(735c) Modeling Layered Crystal Growth at Different Supersaturations: Connecting Growth Regimes

Layered crystal growth occurs via steps flowing across the surface of a face and completing successive layers. These steps appear as a result of screw dislocations (spiral growth), or two-dimensional (2D) nuclei forming on the surface. The mechanism with the largest normal growth rate for that face will dominate, which is spiral growth at low supersaturation and 2D nucleation & growth at higher supersaturation. In addition, incorporation into kink sites in either mechanism can be limited by attachment kinetics or mass transport.
A mechanistic spiral growth model has been developed that performs well at
predicting the crystal habit of organic molecules grown from solution at low supersaturation1 and has also been adapted to consider 2D nucleation and growth2. In the present work, this 2D nucleation & growth model has been generalized and divided into two regimes: birth and spread, with negligible initial nucleus area, and polynuclear, with negligible nucleus growth due to rapid step annihilation. A variety of crossovers exist: 2D birth and spread to 2D polynuclear, spiral to 2D, and the crossover to mass transport-limited, which can happen from any of these regimes. These crossovers are calculated by comparing growth rates and solving for the supersaturation at which they are equal; knowledge of them allows relative growth rates to be calculated at any supersaturation for a given system, and therefore the crystal morphology can be predicted in each regime.
In calculating crossovers or relative growth rates, the rate constants for kink attachment/detachment (k+ & k-) and 2D nucleation rate prefactor (κ2D) appear, which are expensive to determine from molecular simulations. Instead, the ratio of κ2D / k- can be evaluated, adapting theory for the stationary nucleation rate3 to develop an expression for κ2D using a system-specific 2D nucleus geometry. This technique allows crossovers and relative growth rates to be calculated using parameters we can obtain through the mechanistic model, with the exception of mass transport effects that still require estimates for these rate constants. This has been applied to small centrosymmetric molecules such as naphthalene to predict crossovers and supersaturation dependent morphologies.
References
1. Snyder, R. C., & Doherty, M. F. (2009). Predicting crystal growth by spiral

motion. Proceedings of the Royal Society A: Mathematical, Physical and

Engineering Science, 465(2104), 1145-1171.

2. Lovette, M. A., & Doherty, M. F. (2012). Predictive Modeling of

Supersaturation-Dependent Crystal Shapes. Crystal Growth & Design, 12(2),

656-669.

3. Kashchiev, D. (2000). Nucleation: Basic Theory with Applications.
Butterworth-Heinemann, Oxford.