Pb nanoprecipitates in Al: magic-shape effects due to elastic strain.

We present a theory for size-dependent shapes of Pb nanoprecipitates in Al, introducing the concept of "magic shapes," i.e., shapes having near-zero homogeneous elastic strains. Our quantitative atomistic calculations of edge energies show their effect on precipitate shape to be negligible, thus it appears that shapes must be due to the combined effect of strain and interface energies. By employing an algorithm for generating magic shapes, we replicate the experimental observations by selecting magic-shape precipitates with interfacial energies less than a cutoff value.