galena system.