Liquid-drop model for the size-dependent melting of low-dimensional systems

Empirical relations are established between the cohesive energy, surface tension, and melting temperature of different bulk solids. An expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and these empirical relations, and compared with other theoretical models as well as the available experimental data in the literature. The model is then extended to understand (i) the effect of substrate temperature on the size of the deposited cluster and (ii) the superheating of nanoparticles embedded in a matrix. It is argued that the exponential increase in particle size with the increase in deposition temperature can be understood by using the expression for the size-dependent melting of nanoparticles. Superheating is possible when nanoparticles with a lower surface energy are embedded in a matrix with a material of higher surface energy in which case the melting temperature depends on the amount of epitaxy between the nanoparticles and the embedding matrix. The predictions of the model show good agreement with the experimental results. A scaling for the size-dependent melting point suppression is also proposed.