Theoretical calculation of oxygen isotope fractionation factors in carbonate systems

摘要

Using established methods of statistical mechanical calculation and a recent compilation of vibrational frequency data, we have computed oxygen isotope reduced partition function ratios (beta values) for a large number of carbonate minerals. The oxygen isotope beta values of carbonates are inversely correlated to both the mass and radius of the cation bonded to the carbonate anion but neither correlation is good enough to be used as a precise and accurate predictor of beta values. There is an approximately 0.6% relative increase in the beta values of aragonite per 10 kbar increase in pressure. These estimates of the pressure effect on beta values are broadly similar to those deduced previously for calcite using the methods of mineral physics. In comparing the beta values of our study with those derived recently from first-principles lattice dynamics calculations, we find near-perfect agreement for calcite and witherite (<0.3% deviation), reasonable agreement for dolomite (<0.9% deviation) and somewhat poorer agreement for aragonite and magnesite (1.5-2% deviation). In the system for which we have the most robust constraints, CO2-calcite, there is excellent agreement between our calculations and experimental data over a broad range of temperatures (0-900 degrees C). Similarly, there is good to excellent correspondence between calculation and experiment for most other low to moderate atomic mass carbonate minerals (aragonite to strontianite). The agreement is not as good for high atomic mass carbonates (witherite, cerussite, otavite). In the case of witherite and cerussite, the discrepancy may be due, in part, to our calculation methodology, which does not account for the effect of cation mass on the magnitude of vibrational frequency shifts associated with heavy isotope substitution. However, the calculations also reveal an incompatibility between the high- and low-temperature experimental datasets for witherite and cerussite. Specifically, the shapes of fractionation factor versus 1/T-2 curves in the calcite-witherite and calcite-cerussite systems do not conform to the robust constraints on the basic shape of these curves provided by theory. This suggests that either the high- or low-temperature datasets for both minerals is in error. Dolomite-calcite fractionation factors derived from our calculations fall within the wide range of fractionations for this system given by previous experimental and natural sample studies. However, our compilation of available low-temperature (25-80 degrees C) experimental data reveal an unusual temperature dependence of fractionations in this system; namely, the data indicate an increase in the magnitude of fractionations between dolomite (or proto-dolomite) and calcite with increasing temperature. Such a trend is incompatible with theory, which stipulates that fractionations between carbonate minerals must decrease monotonically with increasing temperature. We propose that the anomalous temperature dependence seen in the low-temperature experimental data reflect changes in the crystallinity and degree of cation ordering of the dolomite phase over this temperature interval and the effect these changes have on the vibrational frequencies of dolomite. Similar effects may be present in natural systems at low-temperature and must be considered in applying experimental or theoretical fractionation data to these systems. In nearly all cases, carbonate mineral-calcite fractionation factors given by the present calculations are in as good or better agreement with experimental data tha are fractionations derived from semi-empirical bond strength methods. (C) 2008 Elsevier Ltd. All rights reserved.