The Kinetics of Ordering in Gadolinium Zirconate: an Unusual Oxygen Ion Conductor
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599 Mat. Res. Soc. Symp. Proc. Vol. 398 01996 Materials Research Society
THE STRUCTURES - CRYSTALLOGRAPHY The fluorite structure, space group Fm3m, consists of a face-centered array of cations with anions located in tetrahedral sites between those cations [3,6]. As shown in Fig. la, cations are situated in the 4a site and anions in the 8c site. The ideal stoichiometry of fluorite is MO 2, where M is a quatravalent cation. The defect-fluorite structure of gadolinium zirconate can be described as (Gd 0 5Zr 0 5)(O0 875)2, in which the single crystallographic cation site is randomly occupied by Gd and Zr ions, at a 1:1 ratio, and, similarly, the single crystallographic anion site is randomly occupied by oxygen ions and vacancies, at a 7:1 ratio. The ordering of cations in pyrochlore, space group Fd3m, is reflected in the crystallographically distinct sites that Zr and Gd occupy: 16c and 16d, respectively. Likewise, the anions take on three distinct sites: 48f, 8a and 8b. In fully ordered Gd 2Zr 20 7 the first two of these sites are fully occupied whereas the third is vacant, Fig. lb.
Figure 1(a) The structure of fluorite
(b) The structure of pyrochlore
In addition to chemical ordering, the fluorite to pyrochlore transition is accompanied by a doubling of the lattice parameter. Furthermore, while all anions are located at the ideal centers of cation tetrahedra in the fluorite structure, the 48f oxygen of the pyrochlore structure relaxes in the direction of the smaller Zr cations and the vacant 8b anion site. Accordingly, the 48f oxygen shifts from the equivalent fluorite coordinates of 3/8, 1/8, 1/8 to x, 1/8, 1/8, where x > 3/8. Relative to fluorite, pyrochlore exhibits a number of superstructure peaks in its diffraction pattern, specifically, peaks appear where hp, kp and lp are all odd, or h0 k and lp are all even with the constraint that hp = 4n and kp, l0 = 4n + 2. The intensities of those superstructure peaks reflect the degree of ordering in the material, which, in turn, can be quantified in terms of some thermodynamically relevant order parameter. In the case of the defect-fluorite to pyrochlore transition, a cation order parameter. So~ involving cation occupancies can be readily defined. Following the notation of Warren [7] and the derivation of Moon [8], = [Gd1 6 c]- Gd 16c(F) =
cGd 16 (P)
-
Gdr 6c(F)
where [Gd1 6 c] is the site occupancy of Gd in the 16c site, Gd1 6c(F) is the expected 16c site occupancy in the fluorite phase (= 'f),and Gd1 6e(P) is the expected occupancy in the pyrochlore phase (= I). Similar order parameters can be defined for anions with respect to site occupancies (on all three anion sites) or with respect to the 48f oxygen x-coordinate. However, these are not relevant to
600
a discussion of X-ray diffraction patterns as the superstructure peak intensities are dominated by the cation order parameters. This results from the fact that, in a single-phase, partially ordered pyrochlore, superstructure peak intensities are directly proportional to the difference in scattering powers
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