Surface and finite size effects impact on the phase diagrams, polar, and dielectric properties of (Sr,Bi)Ta₂O₉ ferroelectric nanoparticles

In the framework of the thermodynamic approach Landau-Ginzburg-Devonshire (LGD) combined with the equations of electrostatics, we investigated the effect of polarization surface screening on finite size effects of the phase diagrams, polar, and dielectric properties of ferroelectric nanoparticles of different shapes. We obtained and analyzed the analytical results for the dependences of the ferroelectric phase transition temperature, critical size, spontaneous polarization, and thermodynamic coercive field on the shape and size of the nanoparticles. The pronounced size effect of these characteristics on the scaling parameter, the ratio of the particle characteristic size to the length of the surface screening, was revealed. Also our modeling predicts a significant impact of the flexo-chemical effect (that is a joint action of flexoelectric effect and chemical pressure) on the temperature of phase transition, polar, and dielectric properties of nanoparticles when their chemical composition deviates from the stoichiometric one. We showed on the example of the stoichiometric nanosized SrBi₂Ta₂O₉ particles that except the vicinity of the critical size, where the system splitting into domains has an important role, results of analytical calculation of the spontaneous polarization have a little difference from the numerical ones. We revealed a strong impact of the flexo-chemical effect on the phase transition temperature, polar, and dielectric properties of Sr_yBi_2+xTa₂O₉ nanoparticles when the ratio Sr/Bi deviates from the stoichiometric value of 0.5 within the range from 0.35 to 0.65. From the analysis of experimental data, we derived the parameters of the theory, namely, the coefficients of expansion of the LGD functional, the contribution of flexo-chemical effect, and the length of the surface screening.