Calculations of finite size effects in barium titanate

Abstract

The polarisation and permittivity of barium titanate are calculated as a function of temperature from Landau-Ginzburg-Devonshire theory, taking into account effects due to the finite volume of coherently polarising regions. For regions of less than 10 nm in diameter, in which spatially uniform thermal fluctuations of the polarisation become significant, there are marked departures from the single crystal behaviour, particularly in the vicinity of the ferroelectric phase transitions. The behaviour is similar to aspects of that reported for fine-grained ceramics and thin films, suggesting that limited coherence of the magnitude of polarisation is responsible for a reduction in the permittivity and the appearance of diffuseness of the ferroelectric phase transitions.