The initial stages of the cellular reaction

Abstract

Both the nucleation process per se and the organization of nearby nuclei or precipitates formed at a given disordered grain boundary into a viable cell structure are considered. When the critical nucleus is modeled in simple fashion, based upon a rectangular parallelepiped, the rate of nucleation by the “conventional” mechanism, in which the grain boundary is essentially immobile during the nucleation process, far exceeds that by the Tu-Turnbull “pucker” mechanism, in which the grain boundary is deflected so that its plane is parallel to the habit plane of the nucleus. A more rigorous model of the critical nucleus, based upon the somewhat specialized assumption that an energy cusp facet forms at only one boundary orientation but developed without a preconceived view of the nucleus morphology, leads to this result only when the facet energy is greater than one-half the energy of a disordered grain boundary. In the reverse energetic situation, the nucleus morphology is effectively that supposed by the pucker mechanism. The initial stage of cellular growth is examined in the framework of the question: why do allotriomorphs form at disordered grain boundaries under some conditions of alloy composition and temperature and cells develop under other conditions? The conditions for the two reaction paths are established on the basis of two key ideas: the direction in which the torque term associated with a facet deflects a grain boundary meeting the edge of the facet (deduced from the considerations of Hoffman and Cahn), and the existence of a driving force for the breakaway of a grain boundary from such a junction resulting from the requirement of continuity of path to another junction located nearby.