Three-dimensional domain patterns in tetragonal-to-monoclinic Bi4Ti3O12 ceramics: Nonlinear analysis and piezoresponse force microscopy imaging

Abstract

Tetragonal-to-monoclinic Bi4Ti3O12 (BIT) exhibits complicated domain patterns thanks to its two independently switchable spontaneous polarizations that lie in the ac plane of the monoclinic unit cell. Utilizing the nonlinear theory of ferroelectric phase transformation based on the deformation gradient tensor and spontaneous polarization, we systematically analyzed domain patterns in BIT, classifying its domain walls (DWs) into five different classes. Three-dimensional piezoresponse force microscopy (3D PFM) was then adopted to characterize the ceramic BIT, revealing intriguing domain patterns in planar, lateral, as well as tilted grains. Guided by the nonlinear theoretical analysis, 3D polarization distributions were successfully reconstructed, wherein 9°-, 90°-, 91°-, and 180°-DWs were observed along with 171°-charged DWs. The nonlinear analysis is thus confirmed by 3D PFM characterizations, and the combined theoretical analysis and experimental investigation contribute to our understanding on the 3D tetragonal-to-monoclinic ferroelectric domain patterns.