The effect of a periodic growth rate on the morphological stability of a freezing binary alloy

The effect of a periodically varying growth rate on the morphological instability of a crystal growing from a binary alloy is considered using linear stability theory. We consider a planar interface with a crystal growth rate proportional to 1+? cos ?? (where ? is time) advancing into a liquid of semi-infinite extent. The linearised perturbation equations are solved by four different methods for the case when there is no meltback: (i) the solution in the limit ??0, (ii) a Fourier series expansion, (iii) the limit of the spatial wavenumber of the perturbation tending to infinity with the effect of capillarity constrained to be order one and finally, (iv) a direct numerical integration. The methods are in good agreement over their range of validity. The case of meltback,|1, is also considered using the method (iv). It is found in all cases that the system is stabilised resulting in a decrease in the critical temperature gradient of about 10% for the alloys Ge-Si, Ge-Ga, and Pb-Sn considered here