Melting and freezing of embedded nanoclusters

Small crystals are known to melt at a different temperature than the bulk; it is usually lower for freestanding nanocrystals. However, the size-dependent melting temperature is often analyzed with approximate formulas, corresponding to the limits of metastability of the solid cluster, instead of accounting for nucleation at an intermediate temperature. In addition, the advent of nanofabrication of inclusions in a host matrix adds a parameter to the problem: the different interactions of the matrix with the solid and the liquid phases. We address the issue of freezing and melting of spherical inclusions with a thermodynamically consistent model for nucleation of the new phase. The role of the matrix is included in the model through the contact angle of the liquid-solid interface on the matrix material, which strongly affects the nucleation behavior. We emphasize how the matrix curvature modifies the classical result for heterogeneous nucleation on a plane surface. The proposed formulation is simple and universal and can be easily used to analyze measurements. We illustrate the procedure on two recent experiments.