Size focusing in core-shell precipitates: A phase-field study

Due to their enhanced resistance to coarsening and/or creep, aluminium alloys with precipitates of two distinct phases in a core-shell morphology are of great contemporary interest. In this paper, we focus on the curious observation in two recent studies on Al-Sc-Li and Al-Yb-Li alloys that growth of the shell phase leads to a narrowing of the size distribution. We have studied this phenomenon, known as size focusing, using a theoretical framework (which extends Zener's theory of diffusional growth to a core-shell precipitate) and multi-precipitate simulations based on a phase field model. Our results yield key theoretical insights as well as conclusions with practical significance. (a) On the theoretical front, we show clearly that size focusing is a growth phenomenon: it ends when shell growth ends, and coarsening begins. (b) On the practical front, our results offer guidelines for designing alloys with narrower size distributions: size focusing is promoted in alloys with greater shell volume fractions and greater inter-precipitate spacing.