Boron and oxygen isotopes fractionation between borate minerals and fluids and implications for borate deposit formation

Boron and oxygen isotope studies have the potential to reveal important information regarding the formation of the borate minerals that form in non-marine evaporite deposits and are the major economic source of boron. In particular, boron isotopes can provide information concerning the source of boron and the pH conditions during borate precipitation, and oxygen isotopes can be used to constrain crystallization temperatures and the extent of evaporation of the brines. However, quantitative application of boron and oxygen isotope studies of borate minerals are hindered by the lack of isotope fractionation factors for both isotopes. Experimental determination of these values is difficult because of the problem of achieving equilibrium conditions at low temperatures. Hence, this work systematically calculates the reduced partition function ratios (RPFRs, β values) of boron and oxygen isotopes in borate minerals and brine using density functional theory. The results indicate that the 10³lnβ among these minerals decreases in the sequence of borax ≈ kernite > ulexite ≈ probertite > teruggite > hydroboracite > kurnakovite > colemanite > priceite > pinnoite > howlite for boron isotopes and in the order of howlite > hydroboracite priceite > colemanite > kernite > probertite > pinnoite > ulexite > teruggite > kurnakovite > borax for oxygen isotopes. These 10³lnβ values for boron isotopes are primarily influenced by the BO₃/BO₄ ratio in borate minerals while the chemical composition (cationic type) has a subordinate effect. Thus, the temperature dependence of boron isotope fractionation between borate minerals and fluids at pH of 8.60 has been derived as following: Δ¹¹B_borax-fluid = - 0.0016 T² + 0.1375T - 4.2902, Δ¹¹B_{colemanite-fluid} = - 0.0016 T² + 0.1525T - 8.5653 and Δ¹¹B_{ulexite-fluid} = - 0.0017 T² + 0.1724T - 13.7696. The impact of fluid pH on boron isotope fractionation is also significant, where the pH dependent boron isotope fractionation at 298.15 K can be quantified as: Δ¹¹B_borax-fluid = $\frac{{10}^{8.597-pH}}{1+{10}^{8.597-pH}}\times 25.8853-11.1907$, Δ¹¹B_{colemanite-fluid} = $\frac{{10}^{8.597-pH}}{1+{10}^{8.597-pH}}\times 25.8853-2.526$, Δ¹¹B_{ulexite-fluid} = $\frac{{10}^{8.597-pH}}{1+{10}^{8.597-pH}}\times 25.8853-7.8217$. The heavy isotope, ¹¹B, is preferentially fractionated into borate minerals compared to the fluid phase under basic pH conditions, but prefers the fluid phase in neutral and acidic brine conditions. The calculated fractionation factors, combined with the Rayleigh fractionation model and the diffusion model, help us explain the spatial variation in boron isotopes and constrain the genesis of two typical borate deposits, Kirka and Kramer. A robust geothermometer using oxygen isotopes in the paragenetic mineral pairs of calcite and Ca-borates has been proposed.