Universal Size Dependence of Integral Enthalpy and Entropy for Solid–Solid Phase Transitions of Nanocrystals

There is a significant effect of particle size on the solid–solid phase transition of nanocrystals, but the precise relations of integral enthalpy and entropy of phase transition with particle size have not been reported. In this paper, we deduced the fundamental equations of the integral enthalpy and entropy of solid–solid phase transitions for nanocrystals with different particle sizes, respectively. These universal and precise thermodynamic relations, free of any adjustable parameter, can precisely describe the real process of phase transition. Experimentally, we researched the phase transition from tetragonal to cubic of nano-PbTiO3with different diameters (24.8, 35.6, 41.9, 54.2, 63.7, and 70.1 nm). The regularities obtained from these experiments were consistent with the theoretical relations. There were linear relations between the integral enthalpy and entropy of solid–solid phase transition and the reciprocal of size of nanocrystals as the radius exceeds 10 nm. Our thermodynamic relations and the quantitative size-dependent regularities of solid–solid phase transition can provide references for explaining and confirming the solid–solid phase transitions involved in the real processes of preparation and application of nanocrystals.