(323e) Multi-Site Models to Accurately Determine the Distribution of Kink Sites Adjacent to Low Energy Edges
AIChE Annual Meeting
2011
2011 Annual Meeting
Separations Division
Nucleation and Growth II
Tuesday, October 18, 2011 - 2:10pm to 2:35pm
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 kbT 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.