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 improvements in comparison with the bulk prototypes. At that the shift of the ferroelectric transition temperature can reach as much as hundreds of Kelvins. Phenomenological description of these effects was proposed in the framework of Landau-Ginsburg-Devonshire (LGD) theory using the conceptions of surface tension and surface bond contraction. However, this description contains a series of poorly defined parameters, which physical nature is ambiguous. It is appeared 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 defects 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) originated from defects accumulation the near surface.In the paper we propose a theoretical model that takes into account Vegard strains and perform a detailed quantitative comparison of the theoretical results with experimental ones for quasi-spherical nanoparticles, which reveal the essential (about 100 K) increase of the transition temperature in spherical nanoparticles in comparison with bulk crystals. The average radius of nanoparticles was about 25 nm, they consist of KTa 1х Nb х O 3 solid solution, where KTaO 3 is a quantum paraelectric, while KNbO 3 is a ferroelectric. From the comparison between the theory and experiment we unambiguously established the leading contribution of Vegard strains into the extrinsic size effect in ferroelectric nanoparticles. We determined the dependence of * Corresponding author 1: anna.n.morozovska@gmail.com † Corresponding author 2: isgolovina@ukr.net 1 Vegard strains on the content of Nb and reconstructed the Curie temperature dependence on the content of Nb using this dependence. Appeared that the dependence of the Curie temperature on the Nb content becomes non-monotonic one for the small (< 20 nm) elongated KTa 1-х Nb х O 3 nanoparticles. We established that the accumulation of intrinsic and extrinsic defects near the surface can play the key role in the physical origin of extrinsic size effect in ferroelecric nanoparticles and govern its main features.

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

“…[34]. In particular depolarization field always decreases ferroelectric polarization and transition temperature.…”

“…Note, that an additional size dependence of the Curie temperature shift in comparison with a bulk value is possible due to the excess surface stress [29,34], flexoelectric strains and chemical pressure mechanism [41]. Namely,…”

Size effects of ferroelectric and magnetoelectric properties of semi-ellipsoidal bismuth ferrite nanoparticles

“…Such study may be very useful for science and advanced applications, because the theory of finite size effects in nanoparticles allows one to establish the physical origin of the polar and other physical properties anomalies, transition temperature and phase diagrams changes appeared with the nanoparticles sizes decrease. In particular, using the continual phenomenological approach Niepce [52], Huang et al [53,54], Ma [55], Eliseev et al [56] and Morozovska et al [57,58,59,60,61] have shown, that the changes of the transition temperatures, the enhancement or weakening of polar properties in spherical and cylindrical nanoparticles are conditioned by the various physical mechanisms, such as correlation effect, depolarization field, flexoelectricity, electrostriction, surface tension and Vegardtype chemical pressure.…”

“…It is considered that the size effects are associated either with intrinsic (mainly related to the atomic polarization) or extrinsic (stresses, microstructure, polarization screening etc.) factors [57][58][59][60]. Semi-ellipsoid height is c and lateral semi-axes are a and b.…”

Effect of Defect States on the Upconversion Emission Properties in KLu2F7Nanocrystalline

“…1b, which is consistent with Vagard's law. [23][24][25] Li + ions are expected to replace K + and Lu 3+ ions, which leads to lattice shrinking. When the doped concentration increases, the confusion trend of the cell volume could suggest the occupying of the interstitial sites of host matrix.…”