Descriptor Logic for Disorder in High-Entropy and Compositionally Complex Fluorite Oxides: A Critical Assessment

No single scalar captures disorder in high-entropy and compositionally complex fluorites. This Perspective evaluates compositional and structural descriptors by physical meaning, reference frame, covariance, and transferability. Pairwise cation mismatch contains the same information as size variance, whereas host-referenced misfit adds a reference-dependent mean-radius offset. Analysis of twenty-four published compositions from three systematic datasets illustrates the limits of configurational entropy and size variance as independent descriptors of phase formation and transport. With equal Hf, Zr, and Ce fractions, changing the host reference reverses misfit rankings and alters the host-offset term up to 78-fold. In twelve dual-phase zirconates and mixed zirconate-hafnates, the nominal rA/rB ratio correlates with phase fraction but describes neither coexisting phase, whereas measured phase compositions give non-overlapping fluorite and pyrochlore values, distinguishing descriptor limitations from inappropriate evaluation frames. Structural observables are assessed by specificity, reproducibility, and relevance. Together, these criteria and the compositional analysis define a framework that distinguishes compositional inputs, multiplicity and crystal-chemical mismatch, from their structural realization. Its purpose is to test descriptor relevance and limits rather than predict untested compositions.