In this article we provide some perspectives on a range of pyrochlore and defect fluorite type compounds with nominal A₂B₂O₇, A₂BO₅, ABC₂O₇, and other stoichiometries. Typically, the phase transformations and stability fields in these systems are mapped as a function of the ionic radii of the A and B-site cations, e.g., the A/B cation radius ratio (r_A/r_B). This provides a useful guide to compatible structures and compositions for the development of advanced materials. Pyrochlore commonly transforms to a defect fluorite structure at high temperature in many systems; however, it is not uncommon to observe defect fluorite as the initial metastable phase at low temperature. The patterns of order-disorder observed in these materials are primarily due to the energetics of layer stacking, the defect formation and migration energies of cations and anions, or modulations of the parent cubic structure in 3 + n dimensional space. The first lead to predominantly non-cubic derivatives of the parent defect fluorite structure (e.g., zirconolite polytypes), the second control the order-disorder processes, and the latter lead to a variety of subtle additional scattering features within the cubic parent structure. Although the energetics of cation disorder and anion-vacancy disorder have become more accessible via atomistic approaches (e.g., MD and DFT), we continue to find interesting physical-chemical problems in these materials. For example, although there are significant differences in composition (Tb/Zr ratio and O content) between Tb₂Zr₂O₇ and Tb₂ZrO₅, both of which are defect fluorites, we note that the modulations found in these two compounds by electron scattering are virtually identical with regard to the direction and magnitude of displacement from the normal Bragg diffracted beams. This suggests that neither the A/B cation ratio nor the oxygen stoichiometry have a significant effect on the modulations. The general observations on the systems of compounds noted in this paper rest primarily in the context of industrial materials for nuclear waste disposal, potential applications in inert matrix fuel designs, and other important technological applications such as ionic conductivity, electrical conductivity, and magnetism. Scientific advances in these areas have been underpinned by recent advances in ion irradiation, synchrotron X-ray, neutron scattering, and modelling and simulation capabilities. Furthermore, there has been some renewed interest in natural samples, e.g., Th-U zirconolite and pyrochlore as analogues for potential host phases in nuclear waste forms. In particular, the natural pyrochlores have provided additional details with regard to radiation damage ingrowth, percolation transitions, and the relationships between accumulated dose and physical properties including hardness, elastic modulus. Specific details of the thermal annealing of these samples have also been elucidated in considerable detail.

Some AX₂ binary compounds with the fluorite structure (space group $Fm\bar{3}m$) are well-known examples of materials exhibiting transitions to ionic superconducting phases at high temperatures below their melting points. Such superionic states have been described as either highly defective crystals or part-crystal, part-liquid states where the A ions retain their crystalline order whilst the X ions undergo partial melting. However, no detailed description of the structure of these phases exists. We present here the results of our investigation of the structural changes that occur during these transitions and the structural characteristics of the resulting superionic materials. This work is based on atomic-scale molecular dynamics modelling methods as well as computational diffraction techniques. We employed a set of empirical potentials representing several compounds with the fluorite structure to investigate any potential-dependent effect. We show the importance of small-scale structure changes, with some local environments showing a hexagonal symmetry similar to what is seen in the scrutinyite structure that has been documented for example in UO₂.

Their very flexible chemistry gives oxide materials a richness in functionality and wide technological application. A specific group of oxides that have a structure related to fluorite but with less oxygen, termed anion-deficient fluorite structural derivatives and with pyrochlores being the most notable example, has been shown to exhibit a diversity of useful properties. For example, the possibility to undergo a transition from an ordered to disordered state allows these oxides to have high radiation tolerance. Atomistic-scale calculations in the form of molecular dynamics (MD) and density functional theory (DFT) have been extensively used to understand what drives this order/disorder transition. Here we give a brief overview of how atomistic-scale calculations are utilized in modeling disorder in pyrochlores and other anion-deficient fluorite structural derivatives. We discuss the modeling process from simple point defects to completely disordered structures, the dynamics during the disordering process, and the use of mathematical models to generate ordered solid-solution configurations. We also attempt to identify the challenges in modeling short range order and discuss future directions to more comprehensive models of the disordered structures.