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Crystallization fronts in supercooled liquids: how rapid fronts can lead to disordered glassy solids

We determine the speed of a crystallization front as it advances into the uniform liquid phase after the system has been quenched into the crystalline region of the phase diagram.

The figure shows an example of such a front, with a hexagonal crystal on the left and the liquid phase on the right. There are two mechanisms by which fronts of this type can advance, depending on whether the liquid state is linearly stable or not. When the liquid is linearly unstable, the front speed can be calculated by applying a marginal stability criterion. As the crystallization front advances into the unstable liquid phase, the density profile behind the advancing front develops density modulations and the wavelength of these modulations is a dynamically chosen quantity. For shallow quenches, the selected wavelength is close to that of the crystalline phase and so well-ordered crystalline states are formed. However, when the system is deeply quenched, we find that this wavelength can be quite different from that of the equilibrium crystal, so the crystallization front naturally generates disorder in the system. Significant rearrangement and ageing must subsequently occur for the system to form the regular well-ordered crystal that corresponds to the free energy minimum.

Additional disorder is introduced whenever a front develops from random initial conditions. We illustrate these findings using two different models of a fluid of soft, purely repulsive particles in solution.