Density of the melt - Fe partitioning between bridgmanite and melt and density of the melt

6.2 Fe partitioning between bridgmanite and melt and density of the melt

6.2.4 Density of the melt

Based on the calculated melt composition, melt densities were determined using the second-order Birch-Murnaghan equation of state with the thermal pressure term proposed by Wakabayashi and Funamori (2013): expansion coefficient respectively. The first and second subscripts denote the pressure and temperature respectively. T0 is the reference temperature of 2500 K. Parameters for the equation of state of silicate melt were provided as 𝑉_0,𝑇₁_,𝑖, 𝛼_0,𝑇₁_,𝑖 and 𝐾_0,𝑇₁_,𝑖 for each melt

172 component SiO2, Al2O3, FeO, MgO, and CaO (Wakabayashi and Funamori, 2013). Using 𝑉_0,𝑇₁_,𝑖, the zero-pressure molar volume of silicate melts at T1 could be expressed as:

𝑉_0,𝑇₁ = ∑ 𝑥_𝑖𝑉_0,𝑇₁_,𝑖

𝑖

(6.6)

where 𝑥_𝑖 is the molar fraction of component i and T1 is the reference temperature of 1773 K.

Differentiating equation (6.6) with respect to temperature yields 𝛼_0,𝑇₁𝑉_0,𝑇₁ = ∑ 𝑥_𝑖𝛼_0,𝑇₁_,𝑖𝑉_0,𝑇₁_,𝑖

𝑖

(6.7)

and then the zero-pressure thermal expansion coefficient of silicate melt at T1 is calculated from,

𝛼_0,𝑇₁ = ∑ 𝑥_𝑖 _𝑖𝛼_0,𝑇₁_,𝑖𝑉_0,𝑇₁_,𝑖

𝑉_0,𝑇₁ (6.8)

The zero-pressure thermal expansion coefficient at the temperature of interest is,

𝛼_0,𝑇 =

The zero-pressure molar volume at T0 is calculated from the values of the molar volume and zero-pressure thermal expansion coefficient at T1 according to

𝑉_0,𝑇₀ = 𝑉_0,𝑇₁exp ( ∫ 𝛼_0,𝑇𝑑𝑇

so the zero-pressure bulk modulus at T0 can be calculated by

173 calculated accordingly. The average molecular weight can be calculated from the molecular weight of each component by

Parameters used in this study are listed in Table 6.1 (Wakabayashi and Funamori, 2013). In Fig. 6.5 densities of silicate melts estimated using equation (6.5) and the parameters in Table 6.1 are compared with high-pressure experimental results obtained using the sink-float technique with both olivine and diamond (Agee and Walker, 1993; Ohtani et al., 1997;

Suzuki and Ohtani, 2003; Suzuki et al., 1995, 1998). There is very good agreement for the different melt compositions.

Table 6.1 Parameters for silicate melt density calculation used in this study from Wakabayashi and Funamori (2013).

174 Fig. 6.5 Comparison of silicate melt densities calculated from the equation of state of Wakabayashi and Funamori (2013) with high-pressure experimental results. The calculation was performed under the same conditions (i.e. pressure, temperature and composition) as reported in the experiments.

The solid line indicates the 1: 1 correspondence. The experimental data on peridotitic melt are from Agee and Walker (1993); Ohtani et al. (1997); Suzuki and Ohtani (2003); Suzuki et al. (1995, 1998).

The experimental data on partial melt of peridotite which is melt formed by partial melting of PHN1611 peridotite at 20 GPa is taken from Ohtani et al. (1997). The experimental data on Basaltic and Picritic melt are from Ohtani and Maeda (2001).

Because the melt contains some amount of water, the effect of H2O on the density of silicate melt needs to be considered. The partial molar volume of H2O at the pressure and temperature of interest is calculated using the Vinet equation of state (Sakamaki, 2017):

𝑃 = 3𝐾_𝑇[1 − (𝑉̅_H₂_O 𝑉̅_H₂_O,0)

] (𝑉̅_H₂_O 𝑉̅_H₂_O,0)

𝑒𝑥𝑝 {3

2(𝐾^′− 1) [1 − (𝑉̅_H₂_O 𝑉̅_H₂_O,0)

]} (6.15)

where 𝑉̅_H₂_O is the high-pressure partial molar volume of H2O, 𝑉̅_H₂_O,0 is the zero-pressure partial molar volume taken from Bouhifd et al. (2015) at a reference temperature of 1273 K

175 and 𝐾_𝑇 is the isothermal bulk modulus. The zero-pressure partial molar volume of water at the temperature of interest is calculated from water, 𝑉_{melt,𝑃,𝑇} is the partial molar volume at high pressure and temperature from equation (6.5) and 𝑉̅_H₂_O,𝑃,𝑇 is the high-pressure and high temperature partial molar volume of H2O obtained from equation (6.15).

Table 6.2 Parameters used in this study for the equation of state for the partial molar volume of H2O in magma from Sakamaki (2017).

The obtained densities for hydrous melts at 25 GPa and 1923 K are plotted against the melt water contents for different partial melt fractions in Figure 6.6. The hydrous silicate melts range in density between 3.95 and 3.98 g/cm³ over the range of parameters examined and decrease with the water content. The uncertainties in the melt H2O composition, therefore, have very little effect on the determined densities at these conditions.

176 Figure 6.6 The density of the hydrous melt versus the water content of the melt calculated with different melt fractions at 25 GPa and 1923 K.

The low solubility of H2O in Brg and Fp raises the possibility that water could be released by subducting material as it enters the lower mantle (Bolfan-Casanova et al., 2003). Released H2O would then cause partial melting. The density of the hydrous partial melts then formed is important for determining whether they are likely to rise out of the lower mantle and potentially rehydrate the transition zone or whether they could form neutrally buoyant melt layers that could potentially lead to seismically observable decreases in shear wave velocities (Schmandt et al., 2014). Nakajima et al. (2019) attempted this calculation based on the chemical compositions of experimental melts produced in equilibrium with Brg and Fp and found melts to have a lower density than the lower mantle. However, as described in section 6.2.2 the iron contents of these melts were likely lower than plausible for the lower mantle as a result of the use of a highly oxidized starting material and the strong effect of redox state on the Fe-Mg partitioning between Brg and melt. Nakajima et al. (2019) also made no consideration for the degree of melting and simply used melt compositions found in their experiments. In the mantle the proportion of H2O present will control the

177 melt fraction, which in turn will control the amount of iron in the melt. Although no analysis exists that is specific for the lower mantle, a comparison with a study made for the 410 km discontinuity (Hier-Majumder and Courtier, 2011) implies that observable decreases in shear wave velocity in the lower mantle could result from partial melt fractions that lie in the range of 0.005 to 0.01 (Schmandt et al., 2014).

In Figure 6.7 the densities of hydrous peridotite partial melts with compositions calculated in this study are determined along a mantle geotherm (Brown and Shankland, 1981) using the equations of state (6.5) and (6.15). For comparison, the PREM model for the density of the mantle (Dziewonski and Anderson, 1981) is also shown. The red and blue solid lines show the result for hydrous melts containing 15 wt.% H2O and 30 wt.% H2O produced by 1 wt.% melting of the mantle respectively. The hydrous melt density obtained for 0.1 and 0.5 wt.% partial melting is nearly identical to 1 wt.% melting with a difference of only ~ 0.002 g/cm³, and is therefore not shown. Because the density of water in silicate melt intersects with that of silicate melt at 25.3 GPa, the water content has a negligible effect on the melt density between 25-26 GPa (Sakamaki, 2017). Below 25 GPa, the difference of the two compositions increases with decreasing pressure due to the high compressibility of H2O and the effect of H2O content on the density becomes more significant with decreasing pressure (Fig. 6.7). Extrapolations to higher and lower pressures are isochemical, however, whereas in reality the melt composition will change gradually with pressure to make the prediction increasingly inaccurate. The density of partial melts generated from peridotite under hydrous conditions (Kawamoto, 2004; Nakajima et al., 2019) at ~ 25 GPa and ~1673 K and dry conditions (Ito and Takahashi, 1987; Kuwahara et al., 2018; Trønnes and Frost, 2002;

Wang and Takahashi, 2000) at ~ 25 GPa and 2473-2773 K are also calculated and shown for comparison (Fig. 6.7). The density profile of hydrous melts (Kawamoto, 2004; Nakajima et al., 2019) were calculated along the current mantle geotherm (Brown and Shankland, 1981).

The water content in the melt was assumed to be 30 wt.% by Nakajima et al. (2019) from the deficit in the EDS analysis totals. For Kawamoto (2004) the same technique using the electron microprobe analysis totals leads to a 40 wt.% melt water content. It can be seen that the hydrous melt in our study is denser than both those of Nakajima et al. (2019) and

178 Kawamoto (2004) (Fig. 6.7). As this is the case when both melt H2O contents are identical, the higher density in our study can be wholly attributed to the higher Fe content of the melt, as discussed in section 6.2.2. The density of dry melt generated by peridotite was calculated along the mantle geotherm as well as the peridotite solidus (Herzberg et al., 2000). The composition of the dry melt was taken from the average value from Ito and Takahashi (1987); Kuwahara et al. (2018); Trønnes and Frost (2002); Wang and Takahashi (2000). As can be seen in Fig. 6.7, the density of dry melt along the peridotite solidus is much lower than the hydrous melt in our study and Nakajima et al. (2019) at 22-28 GPa. Compared with the dry melt density calculation along the mantle geotherm (purple line in Fig. 6.7), the smaller density of dry melt is not only caused by the higher temperature but also the smaller Fe content in the melt. At higher temperatures in anhydrous melting experiments, the Fe content in both melt and coexisting Brg decreases, mainly due to the higher melt fractions encountered. Kuwahara et al. (2018), for example, estimated that melts containing 7-8 wt.% FeO account for 81-99 wt.% based on mass balance calculations.

Schmandt et al. (2014) reported a region of low shear wave velocities below the 660 km discontinuity under the south western USA, which from the lateral extent might be interpreted as a region containing neutrally buoyant partial melt. In Fig. 6.7, however, it is clear that the density of such a 1 wt.% hydrous partial melt would be much lower than the density of the lower mantle at this depth, as constrained by the PREM model (Dziewonski and Anderson, 1981). Such a melt composition, however, should also be close to equilibrium with an assemblage compatible with the base of the transition zone, as the solid phases must also be in equilibrium with such an assemblage at slightly lower pressures. This raises the possibility, therefore, that hydrous melts might rise out of the lower mantle but may tend to pond at the base of the transition zone on top of the 660 km discontinuity or that they may freeze due to the increase in H2O solubility of the mantle minerals. The region examined by Schmandt et al. (2014) appears to be down welling, however, with a rate of up to 2 cm/year. It may be that hydrous mantle is continuous dragged down from the transition zone into the lower mantle and that the low velocities arise due to melts forming in this downwelling material and rising back up again in a continuous cycle.

179 Figure 6.7 Calculated densities of the partial melts of anhydrous and hydrous peridotite from the current study and previous studies along the mantle geotherm (Brown and Shankland, 1981). The preliminary reference earth model (PREM) is also plotted (Dziewonski and Anderson, 1981) as a solid black line. The red and blue lines are compositions calculated from the current study for 1 % partial melt containing 15 wt.% and 30 wt.% water respectively. Melt densities based on the results of previous hydrous and anhydrous melting studies are shown for comparison.

180

181

7 Major conclusions

This thesis focused on investigating the substitution mechanisms in bridgmanite (Brg), the speciation of Al and Fe³⁺ as a function of oxygen fugacity and composition, the influence of Fe and Al substitution on the crystal structure of Brg as well as the composition, mainly the Fe content, of hydrous melts coexisting with Brg. The main conclusions can be summarized as follows:

(1) In Fp saturated systems, at low M³⁺ (M³⁺=Fe³⁺+Al³⁺) concentrations (<0.15 atoms pfu in Al bearing system, <0.03 atoms pfu in Fe bearing system and <0.10 atoms pfu in Fe, Al-bearing system), both charge-coupled substitution (CCS) and oxygen vacancy substitution (OVS) mechanisms are important in Brg. At higher trivalent cation concentrations, the charge coupled substitution predominates. The maximum amount of OVS in the current study is 0.04 pfu. This maximum OVS component value was achieved in the sample where the Al content (0.23 atoms pfu) is significantly higher than the Fe³⁺ content (0.11 atoms pfu) in Brg (S7214). The oxygen vacancy proportion shown in Fig. 5.13 is the absolute number of oxygen vacancies pfu in Brg which is half the value of that expressed in mole fraction of MgM³⁺O2.5 component (𝑥_MgM³⁺_O_2.5).

(2) When both Fe³⁺ and Al are present, Al prefers to occupy the B site and Fe³⁺ prefers to go onto the A site, which is confirmed by single crystal X-ray diffraction through refinement of the mean atomic numbers at the A and B sites. FeAlO3 charge coupled substitution is the major substitution mechanism for trivalent cations when the amount of Fe³⁺ and Al in Brg are similar. When there is additional Al or Fe³⁺, MgAlO2.5, MgFe³⁺O2.5 OVS and AlAlO3 or Fe³⁺Fe³⁺O3 CCS are also present. For the samples analyzed in this study it appears that Fe³⁺

enters the B site only when the amount of Fe³⁺ is larger than Al.

(3) The molar volume of Brg increases with increasing Fe and Al substitution. The molar volume of pure MgSiO3 end-member is 24.447(5) cm³/mol. If a linear volume relation is assumed, the molar volumes of the Brg end-members FeSiO3, FeAlO3, MgAlO2.5, MgFeO2.5

and FeFeO3 are determined to be 25.339 cm³/mol, 27.081 cm³/mol, 26.565 cm³/mol, 27.5

182 cm³/mol and 29.494 cm³/mol, respectively. The volumes of these components are essential for any thermodynamic calculation of Brg chemistry at pressures within the lower mantle.

(4) All lattice parameters of Brg increase with increasing M³⁺M³⁺O3 and MgM³⁺O2.5

substitution, with the largest increase being that of the c-axis and the smallest being that of the a-axis. This can, in part, be attributed to changes in the corresponding individual B-O and A-O bond distances. The Fe²⁺SiO3 has only a minor effect on b- and c- axes but results in increases in the a-axis.

(5) All B-O bond distances in Brg increase with increasing M³⁺M³⁺O3 and MgM³⁺O2.5

substitution, with the B-O1 individual length which lies mainly along the c-axis increasing more rapidly than the intermediate B-O2 distances which are mainly in the a-b plane. This gives rise to an elongation of the B site octahedron along the c-axis due to the M³⁺ cation substituting Si at this site. Fe²⁺SiO3 substitution has no obvious effect on the B-O bond distances.

(6) The shortest four A-O bond distances in Brg decrease while the other longer distances increase with increasing M³⁺M³⁺O3 and MgM³⁺O2.5 substitution, leading to a larger distortion of the A-site coordination polyhedral. Fe²⁺SiO3 substitution, on the contrary, decreases the distortion of the A site.

(7) The orthorhombic distortion of Brg has been described using the irreducible representations (Irreps) describing the displacive modes of the A cation and oxygens from the atomic positions of the cubic perovskite aristotype structure. Five mode displacements are allowed for the orthorhombic Brg structure: R4+ and M3+, which describe the out-of-phase tilting along the [110] direction and the in-out-of-phase octahedral tilting along [001]

respectively, are the two primary distortion modes in Brg. The secondary modes include X⁵⁺, which describes the displacement of O and of Mg from the center of the aristotype unit cell and the R5+ mode, which describes the displacement of the Mg atoms along the orthorhombic a-axis. Although these modes are only secondary (i.e. do not drive the cubic to orthorhombic phase transformation) they have a no negligible amplitude which increase with increasing M³⁺M³⁺O3 and MgM³⁺O2.5 substitutions. In contrast, the Fe²⁺SiO3

183 substitution decreases the R4+ tilting and the X5+ and R5+ displacements of the A cations and therefore its distortion in agreement with the variation observed for the A-O individual bond distances.

(8) The spontaneous strain e4 and etx in Brg increases with M³⁺M³⁺O3 and MgM³⁺O2.5

substitution and decreases with Fe²⁺SiO3 substitution. The coupling coefficient between the order parameters (describing the octahedral tilting driving the cubic to orthorhombic phase transition) and the spontaneous strain is strongly dependent on composition.

(9) At constant pressure and temperature, the Fe³⁺/ΣFe ratio in Brg is found to be a function of oxygen fugacity (f_O2) as well as the Al and Fe content. At a fixed oxygen fugacity and Fe content, the Fe³⁺/ΣFe ratio in Brg increases with Al content, whereas this dependency decreases at higher oxygen fugacities. This is simply because the Fe³⁺/ΣFe ratio approaches unity at high f_O2regardless of the Al content. At a fixed Al and Fe content, the Fe³⁺/ΣFe ratio in Brg increases with oxygen fugacity and the dependency is smaller at higher Al content. At fixed Al content and oxygen fugacity, the Fe³⁺/ΣFe ratio in Brg decreases slightly with increasing Fe content. In addition, the Fe³⁺/ΣFe ratio in Brg seems to decrease with increasing temperature if all other parameters remain constant.

(10) Previous studies (Liu et al., 2017, 2019a, 2019b) indicate that for Fe-free Al-bearing Brg, the AlAlO3 CCS increases monotonically with Al content while the MgAlO2.5 component first increases with Al content, reaching a maximum at Al=0.1 pfu and then decreases with Al content. This behavior can be described by a thermodynamic model with 𝑊_Mg^Brg_Al,A=152.6 kJ/mol and ∆𝐺_(5.12)⁰ = - 85(4) kJ/mol for the equilibrium 2MgAlO2.5 = AlAlO3 + 2MgO (5.12) at 27 GPa and 2000 K. The large interaction parameter is necessary because a significant change in the speciation occurs over a relatively narrow Brg Al content.

(11) A similar thermodynamic model can be constructed using the equilibrium 2MgFeO2.5 = FeFeO3 + 2MgO (5.21) in Al-free, Fe-bearing Brg with an additional equilibrium used to determine the oxygen fugacity dependence i.e. 2FeO + 0.5O2 = FeFeO3 (5.27) at 25 GPa and 1973 K. The best solution was achieved with ∆𝐺_(5.21)⁰ = - 27.886 kJ/mol and ∆𝐺_(5.27)⁰ =

184 172.236 kJ/mol. Using activity-composition models does not improve the fitting even with Margules parameters in the order of MJ/mol. Therefore, the resulting model which has only two fitting parameters is considered to provide the best fit within experimental uncertainties.

(12) In order to develop a thermodynamic model to describe the Fe³⁺ and Al speciation in Brg it is necessary to consider mixing of the 3+ cations on both cation sites and to constrain this inter-site mixing using the equilibria: 2MgFeO2.5 = FeFeO3 + 2MgO (5.30) and 2MgAlO2.5

= AlAlO3 + 2MgO (5.31). One further equilibrium is then used to impose the control of f_O2 i.e.

2FeO + AlAlO3 + 0.5O2 = 2FeAlO3 (5.32). The experimental data were then fitted by allowing the site occupancies of 3+ cations for each experimental composition to vary under the constraints of mass balance and finding the sets of site occupancies that allow three constant values of ∆𝐺⁰ values to be determined for all the experiments. Using 11 experimental analyses of coexisting Brg and Fp samples with varying concentrations of total Fe, Al and at different oxygen fugacities the following best fit standard state Gibbs free energies were obtained at 25 GPa and 1973 K: ∆𝐺_(5.31)⁰ = - 180.438 kJ/mol, ∆𝐺_(5.32)⁰ = -32.807 kJ/mol and ∆𝐺_(5.33)⁰ = 24.605 kJ/mol. Brg total Fe³⁺ and Fe³⁺/ΣFe ratio calculated using the model are in good agreement with the experimental data even though the model has only three adjustable parameters. Several activity-composition models were tested but were found not to significantly improve the fitting. This does not imply that the mixing is ideal but that the activity-composition relations do not have a significant effect in the compositional range examined. Using this model, the ferric Fe content of Brg and its distribution over the A and B sites can be determined at 25 GPa and 1973 K as a function of f_O2 for any given bulk Fe and Al content of Brg.

(13) Using this model combined with a mass balance calculation, the composition and proportion of coexisting Brg and Fp were calculated for a pyrolite bulk composition at different oxygen fugacities. The results were compared with the experimental results of Irifune (1994) and Irifune et al. (2010) at 28 GPa that employed the same composition.

The model can reproduce the apparent KD (i.e. the Mg-Fe exchange coefficient between Brg

185 and Fp that assumes all iron is Fe²⁺) and the Fe³⁺/ΣFe ratio in Brg from these experiments if an oxygen fugacity of IW + 1.5 is assumed. This is a quite reasonable assumption for these experiments that employed carbon capsules.

(14) The model shows that KD (app) is a strong function of oxygen fugacity due to the variation of the Brg Fe³⁺ content with f_O2. The changes in KD (app) observed between 28 and 47.4 GPa by Irifune et al. (2010) can be achieved through changes in f_O2 between IW and IW +1.5. While Irifune et al. (2010) attributed changes in KD (app) to an Fe²⁺ spin transition in Fp, the results of this study shown that changes in experimental f_O2 provide at least as good an explanation. The absence of f_O2 measurements in almost all previous experimental

Im Dokument Bridgmanite crystal chemistry and iron content in the Earthʹs lower mantle (Seite 179-200)