LAUSR

In spite of more than 60 years of research, hundreds of publications, and dramatic influence on properties, the driving force of the formation of the polar nanoregion (PNR) in the paraelectric phase of perovskite ferroelectrics and consequent relaxor properties remains uncertain. We show that these peculiar features follow directly from the vibronic, pseudo-Jahn-Teller (PJT) theory of ferroelectricity. Due to the higher disorder (and entropy) in the paraelectric phase (created by the local PJT dynamics), as compared with the polarized phase (where the PJT dynamics is partially quenched), a small PNR of the latter with $n$ unit cells is formed in a dipole-alignment self-assembly process. It emerges encapsulated by a border layer with intermedium ordering that produces ``surface tension'' and limits its size. The thermodynamic equilibrium between the PNR and the bulk cubic phase at temperatures ${T}_{n}$, well above the phase transition ${T}_{\mathrm{C}}$, is reached by compensation of the excessive entropy contribution ${T}_{n}\mathrm{\ensuremath{\Delta}}S$ with ordering energy and the work against this surface tension. The calculations based on the vibronic theory, including the PJT induced local dipolar dynamics and intercell interactions, yield the size of PNR as a function of the temperature increments ${T}_{n}\ensuremath{-}{T}_{\mathrm{C}}$ and some crystal parameters. In accordance with experimental data, the size of the emerging PNR decreases with temperature, $n\ensuremath{\sim}{({T}_{n}\ensuremath{-}{T}_{\mathrm{C}})}^{\ensuremath{-}3}$, becoming undetectable at the Burns temperature ${T}_{\mathrm{B}}$. At temperatures ${T}_{f}$, nearer to the phase transition, the sizes of PNRs grow rapidly, and their interaction leads to the formation of the nonergodic (glasslike) phase.