First-principles calculations of equilibrium isotope fractionation of Cl, Ca, and O in apatites and amphiboles

Apatites and amphiboles are common hydrous minerals in igneous and metamorphic rocks, which can be found from the crust to the lithospheric mantle. These minerals can incorporate chlorine (Cl) and fluorine (F) by substituting for hydroxyl groups (OH). The isotopic compositions of Cl, Ca, and O of apatites and amphiboles are valuable geochemical tools for understanding the terrestrial and extraterrestrial processes over a wide range of temperatures. In the present study, first-principles methods were used to investigate the equilibrium isotope fractionation of Cl, Ca, and O in apatites and amphiboles. Our results reveal that amphiboles are generally more enriched in 37Cl compared to apatites. In apatites, increasing the Cl/(Cl + F) and Cl/(Cl + OH) ratios reduces the βCl-factors of Cl-F-apatites and Cl-OH-apatites, respectively, while substitution between F and OH has a small impact. In amphiboles, Cl contents have little effect on the βCl-factors. For Ca isotopes, the βCa-factors are largely unaffected by substitutions among Cl, F, and OH in either mineral. For O isotopes, the βO-factors vary depending on the type of oxygen atoms. In Cl-F-apatites and Cl-OH-apatites, the βO-factors for total oxygen atoms decrease with increasing Cl/(Cl + F) ratios but increase with Cl/(Cl + OH) ratios, respectively. Hydroxyl oxygen sites in amphiboles exhibit higher βO-factors than those in apatites, whereas silicate oxygen sites are more enriched in 18O than phosphate oxygen sites. Correlations between bond lengths and isotope fractionation properties are also observed: in both apatites and amphiboles, the βCl-factor is negatively correlated with the Cl–Cation bond length, except in the cases of actinolite and richterite, while the βO-factors of phosphate oxygen and silicate oxygen correlate with the O–P and O–Si bond lengths, respectively. These results can enhance our understanding of Cl, Ca, and O isotope behavior in halogen-bearing phosphates and silicates, providing valuable insights into the role of apatites and amphiboles as indicators of evolutionary processes on Earth and in extraterrestrial bodies.