Multi-Site Models to Accurately 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 total surface energy of the edge constant and (2) creates another site with the same properties. [1] These properties allow growth through successive incorporation events to proceed in a self-sustaining manner. Traditionally the distributions of kink sites have been determined using single-site model; whereby, the probabilities of encountering a kink site adjacent to an edge and encountering a disturbance within an edge are assumed equivalent. [2] However, this assumption breaks down for edges where more roughly one out of every five sites (or more) is a disturbance.

In this presentation, we demonstrate a set of multi-site models that accurately determine the probabilities of encountering kink sites; with the requirement that they obey both properties necessary for growth through self-sustaining incorporation events. The probabilities determined using the multi-site models diverge from the classic single-site model for edges with intermolecular interaction strengths less than ~6 k_bT between successive molecules. The probability of encountering a kink site adjacent to an edge using the multi-site model and the probability of encountering a disturbance along edges on the (111) face of an FCC crystal is shown in Figure 1.

 

Figure 1. The probability of encountering a kink site on the (111) face of an FCC crystal determined using the multi-site model.  The curve marked “Disturbance” is identical to the results determined from the single-site model.

Moreover, we show that the results of the multi-site models are applicable to all faces containing two or three centrosymmetric periodic bond chains (PBCs, as defined in [3]). The implications of these findings for the development of predictive shape models and in experimental analysis are discussed.

References

[1] Vekilov, P. G., Cryst. Growth Des., 2007, 7, 2796-2810.

[2] Burton, W. K.; Cabrera, N. & Frank, F. C., Phil. Trans. Roy. Soc. A, 1951, 243, 299-358.

[3] Lovette, M. A.; Browning, A. R.; Griffin, D. W.; Sizemore, J. P.; Snyder, R. C. & Doherty, M. F., Ind. Eng. Chem. Res., 2008, 47, 9812-9833.