5.3 Substitution mechanisms in Bridgmanite
5.3.1 Al-bearing bridgmanite
In order to understand the distribution of cations in Brg in the Fe + Al bearing system it is useful to first examine the speciation in the individual Al and Fe bearing subsystems. For the Al-Mg-Si-O system this is possible using previously published data (Kojitani et al., 2007; Liu et al., 2019a; 2019b; Liu et al., 2017; Navrotsky et al., 2003). In Fig. 5.2a, the Si content of Fe-free Al-bearing Brg is plotted against the Al content. Two solid lines indicate the expected trends for the charge coupled substitution mechanism along the MgSiO3-AlAlO3
join and the oxygen vacancy substitution mechanism along the MgSiO3-MgAlO2.5 join, respectively. Bulk compositions along the MgSiO3-AlAlO3 join (green circles) produce Brg samples that fall along the CCS trend line. Bulk compositions with Mg>Si, on the other hand, result in Brg compositions (orange circles) that fall between the CCS and OVS trend lines.
The proportions of the two substitution mechanisms change with the Al content in bridgmanite, from MgAlO2.5 OVS dominating at low Al content (<0.10 pfu) to equal abundance of OVS and CCS with Al between 0.1-0.15 atoms pfu and finally to AlAlO3
dominance at high Al content > 0.15 atoms pfu. The variation in the two substitution
130 mechanisms for Brg with a bulk starting composition of Mg>Si can be seen more clearly in Fig. 5.2b, where the proportions of the two components are determined from the equation MgxAlzSiyOx+1.5z+2y=yMgSiO3+(x-y) MgAlO2.5+0.5(z-x+y) AlAlO3 (x+y+z=2, Liu et al., 2017). The CCS AlAlO3 component increases monotonically with increasing Al content while the MgAlO2.5 OVS component initially increases to a maximum at Al= ~ 0.1 atoms pfu and then decreases upon a further increase in Al.
131 Fig. 5.2 (a) The variation of the Si content of Brg with Al content at 25-27 GPa and 1873-2000 K. The two solid lines are expected trend lines for CCS along the MgSiO3-AlAlO3 join and the OVS along the MgSiO3-MgAlO2.5 join respectively. The orange symbols indicate Brg with starting bulk composition Mg>Si and the green symbols represent Brg with starting bulk composition Mg=Si. Data are taken from Kojitani et al. (2007); Liu et al. (2017, 2019a, b) and Navrotsky et al. (2003). (b) The mole fraction of AlAlO3 and MgAlO2.5 component in Brg as a function of Al content at 27 GPa and 2000 K.
Open circles represent data from Liu et al. (2019a, b) with a bulk composition Mg > Si in the system.
Solid lines are the calculated values based on the thermodynamics models derived at 27 GPa and
The equilibrium coefficient K for this reaction is defined as:
𝐾 = 𝑎AlAlO
where 𝑎AlAlOBrg 3and 𝑎MgAlOBrg 2.5are the activities of the AlAlO3 and MgAlO2.5 components in Brg respectively. At equilibrium, the standard state Gibbs free-energy change can be expressed by
∆𝐺(5.12)0 = −R𝑇ln 𝑎AlAlOBrg 3 (𝑎MgAlO
2.5
Brg )2 (5.14)
taking the standard state to be the pure end-members at the pressure and temperature of interest. The activities of the Brg component are defined as:
𝑎AlAlOBrg 3 = 𝑥AlAlOBrg 3× 𝛾AlAlOBrg 3 (5.15𝑎) 𝑎MgAlOBrg 2.5 = 𝑥MgAlOBrg 2.5 × 𝛾MgAlOBrg 2.5 (5.15𝑏) where γ is the activity coefficient. Substituting these equations into equation (5.14) yields:
132 which should yield a constant value for a given pressure and temperature regardless of the composition. MgSiO3 bridgmanite has two oxygen sites, O1 with a multiplicity of 1 and O2 with a site multiplicity of 2. If we consider that oxygen vacancies occur on one half of the available O1 sites, then the mole fraction of the MgAlO2.5V0.5 component can be written as,
𝑥MgAlOBrg 2.5V0.5 = 2𝑥Mg,A𝑥Al,B(𝑥V,O1)0.5(𝑥O,O1)0.5 (5.17) where 𝑥Mg,A and 𝑥Al,B are the mole fractions of Mg on the A site and Al on the B site respectively, and XV,O1 and XO,O1 are the mole fractions of vacancies and oxygen on the O1 site where 𝑥V,O1= 0.5 (𝑥Al,B− 𝑥Al,A). The integer 2 in equation (5.17) is required such that the activity of the end-member MgAlO2.5V0.5 is equal to unity. For the coupled substitution of Al, it is assumed that charge balance results in local ordering of Al on each site, such that the mole fraction of the AlAlO3 component is:
𝑥AlAlO
3
Brg = 𝑥Al,A = 𝑥Al,B (5.18)
Using a symmetric mixing model, the deviation from ideal mixing can be described by:
R𝑇ln𝛾AlAlO
133
By using the mole fractions of different ions on A, B and O1 sites in Brg obtained from the experiments, the equation can be fitted using a non-linear least-squares algorithm to determine the three interaction parameters and ∆𝐺(5.12)0 . However, values for the three interaction parameters are highly correlated, and a range of values will provide a satisfactory fit. Refining all three interaction parameters at the same time gives unreasonable solutions, but always gives 𝑊Al
Si,B parameters are shown in Fig. 5.2b and they agree very well with the experimental data.
The very large interaction parameters required to fit the Al distribution in Fe-free Brg imply significant non ideality in the mixing of oxygen vacancies and between Mg and Al mixing on the A site. The magnitude of the interaction parameters is far greater than those normally observed for cation mixing among mantle silicates and is also much greater than the values required to fit AlAlO3 mixing between Brg and corundum in the MgSiO3-AlAlO3
system (Panero et al., 2006). This seems to be inevitable, however, because the concentration of the MgAlO2.5 component goes through a maximum over a relatively small change in Al content. As the excess enthalpy contribution to the free energy is a function of concentration (Eq. 5.19 a, b), large coefficients i.e. interaction parameters, are required in order for the small change in total Al content to have a large effect on the speciation.
134