was increasing linearly. Just as for the case of the open system, a length can be
derived from the slope of the CSD. However, this ‘characteristic length’ does
not have a clear physical meaning, as was the case for the open system.
Experimental or natural validation of these models is lacking – the only
system studied in detail that might replicate closed-system CSDs, the
Makaopuhi lava lake, had CSDs with constant intercept and variable slopes
(see Section 3.4.1.1; Cashman & Marsh, 1988).
3.2.2.3 Other kinetic population models
Lasaga (1998) has explored the CSDs that are produced by Gaussian-shaped
variations of nucleation and growth rates with time. He found that the growth
rate must peak before the nucleation rate reaches its maximum otherwise
totally unnatural CSDs are produced. He also showed that few CSD
models produce straight CSDs on a classical CSD diagram and that minor
variations in the parameters of the rate variations can produce significant
changes in the CSDs.
Eberl, Kile and co-workers have proposed that kinetic growth rate is
proportional to crystal size (Eberl et al., 1998, Kile et al., 2000, Eberl et al.,
2002). They based this idea on their observation that many CSDs are lognor-
mal. However, in many of their studies it is not clear if the CSDs are truly
lognormal when the data have been stereologically corrected and lower analy-
tical cut-off limits are respected. Approximately lognormal CSDs do exist
(Bindeman, 2003) and are easily produced during equilibration (see
Section 3.2.4) and this is most likely the case for their observations.
Maaloe (1989) has proposed that many CSDs are exponential and that a
growth probability model can explain this distribution. However, this effect
was not enough to explain the curvature of his CSDs and hence he also
invoked a two-stage model of crystallisation.
3.2.3 Mechanically modified textures
Populations of crystals can be modified by mechanical processes, such as
compaction, sorting and mixing. Some of these processes are closed, in that
the total mass of the system is unchanged, others are open to the addition of
crystals and magma.
3.2.3.1 Compaction and filter pressing
A common process that can change CSDs is compaction (e.g. McBirney &
Hunter, 1995, Hunter, 1996, Jerram et al., 1996, Higgins, 1998). This process
starts as mechanical compaction, in which reorganisation of the grains enables
52 Grain and crystal sizes