Misfit stress relaxation in composite nanoparticles

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We discuss various mechanisms of misfit stress relaxation in elastically inhomogeneous core–shell nanoparticles. For some of the mechanisms, which are the formation of a prismatic loop of misfit dislocation, the nucleation of mode I cracks in cores and shells, and the delamination of the shell, we obtain quantitative estimates for the necessary conditions of the relaxation onset. These conditions are given in terms of critical parameters of the core–shell nanoparticles. We show that in spherically symmetric core–shell nanoparticles, the formation of a prismatic loop of misfit dislocation around the core is always more preferable than the crack opening inside the core or shell, and than the shell delamination as well. At the same time, we conclude that some other alternative or preliminary mechanisms of misfit stress relaxation can occur.