Potassium Disorder in the Defect Pyrochlore KSbTeO₆: A Neutron Diffraction Study

Abstract

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 $Fd\overline{3}m$, 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.

1. Introduction

Recently, the defect pyrochlore oxide (H₃O)SbTeO₆ 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 HSbO₃·nH₂O or Sb₂O₅·nH₂O) 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 (H₃O)SbTeO₆ [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 H₃O⁺ ion diffusion. The general crystallographic formula of pyrochlore oxides is A₂B₂O₆O′, consisting of a covalent B₂O₆ network of BO₆ corner-sharing octahedra with an approximate B-O-B angle of 130°, and the A₂O′ 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 A₂B₂O₆ or even AB₂O₆ stoichiometry [6].

The full characterization of the crystal structure of (H₃O)SbTeO₆ was performed by neutron diffraction, leading to the location of the protons in the framework [1]. (H₃O)SbTeO₆ has been prepared by ion exchange from KSbTeO₆ pyrochlore in sulfuric acid at 453 K for 12 h [1,2]. The crystal structure of KSbTeO₆ has not been described in detail, although a pioneering study reports the synthesis of the A(SbTe)O₆ pyrochlore family (A = K, Rb, Cs, Tl) [7]. The crystal structures of these oxides were defined in the $Fd\overline{3}m$ 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 KSbTeO₆ from NPD data, followed by a Rietveld refinement from combined XRD and NPD data, yielding complementary information on the K⁺ positions.

2. Experimental

KSbTeO₆ was prepared by the solid-state reaction between potassium oxalate (K₂C₂O₄), TeO₂, and Sb₂O₃ in a 1:2.3:1 molar ratio, providing an excess of TeO₂ 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.

3. Results and Discussion

KSbTeO₆ 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, $Fd\overline{3}m$ 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 (⅛,⅛,0.429) corresponding to 48f Wyckoff sites, Sb positions (½,½,½) corresponding to 16d sites, and two possible Wyckoff sites for K: (⅛,⅛,⅛), 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 $Fd\overline{3}m$ (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 (½,½,½) 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) Ų. 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. Unit–cell, fractional atomic coordinates, atomic displacement parameters, refined occupancy factors and Rietveld agreement factors of KSbTeO₆ in the cubic space group $Fd\overline{3}m$ (No. 227), with Z = 8.

Crystal Data
Cubic, $Fd\overline{3}m$				X-ray radiation, λ = 1.5418 Å
				Neutron radiation, λ = 1.595 Å
a = 10.1226(7) Å				Particle morphology: powder
V = 1037.22(12) Å3				Z = 8
Rietveld Agreement Factors
XRD data				NPD data
Rp = 7.55%				Rp: 4.75%
Rwp = 11.77%				Rwp: 6.27%
Rexp = 9.11%				Rexp: 3.85%
RBragg = 3.40%				RBragg = 3.59%
χ2 = 1.67				χ2 = 2.65
1801 data points				3240 data points
Atomic Coordinates, Isotropic Atomic Displacement Parameters (Å2) and Refined Occupancy Factors
	x	y	z	Ueq	Occupancy
K	0.126(3)	0.126(3)	0.126(3)	0.060(4)	0.256(4)
Sb1	0.50000	0.50000	0.50000	0.0037(3)
Te1	0.50000	0.50000	0.50000	0.0037(3)
O1	0.42760(9)	0.12500	0.12500	0.0099(3)
Anisotropic Atomic Displacement Parameters (Å2)
	U11	U22	U33	U12	U13	U23
K	0.055(3)	0.055(3)	0.055(3)	0.025(8)	0.025(8)	0.025(8)
Sb	0.0037(3)	0.0037(3)	0.0037(3)	−0.0004(3)	−0.0004(3)	−0.0004(3)
Te	0.0037(3)	0.0037(3)	0.0037(3)	−0.0004(3)	−0.0004(3)	−0.0004(3)
O	0.0075(4)	0.0111(3)	0.0111(3)	0.0	0.0	−0.0065(4)

.

In the final Rietveld refinement, the x parameter in the 32e position shifted to 0.126(3). Thus, K practically occupies the (⅛,⅛,⅛) 8a Wyckoff sites. The main interatomic distances and angles are shown in

Table 2. Selected interatomic distances and angles for KSbTeO₆ at 298 K.

Distances (Å)
K-O (x3)	3.05(3)
K-O′ (x3)	3.07(3)
(Sb,Te)-O (x6)	1.9338(6)
Angles (°)
O-(Sb,Te)-O	86.10(3)
	93.90(3)
(Sb,Te)-O-(Sb,Te)	135.45(2)

. Figure 1 and Figure 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.

Figure 3 displays the pyrochlore structure of KSbTeO₆, which can be described as composed of a mainly covalent network of (Sb,Te)O₆ units sharing corners, with a (Sb,Te)-O-(Sb,Te) angle of 135.45(2)° (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 pseudo-octahedral 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 $Fd\overline{3}m$ 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.

4. Conclusions

KSbTeO₆ exhibits a defect pyrochlore structure defined in the cubic $Fd\overline{3}m$ 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].