Melting behaviour of fractal-shaped nanoparticles (the example of Si–Ge system)

In this paper, thermodynamical approach has been used to simulate the influence of shape on phase equilibria in the two-phase-region between liquidus and solidus temperatures in case of Si–Ge alloy nanoparticles. Volumes and shapes of considered nanoparticles have been described by their effective radii and fractal dimensions, the dependence of fractal dimensions on temperature has been obtained using a simple geometrical model. It has been shown that decreasing the volume of a nanoparticle and its fractal dimension (which corresponds to nanoparticles of a more complicated shape) leads to narrowing down the temperature range of the heterogeneous region and changes the phase transition temperatures and equilibrium compositions of co-existing phases. At different temperatures, the dependences of the composition of the liquid phase differ which is explained by implementing different mechanisms of reducing the surface energy.