Within the series of A(2)O(3)-HfO2 phase diagrams (A ranges in cationic radius from Lu3+ to La3+), only those from Gd2Hf2O7 to La2Hf2O7 are known to exhibit a pyrochlore phase field. For A cations smaller than Gd3+, only a disordered fluorite phase field exists. Disorder energies for the entire series of pyrochlore oxides have been determined via atomistic simulation. These energies can be correlated to the order-disorder temperatures from the phase diagrams. Consequently, we predict the. existence of hitherto unobserved pyrochlores: Dy2Hf2O7, Ho2Hf2O7, and Er2Hf2O7.