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Paraelectric-Ferroelectric Phase Transitions in Small Spherical Particles

2008; Taylor & Francis; Volume: 375; Issue: 1 Linguagem: Inglês

10.1080/00150190802437928

1563-5112

O. Hudák,

Dielectric materials and actuators

Abstract A transition in a spheroidal particle from the paraelectric to the ferroelectric phase as well as dynamic susceptibility are studied without approximation in the paraphase. It is assumed that the surface charge is compensated and the boundary condition for the polarisation is P = 0, i.e. with zero polarisation at the surface of the particle. There is an infinite number of resonance frequencies in the dynamic dielectric function within the quasistatic approximation. The paraphase properties of the dielectric response of the particle are discussed. The transition temperature decreases with decreasing diameter d of the particles inverse quadratically. There exists such a critical diameter that for the particles with the diameter below the critical one the ferroelectric phase is absent. Comparison of the experiment with theoretical results is carried out. Introduction of a dead layer thickness leads to a very good agreement of theory with the experiment for PbTiO 3 and to a good agreement with the experiment for BaTiO 3 . Keywords: Paraelectric-ferroelectric phase transitionsmall spherical particlesdynamic dielectric function PbTiO 3 BaTiO 3 Acknowledgment The author wishes to express his sincere thanks to V. Dvorak, J. Petzelt and I. Rychetsky, the Department of Dielectrics, Institute of Physics AS CR, Praha, for their discussions about microcomposite materials and small particle ferroelectric properties, to D. Nuzhnyy from the same Institute for his technical help with the figures, to V. Trnovcova, Department of Physics, Faculty of Materials Science and Technology, Trnava Slovak University of Technology in Bratislava, Trnava, for discussions concerning the microcomposites during the author's stay in Trnava and to V. Sepelak from the Geotechnical Institute, SAS, Kosice for discussions on ferroics. This work was supported partially by the grant VEGA 1/3042/06. This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0728-07 at the final stages of the work. The author wishes to express his sincere thanks to P. Presnajder from the Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, for his kind support.