In the model described in section 5.3.3 the composition of Brg is determined using three equilibria involving different Brg and Fp components, for which standard state Gibbs free energies have been estimated at the pressure and temperature of interest, i.e. 25 GPa and 1973 K. In section 4.2 the volumes of these Brg components have been determined which allows the pressure dependencies of the three equilibria to be estimated. For equilibrium (5.32) for example the pressure dependence can be included using the equation
∆𝐺(5.32)0 − ∫ ∆𝑉. 𝑑𝑝
25 0
+ ∫ ∆𝑉. 𝑑𝑝
𝑃 0
= −R𝑇ln (𝑎FeAlO
3 Brg )2 (𝑎FeOFp )2 𝑎AlAlO
3
Brg (𝑓O2)0.5 (5.39)
155 where the first integral corrects the standard state of ∆𝐺(5.32)0 to room pressure. Similar equations can then be written for equilibrium (5.30) and (5.31). Volumes and equation of state data used to calculate the integrals are given in Table 5.5. The formalism of Holland and Powell (2011) is employed. Equation of state terms for the Brg components are assumed to be the same as those for MgSiO3 Brg. Although there may be significant uncertainties in assuming that the compressibilities of the Brg components are identical, this assumption is unlikely to change the direction of the calculated trends with increasing pressure but there are significant uncertainties in the gradients of the calculated trends with pressure. These uncertainties increase with pressure and for this reason the extrapolation is performed over a relatively small pressure range. The model was calculated from 26-40 GPa at two assumed conditions: (1) at a constant oxygen fugacity of IW+1.5; (2) in equilibrium with Fe-Ni metal. Extrapolation to pressures higher than 40 GPa maybe not suitable due to the possible spin transition in ferropericlase proposed to begin at 40-50 GPa (see Lin et al., 2013 for a review). The predicted Fe3+/ΣFe ratio of Brg versus pressure is plotted in Fig. 5.11 in which the results from previous studies are also shown for comparison. Due to the negative volume change of reaction (5.32), the calculated Fe3+/ΣFe ratio of Brg increases with pressure. The Fe3+/ΣFe ratio of the two multi-anvil studies from Irifune et al. (2010) and Stagno et al. (2011) (open circles in Fig. 5.11) fall well within the range between the two model curves. Although the Al content (0.07 atoms pfu) of Brg in Stagno et al. (2011) is slightly lower than Irifune et al. (2010) and our model (0.10 atoms pfu), it was buffered at an oxygen fugacity of IW+2 that is slightly higher than used in the model calculation. The carbon capsule adopted in Irifune et al. (2010) also implies that the oxygen fugacity in their experiments should not have exceeded approximately IW+2, as discussed in section 6.1. The Fe3+/ΣFe ratios of Brg reported from previous laser heated diamond anvil cell experiments have, in general, lower values (Fig. 5.11). For the studies of in Prescher et al. (2014) and Kupenko et al. (2015) the Al contents of Brg were lower (0.05-0.07 pfu) than our model (0.1 atoms pfu), which as shown in Fig. 5.1a may account for some of the difference in Fe3+/ΣFe ratio compared with the model. The Fe content of Brg in in the study of Shim et al. (2017) and Kupenko et al. (2015) was also much higher (~ 0.2 atoms pfu)
156 than our model (0.1 atoms pfu) which as shown in Fig. 5.1b would also result in lower Fe3+/ΣFe ratios. Shim et al. (2017) performed one of the only studies in DAC where attempts were made to buffer the fO2 with the presence of Fe metal. However, Fp was not present in the experiments, which instead contained an SiO2 polymorph. As such the results are not applicable to the model determined in this study. Andrault et al. (2018) report that the potential presence of garnet in their experimental results up to 30-35 GPa may explain why the Fe3+/ΣFe ratios are low. However if Brg coexisted with garnet at these conditions its Al content would be expected to be very high (Akaogi et al., 2002) and if the bulk Fe contents were comparable, the minimum Fe3+/ΣFe ratio should be greater than that determined from the model. The Al and Fe contents of Brg were not reported in the study of Andrault et al.
(2018), so it is very hard to make a comparison with these results. One point worth noting is that in most of the DAC experiments, the Fe3+/ΣFe ratios measured from the high pressure samples are quite close to those of the starting material, which may indicate a lack of equilibrium. For example, the Fe3+/ΣFe ratios of the starting materials are 0.07, 0.35 and 0.42 for Andrault et al. (2018), Kupenko et al. (2015) and Prescher et al. (2014) respectively and the corresponding Fe3+/ΣFe ratio of Brg at 23-27 GPa are 0.12, 0.38 and 0.42 respectively. This comparison serves to underline the fact that control of factors such as fO2, Brg Al and Fe contents and SiO2 activity are likely essential if any systematic information is to be gained on the evolution of Brg Fe3+/ΣFe ratios with pressure.
157 Fig. 5.11 Fe3+/ΣFe ratio of aluminous bridgmanite as a function of pressure. The red solid line indicates model results calculated with a constant fO2=IW + 1.5 and the blue solid line indicates model results calculated for an assemblage in equilibrium with Fe-Ni metal. Previous diamond anvil cell results from Andrault et al. (2018); Kupenko et al. (2015); (2014); Shim et al. (2017) and multi-anvil experiment results from Irifune et al. (2010) and Stagno et al. (2011) are also shown for comparison. The upper and lower value from Irifune et al. (2010) are measurements made on the same sample using electron energy loss and Mössbauer spectroscopy respectively.
The apparent KD for Mg and Fe exchange between Brg and Fp was also calculated as a function of pressure assuming three different scenarios: (1) at a constant oxygen fugacity of IW+1.5; (2) for constant Fe3+/ΣFe ratio in Brg equal to 0.69; and (3) for an initial whole rock Fe3+/ΣFe ratio of 0.03 which would result in the precipitation of Fe-Ni metal. The results are shown and compared with those of Irifune et al. (2010) in Fig. 5.12. The KD (app) value assuming constant fO2=IW+1.5 is the largest while that with initial whole rock ferric Fe over total Fe ratio of 0.03 is the smallest. For both conditions, the KD (app) does not change very much in the pressure range of 26-40 GPa. In contrast, the KD (app) value for constant Fe3+/ΣFe=0.69 in Brg decreases from 0.67 at 26 GPa to 0.48 at 40 GPa. The KD (app) value of 0.48 at 40 GPa for Brg Fe3+/ΣFe ratio of 0.69 is in good agreement with that from Irifune et
158 al. (2010) which has a Fe3+/ΣFe ratio of 0.67 and a KD (app) of 0.51(7). Therefore for the two data points where Fe3+/ΣFe ratios where measured by Irifune et al. (2010) there is reasonable agreement with the model. The KD (app) decreases because of the effect of pressure on Fe2+-Mg exchange between Brg and Fp. For the other scenarios this is not apparent because the Fe3+/ΣFe ratio increases with pressure. In order for the Fe3+/ΣFe ratio to remain constant the fO2 would have had to decrease in the experiments from IW+1 to IW.
This provides one explanation for the overall decrease in KD (app) but the sharp drop observed in KD (app) can only be explained if some further evolution in the fO2 of the experiments occurred. This again serves to underline the fact that experiments on Fe-Mg partitioning in the lower mantle are simply unconstrained unless the fO2 and Fe3+/ΣFe ratio of Brg, are constrained.
Fig. 5.12 Model curves for Fe-Mg exchange KD between Brg and Fp plotted against pressure at different assumed conditions. Data from Irifune et al. (2010) also are shown for comparison. The arrows represent the two pressure points where the Fe3+/ΣFe in Brg were measured in Irifune et al.
(2010) and the values obtained are indicated. The different Fe3+/ΣFe value shown from Irifune et al.
(2010) are measurements made on the same sample using electron energy loss and Mössbauer spectroscopy respectively.
159 Oxygen vacancies in Brg have aroused great interest as they have been considered to be possible sites for the substitution of hydrogen and noble gasses (Litasov et al., 2003;
Shcheka and Keppler, 2012) and may also influence the compressibility and transport properties of Brg. The model predicts that the proportion of oxygen vacancies in Brg decreases with pressure. As shown in Fig. 5.13, calculated at an fO2=IW + 1.5 and for a pyrolite composition, the proportion of oxygen vacancies deceases sharply up to 32 GPa, reaching practically zero at 40 GPa. This trend is consistent with previous results in Al-Brg in both experimental and theoretical studies (Brodholt, 2000; Liu et al., 2017). Although the proportion of oxygen vacancies in Brg appears relatively small at 26 GPa, no other mantle mineral contains such a large amount of such vacancies. Since the amount of oxygen vacancies should be positively correlated to the rate of chemical diffusion, at least for oxygen anions, the decrease in Brg oxygen vacancies with pressure in the upper part of the lower mantle may influence transport properties in the upper regions of the lower mantle (Karato and Wu, 1993). It might, for example, provide an explanation for a proposed increase in lower mantle viscosity towards 1000 km depth (Rudolph et al., 2015). This viscosity increase was proposed as a possible physical mechanism to explain why some subducting slabs seem to stagnate towards the mid lower mantle (Fukao and Obayashi, 2013).
160 Fig. 5.13 The proportion of oxygen vacancies per formula unit in Brg versus the pressure at a constant oxygen fugacity of IW+1.5 calculated for a pyrolite composition using the thermodynamic model developed in this study. Note that the oxygen vacancy proportion shown here is the absolute number of oxygen vacancies pfu in Brg which is half the value of mole fraction of MgM3+O2.5
component (𝑋MgM3+O2.5) as in Fig. 5.9.
161