Corrigendum to “Origin of Fe³⁺ in Fe-containing, Al-free mantle silicate perovskite” [Earth Planet. Sci. Lett. (2014) 409 (319–328)] ((S0012821X14006979)(10.1016/j.epsl.2014.11.006))

In the main text section 2.1.1 the term Hvib0(Osolid2−) in the equation for Gvib(Osolid2−)–Hvib0(Osolid2−) (Lee et al., 2009; Lee and Morgan, 2012) was miscalculated. The incorrect value was 0.63 eV and the corrected value is 0.095 eV. As discussed below, this correction demonstrated that there was some discrepancy in the DFT oxidation energies, so we now add another correction term with an increase μ(O₂) in main text eq. (4) by 0.4 eV/O_2. These corrections change the reaction energy of Eq. (1), and have the effect of stabilizing oxygen gas and reducing the amount of Fe³⁺ created by oxidation. This change does not significantly impact the curve shapes, the qualitative conclusions, or the discussions, except regarding Fig. 1, which we detail below. Unfortunately, many of the specific values shown in the figures and mentioned in the text related to the oxidation reaction in Eq. (1) are somewhat changed, so below we give revised figures and specific corrections for regions of text or values which need to be updated. Figs. 1, 2, 4(a), and 5 in the main text are changed to the new Figs. E1, E2, E4(a), and E5, respectively. The changes to the text are: Pg 323/lc(left column) ln(line) 11, remove “We don't use any data from FeO or ferropericlase in constructing our model, so being consistent with Fe⁰/ferropericlase equilibrium thermodynamics is an important test of the model.” Pg 323/lc ln33, remove “The ability to define this range consistently for both Mg–Pv and Fp, despite the model being developed without any explicit ab initio calculations on the Fp system, supports the accuracy of our thermodynamic model.” Pg 323/lc ln 25, change “11.6” to “12.8”. Pg 323/lc ln 33,change “11.6” to “12.8”. Pg 323/rc(right column) ln 22, change “0.5” to “0.3”. Pg 323/rc ln 22, change “0.08” to “0.05”. Pg 323/rc ln 24, change “0.7” to “0.6”. Pg 323/rc ln 24, change “0.2” to “0.13”. Pg 326/lc ln 9, change “0.4–0.5” to “0.3–0.35”. Pg 326/lc ln 9, change “0.08–0.1” to “0.05”. Pg 326/lc 2nd ln from the bottom, change “0.05” to “0.03”. Pg 326/rc ln 1, change “0.17” to “0.035”. Pg 326/rc ln 1, change “0.1” to “0.045”. Pg 326/rc ln 2, change “0.89” to “0.19”. Pg 326/rc ln 2, change “0.52” to “0.24”. Our correction to Hvib0(Osolid2−) changes the predicted transition oxygen fugacity, fO2t, which is where the charge disproportionation (chg. disp.) reaction ceases to occur and the oxidation reaction starts to occur. Specifically, in Fig. 1 (main text) fO2t changes from log⁡(fO2t)=log⁡(fO2[Re–ReO])−6.9 to log⁡(fO2t)=log⁡(fO2[Re–ReO])−4.7. Because the bridgmanite (Pv) is in equilibrium with ferropericlase (Fp) (Mg,Fe)O the Fe from the chg. disp. reaction can only exist for oxygen fugacity less than fO2[Fe–(Mg,Fe)O]. We show below that fO2[Fe–(Mg,Fe)O]=log⁡(fO2[Re–ReO2])−5.7. This yields a final change in value from the incorrect value log⁡(fO2t)=log⁡(fO2[Re–ReO])−6.9 to the correct value log⁡(fO2t)=log⁡(fO2[Re–ReO2])−5.7. So in our corrected Fig. E1, we can see the log⁡(fO2t) is at log⁡(fO2[Re–ReO2])−5.7. The determination of log⁡(fO2[Fe–(Mg,Fe)O]) is as follows. We first consider relative difference between fO2[Fe–FeO] and fO2[Re–ReO2] at T=2000 K, P=20 GPa–100 GPa (lower mantle relevant conditions) from experiments (Campbell et al., 2007, 2009). The experimental results show that log⁡(fO2[Fe–FeO]) is −4.5 to −5 with respect to log⁡(fO2[Re–ReO2]). We take an average which is −4.75≈−4.8 to represent the log⁡fO2 difference between Fe–FeO and Re–ReO₂. Now we consider the different between log⁡(fO2[Fe–FeO]) and log⁡(fO2[Fe–(Mg,Fe)O]). In our model the Fe content in Pv is 0.125 per formula unit of MgSiO₃, which is (Mg_0.875Fe_0.125)SiO₃. Based on previous experiments, the Fe partitioning coefficient KD between Pv and Fp is 0.2–0.3 in Al-free condition (Irifune et al., 2010). If we take an average, then we can assume KD≈0.25 in Al-free condition. Then based on the definition of KD(KDPv–Fp=(Fe/Mg)Pv/(Fe/Mg)Fp), we can find that (Mg_0.875Fe_0.125)SiO₃ should be in equilibrium with (Mg_0.64Fe_0.36)O. Under an ideal solution approximation (SI section 5), log⁡(fO2[(Mg0.64Fe0.36)O]) is calculated to be −0.9 with respect to log⁡(fO2[Fe–FeO]). Therefore based on above arguments, we have log⁡(fO2[Fe–(Mg,Fe)O])=log⁡(fO2[(Mg0.875Fe0.125)SiO3])=log⁡(fO2[(Mg0.64Fe0.36)O])=log⁡(fO2[Fe–FeO])−0.9=log⁡(fO2[Re–ReO2])−5.7.