On the strain-induced stabilization of microstructural features formed along dislocations

Capillarity-driven mass transport limits the stability of microstructures with a high surface-to-volume ratio. Fiber reinforcements, dendritic structures, and other wire-like morphologies may be susceptible to Rayleigh instabilities and to concurrent or subsequent coarsening. Decreases in the characteristic length scales of microstructures to the nanoscale make such forms of evolution and instability evident at lower values of homologous temperature, consistent with expectations based on size scaling. Herein, we present a simple continuum theory that predicts that sufficiently small second-phase wires exhibiting dislocation character are stable to both Rayleigh instabilities and coarsening. Thus, defects such as hollow-core dislocations will tend to be stabilized while a freestanding nanowire will tend to be unstable. More generally, the effects of surface-energy anisotropy and strain energy on morphological stability are evaluated in a manner that allows their individual and combined effects on stability to be assessed and mapped. Strain energy and surface/interfacial-energy anisotropy, and normalized wire radius impact the stability of a rod-like particle. The parameter S is the ratio of the minimum stable perturbation wavelength in the actual system to that in an isotropic dislocation-free reference system, λminactual/λminref ; for the reference system, S=1 for all R0 . If a dislocation is present, then S→∞ as R0→2R∗ where R∗ is the Frank radius. The values of S when R0/2R∗>1 hinge on the sign and magnitude of the surface/interfacial-energy anisotropy. [Display omitted]