Li⁺ conductivity of tungsten bronze Li_xSr_1−0.5xTa₂O₆ studied by neutron diffraction analysis

Abstract

The crystal structures of tetragonal tungsten bronze, Li_xSr_1−0.5xTa₂O₆ (x = 0.08, 0.17, 0.25) were investigated by neutron diffraction analysis, focusing on the geometry of the oxide framework as well as the Li distribution. The Rietveld refinement and Fourier mapping of nuclear density indicated that Li atoms are distributed in the pentagonal and rectangular channels of the tungsten bronze lattice, which provide 15-fold and 12-fold coordinated cavities, respectively. Those cavities are interconnected to form a three-dimensional network, which can serve as the Li⁺ conduction pathway in Li_xSr_1−0.5xTa₂O₆. It is proposed that the rhombic faces of the 12-coordinated polyhedra (distorted cuboctahedra) act as the bottleneck for long-range Li⁺ migration.

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1. Introduction

Tungsten bronze type structures possess unique 1-dimensional channels running along the crystal c-axis, which is promising for the insertion/exchange of small cations such as Li⁺.^1–8 In the tetragonal tungsten bronzes (TTBs), three types of c-directional channels are found: the ab unit area (≈12.4 × 12.4 Ų) contains four pentagonal channels, two quadrangular channels, and four triangular channels, with 15, 12, and 9-coordinated cavities, respectively (Fig. 1).^9,10 The ionic conductivity of tungsten bronzes has been reported from several different phases such as A_0.6(M, Nb)O₃ (A = Sr, Ba; M = Mg, Ti), Pb_5−xK_6(1−x)Li_4(1−x)Ta₁₀O₃₀, Ba_0.22TaO_0.72, and Na_1−xH_xNbWO₆·yH₂O.^11–18 In the above, the position of mobile Li⁺ or H⁺ has been estimated diversely depending on the composition, triangular channel in Pb_5−xK_6(1−x)Li_4(1−x)Ta₁₀O₃₀ and Pb_5(1−x)Li_10xTa₁₀O₃₀,^12,15 and pentagonal channel in H_0.8Na_0.4Nb_1.2W_0.8O₆.¹⁶

Fig. 1 (a) Crystal structure of tetragonal tungsten bronze projected along c-axis, and the coordination environments of (b) A2 and (c) A1 sites, using a particular example of β-SrTa₂O₆.

Recently, lithiation of the TTB oxide β-SrTa₂O₆ was accomplished by a solid state ion exchange of Sr²⁺ → 2Li⁺.¹⁹ The ionic conductivity of Li_xSr_1−0.5xTa₂O₆, as a function of Li content, 0 < x ≤ 0.31, was highest for x ≈ 0.17 (σ = 10⁻⁵ Ω⁻¹ cm⁻¹ at 540 K). The scanning and transmission electron microscopic studies strongly suggested that the Li⁺/Sr²⁺ diffusion in Li_xSr_1−0.5xTa₂O₆ occurred along the channel direction (c-axis). As the Sr²⁺ ions in β-SrTa₂O₆ occupy the pentagonal and tetragonal channels, it can be conjectured that Li⁺ ions enter either or both of the above sites, although the distribution of Li⁺ has not been definitely judged for Li_xSr_1−0.5xTa₂O₆.

For better understanding the cation exchange process and the ionic transport in Li_xSr_1−0.5xTa₂O₆, neutron powder diffraction was carried out for three different compositions, x = 0.08, 0.17, and 0.25. The Rietveld refinement and Fourier mapping of the nuclear scattering density were performed, focusing on the Li⁺ locations in Li_xSr_1−0.5xTa₂O₆. It is shown that the 12-coordinate cavities inside the quadrangular channel of Li_xSr_1−0.5xTa₂O₆ are capped with six rhombic faces, the size of which varies along the progress of the lithiation, possibly impacting on the activation barrier of the ion hopping.

2. Experimental

The tungsten bronze oxide β-SrTa₂O₆ was prepared via a solid state reaction using SrCO₃ (Alfa Aesar, 99.95%) and Ta₂O₅ (Alfa Aesar, 99.95%), with a final heating temperature of 1673 K.²⁰ For preparing Li_xSr_1−0.5xTa₂O₆ (x = 0.08, 0.17, and 0.25), a mixture of polycrystalline Li₂CO₃ (Aldrich, 99.99%) and β-SrTa₂O₆ was heated to 873 K in air for 12 h. After heating, the sample was rinsed with distilled water, and dried in air at 328 K for 12 h.¹⁹ The Li concentration of the product sample was controlled by varying the Li : Sr ratio in the starting reactant mixture. The chemical analysis, lattice constants, and ionic conductivity of Li_xSr_1−0.5xTa₂O₆ were reported in a previous work.¹⁹

Powder neutron diffraction (ND) was measured for Li_xSr_1−0.5xTa₂O₆ (x = 0.08, 0.17, and 0.25) in the powder diffractometer, Echidna, at the Australian Nuclear Science Technology Organisation's OPAL facility. The ND data was recorded using ≈2 g of powder sample loaded in a vanadium can, with λ = 2.4395 Å over the 2θ range, 10–164°, at a step size 0.05°. The Rietveld refinement and Fourier map calculation were carried out using the GSAS-EXPGUI software suite.^21,22

3. Results and discussion

Fig. 2 shows the ionic conductivity of Li_xSr_1−0.5xTa₂O₆ as a function of x, measured in the temperature range 298–540 K. The above data were acquired in the dry N₂ atmosphere and represent the Li⁺ conductivity (σ_Li) of Li_xSr_1−0.5xTa₂O₆. Notably, the maximal σ_Li occurred around x = 0.17, which was interpreted as the compromise between structural and compositional factors. The increase of Li content in Li_xSr_1−0.5xTa₂O₆ accompanied the contractions of the ab-dimension and hence the cross-sectional area of the potential Li pathways. That is, the increase of carrier concentration was likely counteracted by the decrease of carrier mobility.

Fig. 2 Temperature-dependent ionic conductivity of Li_xSr_1−0.5xTa₂O₆ (x = 0.08, 0.17, 0.25, and 0.31) measured in N₂.

Although the previous study by synchrotron X-ray diffraction (XRD) determined the crystal symmetry and lattice constants of Li_xSr_1−0.5xTa₂O₆,¹⁹ the detailed information on Li occupancy could not be obtained mainly due to its insignificant scattering power. As a complementary approach, neutron powder diffraction was employed here. The neutron scattering length (b) of Li is of comparable magnitude to those of other elements contained in Li_xSr_1−0.5xTa₂O₆,^23,24 which makes the ND data useful for the structural study.

It was supposed that Li_xSr_1−0.5xTa₂O₆ had quite similar structures to that of β-SrTa₂O₆, and therefore the neutron Rietveld refinements of Li_xSr_1−0.5xTa₂O₆ used a structure model based on β-SrTa₂O₆ (Fig. 1).²⁰ In practice, the Rietveld refinement of Li_xSr_1−0.5xTa₂O₆ was conducted in a semi-constrained manner. While the lattice constants and all the atomic positions were fully refined, the site occupancies for Sr/Li were subjected to two constraints. First, the amounts of Li and Sr were fixed according to the result of chemical analysis for three samples, which were Li_0.08Sr_0.96Ta₂O₆, Li_0.17Sr_0.92Ta₂O₆, and Li_0.25Sr_0.88Ta₂O₆, respectively. Second, Li was distributed only to pentagonal and quadrangular channels, i.e., the A2 and A1 sites shown in Fig. 1.

Fig. 3 shows, as an example, the refinement profile for Li_0.08Sr_0.96Ta₂O₆, and Table 1 lists the corresponding atomic parameters. The plots for x = 0.17 and 0.25, and the associated structural parameters are included in ESI.† Fig. 4 summarizes the structural evolutions upon the Li introduction to β-SrTa₂O₆. The unit cell volume of Li_xSr_1−0.5xTa₂O₆ gradually decreased with increasing x (Fig. 4c), which confirmed the observation from the previous XRD study.¹⁹ Such a result is attributed mainly to the smaller size of Li⁺ as compared with Sr²⁺.²⁵

Fig. 3 Neutron Rietveld refinement of Li_0.08Sr_0.96Ta₂O₆ (R_wp = 5.94%, R_p = 4.72%, χ² = 1.25).

Table 1 Atomic parameters of Li_0.08Sr_0.96Ta₂O₆ obtained from neutron Rietveld refinement^a

Atom		x	y	z	Uiso (Å^2)	occ
a Space group Pnam (Z = 10), a = 12.3604(3) Å, b = 12.4137(4) Å, c = 7.7207(2) Å.b Sr1 site corresponds to quadrangular cavity (A1 in Fig. 1); Sr2 and Sr3 sites correspond to pentagonal cavity (A2 in Fig. 1).c Fixed.d Occupancy factors (occ) for Sr1, Sr2, and Sr3 sites represent the combined contribution from Sr and Li, and are expressed in terms of the neutron scattering length of Sr.
Sr1^b	4c	0.997(1)	0.001(2)	0.25	0.001^c	0.581(7)^d
Sr2^b	4c	0.3487(8)	0.1859(9)	0.25	0.015^c	0.885(4)^d
Sr3^b	4c	0.3374(8)	0.1869(1)	0.75	0.015^c	0.885(4)^d
Ta1	4b	0	0.5	0.5	0.0015^c	1
Ta2	8d	0.0735(4)	0.2080(4)	0.4985(8)	0.0015^c	1
Ta3	8d	0.2860(4)	0.4242(4)	0.5049(9)	0.0015^c	1
O1	4c	0.9824(8)	0.4721(8)	0.25	0.0174(9)	1
O2	4c	0.0525(8)	0.2195(10)	0.25	0.0174(9)	1
O3	4c	0.1121(9)	0.1914(8)	0.75	0.0174(9)	1
O4	4c	0.3199(7)	0.4201(9)	0.25	0.0174(9)	1
O5	4c	0.2726(8)	0.4143(10)	0.75	0.0174(9)	1
O6	8d	0.2234(5)	0.2743(5)	0.4767(8)	0.002(1)	1
O7	8d	−0.0006(6)	0.3463(6)	0.5385(9)	0.019(1)	1
O8	8d	0.3414(6)	0.0066(6)	0.5361(9)	0.019(1)	1
O9	8d	0.1344(6)	0.0621(6)	0.468(1)	0.027(1)	1
O10	8d	0.4353(7)	0.3537(6)	0.530(1)	0.027(1)	1

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Fig. 4 Lattice evolution upon the Li⁺/Sr²⁺ ion exchange in β-SrTa₂O₆: (a) a, b parameters, (b) c parameter, and (c) unit cell volume.

In the neutron Rietveld refinement, it was of main interest to examine the occupancies (occ) of A1 and A2 sites. The model structure of β-SrTa₂O₆, which is an orthorhombic TTB, is rather complex and includes a large number of structural variables.²⁰ Partly because of such a complexity, the site occupancies of Li_xSr_1−0.5xTa₂O₆ were refined under the aforementioned constraints.

The coherent neutron scattering lengths of Li and Sr are −1.90 fm and 7.02 fm, respectively. Therefore, either the Li population or the Sr vacation will only decrease the nuclear density for a given site (A1 or A2). Fig. 5 shows the effective neutron scattering lengths (b_eff) for the A1 and A2 sites, where b_eff = 7.02 × occ(Sr) − 1.90 × occ(Li). With the increase of x in Li_xSr_1−0.5xTa₂O₆, the b_eff(A1) decreased more rapidly than b_eff(A2). It implies that the Sr²⁺ → 2Li⁺ exchange occurred more frequently in the quadrangular channel than in the pentagonal channel, and also that Li⁺ preferred the A1 site. Such a result is reasonable when considering the small size of Li⁺. In fact, there were several cases where Li⁺ occupied even the 9-coordinated A3 site within the triangular channel.^9,12,15

Fig. 5 Effective neutron scattering lengths (b_eff) evaluated for Sr/Li sites, A1 and A2, in Li_xSr_1−0.5xTa₂O₆ (x = 0, 0.08, 0.17, and 0.25).

The orthorhombic distortion of β-SrTa₂O₆ was lessened by the Li/Sr exchange, and this can also be attributed to the size effect. The A1 site of β-SrTa₂O₆ is somewhat smaller than Sr²⁺. As a quick indicator, the bond valence sum (BVS) for Sr, when located at the A1 site of β-SrTa₂O₆, is calculated to be 2.53 valence units²⁰ and the corresponding value becomes even larger in Li_xSr_1−0.5xTa₂O₆. On the other hand, Li is grossly underbonded at the A1 site in Li_xSr_1−0.5xTa₂O₆, with BVS values of ≈0.5. Therefore, it is presumed that the Li/Sr mixing and disorder on the A1 site could alleviate the orthorhombic distortion. In this respect, it is noteworthy that Li_xSr_1−0.5xTa₂O₆ may have rather complex local structures. In particular, it is highly probable that Li is displaced from the ideal A1 site, and/or that the A1-centered polyhedra are distinctly relaxed depending on the cation occupancy (Sr, Li, or vacancy).

To examine whether it is legitimate to rule out the occupation of the A3 site by Li, Fourier nuclear density calculation was employed. Table 2 briefly lists the most prominent peaks from the observed (ρ_obs) and difference (ρ_diff = ρ_obs − ρ_calc) profiles for Li_0.08Sr_0.96Ta₂O₆, Li_0.17Sr_0.92Ta₂O₆, Li_0.25Sr_0.88Ta₂O₆, and β-SrTa₂O₆. Fig. 6 shows the two-dimensional contour diagrams of ρ_diff, taken for the ab-plane with z = 1/4 which corresponds to the c-axial height of the A1, A2, and A3 sites. In each of the above four phases, the maximum and minimum values of ρ_diff were significantly smaller than the respective ρ_obs values. This supports the reliability of the Rietveld analysis. Particularly the absence of the notable minima (negative peak) around the A3 site strongly indicates that Li resides mostly on A1 or A2 sites.²⁶

Table 2 Nuclear scattering density (fm Å⁻³) at the peaks identified from the observed (ρ_obs) and difference (ρ_diff) Fourier profiles

	β-SrTa2O6	Li0.08Sr0.96Ta2O6	Li0.17Sr0.92Ta2O6	Li0.25Sr0.88Ta2O6
ρobs, max	1.690	1.702	1.684	1.679
ρobs, min	−0.505	−0.448	−0.405	−0.414
ρdiff, max	0.028	0.033	0.078	0.079
ρdiff, min	−0.025	−0.028	−0.067	−0.069

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Fig. 6 Difference Fourier nuclear density for Li_xSr_1−0.5xTa₂O₆: (a) x = 0.08 and (b) x = 0.17. Each contour diagram shows an area of 13 × 13 Å centered at (1/2, 1/2, 1/4) and perpendicular to c.

Based on the Rietveld refinement, the Li⁺ conduction pathways in Li_xSr_1−0.5xTa₂O₆ can be proposed as follows. Both A1 and A2 sites are partially filled with Li and Sr, while the A1 site has the greater vacancy fraction than A2 (Fig. 5). Apparently the Li⁺ hopping may occur along the c-axis, that is, between A2 sites through a pentagonal window or between A1 sites through a quadrangular window. But such a migration is not likely to extend to a long range due to the presence of intervening Sr. On the other hand, the A1 and A2 sites also share faces with each other in the ab-plane. Each A1 site is capped with six pseudo-rhombic faces, four of which are shared by A2-centered polyhedra. Meanwhile, each A2 site is immediately surrounded by two A1 sites and three A3 sites on the ab-plane. Therefore, a three-dimensional network of Li⁺ pathway can be suggested as shown in Fig. 7a, where all the A1 and A2 sites are interconnected with one another. Here, the pseudo-rhombic faces of the A1-centered polyhedra are considered to be potential bottlenecks for the Li⁺ migration.

Fig. 7 (a) Two-dimensional connectivity among the A1 and A2 cavities in the TTB lattice and (b) window sizes of the A1-centered polyhedra, represented by the diagonal lengths of the rhombic faces. In (a) open pentagons and squares represent the vertical channels running along c-axis.

Fig. 7b compares the window sizes, represented by the two diagonal lengths, of the rhombic faces adjoining A1 and A1 sites (along 〈001〉), and those adjoining A1 and A2 sites (along 〈120〉 or 〈210〉). In β-SrTa₂O₆ and Li_0.08Sr_0.92Ta₂O₆, the four faces between A1 and A2 sites were similar in size and were more distorted than those between A1 sites. However, in the phases with x = 0.17 and 0.25, the A1-centered polyhedra (distorted cuboctahedra) were formed with more irregular shapes. In any case, the rhombic windows, either the A1–A2 or A1–A1 types, were smaller than the pentagonal window between two A2 sites. This implies that the Li⁺ hopping should be faster in the c-direction than in the ab-plane. However, it should be reminded that the long range Li⁺ migration in Li_xSr_1−0.5xTa₂O₆ will necessarily include the hopping between A1 and A2 sites. As the Li content in Li_xSr_1−0.5xTa₂O₆ increases, the A1–A2 window gets smaller, which seems to be in part responsible for the decrease of the overall Li⁺ mobility. Moreover, the increase of Li content concurrently removes the vacancy of the A1/A2 sites, for instance, from Li_0.08Sr_0.96□_0.16Ta₂O₆ (x = 0.08) to Li_0.25Sr_0.88□_0.07Ta₂O₆ (x = 0.25). In this regard, the observed variation of σ_Li in Li_xSr_1−0.5xTa₂O₆ can be explained by taking into account the carrier concentration, site availability, and the activation of carrier migration. It is suggested that the ionic conductivity of the TTB phase would be optimized far below the full occupation of the A1 and A2 sites, and also by using a composition that can provide enlarged windows for the A1-centered cavities.

4. Conclusions

Neutron Rietveld and Fourier map analyses were employed to examine the intracrystalline structure of TTB Li_xSr_1−0.5xTa₂O₆, from which a three-dimensional Li⁺ pathway is suggested. A close examination indicated that the A1 sites, which have the distorted cuboctahedral environments, play an essential role for the long-range Li⁺ migration within Li_xSr_1−0.5xTa₂O₆. The increase of x in Li_xSr_1−0.5xTa₂O₆ leads to the higher carrier concentration, but accompanies an adverse structural effect on the Li⁺ mobility. Particularly, in the region of x > 0.17, the increase of Li⁺ concentration is more than offset by the combined effect of two factors: the distortion of the rhombic window of the A1-centered polyhedra and the annihilation of the vacancy sites.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Yeungnam University Research Grant (2016A380034).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8ra02779j

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