9.3 Rayleigh Fractionation

Because the value of Di depends so heavily on the mineral for a single magma type like basalt, the trace element content of a rock may be used to help identify the presence of particular minerals during partial melting or the loss of particular minerals during fractional crystallization. To see what to expect for an element based on its distribution coefficient, it is helpful to look at some models of ways the liquid and crystals might be separated during melting or crystallization.

Figure 9.01. Rayleigh Fractionation. 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 the original liquid that remains during crystallization. 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 mineral is removed from contact with a magma instantaneously as it is formed, the maximum effect on the trace element composition is produced. A model of instantaneous removal can be described by the Rayleigh Fractionation equation. The Rayleigh equation gives the ratio (Ci/Co) of the concentration of a trace element (i) in the liquid, Ci, relative to the concentration of element (i) in the liquid before any fractionation has occurred, Co, as a function of the fraction, FL, of the liquid that remains and of the distribution coefficient, Di. The equation is:

(2) Ci/Co = FL (Di - 1)

Figure 9.01 shows the Rayleigh model for various values of Di and liquid fractions, FL. Click on the diagram to see a larger, interactive version. After you look at Figure 9.01, answer the following questions:

1. Which values of Di guarantee a significant decrease the concentration of trace element (i) during fractional crystallization?
Pick one and press "Enter" below.
A high (>>1) value of Di guarantees a significant decrease the concentration of trace element (i) during fractional crystallization.
A Di value of 1 guarantees aa significant decrease the concentration of trace element (i) during fractional crystallization.
A low (<<1) value of Di guarantees a significant decrease the concentration of trace element (i) during fractional crystallization.
The value of Di does not controll the concentration of trace element (i) during fractional crystallization.

2. For a distribution coefficient of 2, what will be the value of Ci/Co when only 70% of the original liquid remains?
Pick one and press "Enter" below.
0.90
0.80
0.70
0.60
0.50
0.40
0.30

3. For a distribution coefficient of 0.002, what fraction of the liquid (FL) must be crystallized for the value of Ci/Co to reach 2?
Pick one and press "Enter" below.
0.90
0.80
0.70
0.60
0.50
0.40
0.30