DISEQUILIBRIUM PARTIAL MELTING MODEL AND ITS IMPLICATIONS FOR TRACE-ELEMENT FRACTIONATIONS DURING MANTLE MELTING

A model to describe trace element evolutions during partial melting is proposed by assuming surface equilibrium instead of complete equilibrium between mineral grains and melt and by considering the following factors: (1) chemical diffusion in minerals; (2) melting and melt extraction. For mantle melting rates of approximately 10(-7) yr-1, inferred from mid-ocean ridge spreading rates, elements with diffusivities (D) in minerals of > 10(-15) cm2/s will be at equilibrium between minerals of 0.5 cm in diameter and melt during mantle melting. However, the anomalous radioactive excess of Ra-226 over Th-230 (up to 300%) in young basalts which cannot be explained by equilibrium melting because of the highly incompatible nature of both elements can be accounted for by the present model only when melting rate is in the orders of 10(-6) to 10(-5) yr-1. The disequilibrium effect cannot be ignored for elements with D < 10(-13) cm2/s if the melting rate is 10(-5) yr-1. Disequilibrium melting lowers the incompatibility of an incompatible element; the high the incompatibility, the more obvious this effect is. Fractionation of trace elements during disequilibrium melting depends both on their equilibrium partition coefficients (k) and their diffusivities. This has two consequences: (1) fractionation of two highly incompatible elements (k less-than-or-equal-to 0.01) by more than 20% is still possible at melting degree as high as 15% if their diffusivities differ by a factor of 5 or more, as compared to the requirement for less than 5% partial melting for the same extent of fractionation by equilibrium melting; and (2) the incompatibility order of two incompatible elements can be reversed under certain circumstances (i.e., k1 > k2, but D1 > D2). The Pb paradox, namely, that the U/Pb ratio in mantle sources inferred from Pb isotopes has increased during the differentiation of the Earth even though Pb is less incompatible than U, is explainable if the diffusivity of Pb is higher than that of U (e.g., by a factor of 10) and if the melting rate is in the order of 10(-5) yr-1.