Batch melting

Partial melting Two types of partial melting process are commonly described in the geological literature and rejpresent end-member inodels of natural processes. Batch melting, equilibrium partial meldng, describes the 

In the se of modal meldng (i.e. where the minerals contribute to the melt in propordon to their concentradoh m the rode), qn [4.8], simplifies to 

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As explained below, most melting models are highly sensitive to the D values chosen for the parent elements U and Th. For example, in the case of simple batch melting, it can be shown that the U- Pa fractionation will only depend on the partition coefficients for U as long as Dpa is essentially zero ... 

Minster JF, Allegre CJ (1978) Systemahc use of trace elements in igneous processes. Part III Inverse problem of batch melting in volcanic suites. Contrib Mineral Pehol 68 37-52 Morgan JW (1971) Convechon plumes in the lower manhe. Nature 230 42-43... 

Where c, is the concentration of an element measured at the surface, Cbt is the concentration of a stable element due to batch melting and a, is the enrichment factor due to transport. The concentrations in the melt are given by the batch melting equation. 

The composition of the melt is then estimated with a batch melting model as follows assuming that there is a total porosity of dfm+fr, where fr is the mass fraction of melt prior to this new melting event ... 

Cooper, A. R. 1986. Differences between gel-derived melts and those prepared by batch melting. In Better Ceramics Through Chemistry II, edited by Brinker, C. J. Clark, D. E. Ulrich, D. R. Mat. Res. Soc. Symp. Proc. 73 421-430. 

Figure 4.7 Assumed probability density function for the degree of melting F (top). Resulting probability density functions for the reduced solid concentration of element i upon fractional melting (middle) and batch melting (bottom) for different solid-liquid partition coefficients D,.

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... 

Table 9.1. Mineral-liquid partition coefficients used for the forward modeling of batch-melting.

Table 9.3. Synthetic example of batch-melting inverse modeling.

Albarede, F. (1983). Inversion of batch melting equations and the trace element pattern of the mantle. J. Geophys. Res., 88, 10573-83. 

It is noted that the relationship between X and F is also important to distinguish the dynamic melting model from both the batch melting and the fractional melting models (Fig. 3). 

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