We have studied diffusion controlled growth of an isolated, misfitting precipitate in a supersaturated matrix using a phase field model. Treating our simulations as computer experiments, we have critically compared our simulation results with those from Zener-Frank and Laraia-Johnson theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the ZF theory is very good for 1D systems. In 2D systems with interfacial curvature, we still get good agreement between simulations and both ZF and LJ theories, but only for large supersaturations. At small supersaturations, the growth coefficient from our simulations does converge towards that from theory, but a large gap does remain when the simulations end due to overlap of diffusion fields. An interesting finding from the simulations is the less complete realization of the Gibbs-Thomson effect during growth, particularly in more supersaturated alloys. Thus, even at the same precipitate size, the curvature effects are less severe in more supersaturated alloys.
A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.
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