We can expect that the changes in tilting and distortion that occur in the perovskite-type structure of bridgmanite due to different cation substitutions play a role in the compression behavior of this mineral and in its transformation to the post-perovskite structure. The compressibilities of the AO12 and BO6 Brg sites i.e. βA and βB, depend on the strengths of the individual bonds that the A- and B- cations have with the oxygens. Cation substitution will affect the bond strength and hence the compressibility behavior of the two sites determining ultimately whether the perovskite-type structure would become more or less distorted with increasing pressure and/or temperature. It has been shown how the relative compressibilities βB/βA can be directly deduced from the basic bond-valence parameters (Brown and Altermatt, 1985) and the bond lengths measured at room pressure (Angel et al., 2005; Zhao et al., 2004), i.e βB:βA=MA:MB. MA and MB represent the site parameters defined as 𝑀𝑖 = ∑𝑁𝑗=1𝑖 𝑅𝐵𝑖𝑗exp(𝑅0−𝑅𝐵 𝑖𝑗) where R0 is the bond-valence parameter that depends only upon the particular cation-anion pair, B is a universal constant equal to 0.37 Å (Brese and O'keeffe, 1991; Brown and Altermatt, 1985) and Rij and Ni are the average bond length and coordination number of the cation site at ambient conditions, respectively. Since the bridgmanites investigated in this study do not have an end-member composition, we have used individual bond lengths and we have calculated R0 as a linear combination of the bond-valence parameters of the different proportions of cations occupying the bridgmanite A and B sites, rather than using simply the average bond distances. The resulting MA/MB ratio (Figure 4.10) are all smaller than 1 implying that the octahedral tilts will increase with pressure because the AO12 site is more compressible than the octahedral site (Angel et al., 2005). This ratio increases with increasing M3+M3+O3 and MgM3+O2.5 substitution suggesting either an increase in B-site compressibility or a decrease of the A-site compressibility as a function of M3+M3+O3 and MgM3+O2.5 substitution, given the inverse proportionality between the B-site/A-site compressibility ratio and the MA/MB ratio. This implies that substitution of mainly Al into the octahedral site increases its compressibility, whereas the
118 substitution of mainly Fe3+ at the A site decreases its compressibility likely due to the decrease of the shortest A-O distances (Fig. 4.5a).
Fig. 4.10 The relative compressibility of the B site over A site (MA/MB=βB/βA) versus the sum of CCS and OVS. Symbols are the same as in Fig. 4.3.
It is been suggested that as octahedral tilting of a perovskite-type structure increases which decreases the polyhedral volume ratio VA/VB, the repulsion between inter-octahedral anions increases and may destabilize the perovskite relative to the post-perovskite structure when the distance of intra-octahedral anions (l) reaches the average separation distance of the intra-octahedral anions (i.e. the average length of the octahedra edges, <X-X>I) (Martin et al., 2006; Martin and Parise, 2008). This critical point (l: <X-X>I=1) is empirically found to occur at VA/VB=4.038 (Martin and Parise, 2008) (Fig. 4.11). The effect of Fe and Al substitution on the perovskite to post-perovskite phase transition in bridgmanite is still a matter of debate, however there is some experimental and theoretical evidence that points to Al and Fe stabilizing the perovskite-type structure (see Hirose et al., 2017 for a review). Although the octahedral tilting increases with M3+M3+O3 and MgM3+O2.5
119 substitution at room pressure resulting in a smaller VA/VB ratio at ambient conditions (Fig.
4.7, 4.11), a more compressible octahedral site in Fe+Al-bearing bridgmanite would imply a less steep increase in the tilting angle or decrease in VA/VB ratio with pressure and therefore we may expect a larger pressure at which repulsion between oxygens will occur driving the phase transformation with respect to the MgSiO3 end-member.
Fig. 4.11 The O2-O2 (Wyckoff position 8d) distance along the [001] direction l(001), the O1-O1 (Wyckoff position 4c) distance along the [hk0] direction l(hk0) and the O2-O2 (Wyckoff position 8d) distance in a general direction l(hkl) normalized to the average octahedron edge length <O-O>I and plotted with the VA/VB ratio in single Brg crystals from the current study. l: <X-X>I=1 and empirical value of VA/VB=4.038 are thought to be the critical point where perovskite structure is not stable anymore. Symbols are the same as in Fig. 4.3.
120
121
5 Speciation of Fe and Al in bridgmanite as a function of composition and oxygen fugacity
As explained in section 1.6, in order to determine the compositions of Brg and Fp in the lower mantle it is essential to understand how iron is accommodated in Brg. The Brg Fe3+
content, for example, is known to be strongly influenced by the presence of Al but must also be a function of the oxygen fugacity. The speciation of Fe and Al in Brg will not only affect the interphase Fe-Mg partitioning with Fp but will also influence the possible formation of metallic iron alloy and the elastic and transport properties in the lower mantle (Frost and Langenhorst, 2002; Frost et al., 2004; McCammon, 1997; Nakajima et al., 2012). Given the difficulty in performing experiments on Brg at conditions that correspond to the entire lower mantle it is essential that a clear understanding of the influences on Brg site occupancies are at least obtained at lower pressures where the conditions can be relatively well constrained.
In this study experiments have been performed to examine the compositions of Brg and Fp at 25 GPa and 1973 K within bulk compositions with varying Fe and Al contents and over a range of oxygen fugacities. The factors affecting the speciation of Fe3+ and Al in Brg are examined and thermodynamic models are developed to describe this speciation in the Fe-Mg-Si-O, Al-Mg-Si-O and Fe-Al-Mg-Si-O systems.