Size effect on the phase stability of nanostructures

An extension of the classical thermodynamics to nanometer scale has been conducted to elucidate information regarding size dependence of phase transition functions and binary phase diagrams. The theoretical basis of the extension is Lindemann's criterion for solid melting, Mott's expression for vibrational melting entropy, and Shi's model for size dependent melting temperature. These models are combined into a unified one without adjustable parameters for melting temperatures of nanocrystals. It is shown that the melting temperature of nanocrystals may drop or rise depending on interface conditions and dimensions. The model has been applied to size dependences of melting enthalpy and atomic cohesive energy, critical temperatures for glass transition, ferromagnetic transition, ferroelectric transition, superconductor transition and ferromagnetic-antiferromagnetic transition. Moreover, the above modeling has been utilized to determine the size-dependent continuous binary solution phase diagrams, bi-layer transition diagrams of metallic multilayers, and solid transition phase diagrams after modeling the transition entropy and atomic interaction energy functions of nanocrystals. Moreover, the model has been used to predict size dependence of diffusion activation energy and diffusion coefficient. These thermodynamic approachs have extended the capability of the classical thermodynamics to the thermodynamic phenomena in the nanometer regime.