  While biological crystallization processes have been studied on the
microscale extensively, models addressing the mesoscale aspects of such
phenomena are rare. In this work, we investigate whether the phase-field theory
developed in materials science for describing complex polycrystalline
structures on the mesoscale can be meaningfully adapted to model
crystallization in biological systems. We demonstrate the abilities of the
phase-field technique by modeling a range of microstructures observed in
mollusk shells and coral skeletons, including granular, prismatic,
sheet/columnar nacre, and sprinkled spherulitic structures. We also compare two
possible micromechanisms of calcification: the classical route via ion-by-ion
addition from a fluid state and a non-classical route, crystallization of an
amorphous precursor deposited at the solidification front. We show that with
appropriate choice of the model parameters microstructures similar to those
found in biomineralized systems can be obtained along both routes, though the
timescale of the non-classical route appears to be more realistic. The
resemblance of the simulated and natural biominerals suggests that, underneath
the immense biological complexity observed in living organisms, the underlying
design principles for biological structures may be understood with simple math,
and simulated by phase-field theory.
