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

This paper examines the factors that determine the position occupied by a v oid associated with an embedded precipitate particle. Analytical expression s are developed for the energy changes associated with positioning the void and the precipitate at various possible locations within a cubic cavity bo unded by interfaces of a single crystallographic type. The calculated energ ies include consideration of the void volume fraction as well as the wettin g criteria to account for interfacial energetics. The results of the analys is are applied to the interpretation of previous experimental results obtai ned on voids associated with Pb precipitates in a Si matrix, where the prec ipitate and void are confined within a more complex cubo-octahedral cavity. By taking into account the volume fraction of the void and the wetting con ditions 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 analys is of three-dimensional voids and particles confined to a cubo-octahedral c avity is found to reproduce the four corner positions observed in the trans mission electron microscopy images of the voids taken along a [110] directi on. These are shown to be equivalent by a suitable set of symmetry operatio ns.