9.4 Partial Melting

Figure 9.02. Batch Model for Partial Melting. The ratio of the concentration (wt.%) of an element (i) in a magma relative to its initial concentration is shown as a function of the fraction of liquid that has been produced by melting. The Ci/Co values are shown on a logarithmic scale for different distribution coefficients (Di). Click on the diagram for a larger, interactive version.

If a rock partially melts and the liquid is removed, the resulting liquid is likely to have a different trace element concentration than the rock that is melting. A way to model fractionation by partial melting is to calculate the equilibrium trace element composition of the liquid (CiL) after a modest fraction of melting (F) and remove that liquid. (CiL) can be calculated using the distribution coefficient (Di) and the composition of the solid rock (CiS) using equation (1). Dividing the system into a liquid fraction (F) and a solid fraction (1-F), by mass balance we have:

(3) CiTotal = F * CiL + (1 - F) * CiS

Using equation (1) to substitute for CiS and rearranging, an equation for batch melting is obtained:

(4) CiL/CiTotal = 1 / [Di * (1 - F) + F]

Figure 9.02 is a graph of equation (4) for several values of the distribution coefficient Di. Click on the figure to see an interactive version that also includes the option to graph a couple of other partial melting models (instantaneous removal and aggregated instantaneous removal of liquid). After you look at the interactive version of Figure 9.02, answer the following questions:

1. If the distribution coefficient Di is 10, for 50% batch melting, what will be the ratio of the ratio of the weight percent of the element i in the melt relative to the weight percent of the element i in the rock before any melting?
Pick one and press "Enter" below.
9.99
3.33
1.01
0.57
0.18
0.06
0.01

2. For incompatible elements, does a 30% partial melt have a higher concentration of the trace element or a lower concentration of the trace element than the rock being melted?
Pick one and press "Enter" below.
Higher
The Same
Lower