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.
(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?
Yes! The concentration of element i with Di=10 in a 50% batch-melted liquid is only 18% of Ci in the original rock. You can see this in Figure 9.02 by choosing 10 for Di and moving the FL slider to 0.50. Mouse over the blue dot to see the Ci/Co value.
No. The concentration of element i with Di=10 in a 50% batch-melted liquid is only 18% of Ci in the original rock. You can see this in Figure 9.02 by choosing 10 for Di and moving the FL slider to 0.50. Mouse over the blue dot to see the Ci/Co value.
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?
Yes! The concentration of an incompatible will be higher in the magma produced by 30% partial melting than it is in the original rock. You can see this in Figure 9.02 by choosing a value for Di that is below 1 and moving the FL slider. Mouse over the blue dot to see the Ci/Co value.
No. The concentration of an incompatible will be higher in the magma produced by 30% partial melting than it is in the original rock. You can see this in Figure 9.02 by choosing a value for Di that is below 1 and moving the FL slider. Mouse over the blue dot to see the Ci/Co value.
