The effect of net-transfer reactions on the isotopic composition of minerals

To interpret correctly the isotopic composition of metmorphic rocks and minerals, the effect of nettransfer reactions must be quantitatively evaluated. Such evaluation requires a complete set of linearly independent, net-transfer reactions that fully describe the reacting system. The set of net-transfer reactions is then coupled with mass-balance equations for stable isotopes. Reaction spaces can be contoured with isopleths of °¹⁸O, °¹³C, and D of minerals which allows evaluation of the effect of different reactions and bulk compositions on the stable isotopic composition of minerals and rocks. Using this approach, we examined the effect of fractionation of isotopes due to net-transfer reactions at the biotite and second-sillimanite isograds in northern New England. Our analysis shows that the shift in °¹³C and °¹⁸O at an isograd depends strongly upon the overall net-transfer reaction at the isograd and the bulk composition of the rock. The use of model isograd reactions to determine isotopic shifts, therefore, can lead to serious errors in the interpretation of isotopic data. At the second-sillimanite isograd °¹⁸O _qtz (quartz), °¹⁸O _kspar (K feldsdpar), and °¹⁸O _wr (whole rock) decrease by 0.5, 1.0, and 0.8 per mil, respectively. Quantitative evaluation of the effect of fractionation of isotopes by net-transfer reactions shows that: (1) the relative changes in oxygen isotopes across the isograd could be caused by distillation of fluids during develatilization reactions; (2) the magnitude of the observed isotopic shifts often differs by a factor of 2 from the calculated shifts due to reaction progress alone. The difference between observed and calculated shifts is attributed to either, differences in bulk composition between individual rocks, or, to isotopic exchange between minerals after peak metamorphism. At the biotite isograd the shifts in carbon and oxygen isotope values are different from predicted shifts caused by net-transfer reactions alone. This discrepancy suggests that fluids infiltrated the rocks during the formation of the biotite isograd.