Coarsening of eutectic structures during and after unidirectional growth

Abstract

Coarsening of eutectics is described by a formalism based on the concept of the “range of approached equilibrium”, ø. Essentially, ø( t) is the range within which deviations from thermodynamic equilibrium have been smoothed out to less than 1/e of their original value. It has therefore the dimension of length and it increases monotonically with time. The driving force for the smoothening is the surface energy (via the Gibbs-Thomson relation), the mechanism is diffusion (either volume or surface diffusion). A dimensional analysis leads to simple laws for ø( t), and the accurate constants in the formulae can be derived from a sineperturbation case. In the coarsening process of eutectic structures we distinguish three types of events: decay to local equilibrium, coagulation and spheroidization. The time spent for each type is estimated by comparing typical size parameters of the eutectic structure with ø( t). This procedure leads to a set of diagrams (figs. 9 and 10) from which the incubation time for each of the coarsening processes can be read for any eutectic structure. Coarsening during growth and the effect of thermal fluctuations during growth are shown to restrict the range of growth velocities where well-controlled structures can be grown, both at the low- and at the high-velocity side. When the interphase interface energy depends on the orientation of the interface, the instability conditions for needle-eutectic structures have to be adapted by an extra factor. In the last section this factor is derived and it is concluded that faceted needles can be completely stabilized against spheroidization.