A PREDICTIVE MODEL FOR RARE-EARTH ELEMENT PARTITIONING BETWEEN CLINOPYROXENE AND ANHYDROUS SILICATE MELT

We present a quantitative model to describe the partitioning of rare e arth elements (REE) and Y between clinopyroxene and anhydrous silicate melt as a function of pressure (P), temperature (T) and bulk composit ion (X). The model is based on the Brice (1975) equation, which relate s the partition coefficient of element i (D-i) to that of element o (D -o) where the latter has the same ionic radius ib as the crystallograp hic site of interest, in this case the clinopyroxene M2 site: D-i = D- o exp(-4 pi EM2NA(ro/2(r(i) - r(o))(2) + 1/3(r(i) - r(o))/RT N-A is Av ogadro's number, E-M2 is the Young's Modulus of the site, R is the gas constant and T is in K. Values of E-M2 Obtained by fitting the Price equation to experimental REE partition coefficient patterns are in goo d agreement with those obtained from the well-known correlation betwee n bulk modulus, metal-oxygen distance and cation charge. Using this re lationship to constrain E-M2 for 3+ cations and then fitting the Price equation to those experimental data where 3 or more REE partition coe fficients had been simultaneously measured we obtained 82 values of D- o and r(o). The latter was found to be a simple and crystallochemicall y reasonable function of clinopyroxene composition. We show that for a ny clinopyroxene-melt pair if D for one middle REE (e.g. Sm or Gd) is known then the Brice equation can be used to predict Ds for all the ot her REE, with uncertainties similar to those involved in the actual me asurements. The model was generalised using thermodynamic descriptions of REE components in crystal and melt phases to estimate the free ene rgy of fusion (Delta G(f))) of the fictive REE components REEMgAlSiO6 and Na0.5REE0.5MgSi2O6. For the melt we find that 6-oxygen melt compon ents (CaMgSi2O6, NaAlSi2O6, Mg3Si1.5O6 etc.) mix with constant activit y coefficient over a wide range of natural compositions. Propagating D elta G(f) into the Price model we obtain an expression for D-o(3+) in terms of the atomic fraction of Mg on the clinopyroxene M1 site, the M g-number of the melt, P and T. The D for any REE can be calculated fro m D-o(3+) using the Price equation. Over 92% of D-REE (454 points) cal culated in this way lie within a factor 0.63-1.59 of the experimental value. The approach can be extended to calculate D for any REE at a gi ven P (less than or equal to 6 GPa) and T (1200-2038 K) to within 0.60 -1.66 times the true value given only the crystal and/or melt composit ion. The model has widespread applicability to geochemical modelling o f all natural processes involving clinopyroxene, e.g. decompression ma ntle melting, enabling for the first time account to be taken of varia tions in partition coefficient in response to changing pressure, tempe rature and phase composition.