Abstract
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.
Highlights
Fifty years ago, Aurivillius [1,2,3] discovered a family of bismuth compounds with a layer structure, and to date, more than 50 compounds are known to belong to this group
The crystal structure of Bismuth Layer-Structured Ferroelectrics (BLSF) consist of [Bi2 O2 ] layer site (Bi2) O2 ]2+ layers interleaved with pseudo-perovskite [Am−1 Bm O3m+1 ]2− units stacked along the c-axis, which can be described by a general chemical formula of (Bi2 O2 )2+ (Am−1 Bm O3m+1 )2−, where A is mono, di, trivalent ions, or a mixture of them and B is tetra, penta, hexavalent ions, or a mixture of both, and the integer m is the number of BO6 octahedral layer, taking any of the values from 1 to 5
The value of tolerance factor may be more limited in BLSF due to the structural instability between the pseudo-perovskite layer and the bismuth-oxygen layer, which is caused by the mismatching of their transverse dimension
Summary
Aurivillius [1,2,3] discovered a family of bismuth compounds with a layer structure, and to date, more than 50 compounds are known to belong to this group. As most of them were found to be ferroelectric, this group was called Bismuth Layer-Structured Ferroelectrics (BLSF), or Aurivillius compounds. Materials 2018, 11, 821 the ABO3 -type perovskite structure can be described by the tolerance factor (t), which can be expressed as [9]:. The value of tolerance factor may be more limited in BLSF due to the structural instability between the pseudo-perovskite layer and the bismuth-oxygen layer, which is caused by the mismatching of their transverse dimension
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