Optimum growth shapes of clusters near planar interfaces

In recent papers, both analytic expressions and the results of numerical calculations were outlined allowing the determination of the optimum shape of a critical cluster forming near or at a planar interface of a solid matrix. Hereby both elastic field and surface energy contributions have been taken into consideration. These results are extended here – employing the same model assumptions – to the determination of the shapes of sub- and super-critical clusters forming as the result of nucleation and subsequent growth. The optimum shape of the newly evolving phase is again determined by the requirement that the work of cluster formation for a given volume of the cluster be minimal. It is shown that for homogeneous and isotropic solids the optimum growth shapes of sufficiently large aggregates of the newly evolving solid phase are hemispheres.