Fig. 8. The relation between thephase transition enthalpy and the reciprocal of the particle sizes of BaTiO3 nanoparticles.
264 W. Zhang et al. / Powder Technology 308 (2017) 258–265
In conclusion, the general equation of phase transition thermody- namics of nanoparticles derived herein provides a foundation and guid- ance for the further research of the phase transition behavior. The Eqs. (20), (21) and (23) were derived based on the above general equation and a thermodynamic model of crystal transition. Furthermore, the re- lation between the temperature at the maximum rate of phase transi- tion and the particle size was interpreted by Eq. (37). The results show that the phase transition enthalpy, the phase transition entropy, the phase transition temperature and the temperature at themaximum rate of phase transition decrease with the decrease of particle size, and are linearly related to the reciprocal of particle size, respectively. This theory can quantitatively describe the size-dependent phase transition behavior of nanoparticles. The experimental results of phase transition for nano-BaTiO3 are consistent well with the above theory relations.
We are thankful to the National Natural Science Foundation of China (No. 21373147 and No. 21573157).
0.004 0.005 0.006 0.007 0.008
Fig. 9. The relation between the phase transition entropy and the reciprocal of the sizes of nano-BaTiO3.
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