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An empirical equation that is a function of mineral-melt partition coefficients is used to explain how the rare earth elements (REE) partition into minerals during closed-system crystallization of coarsely-crystalline rock. The concentration of any REE in a mineral as described by this equation is shown to depend on two factors: (1) the affinity of the mineral to incorporate the REE relative to the affinities of all the other minerals in the rock to incorporate that REE and (2) the modal abundance of the mineral in the rock. The general form of the equation for any REE is (DNDN/sumD) C^/x,^ = C* , where D ** is the mineral-melt REE partition coefficient for a constituent mineral; sumD is the sum of the D 1** values for all the minerals in the rock; C^ is the concentration of a REE in the whole-rock; x* is the weight fraction of the mineral in the rock; and C ** is the concentration of a REE in the mineral. Calculations using this equation and the REE compositions of constituent minerals indicate the proportions of mineral phases in the host rock. These calculations also constrain the values of partition coefficients that must be operative under the conditions of crystallization. The concept of mineral-mineral partitioning represented by this equation accounts for the REE enrichment and the distinctive REE patterns observed in different portions of a metasomatized peridotite-hornblendite xenolith from Dish Hill, CA. A magmatic liquid, now represented by the amphibole-bearing (hornblendite) vein, provided the REE that partitioned into the coexisting peridotite. The present REE patterns are in accordance with the contrasting partition coefficients of the amphibole and the original peridotite and are in response to the time-temperaturepressure conditions of partitioning. Within 1 cm of the vein, the operative partition coefficients for amphibole and peridotite approximate equilibrium values, indicating that equilibrium conditions were attained in this portion of the xenolith. At increasing distance (2-5 cm) from the vein, operative partition coefficients do not correspond to equilibrium values, suggesting that magma-peridotite interactions were incomplete. A third potential application of this equation may include explaining REE redistribution in metamorphic recrystallization.

An empirical equation for modeling rare earth element mineral-mineral partitioning; an application to mantle metasomatism