(683e) Step Velocity of a Crystal Edge with Alternating Rows of Growth Units

The morphology of a crystal impacts bioavailability, catalytic activity, processability, etc. Mechanistic growth models have accurately predicted crystal shapes for a number of organic molecules. [1-3] A critical parameter in these models is the step velocity, i.e., the rate at which a spiral or 2D nucleus edge spreads across the surface. The step velocity depends on the density of kink sites along an edge and the net attachment rate to a kink site; kinks are favorable surface sites for attachment of growth units (atoms, molecules, etc.). [4] Determining these quantities is complicated for non-centrosymmetric crystals, as their multiple growth units can lead to complex step edge configurations.

In this work, we examine an edge with alternating rows of A and B growth units (A-B edge), which can exhibit stable and unstable behavior depending on the supersaturation and anisotropic interactions between A and B. [5] For example, the B row can actually dissolve under supersaturated conditions. We capture these phenomena in a stochastic 1D nucleation model which employs a Fokker-Planck equation to treat formation of an AB nucleus (new A and B rows). This model is used to determine the supersaturation-dependent kink density by balancing kink creation (1D nucleation) with kink annihilation (kink collisions). The resulting step velocity predictions yield great agreement with kinetic Monte Carlo simulations for various supersaturations and anisotropic interactions. We find that the step velocity undergoes a cross-over in supersaturation dependence as the edge changes from unstable to stable (via increasing supersaturation). This suggests the possibility of a supersaturation-dependent aspect ratio of spirals and 2D nuclei with an A-B edge. The step velocity model captures important changes in growth at higher supersaturations and will improve crystal shape predictions.

[1] J. Li, C.J. Tilbury, S.H. Kim, M.F. Doherty, Prog. Mater. Sci. 2016, 82, 1-38.

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

[3] P. Dandekar, Z.B. Kuvadia, M.F. Doherty, Annu. Rev. Mater. Res. 2013, 43, 359-386.

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

[5] C.J. Tilbury, M.N. Joswiak, B. Peters, M.F. Doherty, Cryst. Growth Des. 2017, 17, 2066-2088.