The influence of Fe substitution on the wave velocities of akimotoite

One ultrasonic experiment (T2082) was performed on a Fe-bearing akimotoite sample (Fe10).

Ultrasonic measurements, X-ray diffraction and X-ray radiography for sample length determination were conducted up to 26.4 GPa and 1100 K as described in detail in section 2.8.

Also for this experiment, MgO and Au were used as secondary pressure markers. Their unit-cell lattice parameters and calculated pressures using the EoS reported by Tsuchiya (2003) and Dewaele et al. (2000) are reported in Table 5-1. As for the experiments in Chapter 4.2, the MgO and Au pressures differed by up to 4 GPa possibly due to a different stress distribution on the pressure markers. The absolute pressure could be calculated from the wave velocities and density of akimotoite and is reported in Table 5-2 as well as the travel times, sample lengths and compressional and shear wave velocities of Fe-bearing akimotoite.

After the synchrotron experiment, the assembly T2082 was recovered, cut from top to bottom and polished to perform X-ray diffraction and SEM analyses (Figure 5-3). Electron backscattering imaging showed that brighter secondary phases formed along the grain boundaries of the akimotoite crystals. These additional phases were not present at the beginning of the experiments and due to their very small concentration could not be detected neither in situ by means of the EDXRD nor using the Bruker micro-focus diffractometer on the recovered synchrotron sample.

However, the Mössbauer spectrum of the same recovered sample could be fitted with three distinct doublets (Figure 5-4). The dark green doublet is making up 67(1) % of the total Fe and can be clearly attributed to the Fe²⁺ substituted into the MgO6 site in akimotoite having an isomer shift (IS) of 1.039(2) and a quadrupole splitting (QS) of 1.740(4). This is comparable to the IS and QS obtained for akimotoite (McCammon et al. personal communication).

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Table 5-1: Unit-cell lattice parameter of Au and MgO pressure markers, calculated pressures according to Tsuchiya (2003) and Dewaele et al. (2000), respectively and unit-cell lattice parameters of Fe10 at different pressures and temperatures.

aAu (Å) aMgO (Å) Au P (GPa) MgO P (GPa) temperature (K) aaki (Å) caki (Å) Vaki (ų)

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Figure 5-3: Electron backscattering image of the multi-anvil assembly after the high pressure and temperature ultrasonic experiment. Zooming inside the sample reveals that secondary phases were formed possibly during the high temperature cycle that was performed at 1100 K. The three white spots in the zoomed-in image represent sample damage from the electron beam during EMP analyses.

Figure 5-4: Mössbauer spectrum of the Fe-bearing akimotoite sample after the synchrotron experiment. The dark green doublet (68(1) %) is attributed to Fe²⁺ at the octahedral site of akimotoite, the blue doublet most likely represents Fe²⁺ at the octahedral site of ringwoodite and the bright green doublet has characteristic IS and QS for Fe²⁺ in magnesiowüstite.

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The blue doublet with a IS 1.027(7) of and a QS of 2.72(2) represents most likely the Fe²⁺ in the octahedral site of ringwoodite (Lyubutin et al. 2013) and correspond to 17(1) % of the total Fe.

The light green doublet has IS and QS values of 1.01(1) and 0.70(3), representative of Fe²⁺ at the octahedral site of magnesiowüstite (e.g. McCammon et al. 2004, Otsuka et al. 2010) and corresponds to 16(1) % of the total Fe in the sample. The phase diagram of Fe-bearing akimotoite (Figure 1-7) confirms that the possible additional phases are ringwoodite and magnesiowüstite although at higher pressures relative to the conditions applied during the synchrotron experiment or for a higher FeSiO3 content. This implies that the single-phase stability field of Fe-bearing akimotoite is even smaller than assumed by Ito and Yamada (1982) who reported that at a temperature of 1373 K, akimotoite containing 10 mol.% FeO is stable at least up to ~24-25 GPa.

The composition of akimotoite recovered after the synchrotron experiment and determined from the Mössbauer spectrum is Mg0.93Fe0.07SiO3 i.e. it contains 0.03 atoms per formula unit less than the starting composition of Mg0.9Fe0.1SiO3. This change in composition results in a negligible change of the unit-cell lattice parameters explaining why it was not possible to identify the transformation using EDXRD.

The compressional and shear wave velocities of Fe-bearing akimotoite (Fe10) at room temperature are shown in Figure 5-5 in comparison to the wave velocities of the akimotoite end-member determined using Brillouin spectroscopy (Chapter 3) and ultrasonic interferometry (Zhou et al. 2014) as well as of the Al-bearing akimotoites (Chapter 4.2). Fe-bearing akimotoite has slower compressional and shear wave velocities relative to the MgSiO3 end-member and comparable to the velocities of Ak80. As for the Al-bearing akimotoite samples, the room temperature data were fitted using the third-order finite strain equations derived from the expression of Davies and Dziewonski (1975) as described in chapter 2.8.7. The resulting adiabatic bulk and shear moduli and their first pressure derivatives are KS0 = 197(1) GPa, K’ = 5.2(1), G = 121(1) GPa and G’ = 1.5(1).

High-temperature data have been obtained during three heating cycles up to 800 K and one final heating cycle up to 1100 K (Figure 5-6). Shear wave velocities from the last heating cycle up to 1100 K may show some evidence for a change in the phase assemblage in from of a velocity increase by ~ 0.1 km/s at 600 and 800 K relative to the shear wave velocities collected during previous heating cycles at those temperatures. The secondary phases observed in the recovered

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sample were therefore formed very likely only during the fourth heating cycle that was performed up to 1100 K at 22.6 GPa. Interestingly, no significant velocity difference was observed for the compressional wave velocities during the last heating cycle (Figure 5-6). All data, except for those collected during the last heating cycle were fitted using the Debye-Mie-Grüneisen equation of state after Stixrude and Lithgow-Bertelloni (2005) reported in chapter 2.8.8. As initial values for the bulk and shear moduli and their first pressure derivatives, the EoS parameters obtained by fitting the room temperature data were used. First, V0, KT, K’, G and G’ were let free to vary, then all elastic parameters were refined simultaneously to minimize the discrepancy between the experimental and calculated wave velocities. The resulting elastic parameters obtained are V0 = 26.44 cm³/mol, KT0 = 197(1) GPa, K’ = 5.3(1), G = 123(1) GPa, G’ = 1.4(1), γ = 1.19, q = 2.4 and ηS = 2.9.

Figure 5-5: Compressional (top) and shear (bottom) wave velocities of Fe-bearing akimotoite (Fe10, green) in comparison to the MgSiO3 akimotoite end-member (black circles), Ak97.5 and Ak80 (red and blue, respectively). The wave velocities of Fe10 are slower with respect to the end-member and comparable to Ak80, however, with Ak80 having a different slope.

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Table 5-2: Compressional (vP) and shear wave velocities (vS) calculated from the travel time and sample length at different pressures and temperatures, as well as the density for the Fe10 akimotoite samples.

absolute P (GPa) temperature (K) density (g/cm³) travel time (x10^-9s) sample length (x10^-6 m) vp (km/s) vs (km/s)

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Figure 5-6: Compressional (top) and shear (bottom) wave velocities of Fe-bearing akimotoite (Fe10) up to a temperature of 800 K. Four heating cycles were performed during the synchrotron experiment T2082. The shear wave velocities obtained during the 4^th heating cycle appear faster relative to the velocities of the previous three heating cycles likely due to partial transformation of the sample.

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