The dependence of the Fe²⁺-Mg cation-partitioning between olivine and basaltic liquid on pressure, temperature and composition

Abstract

The equilibrium partitioning of Fe²⁺ and Mg between olivine and liquid along a liquid line of descent has been determined for a calc-alkaline system, ranging in composition from picritic to andesitic. Experiments were conducted between 1000–1450° C and 1 bar to 30 kbar. Within the compositional range investigated ${\text{x}}_{Mg}^{liq} = 0.4 - 0.8$ and $log Kd_{Fe}^{ol - liq} = 0.624 - 4.86 \cdot Mg + 7.3 \cdot Mg^2 + 0.00343 \cdot P$, the compositional dependence of the Fe²⁺ and Mg partitioning is a function of the Mg-content of the liquid. The Mg-content of the liquid correlates strongly with temperature. The variation of the Fe²⁺ and Mg partitioning were therefore evaluated individualy as functions of composition and temperature alone. The composition dependence of the cation-partitioning coefficients (Kd) is given by the following two equations:

$$log Kd_{Fe}^{ol - liq} = 0.624 - 4.86 \cdot Mg + 7.3 \cdot Mg^2 + 0.00343 \cdot P$$

((I))

$$log Kd_{Fe}^{ol - liq} = 1.151 - 4.82 \cdot Mg + 7.3 \cdot Mg^2 + 0.00028 \cdot P$$

((II))

where Mg is the cation-fraction of magnesium in the liquid phase. The temperature dependence of the cation partitioning coefficients can be described by the two equations:

$$log Kd_{Fe}^{ol - liq} = - 1.926 + \frac{{3036}}{T} - \frac{{58.0 \cdot P}}{T} + 0.0364 \cdot P$$

((III))

$$log Kd_{Mg}^{ol - liq} = - 1.456 + \frac{{3117}}{T} - \frac{{67.0 \cdot P}}{T} + 0.0388 \cdot P$$

((IV))

where Kd ^ol-liq _Fe is the cation-partition coefficient (Fe ^/2+ _ol< /Fe ^/2+ _liq< ) and analogous for Mg, temperature T is in Kelvin, pressure P in kbar and Fe²⁺ and Mg are cationfractions. The composition dependence of reactions (I) and (II) as well as the temperature dependence of reactions (III) and (IV) are identical within the statistical errors (Table 4). The Fe²⁺-Mg exchange reaction that is obtained by combining (I) and (II) or (III) and (IV) is therefore compositionand temperature-independent along the liquid lines of descent for the P-T-compositional range investigated, and the experimental data can be fitted to an equation of the form:

$$log Kd_{Fe - Mg}^{ol - liq} = - 0.5214( \pm 0.0023) + 0.00323( \pm 0.00017) \cdot P (kbar)$$

((V))

where $log Kd_{Fe - Mg}^{ol - liq} = \left( {\frac{{Fe_{ol}^{2 + } }}{{Fe_{liq}^{2 + } }}} \right) \cdot \left( {\frac{{Mg_{lig} }}{{Mg_{ol} }}} \right)$.The increase of the Kd for Fe²⁺-Mg partitioning with pressure means that the x ^liq _Mg of primary magmas in equilibrium with an olivine of fixed composition increases with depth. For example, the x ^liq _Mg of a liquid coexisting with an olivine of composition x ^ol _Mg =0.9 increases from 0.73 at 1 bar to 0.77 at 30 kbar. This variation of Kd with pressure may be used either to constrain the depth of phenocryst-liquid equilibration or to test the possible primary nature of magmas of given compositions.