Mass conservation and elemental fractionation - Geochemistry: An Introduction - page 28

10

Garnet

1

Plagioclase Clinopyroxene

0.1

0.01

Olivine

0.001

0.0001

Ba Th U Nb La Ce Pb Sr Nd Sm Zr Hf Eu Gd Dy Er Yb Lu

Figure 2.5 Typical partition coefficients for some important trace elements between the main minerals and

the liquid for a basalt composition.

In this equation, k is a constant related to certain elastic properties of the medium known
as Young's modulus and the Poisson ratio. A measure of the change in elastic energy U
upon compression or expansion is:

F

r 2 d r d U =− P d V =−

r 2 4

π =− F d r (2.12)

π

4

which is integrated between r 0 and r as:

k
2 (

2

U =− r − r 0 ) (2.13)

Most ions of identical charge fit in with such a parabolic relationship between the binding
energy, and therefore ln K , and their squared radius ( Fig. 2.6 ) . Measurement of the differ-
ent H values and evaluation of elastic energies are daunting tasks. Although fractionation

theory applies remarkably well to both low- and high-temperature systems, it is essential
to remember that it requires approximations, however good they may be, and that it cannot
be compared with a zero-order principle such as the conservation of mass.
If one phase plays a particular role, such as seawater or a magmatic liquid from which
minerals precipitate, the fractionation of elements can be described by taking this phase
as a reference and introducing an aggregate (bulk) solid/liquid partition coefficient D s / l
such as:

f j = 1 (2.14)

solids j