Could the Vegard strains govern extrinsic size effects in nanoparticles?
  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 quasispherical 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 K(Ta,Nb)O3 solid solution, where KTaO3 is a quantum paraelectric, while KNbO3 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 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 nonmonotonic one for the small (< 20 nm) elongated K(Ta,Nb)O3 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. 
A.N. Morozovska, I.S. Golovina, S.V. Lemishko, A.A. Andriiko, S.A.   Khainakov, and E.A. Eliseev
cond-mat.mtrl-sci cond-mat.mes-hall