Disorder in Ho₂Ti_2- Zr O₇: pyrochlore to defect fluorite solid solution series

Pyrochlore (A₂B₂O₇) is an important, isometric structure-type because of its large variety of compositions and structural derivatives that are generally related to different disordering mechanisms at various spatial scales. The disordering is key to understanding variations in properties, such as magnetic behavior or ionic conduction. Neutron and X-ray total scattering methods were used to investigate the degree of structural disorder in the Ho₂Ti_2- Zr O₇ (x = 0.0-2.0, Δx = 0.25) solid solution series as a function of the Zr-content, x. Ordered pyrochlores (Fd3̄m) disorder to defect fluorite (Fm3̄m) via cation and anion disordering. Total scattering experiments with sensitivity to the cation and anion sublattices provide unique insight into the underlying atomic processes. Using simultaneous Rietveld refinement (long-range structure) and small-box refinement PDF analysis (short-range structure), we show that the series undergoes a rapid transformation from pyrochlore to defect fluorite at x ≈ 1.2, while the short-range structure exhibits a linear increase in a local weberite-type phase, C222₁, over the entire composition range. Enthalpies of formation from the oxides determined using high temperature oxide melt solution calorimetry support the structural data and provide insight into the effect of local ordering on the energetics of disorder. The measured enthalpies of mixing are negative and are fit by a regular solution parameter of W = -31.8 ± 3.7 kJ mol^-1. However, the extensive short-range ordering determined from the structural analysis strongly suggests that the entropies of mixing must be far less positive than implied by the random mixing of a regular solution. We propose a local disordering scheme involving the pyrochlore 48f to 8a site oxygen Frenkel defect that creates 7-coordinated Zr sites contained within local weberite-type coherent nanodomains. Thus, the solid solution is best described as a mixture of two phases, with the weberite-type nanodomains triggering the long-range structural transformation to defect fluorite after accumulation above a critical concentration (50% Ti replaced by Zr).