Stability of layered bismuth compounds in relation to the structural mismatch

The relation between the stability and the structural mismatch in layered bismuth compounds, (Bi2O2)2+(An−1BnO3n+1)2−, was formulated on the basis of an elastic model. The pseudo-tetragonal lattice parameter, a, of layered bismuth compounds was estimated from the following equation, a=[aB′2ap′2(nK+1)(ap′2+aB′2nK)]12 where aB′ is the lattice parameter of the unconstrained Bi2O2 unit, aP′ the lattice parameter of the unconstrained perovskite-like unit, n the number of perovskite like layer in one structural unit, and K a constant. The change of the strain energy for ionic substitutions was estimated from the elastic relationships. It was found that the increase of n in certain component systems causes the increase of the lattice parameter, a, and the increase of the strain energy. This provides an explanation for the existence of maximum of n. New compounds, Pb3Bi4Ti6O21 (a=5.476, ba=1.000 and c=58.1 Å) and Pb4Bi4Ti7O24 (a=5.485, ba=1.000 and c=66.2 Å) were described.