Mechanochemical Continuum Modeling of Nanovoid Nucleation and Growth in Reacting Nanoparticles

Hollow nanoparticles (NPs) are produced by void nucleation and growth during chemical reactions. However, there is no proper understanding of nucleation and growth mechanisms and their predictive modeling. Models based on the Kirkendall effect predict the process time, which is larger by orders of magnitude than in experiment. This is why some works propose that a large tensile pressure in the core causes void nucleation. Here, a continuum-mechanics approach for nucleation and growth of a nanovoid in reacting NPs based on the Kirkendall effect is developed. In contrast to previous approaches, void nucleation and the effects of stresses are treated explicitly. The void nucleation condition vs pressure, temperature, size of a vacancy, core material, and initial reaction product layer is determined, and a strong multifaceted effect of mechanics is revealed. Thus, with mechanics, a cluster consisting of four vacancies represents the supercritical nucleus. Surprisingly, the core is under compression (which eliminates fracture hypothesis), and compressive pressure and reduced temperature promote void nucleation by decreasing the equilibrium concentration of vacancies at the void surface. However, they suppress void growth by reducing the diffusion coefficients. Our model quantitatively describes the experimental results for oxidation of copper NPs. A thermomechanical loading program is suggested to accelerate and control void nucleation and growth.