Subcritical Bifurcation from Planar to Cellular Interface in Al - 0.5 wt.% Cu Directionally Solidified
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ABSTRACT Samples of the Al - 0.5wt.%Cu system were directionally grown under controlled conditions, to study the role played by the instabilities in the process relatives to the microstructure selection for a given values of interface velocity, and thermal gradient. Using an interface quenching technique and metallographic analysis in longitudinal and transversal cuts of the samples, we determine the transition mechanisms between the different stages of the growth, and associate them to the stability of the solidification front. We study the planar to a cellular transition in different conditions, and although the solidification parameters are in good agreement with the perturbations theory, when analyzing the amplitude of the perturbations during the planar to a cellular transition, the same theory is not able to predict certainly the critical wavelength in this case. Also, we found a subcritical behavior during the transition from a planar to a cellular interface for the diluted Al - Cu system, detecting a hysteresis behavior for the amplitude of the perturbations when it is increasing and then decreasing the interface velocity, through the threshold. INTRODUCTION It is well known that directional solidification is one of the principal techniques for the production of advanced engineering components since it allows to control the microstructure and the properties of the material [1,2]. In the directional solidification the processing variables are the interface velocity V, thermal gradient at the interface GL, and the alloy composition Co. By keeping constant the concentration and the thermal gradient, it is possible to study the microstructure behavior against the interface velocity, that becomes the control parameter of the problem. When an impure material with atomically rough solid-liquid interface is directionally grown, it may exhibit cellular or dendritic structure of solidification front. A planar front of solidification brings a homogenous solid, while a cellular or dendritic front forms a periodic microsegregation map in it. For this reason, the instabilities of a planar front and its development into a periodic array of cells and dendrites have received a particular attention from the metallurgist [2-4]. The nature of these patterns have been explained by the competitive effect between the surface tension, the solute diffusion, and the temperature gradient. The interpretation of the system stability in the basis of "constitutional supercooling" [5,6] has been improved with a complete dynamical out of equilibrium treatment [7-9]. For these studies, in the immediate vicinity of the transition, it is possible to obtain a Landau-like equation for the amplitude Ak, corresponding to a deformation wavevector k dAk ao (k) Ak - al (k)A• (1) dt and, therefore, four different situations can be distinguished, according to the signs of the parameters ao (growth rate) and a, (Landau coefficient): 21 Mat. Res. Soc. Symp. Proc. Vol. 481 ©1998 Materials Research Society
(i) ao < 0; a, > 0: the planar front is stable;
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