Multisite models to determine the distribution of kink sites adjacent to low-energy edges

Kink sites play a critical role in crystal growth. The incorporation of a growth unit into a kink site (1) maintains the free energy of the edge constant and (2) creates another site with the same properties. These properties allow growth through successive incorporation events to proceed in a self-sustaining manner such that the equilibrium spacing between kinks is maintained on average. Traditionally the distributions of kink sites have been determined using a single-site model whereby the probabilities of encountering a kink site adjacent to an edge and encountering a disturbance along an edge are assumed equivalent. In this paper, we develop multisite models that determine the probabilities of encountering kink sites; with the requirement that they obey both properties necessary for growth through successive self-sustaining incorporation events. The probabilities determined using the multisite models diverge significantly from the single-site model for edges with intermolecular interactions ≲6k(b)T between successive molecules. The implications of these findings for the development of predictive crystal shape models and experimental analysis are discussed.