Correction for Righter and Ghiorso, Redox systematics of a magma ocean with variable pressure-temperature gradients and composition

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES Correction for “Redox systematics of a magma ocean with variable pressure-temperature gradients and composition,” by K. Righter and M. S. Ghiorso, which appeared in issue 30, July 24, 2012, of Proc Natl Acad Sci USA (109:11955–11960; first published July 9, 2012; 10.1073/pnas.1202754109).

The authors note the following: “The calculations that we presented for high-MgO concentration silicate melts are unduly sensitive to small variations in the K₂O content of the liquid, stemming from the equation of state (EOS) [(1), hereafter referred to as Part IV EOS] that we utilized to calculate thermodynamic properties of the silicate liquid at high pressure. Although we attributed the strong decrease in ΔIW values for peridotite seen in Figs. 4 and 5 to the possibility of Fe₂O₃ being stabilized in the presence of alkalis in the basalt composition (as well as to the effect of extremely high temperature conditions on the melt volume), the Part IV EOS does not include treatment of Fe₂O₃, so this argument may only be relevant to the natural system; in the Part IV EOS all oxidized iron is treated as FeO. Instead, the strong decrease can be attributed to K₂O contents; above 20 GPa, the Part IV EOS calibration pinned the komatiite fit to a K₂O content of 0.25 wt%; i.e., K₂O is not an independent variable for high-MgO liquid above 20 GPa. A similar conclusion can be reached for the K₂O of MORB liquid above 20 GPa, and to a lesser extent about the other alkali, Na₂O. Given that there are more data constraints in the Part IV EOS to calibrate variation of Na₂O content, we expect the sensitivity of derived thermodynamic properties on Na₂O variation to be muted. However, due caution should be exercised and Na₂O contents should not stray far from the komatiite and MORB calibrants used to derive the Part IV EOS model. We now conclude that the only consistent way to deal with high-magnesia liquids in the context of the Part IV EOS model is to use a K₂O ∼0.25 wt%, instead of the 0.03 wt% K₂O in natural peridotite. As a result, Figs. 4, 5, and 6 and their respective legends appeared incorrectly.

Fig. 4.

A comparison of ΔIW(P.T) calculated for basalt and peridotite (with 0.03 and 0.25 wt% wt% K₂O) (SI Appendix, Table S3) along relatively cool adiabat based the Andrault et al. phase diagram (44). Note that all compositions start slightly oxidized, and then become more reduced at high pressures. The largest error contribution to log fO₂ is from the FeO volume as a function of pressure: Error in FeO at 1 bar is approximately 0.5%, but the error is approximately 3% at 10 GPa, which corresponds to 0.042 J∕bar or 0.1 log₁₀ units at 2,000 K and 10 GPa. The error at 50 GPa is approximately 0.5 log10 fO₂ units. The error contribution from melt and metal activities for these compositions is insignificant relative to the volume integral. ΔIW (ratio) values for these two compositions are −1.9 (basalt) and −2.4 (peridotite).

Fig. 5.

ΔIW (P,T) calculated for peridotite using various PT gradients. Also included are the results for a subsolidus scenario. The hottest gradients also produce low ΔIW (P,T) values at high pressures—lower than the low pressure metal-silicate equilibria values for the early Earth (dashed line).

Fig. 6.

ΔIW (P,T) calculated for scenarios in which the mantle composition starts with low FeO content (reduced), and then changes during accretion to high FeO content (oxidized). Two PT gradients are considered—the hot adiabat (isentrope) based on the Fiquet et al. phase diagram (43), and the relatively cool adiabat (isentrope) based on the Andrault et al. phase diagram (44). Note the narrow oxidizing trends resulting from these scenarios (ΔIW = −2.75 to −2.0).

“Any use of the online fO₂ calculator above 20–25 GPa for peridotite, komatiite or similar high-MgO bulk composition liquids must fix K₂O content of silicate melt to 0.25 wt% K₂O, otherwise erroneous fO₂ values may result.”

The corrected figures and their corrected legends appear below. These errors do not affect the conclusions of the article.