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Perhaps the most characteristic feature
of the crystalline state is the well defined shape or morphology of crystals.
What determines the morphologies
of crystals? Or, to put it another way, which surfaces will be the most
important in the real crystal? Many attempts have been (and are still being)
made to answer this question. Here we will look briefly at two approaches:
the first is based on the energies of surfaces. Forming surfaces
obviously costs energy as bonds are broken when the crystal is cleaved,
although some of this energy will be regained when the crystal surface
relaxes as described in the previous section. And since we can model surface
structures, we can also calculate surface energies. Higher energy surfaces,
that is those that cost more in energy terms to make, would be expected
to be less important; or, to put it the other way round, those surfaces
with low energies will be dominant in the observed crystal morphology.
This idea can be put onto a firm quantitative mathematical basis, and allows
us to predict crystal morphologies. An example is shown on the below.
The predicted morphology of zircon
An alternative (and often more realistic)
approach is to investigate the energies involved in laying down additional
layers of atoms onto a pre-existing surface - the so-called 'attachment
energy'. We might expect that the higher such an energy, the greater the
rate at which atoms will be deposited on that surface. A little thought
shows, however, that the surface which is growing rapidly will not be
important in the resulting crystal morphology; for as shown schematically
on the left, as it grows, it exposes other surfaces.
This model would
indeed lead us to expect that the prevalence of surface will be inversely
dependent on the attachment energy. Once again, the attachment energy
can be calculated and the theory can be made quantitative. The image on
the left
shows resulting predicted morphologies for the case of quartz, which may
be compared with the shape of a real quartz crystal.
The level of the agreement is gratifying.
An illustration of the kinetic control of crystal morphology
The predicted morphology of quartz
Crystal growth is, however, a highly complex
phenomenon and the two approaches described above are only approximate
guides to help us understand the possible shapes that crystals might adopt.
The study of these and related processes is a very active field in contemporary
materials science research.
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