Experimental indications of a low undercooling instability in the cellular mechanism of discontinuous precipitation

For the formation of well formed lamellar cells during discontinuous precipitation, there must be a cooperation between the migration of the grain boundary and the morphological development of the precipitating phase. If the grain boundary velocity is greater than the velocity of the precipitate growth projected along the direction of grain boundary motion, large curvatures may develop leading to temporal oscillations in grain boundary position and/or the eventual separation of the grain boundary from many of the precipitates. For the larger undercoolings, Onsorio (10) has shown by time sequence studies that this does not occur. However, for smaller undercoolings the grain boundary is migrating faster than the projected velocity of the precipitate growth interface, the curvature of the grain boundary increases until the grain boundary separates from the precipitate decreasing the driving force for migration. The cooperation between grain boundary migration and precipitation will break down and the cellular mechanism will be unstable . We have probed the physical basis of the cellular transformation by examining changes in microstructural development as the undercooling is decreased. The expectation that the cooperative effects would break down as the system approached equilibrium (decreasing undercooling) was fulfilled. This leads us to conclude that the cellular mechanism belongs to a general class of cooperative phenomena which are observed to occur in nature and may be successfully investigated using the same general approach outlined in (3) and (4). We do not wish to convey the impression that because the cellular transformation has been grouped (by the authors) with a class of phenomena generally referred to as dissipative (11) that an entropy flux criteria is all that is needed to understand the process. On the contrary, the experimental results presented here should be thought of as guidelines to the development of a microscopic kinetic theory which predicts the onset of the cellular mechanism as the undercooling is increased. As suggested by the experiments, this would require (1) explaining why the grain boundary migrates when essentially equiaxed precipitation occurs, and (2) why the precipitation morphology becomes elongated as the undercooling is increased. In other terms, to understand the cellular transformation we need to understand the transitions from the mechanisms 1-3 as the undercooling is increased. Any application of a macroscopic non-equilibrium stability criteria should only be attempted after the kinetic theory has been sufficiently developed