An analysis of Δ36S/Δ33S dependence on definitions of sulfur mass-independent fractionation

Mass-independent fractionation of stable sulfur isotopes (MIF-S) is believed to be a unique tracer of modern stratospheric eruptions as well as the Archean Earth's reducing atmosphere. The Delta S-36/Delta S-33 ratio has been suggested as a strong constraint to the photochemical origin(s) of MIF-S data, because the variation of Delta S-36/Delta S-33 ratio is commonly thought insignificant when mass-independent fractionated sulfur species (i.e., non-zero Delta S-33 or Delta S-36 values) are mixed with mass-dependent fractionated sulfur species (i.e., Delta S-33 = Delta S-36 = 0 parts per thousand). Given the assumption that mixing makes a straight line in Delta S-33 versus Delta S-36 space, mixing would spread Delta S-33 and Delta S-36 values of geological or atmospheric samples along a line starting from the initial composition of 0 and the original Delta S-36/Delta S-33 slope could be preserved. The Delta S-36/Delta S-33 ratio, however, does not always remain constant during mixing, for the equations that define Delta S-33 and Delta S-36, which by definition represent deviations from mass-dependent behavior, are not linear. Several different definitions (linear, exponential, and logarithmic expressions) have been widely applied for Delta S-33 and Delta S-36, which make the Delta S-36/Delta S-33 ratio a definition-dependent value. Given that each definition has advantages and disadvantages, attention should be paid to the robustness of the Delta S-36/Delta S-33 ratio they predict. To examine the robustness of Delta S-36/Delta S-33 ratio, we performed numerical and analytical analyses of its definition dependence and the behavior during two-component mixing. Our results suggest that the calculated Delta S-33 and Delta S-36 derived from different definitions vary with absolute values of delta S-34 (|delta S-34|): at larger |delta S-34|, the deviations become more prominent, and when |delta S-34| is larger than similar to 34 parts per thousand, the discrepancy of Delta S-36 values determined by different definitions is over 1 parts per thousand, which leads to significant definition-dependent variation in Delta S-36/Delta S-33 at identical delta S-33, delta S-34, and delta S-36 values. This definition-dependence of Delta S-36/Delta S-33 is negligible for most natural samples that show small S-34/S-32 fractionation. However, particular attention should be paid when dealing with processes that yield not only significant MIF-S but also large S-34 isotopic fractionations, such as SO2 photolysis and elemental sulfur polymerization. Among the tested expressions, the linear definitions are the most convenient to model two-component mixing when the delta S-34 difference between the end members is large, because Delta S-33 and Delta S-36 values of the mixture can strictly fall on the linear arrays in Delta S-33 versus Delta S-36 spaces. By applying the linear expression, the Delta S-36-Delta S-33 distributions observed in the modern stratospheric records can be reproduced by SO2 photolysis experiments. This agreement has been previously overlooked because the laboratory-produced Delta S-36/Delta S-33 ratios by exponential and logarithm definitions did not match the values for the modern stratospheric records.