Effects Of The Particle Size On The Phase Transitions Of Nano-PbTiO₃ And Nano-BaTiO₃

Phase transition is always involved in the studies of the preparations, properties and applications of nanomaterials. During the phase transition process, there are great differences between the thermodynamic properties（phase transition temperature, enthalpy and entropy） of nanoparticles and those of their bulk counterparts due to the enormous surface energy of nanoparticles, and the differences mainly dependend on the nanoparticle size. Therefore, it is of important scientific and practical value to research into the influence regularity of particle size on the thermodynamics of the phase transition of nanomaterials.At first, based on the phase transition model proposed in this paper, the universal thermodynamic equation for phase transition temperature of nanoparticles and the thermodynamics equations of nanoparticles with different morphologies were deduced, and the influence regularities of size and morphology on the phase transition temperature of nanoparticles were discussed.Then, the phase transitions of lead titanate and barium titanate nanoparticles were chosen as the research system in experiment. The tetragonal lead titanate（PbTiO₃） and barium titanate（BaTi O₃） nanoparticles with different sizes were prepared by the method of sol-gel, and the particle size, crystal structure and morphology were characterized by X-ray diffractometer, fourier infrared spectrometer and scanning electron microscopy. In addition, the complex permittivity and complex permeability of nano-BaTi O₃ were measured by vector network analyzer, and the influence regularities of size on the dielectric properties were studied. The phase transition temperature, enthalpy and entropy of nano-PbTiO₃ and nano-BaTiO₃ were obtained according to the DSC curves obtained by differential scanning calorimetry. After that, the influence regularities of particle size on the thermodynamic properties of phase transition of nano-PbTiO₃ and nano-BaTiO₃ were discussed and compared with the relevant theoretical functions.The experimental results indicate that,（1） By the method of sol-gel, the tetragonal PbTiO₃ and BaTiO₃ nanoparticles with uniform size distribution and high purity are prepared by controlling the preparation conditions. The calcination temperature, reactant concentration and reaction temperature have effect on the size of PbTiO₃ and BaTiO₃ nanoparticles; the calcining temperature and the reactant concentration have major influence on the particle size, and the influence of reaction temperature is relatively small.（2） The particle size has little effect on the complex permeability of nano-BaTiO₃, the real part and the imaginary are close to 1 and 0, respectively, under different electromagnetic wave frequencies, which indicates that nano-BaTiO₃ is dielectric loss medium; with the particle size decreasing, both the complex permittivity and the dielectric loss present a downtrend.（3） The particle size of nano-PbTiO₃ and nano-Ba TiO₃ has a remarkable influence on the thermodynamic properties of phase transition. With the decrease of particle size, the phase transition temperature, enthalpy and entropy decrease, and present good liner relationships with the reciprocal of radius, respectively. And the influence regularities of particle size on the phase transition temperature obtained from experiments are consistent with the theoretical expression.The thermodynamic equations of phase transition temperature and the influence regularities of particle size on the thermodynamic properties derived in this paper can be used to explain and predict the phase transition behaviors of nanoparticles involved in the preparations and applications of nanomaterials.