A thermodynamic approach at the nanometer scale was performed for the heterogeneous nucleation inside nanocavity, and an analytical expression of the critical energy of nucleation was evaluated considering a rough ball nucleus nucleating inside nanocavity. Compared with the case of the nucleation locating on planar or convex substrate, the critical energy of nucleation inside the concave substrate is the smallest. Based on the thermodynamic and kinetic analyses, at low supersaturation, the smaller the curvature radius of cavity and/or the smaller the contact angle, the smaller the critical energy of nucleation, and the larger the nucleation rate.At high supersaturation, the nucleation rate increases with increasing the contact angle and/or increasing the curvature radius of cavity. In this way, at the low supersaturation, the heterogeneous nucleation rate is larger than the homogeneous one, as the nucleation rate is mainly determined by the heterogeneous nucleation. At the high supersaturation, the heterogeneous nucleation rate is smaller than the homogeneous one, as the nucleation rate is mainly determined by the homogeneous nucleation.
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