A method for parametrizing the A cation size disparity or mismatch in ATO 3 perovskites through the A cation size variance has recently been proposed and experimental studies are reviewed. (A is a mixture of trivalent lanthanide and divalent alkaline-earth cations.) The metal−insulator transition temperature in AMnO 3 perovskites and the critical temperature in A 2 CuO 4 superconductors are both found to decrease linearly with this size variance at constant doping level and average A cation radius. This result enables a pair of quadratic relationships for the mean size and size variance effects to be proposed as the result of changing strain energies associated with small structural distortions at the electronic transitions. Doping level, mean A cation radius, and the size variance are thus the three major parameters that control electronic properties in oxygen stoichiometric perovskite oxides.
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J. Paul Attfield (1998) studied this question.