Chemical composition and tolerance factor at the morphotropic phase boundary in (Bi_0.5Na_0.5)TiO₃-based piezoelectric ceramics

A quantitative relation between the morphotropic phase boundary (MPB) composition and the tolerance factor (t) in (Bi_0.5Na_0.5)TiO₃ (BNT)-based piezoelectric ceramics was established. The t value of the MPB compositions in BNT-based ceramics is around 0.990-0.993 and is independent of the types of added compounds. In order to experimentally demonstrate it, two piezoelectric ceramic systems (1 - x)(Bi_0.5Na_0.5)TiO₃-x(Ba_1-aSr_a)TiO₃, a = 0.05 and 0.3 (BNBST5-x and BNBST30-x, x < 12%), were used. X-ray diffraction patterns and the lattice parameter investigations revealed that these two systems formed solid solutions within the studied stoichiometry and showed a rhombohedral-tetragonal phase transformation. Furthermore, both the structure analysis and electric properties measurements indicated that the MPB compositions were BNBST5-6 and BNBST30-8 and their corresponding t value were 0.9900 and 0.9903, respectively. The results confirm the relation between the MPB composition and t value and provide a method for designing new piezoelectric materials.