Critical sizes for the stabilization of coherent precipitates

Abstract

On growth of a precipitate beyond a critical size (r*), interfacial misfit dislocation loops are energetically stabilized. In the case of precipitation in (small) finite crystals, the energy of both the coherent precipitate and the dislocation loop are altered with respect to bulk crystals. Thus, as the crystal (domain) size approaches nanoscale, the critical size (r*) is expected to be altered with respect to bulk crystals. In the current investigation, finite element simulations are performed to study the variation of critical size (r*) with crystal/domain size and it is shown that below a critical domain size, the coherent precipitate is stabilized. Important findings include: (i) strain energy versus precipitate-size plot shows change in curvature for large precipitate sizes and (ii) coherent state is stable in two distinct regimes of precipitate sizes. Further, a phase diagram showing the stability regions of the coherent and semi-coherent states of the precipitate is drawn.