Oxygen Vacancies in Fast Lithium-Ion Conducting Garnets - Chemistry

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Oxygen Vacancies in Fast Lithium-Ion Conducting Garnets Markus Kubicek,*,† Andreas Wachter-Welzl,† Daniel Rettenwander,§ Reinhard Wagner,‡ Stefan Berendts,∥ Reinhard Uecker,⊥ Georg Amthauer,‡ Herbert Hutter,† and Jürgen Fleig† †

Institute of Chemical Technologies and Analytics, Technische Universität Wien, Getreidemarkt 9/164EC, 1060 Vienna, Austria Department of Chemistry and Physics of Materials, University of Salzburg, Jakob Haringer Straße 2a, 5020 Salzburg, Austria § Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, United States ∥ Department of Chemistry, Technische Universität Berlin, Straße des 17. Juni 124, 10623 Berlin, Germany ⊥ Leibniz Institute for Crystal Growth (IKZ), Max-Born-Straße 2, 12489 Berlin, Germany ‡

ABSTRACT: Fast Li-ion conducting garnets have shown excellent performance as chemically stable solid state Li electrolytes even at room temperature. However, because of phase formation and Li loss during preparation, reliably obtaining high Li-ion conductivities remains challenging. In this work, we show that an additional defect chemical species needs to be considered, namely, oxygen vacancies. We prove the existence of oxygen vacancies in all six investigated sample types: Ta-, Al-, and Ga-stabilized cubic Li7La3Zr2O12 (LLZO) polycrystals and Ta-stabilized LLZO single crystals. Isotope exchange threedimensional analysis was used to characterize surface oxygen exchange (k*) and bulk oxygen diffusion (D*) enabled by the oxygen vacancies present in the LLZO variants. Remarkably high k* values of 10−11−10−8 cm s−1 and D* values of 10−15−10−11 cm2 s−1 were found at 350 °C in air. In a further data analysis, the differences between the compositions are investigated, the concentration of oxygen vacancies is estimated, and the possible effects on the cation defect chemistry and phase formation of LLZO are discussed.

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INTRODUCTION Replacing today’s liquid-electrolyte Li-ion batteries with all-solid state batteries is highly desirable to avoid safety and durability issues such as dendrite-driven short circuit or thermal runaway. Since its introduction by Murugan et al. in 2007,1 the garnet Li7La3Zr2O12 (LLZO) has received a great deal of attention as a solid electrolyte with significant Li-ion conductivity at room temperature in air.2−5 In numerous doping studies since then it was attempted to optimize the cation composition of LLZO with respect to Li-ion conductivity and stability.6,7 Essential is the stabilization of cubic phase(s) and avoiding the tetragonal phase because cubic LLZO shows Li-ion conductivity that is ∼2 orders of magnitude higher.2,6,8 Also the influence of moisture and CO2 on the stability of different LLZO compositions requires attention, because LLZO can degrade or decompose in ambient air.9,10 A common strategy is to introduce substituents acting as donors such as Al3+, Fe3+, or Ga3+ on the Li+ sites or Nb5+, Ta5+, Bi5+, or Mo6+ on the Zr4+ site and thereby reduce the Li stoichiometry per formula unit from 7 to an optimum usually between 6 and 7, depending on the cation substituent.11−25 A great challenge in the preparation of highly conductive LLZO is optimizing the synthesis route. On one hand, high temperatures are necessary to form the garnet phase; on the other, Li loss via volatile Li compounds is commonly observed at high temperatures.26 Therefore, an excess of Li and/or a protective covering to slow Li loss is regularly used during sintering to finally acquire the desired LLZO composition.27,28 In most of today’s research, optimizing the cation compositions of Li garnets is attempted for © 2017 American Chemical Society

improving the properties of LLZO, while oxygen anion stoichiometry is considered to be fixed at 12 oxygen atoms per formula unit and therefore largely ignored. In this work, we show that oxide anion defects indeed exist in LLZO and that their contribution to the total defect chemistry of LLZO cannot be neglected. Only a few studies are known to the authors that speculate about the existence of oxygen vacancies in LLZO or consider them to potentially play a role in the phase formation and defect equilibria of LLZO.13,29−31 The main argument for formation of oxygen vacancies given there is that Li+ loss is connected to simultaneous O2− loss due to charge neutrality. Here, we give direct proof that indeed oxygen stoichiometry can vary in LLZO. Via isotope exchange depth profiling using 18O2 as a stable isotope tracer and by subsequent time of flight secondary-ion mass spectrometry (ToF-SIMS) analysis, we verify that oxygen vacancies are present or even abundant in all investigated LLZO materials, including single crystals, polycrystals, and different cation substituents (Ta5+, Ga3+, and different Al3+ concentrations). The oxide tracer diffusion coefficient at 350 °C is surprisingly high (up to D* = 8.2 × 10−12 cm s−1) and is even close to that of yttria-stabilized zirconia, a fast oxygen-ion conductor. Consequently, we show that oxygen vacancies need to be considered to understand the Li-ion conductivity of LLZO. Acting as donors, they directly Received: March 29, 2017 Revised: August 8, 2017 Published: August 11, 2017 7189

DOI: 10.1021/acs.chemmater.7b01281 Chem. Mater. 2017, 29, 7189−7196

Chemistry of Materials

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RESULTS AND DISCUSSION Structural Characterization. Polycrystalline samples were investigated by XRD and GI-XRD after the 18O2 experiments. Figure 1 displays the smoothed XRD patterns exemplarily for Ta-

affect the defect chemistry of LLZO. Therefore, we expect the true Li content of LLZO compositions to be generally lower than the values reported in the literature. Also, elastic effects on the crystal lattice due to the different size of oxide ions and oxygen vacancies require that attention be paid to influencing phase formation and Li mobility. Oxygen vacancies could turn out to be an important, previously hidden parameter to explain the large scatter in Li-ion conductivities found in the literature for the same nominal LLZO compositions.

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Article

MATERIALS AND METHODS

A total of five different LLZO compositions were analyzed, either single crystals (∼3 mm edge lengths) or polycrystalline pellets (Ø 7 mm × 2 mm). The single-crystal Ta−LLZO samples were grown by the Czochralski method directly from the melt. The starting materials, Li2CO3 (99%, Merck), La2O3 (99.99%, Aldrich), ZrO2 (99.0%, Aldrich), and Ta2O5 (99.99%, Aldrich), were dried, mixed in a stoichiometric ratio with a 10 wt % excess of Li2CO3, and then pressed and sintered at 850 °C for 4 h at a heating rate of 5 °C min−1. The pellet was then melted in an iridium crucible by RF induction heating using a 25 kW microwave generator. An iridium rod was used as a seed for crystal growth under a nitrogen gas atmosphere. The seed pulling and rotation rates were 1.5 mm h−1 and 10 rpm, respectively. The transparent crystal was then cut into ∼3 mm × ∼3 mm × ∼3 mm cuboidal LLZTO samples.32 The synthesis route for polycrystalline pellets is based on the procedure described by Wagner et al.33 Li2CO3 (99%, Merck), La2O3 (99.99%, Roth), and ZrO2 (99.0%, Roth) were weighed to reach the intended stoichiometry. To compensate for Li loss during heat treatment, an excess of 10 wt % Li2CO3 was added with respect to the stoichiometrically required amount of Li2CO3. The reagents were ground and mixed in an agate mortar after the addition of isopropyl alcohol and subsequently pressed into pellets. The pellets were heated to 850 °C at a rate of 5 °C min−1 and calcinated for 4 h. The resulting pellets were again ground in an agate mortar and ball-milled for 1 h under isopropyl alcohol (FRITSCH Pulverisette 7, 800 rpm, 2 mm ZrO2 balls). After being dried, the powder was pressed again into pellets and placed in an alumina crucible. To avoid undesired incorporation of Al3+ from the crucible and to suppress evaporation of lithium from the sample, the actual pellets were always placed between two pellets of stoichiometric Li7La3Zr2O12. The final sintering step was performed by heating with a rate of 5 °C min−1 and holding at 1230 °C for 6 h. Typical densities of these samples are 92−93%, as measured with a Hepycnometer. Polycrystalline pellets were formed with different cation substituents, Ta (Li6La3ZrTaO12), Ga (Li6.4Ga0.2La3Zr2O12), and Al, for which three compositions (Li7−3xAlxLa3Zr2O12, where x = 0.15, 0.20, or 0.30) were investigated. X-ray diffraction was performed using θ−2θ scans (X’Pert PRO PW 3050/60, PANalytical) and 2° grazing incidence X-ray diffraction (GI-XRD). Isotope exchange experiments were performed at 350 °C in 200 mbar 18O2 (97.1% isotope-enriched, CAMPRO) in a special quartz setup using samples with a polished surface. The elevated temperature is necessary for oxygen ions to become sufficiently mobile for exchange and diffusion; 350 °C was chosen as the upper limit as no mass loss of LLZO can be measured by thermogravimetric analysis up to this temperature26 and therefore no changes in O2− stoichiometry from room temperature are expected. Subsequent three-dimensional (3D) analysis of the oxygen isotope distribution was performed on a TOF.SIMS 5 instrument (ION-TOF) using 25 kV Bi3++ primary ions (∼0.03 pA), 2 kV Cs+ for sputtering (∼155 nA), and a low-energy electron gun (20 V) for charge compensation. Negative secondary ions were measured. Details on the used measurement mode (“CBA” mode) are given in refs 34 and 35. Areas of 100 μm × 100 μm were analyzed, and sputter crates were 300 μm × 300 μm wide and up to 7.9 μm deep to avoid any possible influence of surface roughness on the profiles. Depth information was calculated from sputter currents and times and referenced by depth measurement of deep craters by confocal microscopy (Axio CSM 700, Zeiss).

Figure 1. XRD patterns of Ta− and Ga−LLZO (Li6La3ZrTaO12 and Li6.4Ga0.2La3Zr2O12, respectively). The asterisk shows a minor impurity phase found for Ta−LLZO. For Ga−LLZO, a grazing incidence measurement is also shown. The sampling depth is ∼10 μm for XRD and ∼0.5 μm for GI-XRD. For comparison, a reference diffraction pattern of cubic LLZO is shown at the bottom.36

and Ga-doped LLZO as well as a reference pattern of cubic LLZO.36 Each sample shows the reflections of the cubic garnet structure. For Ta-doped LLZO, one minor additional peak was found at 2θ = 21°, which could not be explained, despite the fact that no more impurities were found. Formation of the cubic phase could be shown for all LLZO samples. To investigate if secondary phase formation in air plays a role in our isotope exchange experiments, additional grazing incidence XRD measurements were performed after polishing a Ga−LLZO sample and keeping it in ambient air for 48 h. The sampling depth for XRD is ∼10 μm and for GI-XRD ∼0.5 μm. As shown in Figure 1, no secondary phase formation could be detected by GIXRD on the Ga−LLZO sample. The microstructure of the samples was investigated by scanning electron microscopy (SEM) as shown for four different sample types in Figure 2. For Ga−LLZO and Al−LLZO in the overview images in panels a and b of Figure 2, inhomogeneities of the size of a few micrometers are visible. We expect those inhomogeneities to be only very close to the surface as no secondary phases could be detected via either XRD or GI-XRD. The magnified images (Figure 2c−f) show smooth surfaces with only scratches from polishing. No cracks or grain boundaries could be detected. For Ga−LLZO and Ta−LLZO, small inhomogeneities are visible. Characterization of the Oxygen Nonstoichiometry. In this work, isotope exchange 3D profiling was applied, using the stable oxygen isotope 18O for an oxygen exchange experiment at 7190

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(positively charged, donor-type) and are therefore much more likely to exist in LLZO. For our chosen method and the investigated LLZO compositions, we therefore ascribe incorporation of 18O into LLZO to a surface process in which oxygen vacancies are involved. The kinetics of this surface process can be quantified by the tracer surface exchange coefficient (k*). Accordingly, we ascribe the transport in LLZO to an oxygen vacancy diffusion mechanism that can be quantified by the tracer diffusion coefficient (D*). Significant incorporation and diffusion of the 18 O isotope were observed in all investigated LLZO compositions, proving the existence of oxygen vacancies as described below. Ta-Substituted LLZO. For the Ta−LLZO composition Li6La3ZrTaO12, two different sample types were investigated, namely, single crystals and polycrystalline sintered pellets. In Figure 3, the results of isotope exchange experiments and 3D

Figure 2. SEM images of the different LLZO samples. (a and b) Overview images for Ga−LLZO and Al−LLZO, respectively. Here, inhomogeneities of the size of a few micrometers are visible. We expect those to be only very close to the surface as no secondary phases were present in either XRD or GI-XRD. The magnified images (c−f) show small inhomogeneities for Ga−LLZO and Ta−LLZO as well as scratches from polishing on all samples. No grain boundaries or possible secondary phases are visible therein.

Figure 3. Isotope exchange depth profile of a Li 6 La 3 ZrTaO 12 polycrystalline pellet. The isotope exchange was performed at 350 °C in 200 mbar 18O2 for 45 min. No significant lateral inhomogeneities were observed in the measured area of 100 μm × 100 μm.

SIMS profiling on polycrystals are shown. The graph in Figure 3 shows the relative 18O isotope concentration with depth, while the insets show the lateral 18O distribution that was in good approximation homogeneous for the samples. The red fit curves are non-linear least-squares fits of the data using an analytical solution of Fick’s diffusion equation for a semi-infinite solid and a constant 18O concentration in the gas.37 Via this fitting, it is possible to quantify the surface exchange and diffusion coefficients of oxygen. The very first measured points close to the surface (shown in light colors in Figure 3) show a strongly reduced 18O concentration, which we attribute to effects after the isotope exchange experiment. As the LLZO samples were in air after the isotope exchange experiment and before the SIMS measurement, we expect surface hydroxides and carbonates to form29,38,39 with oxygen from air that has a natural abundance of 18 O of only 0.00205 (see Figure 3). Therefore, the 18O content of such surface layers can be expected to be depleted, and those layers were consequently ignored in the analysis. The same effect was observed for Ga−LLZO as shown below. The tracer surface exchange coefficient at 350 °C (k*) was calculated to be 4 × 10−11 cm s−1, and the tracer diffusion coefficient (D*) was 1.5 × 10−12 cm2 s−1.

350 °C. With subsequent TOF-SIMS 3D profiling at room temperature, we then image the frozen-in isotope distribution. The underlying principle behind this isotope exchange technique is that incorporation and diffusion of oxide ions require defects in the LLZO lattice. These defects can be either oxygen vacancies or oxygen interstitials. For two reasons, we exclude oxygen interstitials as being relevant in our experiments. (i) The oxide ion is relatively large like most anions, and the involved large lattice distortions upon addition of an additional ion make oxygen interstitials energetically unfavorable in tightly packed structures. They are known to exist in layered structures, which LLZO does not adopt. (ii) Analyzing the system from a defect chemistry point of view, it is known that Li can evaporate at the high temperatures involved in the preparation of LLZO single crystals or polycrystalline pellets. The thereby missing Li+ ions (Li vacancies) in LLZO act as negatively charged acceptor defects, just the same as oxygen interstitials. The existence of both defects in significant numbers would again be energetically unfavorable. If the argument is turned around, however, oxygen vacancies would act as a counterbalancing defect to Li vacancies 7191

DOI: 10.1021/acs.chemmater.7b01281 Chem. Mater. 2017, 29, 7189−7196

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Chemistry of Materials Equivalent measurements were performed on single crystals of the same composition (Li6La3ZrTaO12) as shown in Figure 4.

Figure 5. Isotope exchange depth profile of two different grains of a Li6.4Al0.2La3Zr2O12 polycrystal found in a total measured area of 100 μm × 100 μm as shown in the inset. The isotope exchange was performed at 350 °C in 200 mbar 18O2 for 335 min. A clear difference in isotope exchange and diffusion can be observed in different grains. The fit curves of the isotropic diffusion model cannot reproduce the profiles and give only a very rough estimate of the oxygen exchange and diffusion parameters.

Figure 4. Isotope exchange depth profile of a Li6La3ZrTaO12 single crystal. The isotope exchange was performed at 350 °C in 200 mbar 18O2 for 160 min. No significant lateral inhomogeneities were observed in the measured area of 100 μm × 100 μm.

Also here, a homogeneous lateral 18O concentration was found as shown in the inset. Again, the measured data could be described well by using the analytical solution of Fick’s diffusion equation for fitting. The calculated parameters for the measurement shown in Figure 4 are k* = 6.1 × 10−10 cm s−1 for tracer surface exchange and D* = 8.2 × 10−12 cm2 s−1 for tracer diffusion. Both values are considerably higher than those for the polycrystal. One possible explanation could be grain boundaries. However, grain sizes in the polycrystal were ∼10 μm, so pronounced effects from blocking grain boundaries cannot be expected in the 1.2 μm deep profile. A more convincing explanation would be a difference in the concentration of oxygen vacancies between the two samples. Even though they have nominally the same cation composition, their preparation route and the temperatures and atmospheres involved are different. Depending on the actual vacancy concentration, such different preparation parameters can easily lead to a relative difference of ∼1 order of magnitude in the oxygen vacancy concentration of the polycrystal and single crystal, which is necessary to explain the calculated parameters. Al-Substituted LLZO. All three investigated Al-doped LLZO compositions (Li7−3xAlxLa3Zr2O12, where x = 0.15, 0.20, or 0.30) showed similar results in isotope exchange profiling, which were however clearly different from those of the Ta-doped samples. For all Al−LLZO compositions, lateral inhomogeneities were observed as exemplarily sh own in Figure 5 for Li6.4Al0.2La3Zr2O12. The depth profiles shown in Figure 5 were reconstructed from two different areas of the total measured area of 100 μm × 100 μm as shown in the inset. The “fast” area (black squares) showed a significantly larger amount of 18 O incorporated over a depth of several micrometers, while the isotope depth profile of the slow area (blue circles) decayed much faster. During the analysis, it became clear that neither area could be well represented by the used diffusion model (see the red fit curves). This is most probably caused by the diffusion not being homogeneous in those areas. Reasons can be manifold, e.g., grain boundaries, dislocations, secondary phases, etc. The nature of the inhomogeneous diffusion is detrimental for an analysis of the diffusion parameters, which makes an exact analysis

impossible without further knowledge. A detailed investigation is beyond the scope of this study but will be addressed in followup investigations. To roughly compare the oxygen exchange parameters to those of other samples, however, we still use the inappropriate fits shown in Figure 5 to estimate at least the correct order of magnitude. Thus, values were extracted for the fast area: k* ∼ 9 × 10−10 cm s−1, and D* ∼ 3 × 10−12 cm2 s−1. Values for the slow area were as follows: k* ∼ 9 × 10−11 cm s−1, and D* ∼ 4 × 10−15 cm2 s−1. Interestingly, there is a 1 order of magnitude difference in the surface exchange coefficient and even a 3 order of magnitude difference in the diffusion coefficient between different areas on the same polycrystal. When comparing these values to those of the Ta−LLZO single crystal, we find the fast area to be on the same order of magnitude in both k* and D*. Assuming the same mobility for oxide ions, this would mean that the concentration of oxygen vacancies is similar to that of Ta− LLZO in the fast area and decreased by ∼3 orders of magnitude in the slow area of Al−LLZO. However, possible porosity in the fast areas (compare the SEM image in Figure 2b) could also cause an apparent increase in the oxygen exchange parameters. Ga-Substituted LLZO. For Ga−LLZO, 3D isotope profiles similar to those of Al−LLZO were measured. Again, lateral inhomogeneities were observed as shown in Figure 6. However, here no large “fast” areas were detected, but a few small areas in the range of ∼2−10 μm were found with more 18O incorporated than in the homogeneous matrix with a low 18O content. In Figure 6, two of the faster areas were investigated individually (1 and 2 in the inset) together with a larger area without any “18O hot spots” (3 in the inset). As already observed for the Ta−LLZO polycrystals, a decrease in the 18O concentration was found at the surface and ignored for the purpose of fitting. These surface effects were even more pronounced for Ga-doped LLZO polycrystals. One reason for this could be the considerably higher 18O concentration close to the surface, so that re-equilibration in ambient oxygen leads to a stronger effect. In particular, for areas 1 and 2, very high 18O 7192

DOI: 10.1021/acs.chemmater.7b01281 Chem. Mater. 2017, 29, 7189−7196

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Chemistry of Materials

Table 1. Oxygen Exchange Parameters Extracted from Isotope Exchange at 350 °C and Depth Profilinga k* (cm s−1)

D* (cm2 s−1)

Shown Fit Curves Figure 2, Ta-poly “1” 5.2 × 10−11 1.7 × 10−12 Figure 2, Ta-poly “2” 2.1 × 10−11 1.2 × 10−12 −10 Figure 3, Ta-single 6.1 × 10 8.2 × 10−12 −10 Figure 4, Al-poly “fast” ∼9 × 10 ∼3 × 10−12 Figure 4, Al-poly “slow” ∼9 × 10−11 ∼4 × 10−15 Figure 5, Ga-poly “1” 1.8 × 10−8 1.4 × 10−13 −9 Figure 5, Ga-poly “2” 3.3 × 10 4.3 × 10−14 −10 Figure 5, Ga-poly “3” 5.6 × 10 9.4 × 10−14 Average Values of All Measurements on Different LLZO Compositions Li6La3ZrTaO12 poly 3.0 × 10−11 1.5 × 10−12 −10 Li6La3ZrTaO12 single 5.6 × 10 7.3 × 10−12 −11 Li6.55Al0.15La3Zr2O12 poly 3.7 × 10 1.2 × 10−14 Li6.4Al0.2La3Zr2O12 poly 2.7 × 10−11 9.7 × 10−15 Li6.1Al0.3La3Zr2O12 poly 6.3 × 10−11 4.3 × 10−14 −10 Li6.4Ga0.2La3Zr2O12 poly 8.1 × 10 9.6 × 10−14 YSZ (100) Single Crystal at 350 °C 9.5 mol % Y2O3:ZrO2 1.4 × 10−11

Figure 6. Isotope exchange depth profile of three different areas of a Li6.4Ga0.2La3Zr2O12 polycrystal from a total measured area of 100 μm × 100 μm as shown in the inset. The isotope exchange was performed at 350 °C in 200 mbar 18O2 for 45 min. A clear difference in isotope exchange and diffusion can be observed in the different regions. The fit curves of the isotropic diffusion model are used to estimate the oxygen exchange and diffusion parameters in the respective regions.

a

Single and poly refer to single-crystalline and polycrystalline samples, respectively.

concentrations of up to ∼0.6 were found close to the surface, much higher concentrations than with the other compositions. However, also, the decay of the 18O profiles was fast. Converted into values for highest active area 1, the tracer surface exchange rate is very high (k* = 1.8 × 10−8 cm s−1) and the diffusion coefficient is rather low (D* = 1.4 × 10−13 cm2 s−1). This could be caused by possible secondary phases at the hot spot. Such phases would, however, have to be located only at the surface as no such phases could be detected, even by GI-XRD. Interestingly, the diffusion coefficient is similar over the whole sample, which is a further indication that the bulk LLZO is homogeneous and only tiny changes at the surface are present. Further investigations are necessary to understand the connection among the surface of LLZO, its changes due to interaction with ambient air, and the effect on isotope experiments. On the basis of existing SIMS data, we could not identify changed surface compositions or cation inhomogeneities (negative ions were measured). Parameters of Oxygen Exchange and Oxygen Diffusion. A summary of the values for oxygen exchange found for the different LLZO is given in Table 1. First, the parameters of the shown fit curves in Figures 3−6 are presented, and underneath the average values from all measured 100 μm × 100 μm areas (three to five each) of the six different samples are shown in the table. Focusing first on average surface exchange parameter k*, we find that the Ta−LLZO single crystal and the Ga−LLZO polycrystal surfaces are ∼1 order of magnitude more active for oxygen exchange than those of other LLZO compositions do. More specifically, the Ga−LLZO “hot spots” as also shown in Figure 6 exhibited the fastest oxygen exchange with a k* of >10−8 cm s−1. Because of the lack of electronic charge carriers in LLZO, we expect a dominating water-catalyzed oxygen incorporation mechanism as described in ref 40. Therefore, a direct comparison to oxygen exchange coefficients of mixed electronic ionic conducting oxides is not really meaningful. For this study, the rather fast surface exchange parameters (k*) found act mainly as a necessary requirement to incorporate enough 18O to be able to measure depth profiles. The thin layers of hydroxide or carbonate

species at the surfaces of different LLZO compositions will strongly affect the surface exchange kinetics, which further hampers an unambiguous discussion of the k* values. We therefore put the emphasis on the tracer diffusion coefficient, which indeed characterizes bulk LLZO of the desired composition. The values of the tracer diffusion coefficient D* are surprisingly high for all measured samples. Values in the range of ∼10−14 cm2 s−1 to almost 10−11 cm2 s−1 were found. The highest values were found for the Ta−LLZO samples and here especially for the single crystal. The diffusion coefficients there are already close to those of materials optimized for their oxygenion conductivity such as 9.5 mol % yttria-stabilized zirconia (YSZ) for which D* = 1.4 × 10−11 cm2 s−1 at 350 °C in air. This points toward a significant or even very large amount of oxygen vacancies present in the investigated LLZO samples. Oxygen Vacancy Concentration and Its Impact on Defect Chemistry. An exact quantification of the vacancy concentration based on only the tracer diffusion coefficient is not possible, but an estimation can be attempted. First, the measured tracer diffusion coefficient (D*) needs to be converted into the oxygen self-diffusion coefficient (DO). D* differs from DO by Haven ratio H, typically a factor slightly smaller than 1.41 DO depends (for diffusion via vacancies) on two factors, the diffusion coefficient of the oxygen vacancies (DV) and the vacancy concentration (cV). Knowing DO, with the diffusivity of vacancies, one can calculate the vacancy concentration or vice versa. However, for our case of LLZO, neither the diffusion coefficient of oxygen vacancies nor their concentration is known so far. While the concentration of oxygen vacancies can vary over many orders of magnitude in different oxides, the vacancy diffusion coefficients are typically more similar. At least a very rough estimation can therefore be attempted by comparison with other oxides. Data for DV are available for some well-investigated oxide materials, for example, in slightly doped strontium titanate (SrTiO3). Using De Souza’s equation interpolated from numerous studies in ref 42, we obtain a DV value of 2.7 × 10−8 cm2 s−1 at 350 °C. Assuming further a Haven ratio H of 0.7, we 7193

DOI: 10.1021/acs.chemmater.7b01281 Chem. Mater. 2017, 29, 7189−7196

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Chemistry of Materials can estimate the vacancy concentration according to eq 1, with cO being the oxygen site concentration. cV D* = cO HD V

Table 2. Li-Ion Conductivity Data of Different LLZO Compositions Measured at Room Temperature in Aira σ (S cm−1) Li6La3ZrTaO12 Li6La3ZrTaO12 Li6.55Al0.15La3Zr2O12 Li6.4Al0.2La3Zr2O12 Li6.1Al0.3La3Zr2O12 Li6.4Ga0.2La3Zr2O12

(1)

For the measured D* values of LLZO in Table 1, we obtain relative vacancy concentrations (cV/cO) between ∼2 × 10−7 and ∼4 × 10−4. For the highest values measured on the single crystal, this would mean an oxygen nonstoichiometry of ∼5 × 10−3 per unit cell as a first rough estimate. Another comparison can be made for the highly doped fluorite-type oxygen-ion conductor yttria-stabilized zirconia. The oxygen ionic conductivity of 9.5 mol % single-crystalline YSZ at 350 °C in air (σ) was measured as 1.4 × 10−5 S cm−1. The tracer diffusion coefficient can be calculated to be 1.4 × 10−11 cm2 s−1 via the Nernst−Einstein relation43,44 with H = 0.65 for YSZ. From the known oxygen vacancy concentration of 4.3% of oxygen sites in YSZ, we can now as a rough estimate assume the same oxygen-ion mobility for LLZO and YSZ. For the highest measured diffusion coefficient (D* = 8.2 × 10−12 cm2 s−1) in Ta− LLZO single crystals, this estimation would suggest a vacancy concentration of even 2.5% of the oxygen sites in LLZO, approximately half of that in YSZ. We can conclude that an exact quantification is not possible at this point of the investigations, but vacancy concentrations on the parts per million scale in the areas with the lowest measured diffusion coefficients up to the parts per thousand range or even the low percent range in the fastest diffusion areas can be expected. At these concentrations, oxygen vacancies become very important to understanding the entire defect chemistry of LLZO. For typical operation conditions of a Li battery close to room temperature, direct electrical contributions of oxygen vacancies can be neglected. However, even though oxygen vacancies are not mobile then, they still act as a donor and thus affect other defect concentrations. In particular, oxygen vacancies will decrease the Li stoichiometry. Assuming doubly positive oxygen vacancies (with no trapped electrons), every oxygen vacancy needs two Li vacancies for compensation; e.g., 1% oxygen vacancies per oxide site lead to a decrease of 0.24 in the Li stoichiometry per LLZO formula unit Li7La3Zr2O12. From the existence of oxygen vacancies in all LLZO compositions, we conclude that considering oxygen vacancies, the Li content in LLZO is typically lower than nominally reported values in the literature. Li-Ion Conductivity. The technically most relevant property of LLZO garnets is their high Li-ion conductivity. The question of whether and how oxygen vacancies are relevant here remains. For this study, the Li-ion conductivities of the different LLZO compositions were measured at room temperature directly before the isotope experiment at 350 °C. As all samples were sintered at >1200 °C and thermogravimetric data show no change in mass, we assume all samples remain unchanged during the isotope exchange experiment at 350 °C. Several compositions showed high Li-ion bulk conductivities at room temperature in air as shown in Table 2. Values of σ of up to 6 × 10−4 S cm−1 (for Ga−LLZO) were obtained. A complex picture arises when trying to correlate for the different LLZO compositions, the Li-ion conductivity, and the D* values, which are in our approximation directly proportional to the oxygen vacancy concentrations as shown in Figure 7. For the Ta-doped single crystal and polycrystal, we find the higher conductivity for the polycrystal but a higher vacancy concentration for the single

polycrystal single crystal polycrystal polycrystal polycrystal polycrystal

4.26 × 10−4 1.84 × 10−4 6.05 × 10−5 2.47 × 10−5 1.79 × 10−4 6.07 × 10−4

a

Values are from the LLZO samples measured before the isotope exchange experiment.

Figure 7. Double-logarithmic plot of tracer diffusion coefficient D* and Li-ion conductivity of the six investigated sample types. Li+ site substituents (Al3+ and Ga3+) and the Zr4+ site substituent (Ta5+) show different trends.

crystal. On the other hand, for the Al− and Ga−LLZO samples, we find the four investigated compositions following the opposite trend: the higher the conductivity, the higher also the oxygen vacancy concentration. Interestingly, the vacancy concentration is considerably higher for Ta−LLZO than for Al− and Ga−LLZO, even though their Li-ion conductivity is similar. The different cation site for substitution (the Zr4+ site for Ta5+ and the Li+ site for Al3+ and Ga3+) might have a large impact on oxygen vacancy formation. We can conclude that the impact of oxygen vacancies on Li-ion conductivity is rather complex. This becomes clear when considering the different influences oxygen vacancies can have on the Li-ion conductivity of LLZO. (i) By acting as a donor, oxygen vacancies reduce the Li stoichiometry. (ii) By elastically deforming the LLZO lattice, oxygen vacancies can impact phase formation and stabilization. (iii) In a closely related manner, and dependent on the exact location of the oxygen vacancies in the lattice, the elastic deformations can also affect the migration barriers and conduction paths of Li+ in LLZO. Considering points (ii) and (iii), it is not surprising to find different relations between oxygen vacancy concentrations and Li conductivities for substitution either with Ta5+ on the Zr4+ site or with Al3+ or Ga3+ on the Li+ sites of LLZO or also for using different concentrations. Further studies of the topics mentioned above are necessary, namely, the exact effect of Li stoichiometry on the conductivity and the elastic effects of changes in the oxygen and lithium stoichiometry and their impact on phase formation and on Li migration barriers. Comparison with Other Garnet Oxides. The high oxygen diffusion coefficients measured in this study induce the question if this is also observed in other garnet oxides. Experimental studies of oxide diffusion and/or conductivity for the garnets 7194

DOI: 10.1021/acs.chemmater.7b01281 Chem. Mater. 2017, 29, 7189−7196

Article

Chemistry of Materials yttrium aluminum garnet (Y3Al5O12, YAG),45−48 yttrium iron garnet (Y3Fe5O12, YIG),49,50 and gadolinium iron garnet (Gd3Fe5O12, GIG)50 in the temperature range of 800−1300 °C have been published. These garnets all have in common a rather poor oxygen diffusion coefficient of oxygen ionic conductivity. Because of the high activation energies typically in the range of 3−4 eV, D* values of ∼10−30 cm2 s−1 or even lower result, when extrapolating to 350 °C, at which this study was conducted.45,46,48,49 This is more than 15 orders of magnitude lower than the values found for LLZO in this study. Even though a computational study has found energy barriers of only 2.6 eV for YAG,51 the difference after extrapolating to 350 °C would still remain extremely large. The reasons for this large difference between LLZO and other garnets can be caused by a higher oxygen vacancy concentration or a higher mobility, or as we suspect by a combination of both. Some indication of the reasons for these enormous differences can be found in the garnet structure. It is appropriate to use the formula X3Y2Z3 for garnets with the structure element X being the larger cation, Y being the smaller cation, and Z being a very large anion; e.g., for YAG, X = Y3+, Y = Al3+, and Z = AlO45−. For Li7La3Zr2O12 in this nomenclature, X = La3+ and Y = Zr4+, which is quite straightforward, whereas Z as the very large anion now consists of a structure already defective in the cations, nominally Li7/3O417/3−. Here in contrast to the other garnets discussed, not only MO4x− tetraeders exist, but some Li+ ions also have to occupy some of several additional other sites and their mobility is extremely high. We expect that this flexibility in the cations strongly increases the oxygen diffusion coefficient compared to other garnets. This increase might be realized (i) by reducing the formation enthalpy of oxygen vacancies by the possibility of rearranging Li+ cations around the defect and (ii) by an increased mobility of the O2− ions caused by a lower energy barrier of an individual hop into an oxygen vacancy due to the same possibility of fast rearrangement of Li+ ions. A recent computational study suggests that Li ions in the vicinity of an oxygen vacancy prefer the octahedral (>2.2 Å distance to a vacancy) over the tetrahedral sites (