Dependence of critical radius of the cubic perovskite ABO3 oxides on the radius of A- and B-site cations

Critical radius (rC) for cubic perovskite structure is an important factor affecting the migration energy of oxygen ions. The monotonic dependence of the critical radius on the ionic radii of A- and B-site cations in cubic perovskite ABO3 structure was systematically investigated by strict mathematical derivation. When the tolerance factor (t) < 1, the critical radius is a decreasing function but an increasing function with respect to the radius of A-site cation (rA) and B-site cation (rB), respectively. For the case of t > 1, there is a reverse dependence of rC on rA and rB. With respect to the case of t = 1, rC displays a decreasing function with respect to both rA and rB.