Fe2+–Mg partitioning between olivine and liquid at low oxygen fugacity: an experimental and thermodynamic framework

Saper, L. M.; Baker, M. B.; Stolper, E. M.

doi:10.1007/s00410-022-01955-0

Table 4 Values of fit parameters for \({\mathrm{ln K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\), \(\mathrm{ln }{\mathrm{D}}_{\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\), and \(\mathrm{ln}{\mathrm{ D}}_{\mathrm{Fe}^{2+}}^{\mathrm{ol}/\mathrm{liq}}\)

From: Fe²⁺–Mg partitioning between olivine and liquid at low oxygen fugacity: an experimental and thermodynamic framework

		B_Si	B_Ti	B_Si–(Na+K)	\({\mathrm{W}}_{\mathrm{Fe}-\mathrm{Mg}}^{\mathrm{ol}}\)	∆G° (Toplis 2005)	\(\overline{\Delta {\mathrm{K}}}_{\mathrm{D},\mathrm{Fe}^{2+}-\mathrm{Mg}}^\text{ol/liq}{\text{ (Exp-Calc)}}\)	\(\|\Delta {\mathrm{K}}^\text{ol/liq}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}\|\)(a.a.d.)
Model 1		1.0259			3291	–6766 – 7.34 T	–0.0007	0.0026
(n = 14)	1σ	0.0213			182
Model 2		1.0445	–1.3125	–3.0550	3040	–6766 – 7.34 T	–0.0016	0.0141
(n = 201)	1σ	0.0202	0.1076	0.1851	158

		A_i	C_i	F_i (Beattie 1993)	SSR	\(\overline{\Delta {\mathrm{T}}}\) (Exp-Calc)	\|∆T\| (a.a.d.)	\|∆\({\mathrm{D}}_{\mathrm{i}}^{\mathrm{ol}/\mathrm{liq}}\)\| (a.a.d.)
\({\mathrm{lnD}}_{\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\)		13,428	6.224	0.049	1.24× 10⁵	+ 0.02°	19°	0.353
(n = 201)	1σ	284	0.191
\({\mathrm{lnD}}_{\mathrm{Fe}2+}^{\mathrm{ol}/\mathrm{liq}}\)		12,592	7.916	0.048	1.82× 10⁵	+ 0.05°	23°	0.147
(n = 201)	1σ	335	0.225

Fitted parameters for the olivine–liquid exchange coefficient, \( \ln K_{{{\text{D,Fe}}^{{{\text{2 + }}}} {\text{ - Mg}}}}^{{{\text{ol/liq}}}} = \frac{{\Delta G^{^\circ } }}{{{\text{RT}}}} + \sum\limits_{j} {B_{j} } X_{j}^{{{\text{liq}}}} + \frac{{W_{{{\text{Fe - Mg}}}}^{{{\text{ol}}}} }}{{RT}}\left( {1 - 2X_{{{\text{Fo}}}}^{{{\text{ol}}}} } \right) \), Eq. (9), and for the individual partition coefficients, \(\text{lnD}_{{\text{i}}}^{{\text{ol/liq}}} = 0.5({\text{A}}_{\text{i}}/\text{T} + (\text{P} - 1)\text{F}_{\text{i}}/\text{T} - \text{C}_{\text{i}} - 2\text{ln(1.5NM)} - 2\text{ln(3}{\text{X}}_{{{\text{Si}}}}^{{{\text{liq}}}} ) + \text{NF})\), where i = Mg or Fe²⁺, Eqs. (11) and (12); T is in Kelvin and R is in J/(mol K). Model 1 refers to the fit to the RKD experiments only (n = 14, see Parameterizing the compositional dependence of \({\mathrm{K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\) using the RKD data); Model 2 is fit to both the RKD experiments (n = 14) and the preferred low-ƒO₂ compilation of literature experiments (n = 187; see Modeling the compositional dependence of \({\mathrm{K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\) using the RKD and literature data sets). The ∆G° term was adopted from Toplis (2005) and is not a fitted parameter. \(\overline{\Delta {\mathrm{K}}}^\text{ol/liq}_{\mathrm{D},\mathrm{Fe}^{2+}-\mathrm{Mg}}\) is the average difference between the experimental and calculated value for \({\mathrm{K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\), whereas \(|\Delta {\mathrm{K}}^\text{ol/liq}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}|\) is the average absolute deviation (a.a.d.) between the experimental and calculated values. Uncertainties in Model 1 and Model 2 are based on the 1σ errors in \({\mathrm{K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\) used as weights in the fitting procedure and do not include errors for the liquid compositional variables used in the fits. The individual partition coefficients, \({\mathrm{lnD}}_{\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\) and\({\mathrm{lnD}}_{\mathrm{Fe}^{2+}}^{\mathrm{ol}/\mathrm{liq}}\), were fit to the combined low-ƒO₂ compilation (n = 201) as described in Practical application of the model for \({\mathrm{K}}_{\mathrm{D},{\mathrm{Fe}}^{2+}-\mathrm{Mg}}^{\mathrm{ol}/\mathrm{liq}}\). The values for the F_i pressure term for both the Mg and Fe²⁺ models were taken from Beattie (1993) and were not fitted parameters. \({\text{X}}_{\text{Si}}^{\text{liq}}\) is the single-cation mole fraction of Si in the liquid, NM = \({\text{X}}_{\mathrm{Fe}}^{\text{liq}}+ {\text{X}}_{\mathrm{Mn}}^{\text{liq}}{+ \text{ X} }_{\mathrm{Mg}}^{\text{liq}}{+ \text{ X} }_{\mathrm{Ca}}^{\text{liq}}{\text{ + X}}_{\mathrm{Ni}}^{\text{liq}}\), and NF = \(7/2\mathrm{ ln}(1-{\text{X}}_{\mathrm{Al}}^{\text{liq}}) + 7\mathrm{ ln}(1-{\text{X}}_{\mathrm{Ti}}^{\text{liq}})\). SSR is the sum of the squared residuals. ∆T is the average of the differences between the experimental and calculated temperatures in degrees, whereas |∆T| is the average absolute deviation (a.a.d.) between the experimental and calculated temperatures

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