A method for parametrizing the A cation size disparity or mismatch in
ATO(3) perovskites through the A cation size variance has recently bee
n proposed and experimental studies are reviewed. (A is a mixture of t
rivalent lanthanide and divalent alkaline-earth cations.) The metal-in
sulator 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 res
ult of changing strain energies associated with small structural disto
rtions at the electronic transitions. Doping level, mean A cation radi
us, and the size variance are thus the three major parameters that con
trol electronic properties in oxygen stoichiometric perovskite oxides.