Step bunching on a vicinal face of a crystal growing in a flowing solution

The effect of a parallel shear flow and anisotropic interface kinetics on the onset of (linear) instability during growth from a supersaturated solution is analyzed including perturbations in the flow velocity. The model used for anisotropy is based on the microscopic picture of step motion. A shear flow (linear Couette flow or asymptotic suction profile) parallel to the crystal-solution interface in the same direction as the step motion (negative shear) decreases interface stability. For large wavenumbers k(x), the perturbed flow field can be neglected and a simple analytic approximation for the stability-instability demarcation is found. A shear flow counter to the step motion (positive shear) enhances stability and for sufficiently large shear rates (on the order of 1 s(-1)) the interface is morphologically stable. Alternatively, the approximate analysis predicts that the system is unstable if the solution flow velocity in the direction of the step motion at a distance (2k(x))(-1) from the interface exceeds the propagation rate upsilon(x) of step bunches induced by the interface perturbations. The approximate results are applied to the growth of ADP and lysozyme. For sufficiently low supersaturations, the interface is stable for positive shear and unstable for negative shear. More generally, there is a critical negative shear rate for which the interface becomes unstable as the magnitude of the shear rate increases. For a range of growth conditions for ADP, the magnitude of this critical shear rate is 2k(x) upsilon(x). Even shear rates due to natural convection may be sufficient to affect stability for typical growth conditions.