Why $\mathrm{Pb}{(B,B}^{\prime }){\mathrm{O}}_3$ perovskites disorder at lower temperatures than $\mathrm{Ba}{(B,B}^{\prime }){\mathrm{O}}_3$ perovskites

Plane-wave pseudopotential calculations of total energies were performed for three ordered perovskite related supercells in each of the eight stoichiometries of ${A(B}_{1/3}{B}_{2/3}^{\prime }){\mathrm{O}}_3;$ $A=\mathrm{P}\mathrm{b},\mathrm{}\mathrm{Ba},B=\mathrm{Z}\mathrm{n},\mathrm{}\mathrm{Mg}$ and, $B^{\prime }=\mathrm{N}\mathrm{b},\mathrm{T}\mathrm{a};$ and the eight stoichiometries of ${A(B}_{1/2}{B}_{1/2}^{\prime }){\mathrm{O}}_3;$ $B=\mathrm{S}\mathrm{c},\mathrm{I}\mathrm{n}.$ A striking difference between the Pb and $\mathrm{Ba}{(B}_{1/3}{B}_{2/3}^{\prime }){\mathrm{O}}_3$ systems is that the differences in total energies for Pb systems span ranges that are roughly an order of magnitude smaller than those for the corresponding Ba systems. This indicates much lower energetic barriers to disordering in the Pb systems, consistent with experiments. We explain this trend as a consequence of enhanced $\mathrm{Pb}-\mathrm{O}$ bonding to underbonded oxygens in $B^{2+}-\mathrm{O}-B^{2+}$ environments.