Optimum growth shapes of clusters near planar interfaces

In recent papers, both analytic expressions and the results of numerical ca lculations 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 take n into consideration. These results are extended here employing the same mo del assumptions - to the determination of the shapes of sub- and super-crit ical clusters forming as the result of nucleation and subsequent growth. Th e optimum shape of the newly evolving phase is again determined by the requ irement that the work of cluster formation for a given volume of the cluste r be minimal. It is shown that for homogeneous and isotropic solids the opt imum growth shapes of sufficiently large aggregates of the newly evolving s olid phase are hemispheres. (C) 2001 Elsevier Science B.V. All rights reser ved.