Mass conservation and elemental fractionation - Geochemistry: An Introduction - page 35

Table 2.1 Distillation processes

Parent Evolving Partition

Process a phase phase coefficient Environment

Crystallization Liquid Solid Solid/liquid Magmatic

Magma Cumulate Magma/cumulate Magmatic

Brine Salt Salt/brine Evaporitic

Melting Source rock Magma Liquid/solid Magmatic

Evaporation Solution Vapor Vapor/liquid Hydrothermal

Condensation Vapor Liquid water Liquid/vapor Atmospheric

a Add “fractional” to the term describing the process.

magma for low variations of f . Thus the precipitation of 10-20% olivine removes most of
the nickel initially present in the magma ( Fig. 2.10 ) .
Conversely, the coefficients of interest for the fractional melting in which the liquid is
progressively drawn off will be the liquid/solid fractionation coefficients. This gives the
equation:

C 0
D i

1
D i − 1

C liq = ( 1 − F ) (2.30)

f is the liquid fraction extracted, but C 0 is now the concentration of the
source (mantle, crust, etc.). In a system with a low degree of melting, which is the usual
case in nature, the value of F is close to 0. By symmetry with the foregoing reasoning,
it can be seen that the concentrations of incompatible elements, which have very high
liquid/solid partition coefficients (note the reverse order of phases), will vary greatly with
the degree of melting. As in the case of partial fusion at equilibrium, concentrations of
compatible elements remain buffered, however, by the residual solid. A simple, but crucial,
principle is inferred: melting should be preferably investigated with incompatible elements,
crystallization with compatible elements ( Fig. 2.10 ) .
Dividing (2.20) written for A by the ratio of the same equation written for B, the variable
f can be eliminated:

where F = 1 −

dln C res D A

− 1

dln C res =

(2.31)

D B

− 1

In a logarithmic plot, the so-called log-log plot, (ln C A ,ln C B ), concentrations of the dif-
ferent phases present therefore form parallel alignments. Examples of this type of relation
abound in the geochemical literature ( Table 2.1 ). An important application is the demon-
stration that mid-ocean ridge basalt chemistry can be accounted for by fractional melting
of the mantle, in which case the differential form of (2.30) applies:
dln C MORB

1

D A −

dln C res

/ 1

1

D B −

dln C MORB =

dln C res =

(2.32)

/ 1

where res stands for residue and D for the bulk-solid partition coefficients during MORB
melting.