Equilibrium indium isotope fractionation between indium-bearing minerals: Insights from first-principles calculations

Indium (In) is a critical element for electronics and catalysis industries and a volatile metal during planet accretion. Indium isotopes can be used to study cosmochemical and geochemical processes, but no equilibrium indium isotope fractionation factor is available, which restricts our knowledge of indium enrichment and incorporation during geological processes. Here, we investigate the reduced partition function ratios (10³lnβ) of ¹¹⁵In/¹¹³In in indium-bearing minerals using first-principles calculations. The results show that 10³lnβ decreases in the following sequence of dzhalindite > laforetite > roquesite > cadmoindite > Ag-Sn-In-doped sphalerite ≈ Cu-In-doped sphalerite ≈ Cu-Sn-In-doped sphalerite > yixunite > indite > damiaoite > native indium. We found that chemical composition may affect indium isotope fractionation factor in indium-doped sphalerite with Zn/In from 4 to 80 and indium alloys by changing the length of indium bonds. Furthermore, the chemical composition is not only related to the bond length and coordination number (CN) of the target element but also to the electronegativity of other doped elements, which can influence equilibrium indium isotope fractionation. The variation in 10³lnβ of indium-doped sphalerites and independent minerals predicts measurable isotopic differences between indium-bearing minerals. The equilibrium indium isotope fractionation factors calculated in this study provide important guides for the potential applications of indium isotopes in geological processes.