A Critical Review of Existing Criteria for the Prediction of Pyrochlore Formation and Stability

Abstract

Depending on intrinsic (e.g., radius ratio rule r/ r) and extrinsic factors (e.g., processing conditions), pyrochlore-type LnZrO oxides achieve variable degrees of structural disorder. We report on a systematic study of the structural and microstructural characteristics of the GdLn ZrO system, exploring the effect of replacing Gd with a wide range of homovalent lanthanide ions (Ln = Nd, Sm, Dy, Ho, Y, and Er; x = 0.20 and 0.80). All compositions were prepared via a mechanochemical reaction between the corresponding oxides and characterized by X-ray diffraction (standard and synchrotron sources) using the Rietveld method, as well as by Raman spectroscopy. Irrespective of chemical composition, this study reveals that all compositions exhibit a fluorite-like structure. Furthermore, by firing each sample at 800 and 1400 °C, we are able to analyze the transition to pyrochlore-like structures, featuring different degrees of disorder, in all but GdYZrO, which retains the fluorite structure even after heating. The structural data are used to assess the existing criteria for predicting the formation and stability of the pyrochlore structure; according to this analysis, the simple radius ratio rule ( r/ r), provides a useful and sufficiently robust criterion. Because the pyrochlore structure has a strong tendency to disorder, it is not possible to define an empirical index similar to the Goldschmidt tolerance factor for perovskite.

Defining the Structural Stability Field of Disordered Fluorite Oxides

“…Reynolds et al (2013) studied the long-range structure of series members between the ordered pyrochlore Gd 2 Zr 2 O 7 and disordered fluorite Tb 2 Zr 2 O 7 . Fuentes et al (2018) probed similar zirconate oxides ( A x Gd 2-x Zr 2 O 7 ) and based on the experimental data of both studies, the phase boundary for the stability field of disordered fluorite occurs at ρ a ∼ 0.756. This agrees very well with work by Clements et al (2011) who investigated a solid solution of ordered Nd 2 Zr 2 O 7 and disordered Ho 2 Zr 2 O 7 and reported a critical transformation from ordered pyrochlore to disordered fluorite that corresponds, in our phase space calculated with univalent radii, to 0.757 < ρ a < 0.760.…”

“…The ordered pyrochlore structure can be imagined as a 2 × 2 × 2 supercell of the fluorite unit cell in which the stoichiometric oxygen vacancy is ordered at a specific location creating distinct coordination polyhedra for the two cations: an 8-fold cubic polyhedron for the larger A-cation and a smaller 6-fold octahedron for the B-cation. The commonly used rule to explain or predict the boundary of the compositionally-induced transition between disordered fluorite ordered and ordered pyrochlore is when the ionic radius ratio of the 8-coordinated A-site cation (conventionally Shannon, 1976 ) and the 6-coordinated B-site cation exceeds 1.46 ( Subramanian et al, 1983 ; Minervini et al, 2000 ; Sickafus et al, 2000 ; Fuentes et al, 2018 ). Experimental and computational studies have shown that this ionic radius ratio is strongly correlated with the cation anti-site defect formation energy in A 2 B 2 O 7 ( Minervini et al, 2000 ; Sickafus et al, 2000 ) with an increased propensity for a disordered cation sublattice and a disordered fluorite structure for lower defect energies.…”

Spectroscopic insight into the interplay between structural disorder and oxidation degree in melt‐grown Ce0.5Zr0.5O2‐y compounds

“…The instability of Ce 2 Zr 2 O 7+ z pyrochlores upon oxidation and the appearance of a domain structure can be related to the evolution of the R 2 Zr 2 O 7 pyrochlores upon decreasing the lanthanide size. The pyrochlore structure is stable if 1.46≲ r ≲1.80, r being the ratio of the R 3+ and Zr 4+ ionic radii in VIII and VI coordination, respectively . As r approaches the lower limit of 1.46, increasing disorder develops in the form of cation antisite defects and anion‐vacancy population, eventually leading to a fluorite phase.…”

Kagomé networks of octahedrally coordinated metal atoms in minerals: Relating different mineral structures through octahedral tilting

“…This is an inherent source of strain in pyrochlore structures. The pyrochlore structure is usually described as an aniondeficient fluorite derivative structure with face-centred cubic ( fcc) stacking of alternating A 3 B and B 3 A metal atom layers parallel to the {111} fluorite planes (Subramanian et al, 1983;Fuentes et al, 2018;Trump et al, 2018). Both the A and B atoms form 3D kagomé arrays of anion-centred corner-connected tetrahedra, YA 4 and □B 4 (□ = vacancy) (Pannetier and Lucas, 1970) as shown in Fig.…”