Finite-size effects of lattice structure and soft mode in bismuth titanate nanocrystals

Bismuth titanate nanocrystals with grain size from 25 to 83 nm were synthesized by chemical coprecipitation via heat treatment. Lattice structures of the nanocrystals were determined by X-ray diffraction and refined by using the Rietveld method. An empirical relationship a / b ∼ 1 − e − d is established between the orthorhombic distortion ratio a / b and the grain size d , from which a critical grain size d c for vanishing of ferroelectricity of bismuth titanate nanocrystals was found to be 38 nm. Low-frequency Raman spectra were investigated at various grain sizes in the nanocrystals. The results show that the soft mode obviously softens and ferroelectricity weakens with decrease in the grain size. An empirical formula ω 2 = ω 0 2 ( 1 − d 0 / d ) is found to describe the relationship between the soft-mode frequency ω and the grain size d with two fitting parameters ω 0 = 29 cm − 1 and d 0 = 23  nm.