Microelectrodes for local conductivity and degradation measurements on Al stabilized Li₇La₃Zr₂O₁₂ garnets

Samples with a nominal composition of Li_6.40Al_0.20La₃Zr₂O₁₂ were investigated. The synthesis route is based on the procedure described by Wagner et al. [23]. Li₂CO₃ (99%, Merck), Al₂O₃ (99.5%, Aldrich), La₂O₃ (99.99%, Roth), and ZrO₂ (99.0%, Roth) were weighed to reach the intended stoichiometry with an excess of 10 wt% Li₂CO₃, with respect to the stoichiometric amount of Li₂CO₃. The reagents were ground and mixed in an agate mortar under addition of isopropyl alcohol and then pressed into pellets. The pellets were heated to 850 °C with a rate of 5 °C min⁻¹ and calcinated for 4 h. After cooling down, the 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 drying, the powder was pressed into pellets and put into an alumina crucible. To avoid undesired incorporation of Al³⁺ from the crucible and to suppress evaporation of Li₂O from the material, the sample pellets were placed between two additional pellets of pure Li₇La₃Zr₂O₁₂. The final sintering step was performed at 1230 °C for 6 h in ambient air. This results in a polycrystalline pellet with a diameter of about 7 mm, 4.6 mm thickness and typical LLZO-grain sizes of about 100–200 μm (Fig. 1). The density of the sample, measured by a pycnometer (Brand GmbH), is 91%.

The ionic conductivity was measured by electrochemical impedance spectroscopy (EIS). For measurements of the effective conductivity of macroscopic samples (macroelectrode measurements), samples were polished by grinding paper (#4000), and thin films of Pt (200 nm) and Ti (10 nm) were deposited on top and bottom as ionically blocking electrodes. A thin film of titanium is required in order to improve the adhesion of platinum. For the EIS measurements, a Novocontrol Alpha Analyzer was used in the frequency range of 3 × 10⁶–10 Hz. For such macroelectrode measurements the temperature was controlled by a Julabo F-25 HE thermostat, the exact temperature was 25.3 °C, determined by a thermocouple at the sample.

Local conductivities were measured by means of microelectrodes. Using photolithographic techniques in combination with ion beam etching, circular electrodes with diameters of 20–300 μm were prepared from the macroscopic Pt/Ti thin films on top of the samples. Microelectrode measurements were performed at ambient temperature (T = 23.5 °C). Tungsten needles were used to contact the microelectrodes under an optical microscope. The position of the needles was adjusted by mechanically controlled micromanipulators. Figure 2 (a) illustrates the measurement setup and (b) shows a part of the microelectrode array on top of the sample. Impedance measurements (Novocontrol Alpha Analyzer) were performed between a microelectrode and the counter electrode on the bottom side (Pt thin film with Pt paste at the sample edges for contact reasons).

Before microelectrodes were prepared from the Pt thin film the sample’s overall performance was measured with the two macroscopic electrodes. The impedance spectrum of the Al stabilized LLZO garnet determined at 25.3 °C is plotted in Fig. 3. It shows a part of a “semicircle” at high frequencies, followed by a well separated low frequency contribution which represents the impedance of the ionically blocking electrodes (Ti/Pt). In agreement with earlier studies we attribute the resistance of the high frequency feature to ion conduction in the bulk [24, 25].

In order to quantify the impedance spectrum properly, a resistor in parallel to a constant phase element (R ₁ ||CPE ₁ ) is used for the bulk contribution, in series to a constant phase element CPE ₂ describing the blocking electrodes. Additionally, an inductive element (L) is required due to wiring; this is responsible for the strong distortion of the bulk semicircle and the real axis intercept at finite Z_Re, rather than at Z_Re = 0. Hence, the intercept at 2000 Ω in Fig. 3 is not an ohmic offset but the result of the serial inductance. The equivalent circuit shown in Fig. 3 leads to a reliable fit (dashed line) of the impedance spectrum and relative permittivities (ε_r) calculated from CPE ₁ are in the range of 70, which confirms the bulk character of this part of the spectrum. The fit parameters of the spectrum in Fig. 3 are given in Table 1.

From the resistance R ₁ , the effective bulk conductivity σ _macro can be calculated bywith h being the sample thickness and A the surface area. In this specific case a bulk conductivity of 3.3 × 10⁻⁴ S cm⁻¹ results.

This is within the range typically found for such LLZO samples stabilized with aluminium [8, 13, 27‐31]. However, literature data reveal a large scattering of bulk or total conductivities, and in a separate paper we will show that a substantial variation also exists between numerous nominally identical samples prepared in our labs. Compared to all data of our extensive study, the sample shown here has a rather good effective ionic bulk conductivity, even though also two times higher values were measured (A. Wachter-Welzl, et al. unpublished data).

While macroscopic electrodes only yield mean sample conductivities, microelectrodes provide the possibility to measure spatially resolved conductivities. Based on the principle that most of the voltage between a microelectrode and an extended counter electrode drops very close to the microelectrode, the diameter of the electrode (d) determines the investigated volume beneath. The measured resistances are largely determined by the conductivity of a hemisphere with a radius of 2d [16]. An array of microelectrodes with different diameters (20–300 μm) was measured at room temperature. Figure 4 displays typical impedance spectra found in such microelectrodes measurements on the LLZO sample.

The high frequency arc corresponds to charge transport in the probed sample volume and is described by a resistive element (R _Spread ) in the equivalent circuit. The low frequency capacitive increase is caused by the ionically blocking microelectrode and can be modelled by a constant phase element (CPE2), in agreement with the macroscopic electrodes. In many cases, the electrode response of microelectrodes was even steeper than for macroelectrodes and thus the exponent of the CPE closer to 1. Since macro- and microelectrodes consist of the same material, this suggests the existence of some regions with very non-ideal ion blocking, distributed across the sample. The latter probably cause the less steep electrode response in the macroelectrode measurements. In parallel to R _Spread and CPE ₂ , a stray capacitance (CPE ₁ ) has to be introduced due to the measurement setup with a value in the range of 200 fF. This value is larger than what was expected for the bulk capacitance of most microelectrodes. Only for d ≥ 200 μm a geometrical bulk capacitance (C = 2 ε _r  ε ₀ d, ε ₀ = vacuum permittivity) in the 200 pF range results from ε _r ≈ 60. However, adding the bulk capacitance to the equivalent circuit leads to an over parameterization and was therefore avoided here.

A fit of the impedance spectra to the equivalent circuit shown in Fig. 4 (dashed line) reveals R _Spread values. If this “spreading resistance” R _Spread is only due to the charge transport in the bulk, it can be used to calculate the local conductivity, see below. In principle, grain boundary resistances or other interfacial resistances with parallel capacitances being smaller than the stray capacitance cannot be separated from the high frequency arc and may thus also contribute to R _Spread ¹². Grain boundary related effects could not be observed in macroscopic impedance spectra and we do not expect an effect in the microelectrode measurements either. However, additional interfacial resistances cannot be excluded, cf. Sec. 3.3.

Figure 5 shows the resulting “spreading resistances” R _Spread of microelectrodes with a diameter of 100 μm (blue) and 200 μm (red). Variations are very moderate with standard deviations in the range of 9.5%. From the spreading resistance R _Spread and the microelectrode diameter d, a nominal bulk conductivity σ _me can be calculated [32] according to

Provided the sample is homogeneous in the region beneath a microelectrode, this value reflects the true local Li-ion conductivity. Figure 6 displays nominal σ _me values for microelectrodes with different diameters. The solid line σ _macro represents the effective conductivity of the sample, measured with macroelectrodes before microelectrodes were prepared from the macroelectrode on top. Within a factor of about two, macroscopic and microscopic conductivities agree. This indicates that local conductivity measurements using microelectrodes are meaningful and that microelectrode measurements are indeed possible on LLZO. However, the ionic conductivity from microelectrodes seems to depend on their diameter. The averaged local conductivities found for 100 and 300 μm are 4.1 × 10⁻⁴ S cm⁻¹ and 4.9 × 10⁻⁴ S cm⁻¹ (Fig. 7), respectively and thus somewhat larger than the mean conductivity of the sample (3.3 × 10⁻⁴ S cm⁻¹). The highest value found for a 300 μm microelectrode (6.3 × 10⁻⁴ S cm⁻¹) is even significantly higher than the values typically reported for LLZO stabilized with Al_0.20 (σ _macro : 2.4–3.4 × 10⁻⁴ S cm⁻¹) [7, 8, 31]. Plotting the averaged conductivity for every microelectrode diameter shows a clear trend (Fig. 7): For the smallest microelectrodes the measured conductivities are smallest and even slightly below σ _macro .

As small microelectrodes are most sensitive to near-surface effects, this suggests that near to the surface less conductive regions exist. Possibly, local stoichiometric deviations near to the surface or the formation of impurity phases or secondary phases (e.g. La₂Zr₂O₇, LaAlO₃, La₂O₃, La(OH)₃, Li₂CO₃, LiOH), are responsible for the lower nominal conductivities σ _me [14, 33‐35], since preparation as well as measurements include exposure to air. Hou et al. investigated Al stabilized LLZO, sintered at 1100 °C, by means of laser induced breakdown spectroscopy (LIBS) as a surface sensitive measurement method [36]. The maximum depth reached in that contribution was about 35 μm, which is comparable to the range covered by microelectrodes with a diameter of 20 μm. LIBS measurements detected aluminium and lithium rich phases in the first micrometres before the elemental distribution returns to a more or less equilibrated state. In addition, also misorientation angles may affect the ionic conductivity [35]. This could also contribute to the lower local conductivities found here.

The higher conductivity found for larger microelectrodes however, has to have a different reason. Most probably, the samples exhibit spatially inhomogeneous cation compositions and thus the effective conductivities from macroscopic measurements also include sample regions with smaller conductivity while the microelectrodes used in this study seem to be located on regions with higher conductivity. Indeed, in a related study on the scatter of effective sample conductivities of nominally identical samples we could identify significant conductivity variations not only from sample to sample but also within a given sample (A. Wachter-Welzl, et al. unpublished data).

Owing to their near-surface sensitivity, microelectrodes can also be used to investigate degradation phenomena originating close to the surface. Here, the same microelectrodes were measured again after three weeks of storage in ambient air. The impedance spectra in Fig. 8 display three different microelectrodes in their pristine state (cycle 1 – open symbols) and after long-time exposure to air (cycle 2 – filled symbols). Independent of the electrode diameter all impedance spectra indicate an increase in the resistance R _Spread compared to the pristine state.

These changes are probably related to near-surface degradation effects such as the formation of LiOH and Li₂CO₃ caused by a reaction with moisture and CO₂ from ambient air and the exchange of Li⁺ by H⁺ [9‐11, 14]. Figure 9 summarize the measurements and illustrates the resistive changes between the pristine and the degraded state in dependence of the microelectrode diameter. Microelectrodes with a diameter of 20–50 μm show the largest changes with a maximum of 80% resistance increase. With increasing diameter, the variations become smaller. This supports the assumption of near-surface degradation, which becomes less important as the probed volume beneath the electrode increases, i.e. as microelectrode diameters increase. Possibly a similar near-surface degradation already before the very first microelectrode measurements was also responsible for the low conductivities found for 20 μm microelectrodes on pristine samples (see Sec. 3.2).