Effect of Vegard strains on the extrinsic size effects in ferroelectric nanoparticles

Abstract

By changing the size and the shape of ferroelectric nanoparticles, one can govern their polar properties, including their improvement in comparison with the bulk material. The shift of the ferroelectric transition temperature can reach hundreds of degrees Kelvin. A phenomenological description of these effects was proposed in the framework of Landau-Ginsburg-Devonshire (LGD) theory using the concepts of surface tension and surface bond contraction. However, this description contains a series of poorly defined parameters, and the physical nature is ambiguous. It appears that the size and shape dependences of the phase transition temperature, along with all polar properties, are defined by the nature of the size effect. Existing LGD-type models do not take into account that defect concentration strongly increases near the particle surface. In order to develop an adequate phenomenological description of size effects in ferroelectric nanoparticles, one should consider Vegard strains (local lattice deformations) originating from defect accumulation near the surface. In this paper, we propose a theoretical model that takes into account Vegard strains and performs a detailed quantitative comparison of the theoretical results with experimental ones for quasispherical ${\mathrm{KTa}}_{1\text{\ensuremath{-}}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ nanoparticles (average radius 25 nm), which reveal the essential (about 100 K) increase of the transition temperature in spherical nanoparticles in comparison with bulk crystals. From the comparison between the theory and experiment, we established the leading contribution of Vegard strains to the extrinsic size effects in ferroelectric nanoparticles. We determined the dependence of Vegard strains on the content of Nb and reconstructed the Curie temperature dependence on the content of Nb using this dependence. The dependence of the Curie temperature on the Nb content becomes a nonmonotonic one for the small (20 nm) elongated ${\mathrm{KTa}}_{1\text{\ensuremath{-}}x}{\mathrm{Nb}}_{x}{\mathrm{O}}_{3}$ nanoparticles. We established that the accumulation of intrinsic and extrinsic defects near the surface can play a key role in the physical origin of extrinsic size effects in ferroelectric nanoparticles and govern its main features.