A stochastic model for the critical length of a spiral edge

We adopt a stochastic viewpoint for the critical length lc of an edge on the side of a spiral of a crystal growing from solution at low supersaturations. It is argued that the nature of the critical length arises from a transition caused by a dynamical exchange as molecules at the edge go from a “fluid-like” coordination to a crystalline coordination. The expression for the critical length derived from such a mechanism exhibits a dependence on the energy or work required to remove a molecule from a kink site to the crystal terrace and on the supersaturation. Predictions of lc by our model compare well to stochastic simulations of spirals of a Kossel crystal, and provide reasonable order-of-magnitude estimates of spiral behavior of n-methyl urea growing from methanol.