Shape of grain boundaries during phase transformations

Abstract

A simple and general formalism for the analysis of the grain boundaries in specimens solidified under local conditions of uniform temperature is presented. It is applied to two specific cases: the solidification of regular eutectics for which the growth rate is the same for all the grains and the solidification of nodular cast iron where the growth kinetics is inversely proportional to the radius of the grain. In the first situation, hyperbolic grain boundaries typical of different nucleation times are obtained. For the second case, it is shown that the specific growth kinetics leads to planar grain boundaries regardless of the nucleation times and cooling conditions. Quenched and fully solidified grain structures observed in a lead-tin alloy and in nodular cast iron are compared with the predictions of a stochastic solidification model.