Potassium Disorder in the Defect Pyrochlore KSbTeO 6 : A Neutron Diffraction Study

KSbTeO6 defect pyrochlore has been prepared from K2C2O4, Sb2O3, and 15% excess TeO2 by solid-state reaction at 850 ◦C. Direct methods implemented in the software EXPO2013 allowed establishing the basic structural framework. This was followed by a combined Rietveld refinement from X-ray powder diffraction (XRD) and neutron powder diffraction (NPD) data, which unveiled additional structural features. KSbTeO6 is cubic, a = 10.1226(7) Å, space group Fd3m, Z = 8 and it is made of a mainly covalent framework of corner-sharing (Sb,Te)O6 octahedra, with weakly bonded K+ ions located within large cages. The large K-O distances, 3.05(3)–3.07(3) Å, and quite large anisotropic atomic displacement parameters account for the easiness of K+ exchange for other cations of technological importance.


Introduction
Recently, the defect pyrochlore oxide (H 3 O)SbTeO 6 has been described as an excellent proton conductor [1,2], showing a conductivity (σ) of 10 −1 S·cm −1 at 30 • C under saturated water vapor partial pressure, matching the performance of Nafion © as proton conductor for low-temperature fuel cells. Among the most promising candidates to replace Nafion, the so-called antimonic acids (of general stoichiometry HSbO 3 ·nH 2 O or Sb 2 O 5 ·nH 2 O) show a relatively high proton conductivity of~10 −4 S·cm −1 at room temperature (RT) [3], and some yttrium-doped derivatives reach conductivities as high as 10 −3 S·cm −1 [4]. An even larger σ value of 10 −1 S·cm −1 at 30 • C under saturated water vapor partial pressure was described by Turrillas et al. [5], for an original derivative of the antimonic acid obtained by partial replacement of Sb by Te, giving rise to a well-defined oxide with pyrochlore structure and composition (H 3 O)SbTeO 6 [5]. The pyrochlore structure is very appealing while searching for materials of high ionic conductivity, since its open framework containing three-dimensional interconnected channels enables H 3 O + ion diffusion. The general crystallographic formula of pyrochlore oxides is A 2 B 2 O 6 O , consisting of a covalent B 2 O 6 network of BO 6 corner-sharing octahedra with an approximate B-O-B angle of 130 • , and the A 2 O sub-lattice forming an interpenetrating network which does not interact with the former. It is well known that both A cations and O oxygens may be partially absent in defect pyrochlores with A 2 B 2 O 6 or even AB 2 O 6 stoichiometry [6].
The full characterization of the crystal structure of (H 3 O)SbTeO 6 was performed by neutron diffraction, leading to the location of the protons in the framework [1]. (H 3 O)SbTeO 6 has been prepared by ion exchange from KSbTeO 6 pyrochlore in sulfuric acid at 453 K for 12 h [1,2]. The crystal structure of KSbTeO 6 has not been described in detail, although a pioneering study reports the synthesis of the A(SbTe)O 6 pyrochlore family (A = K, Rb, Cs, Tl) [7]. The crystal structures of these oxides were defined in the Fd3m space group (No. 227), with Z = 8. For A = K, the unit-cell parameter reported is a = 10.1133(2) Å. Sb and Te atoms were defined to be statistically distributed at 16d Wyckoff sites; oxygen atoms were placed at 48f sites, and A cations at 32e (x,x,x) Wyckoff positions with x = 0.109, from XRD data [7]. In the present work, we report the ab-initio crystal structure determination of KSbTeO 6 from NPD data, followed by a Rietveld refinement from combined XRD and NPD data, yielding complementary information on the K + positions.

Experimental
KSbTeO 6 was prepared by the solid-state reaction between potassium oxalate (K 2 C 2 O 4 ), TeO 2 , and Sb 2 O 3 in a 1:2.3:1 molar ratio, providing an excess of TeO 2 to compensate for volatilization losses. The starting mixture was thoroughly ground and heated at 823, 973, 1073, and 1123 K for 24 h at each temperature, with intermediate grindings in order to ensure total reaction.
The initial product characterization was carried out by XRD with a Bruker-AXS D8 Advance diffractometer (40 kV, 30 mA) (Germany) controlled by the DIFFRACT PLUS software, in Bragg-Brentano reflection geometry, with Cu K α radiation (λ = 1.5418 Å). A nickel filter was used to remove Cu K β radiation. NPD experiments were carried out in the D2B high-resolution powder diffractometer (λ = 1.595 Å) at the Institut Laue-Langevin, in Grenoble, France. About 2 g of sample was contained in a vanadium can. The full diffraction pattern was collected in 3 h.
The crystal structure was solved ab-initio from NPD data using direct methods and the software EXPO2013 [8]. The model obtained was refined by the Rietveld method [9] with the program FULLPROF (Grenoble, France, version Nov. 2016) [10], from combined XRD and NPD data. A pseudo-Voigt function was chosen to generate the line shape of the diffraction peaks. The following parameters were refined in the final Rietveld fit: scale factor, background coefficients, zero-point error, pseudo-Voigt profile function parameters corrected for asymmetry, atomic coordinates, anisotropic atomic displacement parameters for all atoms, and the occupancy factor of the K + positions. The coherent scattering lengths of K, Sb, Te and O were 3.67, 5.57, 5.80 and 5.803 fm, respectively.

Results and Discussion
KSbTeO 6 oxide was obtained as a well-crystallized powder. The XRD pattern, shown in Figure 1, is characteristic of a pyrochlore-type structure, with a = 10.1226(7) Å. As input data for EXPO2013 [8], the unit-cell parameters, Fd3m space group symmetry and unit-cell contents were given: 8 K, 48 O and 16 Sb, due to the similar Sb and Te scattering lengths. NPD data were used for the crystal structure determination, given their monochromaticity, well-defined peak shape, and the large 2θ range covered (from 0 to 159 • ). EXPO2013 readily gave a structural model with O positions ( 1 ⁄8, 1 ⁄8,0.429) corresponding to 48f Wyckoff sites, Sb positions ( 1 ⁄2, 1 ⁄2, 1 ⁄2) corresponding to 16d sites, and two possible Wyckoff sites for K: ( 1 ⁄8, 1 ⁄8, 1 ⁄8), i.e., 8a sites; and (x,x,x), i.e., 32e sites with x = 0.248, defined in the origin choice 2 of the space group Fd3m (No 227). A combined XRD and NPD Rietveld refinement was carried out in that setting. The Sb and Te atoms were considered to be statistically distributed at ( 1 ⁄2, 1 ⁄2, 1 ⁄2) 16d Wyckoff sites, and K at (x,x,x) 32e sites. The K + ions were allowed to shift along the (x,x,x) 32e position adopting intermediate x values between those suggested by the ab-initio crystal structure determination. At the stage of refining isotropic atomic displacement parameters, x = 0.1429(6) was reached for the (x,x,x) 32e Wyckoff position after convergence, accompanied by large temperature factors (B) of 1.2(2) Å 2 .
A further fit improvement was achieved by refining anisotropic atomic displacement parameters, leading to the crystallographic data and Rietveld agreement factors gathered in Table 1.     In the final Rietveld refinement, the x parameter in the 32e position shifted to 0.126(3). Thus, K practically occupies the ( 1 ⁄8, 1 ⁄8, 1 ⁄8) 8a Wyckoff sites. The main interatomic distances and angles are shown in Table 2. Figures 1 and 2 illustrate the good agreement between the observed and calculated XRD and NPD patterns, respectively.
The Sb:Te ratio could not be refined, given the similar scattering factors (or scattering lengths for neutrons) of both elements using XRD or NPD. This ratio has to be 1:1 if K fully resides at 8a Wyckoff sites, or at 32e sites with an occupation of 1/4. The excess of TeO 2 added to compensate for volatilization losses could also result in a slight over-occupation of the position with Te; therefore, an even lower occupation of the K position would occur. To address this problem, the occupancy of K was also refined: it converged to 1 atom per formula unit, within standard deviations (see Table 1), thus confirming the 1:1 Sb:Te ratio. shown in Table 2. Figures 1 and 2 illustrate the good agreement between the observed and calculated XRD and NPD patterns, respectively. The Sb:Te ratio could not be refined, given the similar scattering factors (or scattering lengths for neutrons) of both elements using XRD or NPD. This ratio has to be 1:1 if K fully resides at 8a Wyckoff sites, or at 32e sites with an occupation of 1/4. The excess of TeO2 added to compensate for volatilization losses could also result in a slight over-occupation of the position with Te; therefore, an even lower occupation of the K position would occur. To address this problem, the occupancy of K was also refined: it converged to 1 atom per formula unit, within standard deviations (see Table 1), thus confirming the 1:1 Sb:Te ratio.    Table 2). The cage-like holes within this network contain the K + ions statistically distributed at 32e Wyckoff positions, with four times the required multiplicity to host K + ions (eight per unit cell); thus, only one in four lobes within each K + cluster shown in Figure 3 must be considered as occupied.   Table 2). The cage-like holes within this network contain the K + ions statistically distributed at 32e Wyckoff positions, with four times the required multiplicity to host K + ions (eight per unit cell); thus, only one in four lobes within each K + cluster shown in Figure 3 must be considered as occupied. The so-called (Sb,Te)O6 octahedra are in fact slightly axially distorted, but they contain six equal (Sb,Te)-O interatomic distances of 1.9338(6) Å (Table 2), which compare well with 1.96 Å, Shannon's ionic radius sum [11].
The location of K + ions at 32e Wyckoff sites has been previously reported for the ASbTeO6 series [6]. It is noteworthy that, in pioneering work on defect AB2O6 pyrochlores [12][13][14], the position of the A atoms was thought to be 8a; later on, the occupancy of (x,x,x) 32e positions, with x close to 1/8 was suggested [15][16][17]. For KSbTeO6, the present work underlines the different results obtained refining isotropic atomic displacement parameters [x(K) = 0.1429(6)], thus with K + at 32e Wyckoff sites; or anisotropic atomic displacement parameters, resulting in x(K) = 0.126(3), very close to 1/8 and thus equivalent (within experimental error) to 8a Wyckoff sites. If the K + positions are fixed at the 8a site, the Rietveld fit does not improve and the atomic displacement parameters of all atoms remain similar.
The K + coordination is shown in Figure 4, with K-O distances of 3.05 and 3.07 Å (Table 2) in a pseudooctahedral coordination to oxygen atoms. In defect AB2O6 pyrochlores, it is worth recalling that for x equal or close to zero, the A atom can be considered as coordinated to six oxygen atoms only, forming a corrugated hexagon normal to the three-fold axis along the [111] direction. For increasing x, some new A-O distances decrease in such a way that for x equal to 1/8 (8a Wyckoff position in the m Fd 3 space group), A atoms occupy the center of a wide cage formed by 18 oxygens, six of them at relatively short distances (3O + 3O′), and 12 at larger distances (3O″ + nine-additional oxygens, which are not shown in Figure 4).
In the present structural description, with x virtually 1/8, quite large anisotropic thermal ellipsoids ( Figure 4) were determined, with r.m.s. displacements of 0.324 Å and 0.172 Å along the long and short ellipsoid axes, respectively. Furthermore, the crystal structure described accounts for the large mobility of K + ions within the pyrochlore cages and the easiness of ion exchange that leads to (H3O)SbTeO6 by treatment in H2SO4 [1,2], thus enabling the conversion of the present material in a technologically important compound with exceedingly high ionic conductivity. The so-called (Sb,Te)O 6 octahedra are in fact slightly axially distorted, but they contain six equal (Sb,Te)-O interatomic distances of 1.9338(6) Å (Table 2), which compare well with 1.96 Å, Shannon's ionic radius sum [11].
The location of K + ions at 32e Wyckoff sites has been previously reported for the ASbTeO 6 series [6]. It is noteworthy that, in pioneering work on defect AB 2 O 6 pyrochlores [12][13][14], the position of the A atoms was thought to be 8a; later on, the occupancy of (x,x,x) 32e positions, with x close to 1/8 was suggested [15][16][17]. For KSbTeO 6 , the present work underlines the different results obtained refining isotropic atomic displacement parameters [x(K) = 0.1429(6)], thus with K + at 32e Wyckoff sites; or anisotropic atomic displacement parameters, resulting in x(K) = 0.126(3), very close to 1/8 and thus equivalent (within experimental error) to 8a Wyckoff sites. If the K + positions are fixed at the 8a site, the Rietveld fit does not improve and the atomic displacement parameters of all atoms remain similar.
The K + coordination is shown in Figure 4, with K-O distances of 3.05 and 3.07 Å (Table 2) in a pseudo-octahedral coordination to oxygen atoms. In defect AB 2 O 6 pyrochlores, it is worth recalling that for x equal or close to zero, the A atom can be considered as coordinated to six oxygen atoms only, forming a corrugated hexagon normal to the three-fold axis along the [111] direction. For increasing x, some new A-O distances decrease in such a way that for x equal to 1/8 (8a Wyckoff position in the Fd3m space group), A atoms occupy the center of a wide cage formed by 18 oxygens, six of them at relatively short distances (3O + 3O ), and 12 at larger distances (3O" + nine-additional oxygens, which are not shown in Figure 4).
In the present structural description, with x virtually 1/8, quite large anisotropic thermal ellipsoids ( Figure 4) were determined, with r.m.s. displacements of 0.324 Å and 0.172 Å along the long and short ellipsoid axes, respectively. Furthermore, the crystal structure described accounts for the large mobility of K + ions within the pyrochlore cages and the easiness of ion exchange that leads to (H 3 O)SbTeO 6 by treatment in H 2 SO 4 [1,2], thus enabling the conversion of the present material in a technologically important compound with exceedingly high ionic conductivity.

Conclusions
KSbTeO6 exhibits a defect pyrochlore structure defined in the cubic m Fd3 symmetry. The mainly covalent network formed by vertex-sharing (Sb,Te)O6 octahedra enables weak interatomic interactions with K + ions. A combined XRD and NPD study showed that K + occupies 32e Wyckoff sites indistinguishable (within experimental error) from 8a sites, placed in the center of a large cage determined by 6 K-O distances in the range 3.05(3)-3.07(3) Å. The quite big anisotropic atomic displacement parameters account for the easiness of ion exchange of this material to yield a product of technological importance, (H3O)SbTeO6 [2].

Conclusions
KSbTeO 6 exhibits a defect pyrochlore structure defined in the cubic Fd3m symmetry. The mainly covalent network formed by vertex-sharing (Sb,Te)O 6 octahedra enables weak interatomic interactions with K + ions. A combined XRD and NPD study showed that K + occupies 32e Wyckoff sites indistinguishable (within experimental error) from 8a sites, placed in the center of a large cage determined by 6 K-O distances in the range 3.05(3)-3.07(3) Å. The quite big anisotropic atomic displacement parameters account for the easiness of ion exchange of this material to yield a product of technological importance, (H 3 O)SbTeO 6 [2].