Size dependence of phase transition thermodynamics of nanoparticles: A theoretical and experimental study

Abstract The phase transitions of nanoparticles are involved in almost every field, which present amazing difference compared with the corresponding bulk materials. Indeed despite extensive studies into phase transition temperature, little is known about the relationships between the temperature at the maximum rate of phase transition, the phase transition enthalpy, the phase transition entropy and the particle size. Hence, it is urgent to complete the size dependence of phase transition thermodynamics of nanoparticles. In this paper, the general equation of thermodynamic properties of phase transitions for nanoparticles was presented. Then the relations of the thermodynamic properties of crystal transition and the particle size were derived based on a thermodynamics model of crystal transition. The theoretical results indicate that the particle size of nanoparticles can remarkably influence the phase transition thermodynamics: with the decreasing particle size, the phase transition temperature, the temperature at the maximum rate of phase transition, the phase transition enthalpy and the phase transition entropy decrease, which are linearly related to the reciprocal of particle size. In experiment, the phase transitions from tetragonal to cubic of nano-BaTiO 3 with different sizes were determined by means of Differential Scanning Calorimetry (DSC); then the regularities of influence of particle size on the phase transition thermodynamics were obtained. The experimental results are consistent with the above relations. The phase transition theory provides a quantitative description of phase behavior of nanoparticles.