Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals. I. Nanoparticle size-dependent tetragonal phase stability

E. K. Akdogan, Ahmad Safari

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We propose a phenomenological intrinsic finite-size effect model for single domain, mechanically free, and surface charge compensated PbTiO3 (PT) nanocrystals with no depolarization fields, undergoing a first-order tetragonal → cubic ferrodistortive phase transition. We then derive a Landau-Devonshire type free-energy functional, which is commensurate with the solution of the free-energy equation for the polar point group 4mm, wherein the nanoparticle size (ξ) is a variable. By using experimental particle size-dependent spontaneous polarization (P→s) data for PbTiO3, we compute the Landau coefficients up to the sixth order in the range <150 nm as a function of ξ. This thermodynamic potential takes into account the size dependence of the Landau coefficients in a consistent manner, and is able to predict the size-induced phase transition as well as the metastable tetragonal phase in the cubic phase field. We then construct a free-energy density surface in ΔG-P→s-ξ space, which describes the decrease in tetragonal phase stability with decreasing ξ rigorously.

Original languageEnglish (US)
Article number064114
JournalJournal of Applied Physics
Issue number6
StatePublished - Apr 8 2007

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Thermodynamic theory of intrinsic finite-size effects in PbTiO<sub>3</sub> nanocrystals. I. Nanoparticle size-dependent tetragonal phase stability'. Together they form a unique fingerprint.

Cite this