Ion Doping Effects on the Lattice Distortion and Interlayer Mismatch of Aurivillius-Type Bismuth Titanate Compounds

Taking Bismuth Titanate (Bi₄Ti₃O₁₂) as a Aurivillius-type compound with m = 3 for example, the ion (W⁶⁺/Cr³⁺) doping effect on the lattice distortion and interlayer mismatch of Bi₄Ti₃O₁₂ structure were investigated by stress analysis, based on an elastic model. Since oxygen-octahedron rotates in the ab-plane, and inclines away from the c-axis, a lattice model for describing the status change of oxygen-octahedron was built according to the substituting mechanism of W⁶⁺/Cr³⁺ for Ti⁴⁺, which was used to investigate the variation of orthorhombic distortion degree (a/b) of Bi₄Ti₃O₁₂ with the doping content. The analysis shows that the incorporation of W⁶⁺/Cr³⁺ into Bi₄Ti₃O₁₂ tends to relieve the distortion of pseudo-perovskite layer, which also helps it to become more stiff. Since the bismuth-oxide layer expands while the pseudo-perovskite layer tightens, an analytic model for the plane stress distribution in the crystal lattice of Bi₄Ti₃O₁₂ was developed from the constitutive relationship of alternating layer structure. The calculations reveal that the structural mismatch of Bi₄Ti₃O₁₂ is constrained in the ab-plane of a unit cell, since both the interlayer mismatch degree and the total strain energy vary with the doping content in a similar trend to the lattice parameters of ab-plane.