The effect of oscillatory shear flow on step bunching

Abstract

During crystal growth, an imposed shear flow at the crystal–fluid interface can alter the conditions for the onset of morphological instability. In previous work, we studied the effect of time-independent shear flows and anisotropic interface kinetics on the morphological stability of a crystal growing from supersaturated solution. The model assumes that growth is by the motion of elementary steps, which is treated by a macroscopic anisotropic kinetic law; morphological instability corresponds to the bunching of elementary steps. Predictions from linear stability theory indicate that a solution flowing above a vicinal face of a crystal can either enhance or prevent the development of step bunches, depending on the direction of the steady shear flow in relation to the direction of step motion; this is also observed in experiments. Here we extend the linear stability analysis to include the effect of an oscillatory shear flow on the morphological stability of a crystal growing from solution and present results for a model system for a range of oscillatory shear rate amplitudes and frequencies both with and without a steady shear component. In the presence of a steady shear flow, modulation can either stabilize or destabilize the system, depending on the modulation amplitude and frequency. Numerical solutions of the linearized Navier–Stokes and diffusion equations and an approximate analytical treatment show that the flow oscillations weakens both the stabilization and destabilization induced by steady-state flow. This weakening comes from mixing of solution above the perturbed interface and a modification to the phase shift between the interface perturbation wave and the corresponding concentration and flow waves. Optimal values of modulation frequency and amplitude are found when the steady flow is destabilizing.