(323e) 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.