equilibrium effects cannot be overstated – it is frequently a source of significant
confusion in the interpretation of CSDs. Melting of igneous rocks will probably
be more controlled by equilibrium textural processes, as it is easier to destroy a
crystal lattice than to make one. But again we must consider mechanical effects
on the crystal population. Kinetics and equilibrium are also important in
metamorphic rocks, but deformation clearly plays a more important role than
in igneous rocks. Finally, I will consider the most generally applicable constraint
on grain and crystal populations, closure: this is the fact that a rock cannot
contain more than 100% crystals or grains. As in geochemistry, this constraint is
commonly acknowledged but it is ignored (Higgins, 2002a).
3.2.1 Primary kinetic crystallisation processes
In many branches of geology the roles of kinetics and equilibrium are impor-
tant, and that is certainly the case here: kinetics will control the speed at which
crystals can nucleate and grow (or dissolve) and equilibrium will dictate the
final amount of the phases. The most common way of expressing the kinetic
effect is in terms of undercooling: a certain overstepping of equilibrium is
necessary to force the nucleation and/or growth of a new phase. However, the
amount of undercooling encountered during the crystallisation of rocks is
probably strongly dependent on the crystallisation environment and minerals
present, and is not well established so far.
The fundamental functions that control growth textures are simply
expressed: during solidification the nucleation rate is a function of time J (t),
whereas the growth rate is a function of both time and crystal size G (t,l). If
both functions are known, then the evolution of the crystal size distribution
with time, n (t,l) can be determined. Generally speaking we are more interested
in the inverse problem: that is we have measured the final crystal size distribu-
tion and we want to know the nucleation and growth rate variations during
solidification. There is no unique solution to this problem, but many attempts
have been made by making assumptions about the form of G (t,l) and J (t)
(e.g. Brandeis & Jaupart, 1987, Marsh, 1988b, Lasaga, 1998, Marsh, 1998,
Zieg & Marsh, 2002).
It is commonly overlooked that significant undercooling is not necessary for
crystallisation: equilibrium requires that the total volume of crystals will
increase during cooling. The texture of the crystals responds to equilibrium
effects to minimise the total energy of the crystal population. This process is
common and has many names: the effect on crystal size is referred to here as
coarsening (see Section 3.2.4). Hence, the final texture of most igneous rocks
will reflect some combination of kinetic and equilibrium effects.
3.2 Brief review of theory 43