| The manufacturing of single crystals with uniform material properties is frequently hampered by the presence of morphological instabilities during the solidification of multi-component materials. Nonuniformities result from an interaction between surface morphology and the concentration gradients created by solute rejection. In order to eliminate these nonuniformities, it is necessary to suppress the instability. In the context of directional solidification, this can be done by producing materials with sufficiently low solute concentrations, or by reducing the pulling speed of the solidification.;When it is undesirable to operate within this restricted range of parameters, some other method of stabilization is necessary. In this thesis we examine the influence of time-periodic shear flows on the interfacial stability of directionally solidifying binary alloys. The flows are generated by one or two-dimensional harmonic oscillations of the crystal parallel to the mean interface position.;A linear stability analysis shows that the critical morphological number for the onset of instability may be increased when oscillations fall within a calculatable range of frequencies. In some cases the critical morphological number may be increased indefinitely by using oscillations with sufficiently large amplitude.;A strongly nonlinear equation governing the evolution of the interface in the limit of high surface energy and a weak flow is derived, and a bifurcation analysis of this equation is performed. For the two-dimensional system, it is found that oscillations with sufficiently large amplitude will change the initial bifurcation from super- to subcritical. For the three-dimensional system, it is found that subcritical instability of parallel, square and hexagonal cells is favored as the amplitude of the flow is increased. |
