The effect of a periodic growth rate on the morphological stability of a freezing binary alloy
Wheeler, A.A. (1984) The effect of a periodic growth rate on the morphological stability of a freezing binary alloy. Journal of Crystal Growth, 67, (1), 8-26. (doi:10.1016/0022-0248(84)90125-8).
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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+α cos ωť (where ť 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 α→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.
|Digital Object Identifier (DOI):||doi:10.1016/0022-0248(84)90125-8|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
|Date Deposited:||05 Apr 2004|
|Last Modified:||06 Aug 2015 02:10|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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