Fe-bearing bridgmanite

Experiments performed in the Fe-Mg-Si-O system coexisting with ferropericlase are plotted in Fig. 5.3a, with the trends expected for the OVS (Mg,Fe)FeO2.5 and the CCS FeFeO3

substitution shown. As for the periclase saturated Al-Mg-Si-O system, the data fall very close to the OVS mechanism when Fe³⁺ is less than 0.03 atoms pfu although uncertainties here are high due to the relatively low concentrations. At higher Brg bulk Fe³⁺

concentrations, i.e. higher oxygen fugacity, the data move closer to CCS substitution. This indicates that the substitution mechanism is changing with Fe³⁺ concentration: MgFeO2.5

OVS appears to dominate at low Fe³⁺ abundance (<0.03 atoms pfu) and FeFeO3 CCS dominates at higher Fe³⁺ concentration (≥ 0.04 atoms pfu). The change between these two substitution mechanisms, as for the Al-bearing system, appears to occur rapidly over within a narrow Fe³⁺ range of ~ 0.02 atoms pfu. Data from Frost and Langenhorst (2002) and McCammon et al. (2004b) saturated with MgO and Lauterbach et al. (2000) and Hummer and Fei (2012) where MgO is undersaturated are also shown for comparison. Compared with data from Lauterbach et al. (2000) and Hummer and Fei (2012) conducted at MgO undersaturated conditions, there seems to be no obvious effect of whether starting compositions are Fp-saturated or SiO2-saturated on the substitution mechanism (Fig. 5.3).

However, the EPMA composition measurement in these studies were performed using a high beam current of 15 nA and 30 nA respectively, which may have resulted in an incorrect Mg/Si ratio since Brg is metastable under electron beams especially for samples with low Fe content. Note, moreover, that the errors of the chemical compositions were not given in Lauterbach et al. (2000). The point at Fe³⁺=0.074 atoms pfu from Hummer and Fei (2012) is far above the region constrained by the CCS and OVS mechanism, indicating more Fe³⁺ on the A site than on the B site which requires the formation of Mg²⁺ vacancies on the A site for charge balance. However, the Fe³⁺/ΣFe ratio in this sample was not measured and the sample may in fact contain some ferrous iron. Moreover, the experiment may be not in equilibrium since, as mentioned in their study, in the run products Brg coexisted with small amounts of unreacted MgO and SiO2 (Hummer and Fei, 2012).

135 In Fig. 5.3b, the mole fractions of FeFeO3 CCS and MgFeO2.5 OVS are plotted as a function of the oxygen fugacity (thus total Fe³⁺ content). As in Al-bearing Brg, the CCS component increases with increasing ferric Fe content and the OVS first increases and then decreases with increasing Fe³⁺ content. However, the OVS component appears to reach a maximum at much lower trivalent cation concentrations (0.03 atoms pfu Fe³⁺) compared with Al-bearing samples (0.1 atoms pfu Al) and the proportion of the OVS component is also smaller being at most 2 mol% in the Fe-bearing system compared to 5 mol% in the Al-bearing system (Liu et al., 2017).

136 Fig. 5.3 (a) The variation of the Si content of Brg with the Fe³⁺ content at 25-26 GPa and 1923-2073 K.

The two solid lines are expected trend lines for CCS along the MgSiO3-Fe³⁺Fe³⁺O3 join and the OVS along the MgSiO3-MgFe³⁺O2.5 join respectively. The solid orange diamonds and the open orange circles represent the current study and data from Frost and Langenhorst (2002) and McCammon et al. (2004b) respectively where Brg coexisting with Fp. The open green circles are data from Lauterbach et al. (2000) and Hummer and Fei (2012) where Brg is not in equilibrium with Fp. (b) The mole fraction of FeFeO3 and MgFeO2.5 component in Brg as a function of oxygen fugacity at 25 GPa and 1973 K. Solid lines are the calculated values based on the thermodynamics models derived at 25 GPa and 1973 K.

A similar equilibrium to that in the Al-bearing system can be written to describe the distribution of Fe³⁺ between cation sites in Brg i.e.,

2MgFeO_2.5 = FeFeO₃+ 2MgO (5.21) Brg Brg Fp

The equilibrium coefficient K for this reaction is:

𝐾 =𝑎_FeFeO^Brg ₃𝑎_MgO^Fp (𝑎_MgFeO

2.5

Brg )² (5.22)

137

As will be seen later the Brg components are assumed to mix ideally so that

𝑎_MgFeO^Brg _2.5V0.5 = 2𝑥_Mg,A𝑥_Fe,B(𝑥_V,O1)^0.5(𝑥_O,O1)^0.5 (5.24) where 𝑥_MgO^Fp is the mole fraction of MgO in ferropericlase and the activity coefficient, 𝛾_MgO^Fp , is determined from the interaction parameters given by Frost (2003).

Because the proportions of Fe³⁺ and Fe²⁺ in Brg depend on the f_O2 a further equilibrium is The activity of FeO in ferropericlase is defined as in equation (5.26) and calculated using the same activity composition data. For each experimental data point obtained in this study standard state Gibbs free energy terms can be calculated from equations (5.23) and (5.28).

138 Two constant values of ∆𝐺_(5.21)⁰ and ∆𝐺_(5.27)⁰ should then be obtained for all data, which in theory would also require activity composition relations to be considered. Brg site assignments estimated from EPMA data and Mössbauer Fe³⁺/ΣFe ratios have large uncertainties, however, relative to the small concentrations of Fe³⁺ involved. One way to fit the relationship between the Fe³⁺ content and f_O2 is to allow the site occupancies of Fe³⁺ on the A and B Brg sites to vary under the constraint of mass balance and to find the Fe³⁺ site occupancies where constant values of the two ∆𝐺⁰terms are found for each experiment. In fact this method leads to a range of solutions with the best result judged by the degree of agreement with the experimental f_O2-Fe³⁺ relationship, shown in Fig 5.4a, and with the proportions of the two components, shown in Fig 5.3b. This result is achieved with ∆𝐺_(5.21)⁰ = - 27.886 kJ/mol and ∆𝐺_(5.27)⁰ =172.236 kJ/mol. Note that in Fig 5.4a the data that appear to be in poor agreement with the model at IW +7.7 have a Brg bulk Fe content of only 0.05 atoms pfu, whereas the other data points as well as the model have 0.1 atoms pfu of Fe. In fact all data fit the model reasonably well once the different total Fe content is accounted for (Fig. 5.4b). It was not possible to find a solution that fitted both the total Fe³⁺ and the Fe³⁺ speciation perfectly, slightly better solutions could be found that assumed very little of the CCS component, but this was deemed to be in poor agreement with the experimentally determined site occupancies. Activity composition models similar to those described in equations (5.19a, b) were found to provide very little improvement in the fitting even when Margules terms of the order of mega Joules per mole were employed. Similarly, an activity model that accounts for the Brg reciprocal solution:

FeFeO_2.5+ MgSiO₃ = MgFeO_2.5+ FeSiO₃ (5.29) Brg Brg Brg Brg

provided very little overall improvement of the fit. As a result, it was considered that the resulting model, which has only 2 fitting terms, provides the best fit within the uncertainties.

139 Fig. 5.4 (a) The ferric iron content in Brg and (b) the ferric iron over total iron ratio in Al-free Brg as a function of oxygen fugacity at P=25 GPa, T=1973 K and fixed Fe content of 0.10 atoms pfu (except for the data points indicated) in Brg. The solid lines are calculated model curves.

140