USING d-D DIAGRAMS TO INTERPRET SULFIDE-SULFATE SULFUR ISOTOPIC DATA FOR MAGMATIC HYDROTHERMAL SYSTEMS

The sulfur isotopic compositions of coeval sulfide and sulfate minerals provide a robust means of inferring hydrothermal conditions including temperature, redox state, sulfur source, isotopic exchange kinetics, and residence time of sulfur species. Plotting sulfate-sulfide data from magmatic systems on a d-D diagram (mineral values vs. difference) commonly produces a sulfate trend with a positive slope and a complementary sulfide trend of negative slope. The slopes and intersection of the trends have been used to estimate R (SO₄/H₂S) and d³⁴S_SS, respectively, assuming equilibrium exchange in a closed system over a range of temperatures at constant R and d³⁴S_SS. However, the use of d-D diagrams has been challenged on the basis that they involve dependent variables and induce a correlation of the data. Plotting pairs of randomly generated values on a d-D diagram readily demonstrates the effect and magnitude of this induced correlation.

Alternatively, plots of d_sulfide vs. d_sulfate for magmatic systems typically produce a single trend of negative slope. Two phase (H₂S, SO₄), closed system, equilibrium isotopic exchange modeling indicates such trends cross isotherms with +1 slopes corresponding to the temperature range of sulfide-sulfate equilibration. Furthermore, the slope (absolute value) of the data trend is equivalent to R and the intercept of the projected data trend with the isotherm that passes through the origin provides an estimate of d³⁴S_SS. This latter isotherm represents the theoretical upper temperature limit where D_{sulfide-sulfate}=0 and, therefore, d³⁴S_SS =d³⁴S_H2S=d³⁴S_SO4.

Potential complications arise when mineral data are used to estimate aqueous values and when closed system behavior is used to model geochemically open processes. However, equilibrium sulfide-sulfate isotopic exchange in magmatic systems effectively exhibits two phase close system behavior on d-d diagrams because sulfur isotopic fractionation between solid and aqueous species is negligible and governing mineral and crystal surface reactions generally fix H₂S and SO₄ concentrations at constant levels and proportions. Consequently, d-d diagrams can provide reasonably accurate estimates of important magmatic hydrothermal parameters that are not compromised by mathematical artifacts.