Equilibrium partial melting

Weill D. E. and McKay G. A. (1975). The partitioning of Mg, Ee, Sr, Ce, Sm, Eu and Yb in lunar igneous system and a possible origin of KREEP by equilibrium partial melting. Proc. Sixth Lunar Sci Conf, 1143-1158. 

Green D. H. (1976) Experimental testing of equilibrium partial melting of peridotite under water saturated, high pressure conditions. Can. Mineral 14, 255-268. 

Batch partial melting will hereafter be understood as equilibrium melting, which is in contrast to fractional melting discussed in Section 9.3.3. The foundation of this model is remarkably simple and was first laid down by Schilling and Winchester (1967). A number of more or less complex modifications enabling useful information to be extracted from the data were later introduced by Gast (1968), Shaw (1970) and Albarede (1983). Bulk equilibrium crystallization of a liquid batch can be handled with equations identical to those for batch-melting. 

The sum of the f over all the n — 1 residual mineral phases is unity. This leads to the equation known as the equilibrium, partial, or batch-melting equation... 

Fig. 3.8 Plot of 8 0 values vs Mg numbers for oceanic basalts filled circles) and continental basalts open circles). The shaded field denotes the 20 range of a MORE mean value of +S.l%o, the clear vertical field denotes the range for primary basaltic partial melts in equilibrium with a peridotitic source (Harmon and Hoefs, 1995)...

During mantle partial melting, the partition coefficients of Th, Pa, and Ra are different from that of U. Assuming the melt and the mantle residue as a whole maintains secular equilibrium, if the melting process is slow, there is chemical equilibrium between the phases, which means each phase (such as the melt phase) is out of secular equilibrium because of different partition coefficients (McKenzie, 1985). 

If solid and melt are in equilibrium during partial melting, the conservation law which is concerned with the concentration of a radioactive and radiogenic nuclide in the solid and melt is given by McKenzie (1985) as the following differential equation... 

Equation (5.31) can be used to model the uranium decay series (U-series) nuclides in the residual melt that is in chemical equilibrium with the solid during dynamic partial melting ... 

The divergence of the LREE/MREE ratios from the evolution predicted by the partial melting models may indeed be partly explained by small amounts of equilibrium melt trapped as... 

Figure 23 Chondrite-normalized abundances of REEs in representative harzburgites from the Oman ophiolite (symbols—whole-rock analyses), compared with numerical experiments of partial melting performed with the Plate Model of Vemieres et al. (1997), after Godard et al. (2000) (reproduced by permission of Elsevier from Earth Planet. Set Lett. 2000, 180, 133-148). Top melting without (a) and with (b) melt infiltration. Model (a) simulates continuous melting (Langmuir et al., 1977 Johnson and Dick, 1992), whereas in model (b) the molten peridotites are percolated by a melt of fixed, N-MORB composition. Model (b) is, therefore, comparable to the open-system melting model of Ozawa and Shimizu (1995). The numbers indicate olivine proportions (in percent) in residual peridotites. Bolder lines indicate the REE patterns of the less refractory peridotites. In model (a), the most refractory peridotite (76% olivine) is produced after 21.1% melt extraction. In model (b), the ratio of infiltrated melt to peridotite increases with melting degree, from 0.02 to 0.19. Bottom modification of the calculated REE patterns residual peridotites due to the presence of equilibrium, trapped melt. Models (c) and (d) show the effect of trapped melt on the most refractory peridotites of models (a) and (b), respectively. Bolder lines indicate the composition of residual peridotites without trapped melt. Numbers indicate the proportion of trapped melt (in percent). Model parameters...

---