Crystal structure and spontaneous polarization of Bi_4-xNd _xTi₃O₁₂ studied by using neutron powder diffraction data

Crystal structural parameters of Bi_4-xNd_xTi ₃O₁₂ (BNT, x ≤ 0.25, 0.5, 0.75 and 1.0) were determined by means of neutron powder diffraction and Rietveld analysis based on the monoclinic space group of B1a1. The a-axis has been found to shrink monotonically from 5.4475(8) to 5.4100(1) with x increasing from 0 to 0.75. The orthorhombicity defined as 2(a-b)/(a+b) decreased with increasing x because the b-axis lattice parameter remained almost constant. The c-axis increases monotonically up to x ≤ 0.75. The spontaneous polarization, which is oriented along the a-axis (P_s//a), decreased from 35.4 to 28.3, 24.8 and 22.2 νC cm^-2 with x increasing from 0 to 0.25, 0.5 and 0.75, respectively as calculated by using the refined structural parameters. Thus, the substitution of Nd for Bi has been found to cause a considerable structural relaxation. Bi₃Nd₁Ti₃O₁₂ showed a considerably small a-lattice parameter of 5.4004 (1) and a very small P _s value of only 7.5 νC cm^-2 indicating that its structure is orthorhombic or close to tetragonal.