D/H isotopic fractionation between brucite Mg(OH) 2 and water from first-principles vibrational modeling

Abstract

Isotopic fractionation between two phases can be calculated if the vibrational properties of isotopic end-members are fully characterized. We assessed a theoretical approach based on first-principles density-functional density (DFT) prediction of vibrational frequencies by comparing with spectroscopic data on isotopically substituted brucite, a model mineral for which detailed experimental data on isotopic effects and brucite–water D/H partitioning exist. The deviation from experimental values averages to less than 1% for lattice modes, and 4% for OH stretching modes. The reduced partition function ratio (RPFR) for D/H substitution in brucite was combined with experimental RPFR for water to calculate D/H fractionation factor between water and brucite. Results within the harmonic approximation systematically deviate from experimental data by + 20–25‰. RPFR is very sensitive to the frequency and isotopic shift of high frequency OH stretching modes, for which anharmonic effects are important and usually not explicitly taken introduced in calculations for minerals. The asymmetry of the O–H potential was calculated by DFT and accounts for spectroscopic measurements of the anharmonic shifts of OH stretching mode overtones and isotopic frequency ratio. Calculations of D/H fractionation introducing anharmonic corrections to the RPFR of brucite are fitted with the expression 1000ln α D/H(brucite/H 2O) = − 23.3 10 3 / T + 2.55 10 6 / T 2 − 1.51 10 9 / T 3, that yields an improved agreement with experiments at high temperature, but the deviation at 25 °C is − 30‰. Uncertainties in calculated fractionation factors can arise from dispersion effects or from DFT errors. For instance, a 1% change of the stretching mode frequencies or a 3% change of lattice mode frequencies could account for the discrepancy between model and experimental fractionation factors. The pressure dependence of brucite RPRF was calculated, and is given by 1000ln Г Pbrucite = P (− 1.005 10 3 / T + 2.18 10 6 / T 2 − 0.213 10 9 / T 3), with P in GPa. The large calculated temperature dependence of the fractionation factor suggests that a single experimental fractionation curve can be fitted to a partial consistent set of experimental data as 1000ln α D/H(brucite/H 2O) = − 27.9(30) 10 3 / T + 8.8(29) 10 6 / T 2 − 2.24(63) 10 9 / T 3. These equations allow calculating the temperature and pressure dependence of the D/H fractionation factor between brucite and water in the 300–900 K and 0.1–100 MPa range when combined with the pressure correction for water RPFR [Polyakov, V.B., Horita, J. and Cole, D.R., 2006. Pressure effects on the reduced partition function ratio for hydrogen isotopes in water. Geochimica Cosmochimica Acta, 70: 1904–1913.] for geochemical applications. The DFT model used here for estimating RPFR of the model mineral brucite can be extended to other hydrous minerals using vibrational spectroscopy as a test for the accuracy of the DFT prediction, and the brucite–water equations proposed here as a reference for determining mineral–water fractionation factors and geochemical applications.