Surface and bulk melting of small metal clusters

We present an analytical solution to the two-parabola Landau model, applied to melting of metal particles with sizes in the nanoscale range. The results provide an analytical understanding of the recently observed pseudo-crystalline phase of nanoscale Sn particles. Liquid skin formation as a precursor of melting is found to occur only for particles with radii, greater than an explicitly given critical radius. The size effect of the melting temperature and the latent heat has been calculated and quantitative agreement with experiments on Sn particles was found. Introduction Among the thermodynamical effects that depend on the size of the system, the depression of melting temperature when one or more dimension of a crystal is reduced to nanometer scale, is one of the best known. The melting point depression has been intensively investigated since it was experimentally discovered by Takagi [1] in 1954. Melting of small metal particles [2, 3, 4, 5] as well as semiconductor particles [6] at temperatures below the bulk melting temperature is now experimentally well established. The phenomenon was already predicted theoretically by Pawlow [7] in 1909. Since then several models have been proposed, for a review see [8, 9]. Commonly these models predict a linear relationship between the depressed melting temperature and the inverse radius of the particle owing to the increase in the role of the surface free energy. More recently, studies of ultra-fine particles have indicated that small scale systems may exhibit quantum-size effects that modify the electronic states. Observations of morphology and internal structures of ultra-fine particles show the presence of a pseudo-crystalline phase (where the particles are continuously fluctuating between different structures) [4, 10]. The pseudo-crystalline phase has been discussed theoretically by [11]. The quantum-size effects occur when the number of surface atoms Ns are comparable to the