First-principles prediction of disordering tendencies in pyrochlore oxides

Using first-principles calculations, we systematically predict the order-disorder energetics of series of zirconate $({A}_{2}{\text{Zr}}_{2}{\text{O}}_{7})$, hafnate $({A}_{2}{\text{Hf}}_{2}{\text{O}}_{7})$, titanate $({A}_{2}{\text{Ti}}_{2}{\text{O}}_{7})$, and stannate $({A}_{2}{\text{Sn}}_{2}{\text{O}}_{7})$ pyrochlores. The disordered defect-fluorite structure is modeled using an 88-atom two-sublattice special quasirandom structure (SQS) that closely reproduces the most relevant near-neighbor intrasublattice and intersublattice pair-correlation functions of the random mixture. The order-disorder transition temperatures of these pyrochlores estimated from our SQS calculations show overall good agreement with existing experiments. We confirm previous studies suggesting that the bonding in pyrochlores is not purely ionic and thus electronic effects also play a role in determining their disordering tendencies. Our results have important consequences for numerous applications, including nuclear waste forms and fast ion conductors.