Size-Dependent Thermodynamic Properties of Two Types of Phase Transitions of Nano-Bi₂O₃ and Their Differences

The thermostability of nanomaterials has crucial influences on their performances and applications, but the effect of regularities of particle size on the crystal transition and melting thermodynamics for the same kind of nanoparticles and the relationships of the thermodynamics between the two types of phase transitions are unclear. In this paper, we proposed a core–shell model applied to the crystal transition and melting of nanospheres, and on this basis, the equations of size-dependent thermodynamic properties for crystal transition and melting were deduced. Experimentally, we prepared nano-Bi₂O₃ with different particle diameters by the hydrothermal method and determined the crystal transition (from phase α to δ) and melting behaviors of nano-Bi₂O₃ by differential scanning calorimetry. The experimental results indicate that the effects of particle size on the two types of phase-transition thermodynamic properties of nano-Bi₂O₃ are dramatic. We found that the effect of regularities of particle size on the thermodynamic properties of the two types of phase transitions are uniform; with the particle size of nano-Bi₂O₃ decreasing, the temperatures, enthalpies, and entropies of the phase transitions decrease, the thermodynamic properties are all linearly related to the reciprocal of the particle diameter, and all of the experimental results of the two types of phase transitions are consistent with the theoretical formulas. Surprisingly, we found that the two types of phase transitions are correlative. The differences in temperature and thermodynamic properties of phase transitions between the two types of phase transitions are also size-dependent and linearly related to the reciprocal of the particle diameter. The results are consistent with the theoretical analysis. The theory and size-dependent regularities can provide important references for the preparations, researches, and applications of nano-Bi₂O₃ and other nanoparticles.