The shapes of two-phase particles: the case of trapped voids in lead particles embedded in silicon

摘要

This paper examines the factors that determine the position occupied by a void associated with an embedded precipitate particle. Analytical expressions are developed for the energy changes associated with positioning the void and the precipitate at various possible locations within a cubic cavity bounded by interfaces of a single crystallographic type. The calculated energies include consideration of the void volume fraction as well as the wetting criteria to account for interfacial energetics. The results of the analysis are applied to the interpretation of previous experimental results obtained on voids associated with Pb precipitates in a Si matrix, where the precipitate and void are confined within a more complex cubo-octahedral cavity. By taking into account the volume fraction of the void and the wetting conditions for Pb on Si, it is verified that voids in Pb precipitates embedded in Si should be convex and occupy corner sites. A computer graphics analysis of three-dimensional voids and particles confined to a cubo-octahedral cavity is found to reproduce the four corner positions observed in the transmission electron microscopy images of the voids taken along a [110] direction. These are shown to be equivalent by a suitable set of symmetry operations. [References: 15]