Microscale mechanical property variations of Al-substituted LLZO: insights from compression testing and molecular dynamics simulations†

Jaron V. Moon^a, Md Takmil Sakir^c, Wooseok Go^b, Rui Xie^a, Michael C. Tucker^b, Marca Doeff^b, Haoran Wang^c and Roseanne Warren*^a
aUniversity of Utah, Department of Mechanical Engineering, 1495 E 100 S, Salt Lake City, UT 84112, USA. E-mail: roseanne.warren@utah.edu
^bEnergy Storage and Distributed Resources Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
^cMechanical and Aerospace Engineering, Utah State University, Logan, UT 84322, USA

First published on 9th August 2024

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Introduction

Lithium lanthanum zirconium oxide (LLZO) is a garnet ceramic solid electrolyte (SE) with great promise for use in all-solid-state lithium metal batteries. Its advantages include enabling the use of a lithium metal anode with a high theoretical specific capacity (3860 mA h g⁻¹), and improved safety in the absence of flammable electrolytes.¹ In an all-solid-state battery, the SE is subject to myriad compressive and tensile stresses (Fig. 1a). Although LLZO is a ceramic material with a large Young's modulus (∼150 GPa) and high hardness (∼6–11 GPa), it is prone to failure from short-circuiting due to dendrite propagation through the SE.² Prior research has shown the susceptibility of ceramic SEs to lithium metal penetration via inter- and intragranular mechanisms.^3,4 Many studies have investigated the propensity for lithium metal to nucleate at voids within the SE,⁵ producing tensile stresses that induce SE failure by mode I crack propagation⁶ (Fig. 1b). In addition to tensile stresses, LLZO polycrystalline grains may also transition into a compressed state during lithium intrusion into the SE, with stress concentrations large enough to initiate crack propagation parallel to the direction of compressive loading⁷ (Fig. 1c). Increasing cell stack pressure has been shown to allow better cycling of solid-state batteries by improving contact between the electrodes and the SE.^8,9 The introduction of cell stack pressure is another probable cause of SE failure in compression (Fig. 1d).

The plausibility that large compressive stresses exist within the SE during cycling offers the need to further study the mechanical response of LLZO under compression. Instrumented indentation testing of LLZO to-date has been limited to reports of bulk sample Young's modulus, hardness, and fracture toughness¹⁰ (ESI Table S1†^11–14). LLZO is a brittle material with low deformability and a tendency to fracture under compressive loading. Compressive strength is a material property that describes the stress at which a material will fail under uniaxial compression; compressive strain describes the corresponding strain at failure. Despite the importance of compressive strength and strain for ceramic solid electrolyte performance, to-date no reported work has attempted to define these properties of LLZO experimentally or computationally.

A further question requiring investigation is the extent to which LLZO mechanical properties, including Young's modulus and compressive strength, may vary spatially across the SE. We hypothesize that microscale property changes arising from defects and/or density variations within the SE produce significant effects on the mechanical properties of LLZO. Microscale property variations are highly applicable to battery materials, as Li nucleation occurs on such length scales. Defects may present in LLZO as localized porosity, pre-existing cracks, voids, impurities, high-density dislocations, stacking faults, chemical segregation, and surface flaws.^15,16 Such defects, specifically nanocracks, have been shown as a leading cause of lithium intrusion into the SE.¹⁷ At the macroscale, Kim et al. showed that changing the density of cubic LLZO results in significant changes in fracture toughness and hardness.¹⁴ Hu et al. also presented the effect of relative density on the bulk properties of Ta-doped LLZO pellets, reporting disparate mechanical properties for pellets with varying densities.¹⁸

This work reports the first compressive strength measurement of Al-substituted LLZO and investigates microscale spatial variations in mechanical properties of LLZO SE using instrumented indentation testing. Microscale pillars were milled via focused ion beam (FIB) milling at various locations across a SE pellet and compressed until failure using a flat punch (Fig. 1e and f). Failure modes of the ceramic pillars are shown to be axial splitting, top surface splitting, shearing, and complete failure across/through grain boundaries due to crack propagation, where all failure modes result in cracking parallel to the compressive force (Fig. 1c and d). The results show a surprising degree of correlated variation in Young's modulus and compressive strength across the SE—variations that to-date have remained undetected or unreported through macroscale property testing alone. Attributing such variations to specific process-structure causes is an important but challenging endeavor. In this work, we attempt a preliminary explanation of the observed process variations by: (1) fitting a linear model relating Young's modulus and compressive strength across all measurements, and (2) conducting molecular dynamics (MD) simulations of LLZO with voids (porosity) representing localized defects in the pillars. The results indicate the importance of compressive strength as a mechanical property of interest for LLZO and the importance of characterizing mechanical properties of SEs at the microscale.

Methods

LLZO preparation

LLZO solid electrolyte pellets were prepared with purchased Al-substituted LLZO powder (Li_6.25Al_0.25La₃Zr₂O₁₂) from Ampcera having an average grain size of 500 nm. This material is cubic at room temperature.¹⁹ Al-substituted LLZO powder was mixed with 5 wt% MgO nanopowder (50 nm) and 5 wt% Li₂CO₃. MgO nanopowder was used to suppress abnormal grain growth during sintering.^20,21 Li₂CO₃ was used to offset lithium loss during sintering. Mixed powder (0.5 g) was put into a die and pressed with 150 MPa of force for 30 s. After removal from the die, green pellets were placed in a tube furnace and heated to 1200 °C for 4 hours under Ar atmosphere. Fully prepared pellets had a diameter of 14.9 mm and a thickness of 0.74 mm. X-ray diffraction (XRD) was completed with a Bruker D2 Phaser to confirm cubic phase stability 24 hours after sintering. Relative density was estimated by measuring the volume and weight of a pellet. Samples were stored in an LC Technology glovebox (H₂O, O₂ <0.1 ppm) to reduce oxidation and surface contamination. Ionic conductivity of an LLZO pellet of known area was measured after coating both sides of the pellet with gold. Gold sputtering was done at 30 mA for 120 s. Electrochemical impedance spectroscopy (EIS) was conducted using point contacts on each side of the pellet with a Bio-Logic VSP-300 potentiostat over a frequency range of 0.1 Hz to 7 MHz. Ionic conductivity was determined from the intercept of the high-frequency semi-circle with the x-axis (Table S2†). Symmetric cells were assembled with the LLZO pellet to report cycling performance and critical current density. Symmetric cells were assembled with gold-coated LLZO pellets. Lithium metal was then melted on the pellets at 200 °C in an Ar-filled glovebox. Cells were assembled in a 2032 coin cell case pressed with an MSE PRO hydraulic manual crimper.

Instrumented indentation testing

LLZO SE was prepared for mechanical property characterization by dry polishing the top surface until an average surface roughness (R_a) of ∼10 nm was achieved. Surface roughness was measured using scanning probe microscopy with a Bruker Hysitron TI Premier nanoindenter. Pillars were milled into the top surface of the LLZO SE using a four-step concentric ring milling process with an FEI Helios Nanolab 650 dual beam FIB and scanning electron microscope (SEM). First, a volume for the punch to travel into the surface was created by milling a 30 μm outer diameter ring (inner diameter 12 μm) using a beam voltage of 30 keV and a current of 21 nA. Next, the pillar was refined with two more millings at 2.5 nA and 0.79 nA. Lastly, the pillar was milled at a current of 80 pA to minimize the taper angle. Pillars were visually inspected to ensure no surface artifacts or additional porosity were introduced during the milling process. Pillars were compressed with a 20 μm diameter flat punch tip using a Bruker Hysitron PI89 SEM Picoindenter stage loaded into an FEI Quanta 600F SEM. Pillars were located and indented using in situ SEM imaging. Loading rates from 100 μN s⁻¹ to 3500 μN s⁻¹ were applied. Load-controlled indentation to pillar failure is a well-established method to determine the compressive strength of ceramics with instrumented indentation testing.^22–24 The loading/unloading curve was translated into an engineering stress–strain curve given the starting pillar diameter (measured at half the height of the pillar) and the pillar height. Pillar densification was neglected when calculating stress. Pillar compression experiments were performed on three LLZO pellets, with two testing sites located on each pellet. Testing sites were located at least 5 mm apart. At least four pillars were milled at each testing site, avoiding obvious surface porosity. During milling, transfer, and imaging, a number of pillars were compromised and could not be tested. Between one and four pillars were successfully tested to failure at each site.

Nanoindentation was completed using a Bruker Hysitron TI Premier nanoindenter to determine the Young's modulus and hardness of the LLZO pellet with a Berkovich tip. Tip calibration was completed periodically using a standard Si sample. Indentation allows for the reduced modulus to be calculated from the slope of the unloading curve and the tip area, which is derived from the tip function. The reduced modulus is the modulus measured taking into account the interaction of the tip and substrate on the response. Hardness was calculated from the maximum load applied and the tip area. Young's modulus for the SE was calculated knowing the reduced modulus, the Young's modulus of the indenter tip, and the Poisson's ratio of the tip and LLZO.²⁵ Nanoindentation results were averaged from more than 20 indentations across three different areas.

Molecular dynamics simulations

MD simulations of Al_0.25Li_6.25La₃Zr₂O₁₂ were conducted in LAMMPS²⁶ using the Buckingham-Coulomb interatomic potential with details provided in the ESI (Table S3).† The initial cubic LLZO crystalline structure consisted of a 188-atom unit cell obtained from quantum mechanical relaxation using VASP.^27–30 Subsequently, the unit cell was replicated in a 10 × 10 × 10 arrangement, resulting in a structure containing 188000 atoms. This structure was then equilibrated at 300 K and zero pressure with an NPT ensemble for 15 ps using LAMMPS. To study the effect of porosity on LLZO mechanical response, spherical voids of varying sizes were introduced into the relaxed LLZO model. Stoichiometry and electrical charge neutrality were maintained when removing atoms. Void-containing models were equilibrated at 300 K and zero pressure in the NPT ensemble for 10 ps to achieve stable configurations. Void volumes determined from these stable configurations were used to calculate porosity. All models were periodic in x, y, and z directions. The resulting structures were subjected to uniaxial loading until failure. A timestep of 1 fs and a strain rate of 10⁹ s⁻¹ were applied to all simulations. Nine models, with porosity ranging from 0 to 42.18%, were built and tested. OVITO was used for visualization and post-simulation analysis.³¹

Results and discussion

Material characterization

Electrochemical testing and XRD measurements were used to confirm the SE properties of LLZO pellets undergoing mechanical testing. The Al-substituted LLZO pellets maintained their cubic structure after sintering, as shown from XRD results (Fig. 2a). The cubic phase is desired due to its higher ionic conductivity,^32–34 where ion migration pathways have shorter distances compared to the tetragonal phase.³⁵ The ionic conductivity of the LLZO pellets used in this study is 0.13 mS cm⁻¹, as calculated from EIS measurements (Fig. 2b), which matches well with other literature values (Table S2†). Symmetric cell electrochemical testing results (Fig. 2c) show stable charge–discharge cycling up to a critical current density of 1.0 mA cm⁻², after which short-circuiting occurs due to lithium intrusion through the SE. The relative density of the full pellets was determined to be 96% given a weight and volume measurement (4.91 g cm⁻³). After confirmation of the stable electrochemical performance of the LLZO SE used in this study, mechanical properties were characterized on pristine LLZO pellets.

Instrumented indentation testing

Fig. 3 illustrates the process of instrumented indentation testing by pillar compression (Fig. 3a–d) and nanoindentation (Fig. 3e–h). The geometry of pillar compression is shown schematically in Fig. 3a. Important pillar parameters include the pillar taper angle (θ), the radius of curvature at the base (ρ), the height (H), and the diameter (D₀). The pillar compression experiment proceeds as follows: (1) pillars are located using in situ SEM imaging (Fig. 3b); (2) the flat punch tip is brought into contact with the pillar, ensuring that the pillar is centered in the middle of the flat punch tip and that the tip will not contact the bulk LLZO; (3) the pillar is loaded to a force below the expected fracture load, then unloaded at the same rate (Fig. 3c); (4) the pillar is loaded and unloaded several times at varying loading rates (μN s⁻¹) with increasing maximum load until failure occurs. Fig. 3d provides an example of the load–displacement curve to failure.

Using the described FIB milling process, the achieved pillars had measured diameters ranging from 2.5–3 μm and heights ranging from 6–8 μm. The relatively low aspect ratios were chosen to reduce the effects of bending during pillar compression. The resulting pillars are multi-grain, with ∼3–6 grains present across the pillar diameter and ∼12–16 grains along the height. Multi-grain pillars allow exploration of the effects of defects and grain–grain interactions on the mechanical properties of the SE. The taper angle was minimized to ∼2° by successive annular milling. “Stopping and Range of Ions in Matter” (SRIM)³⁶ modeling was used to quantify the extent of gallium ion implantation during FIB milling of Al-substituted LLZO. At 0° incident angle, gallium ions will be implanted ∼20 nm into the pillar surface; at 89° incident angle, ions will be implanted ∼6 nm into the surface (Fig. S1†). Given the μm-scale pillar height and diameter, ion implantation is considered a surface effect that will not significantly impact the measured results.³⁷ Using the method of pillar compression, the largest compressive strength measured was 2.63 GPa, corresponding to a Young's modulus of 150.97 GPa for the same pillar.

Nanoindentation provides a complementary measure of Young's modulus to that obtained by pillar compression, and the additional measure of hardness. In this work, nanoindentation of LLZO SE pellets was done with a Berkovich tip. The sharp tip indenter is brought to the surface of the material and loaded into the surface until a desired load is reached, after which the indenter is unloaded from the surface (Fig. 3e–h). The unloading of the indenter allows for the elastic/plastic deformation of the material to be measured. Distinct from pillar compression, no pillars are milled in the nanoindentation experiment and the average depth of the tip displacement is much smaller, approximately 200 nm (Fig. 3e). This shallow displacement means that nanoindentation is not as influenced by defects that may be present in the LLZO SE compared to pillar compression. Fig. 3g shows a noticeable pile-up of LLZO after nanoindentation. Pile-up is caused by plastic flow of material upwards around the indenter due to strain hardening below the tip. A pile-up correction was applied and is described in the ESI.†³⁸ Nanoindentation of the same LLZO pellets tested by pillar compression provides a Young's modulus of ∼145 GPa and a hardness of ∼11.1 GPa (Table S1†). The close agreement between nanoindentation and pillar compression results for Young's modulus and hardness indicates that size-dependent effects are unlikely for the pillar diameter used here.³⁹

Fig. 4 provides results of pillar compression loading/unloading experiments to failure. Load–displacement curves for varying loading rates are provided in Fig. 4a. The load–displacement curves of each LLZO pillar after failure are translated into engineering stress–strain curves given the pillar's initial height and diameter at half height. The engineering stress–strain curves are presented in Fig. 4b for all pillars loaded until failure.

Pillar compression provides three methods with which Young's modulus can be estimated: (1) from the average slope of multiple unloading stress–strain curves before failure; (2) from the linear elastic region of the pillar's stress–strain curve when loaded until failure; and (3) using eqn (1) to account for detailed pillar geometry, as presented in Yang et al.⁴⁰ By estimating the Young's modulus from averaging the unloading curves (Method 1) it is assumed that elastic deformation of the flat punch tip is minimized. During some tests, the pillar would fail during the first loading, meaning the Young's modulus could not be estimated during the unloading. Predicting Young's modulus from the fracture curve (Method 2) is common in mechanics testing but may suffer inaccuracies from elastic compliance of the flat punch tip itself. Eqn (1) considers non-idealities of pillar geometry when estimating Young's modulus, E, as:

	(1)

where D₀, H, and θ are as defined above (Fig. 3a), δ_t is the pillar displacement under applied load P, and ν is Poisson's ratio. The correction factor, ψ, is estimated given the pillar radius of curvature, top diameter, and height.⁴⁰

Fig. 4c plots compressive strength vs. Young's modulus for all pillars loaded until failure. Compressive strength was recorded when catastrophic failure of the pillar occurred. Young's modulus was calculated using the methods described above and the results differentiated in Fig. 4c. A discussion comparing the results of all three methods is provided in the ESI (Table S4),† where all three methods, statistically, estimate the same values. The effect of loading rate on LLZO Young's modulus and compressive strength was evaluated using the variable loading rate data from Fig. 4a. Both properties were determined to be independent of loading rate (Fig. S2†).

The results of Fig. 4 display several noteworthy features. First and foremost is the large range of strength (0.93–2.63 GPa) and Young's modulus (72.1–150.97 GPa) values measured. A high degree of variability in compressive strength and Young's modulus occurred routinely within a single test site of one pellet, meaning that two pillars directly next to each other would produce different mechanical properties (Fig. S3†). This indicates that mechanical property variations between pillars are due to structural changes of the LLZO SE across small length scales. The second noteworthy feature is the single, strong linear relationship between compressive strength and Young's modulus values observed across multiple areas and multiple pellets (Fig. 4c), with a regression model for the two variables resulting in a significant relationship (F_1,12 = 45.85, p < 0.001). Finally, we note that all pillars tested have nearly identical failure strain, despite large differences in failure stress. When comparing all stress–strain curves for the fractured pillars (Fig. 4b), the average strain at failure is measured to be 2.2 ± 0.3%. Compressive strength tests are often plagued with variance and uncertainty due to complex failure modes.⁴¹ In cases where the results are highly influenced by variations in failure mode geometry and/or loading methods, we would expect large differences in failure strain across tests. The fact that all compression tests shown here have statistically the same failure strain indicates that the observed differences in failure stress of each pillar are likely pillar dependent, not method dependent. Interestingly, this result also indicates that all LLZO pillars tested here fail under approximately the same amount of deflection. Overall, these features of the results indicate that the large variance in compressive strength observed could be due to microscale variations between pillars, particularly defects, with more defects reducing the stress needed to reach the failure strain.

SEM images obtained during pillar compression provide further insight into failure modes and crack initiation/propagation in LLZO. LLZO used in this study shows the tendency for axial splitting, top surface splitting, shearing, and complete failure across/through grain boundaries due to crack propagation. Axial splitting occurs when angled slip planes intersect at some depth of the pillar where a crack will initiate due to increased stress concentrations at that location (Fig. 5a).⁴² Top surface splitting occurs perpendicular to slip planes, where cracks originate at the flat punch tip interface and cause parallel cracks to travel down the height of the pillar (Fig. 5b).⁴² Shearing, or diagonal splitting, may be caused by a shear plane existing within the pillar at some angle. Maximum shear stress occurs along this plane, resulting in failure and the release of material from the pillar.⁴³ The observed failure modes arise from the brittle nature of LLZO. Strong covalent bonds prohibit plastic flow across slip planes, resulting in cracking and chipping before catastrophic failure. SEM imaging of one LLZO pillar before compression shows significant microscale porosity present below the top surface (Fig. 5c). FIB cross-sectional analysis of another pillar after compressive failure shows internal porosity and cracks present (Fig. 5d). Such defects do not arise from the FIB milling process, as shown through SEM imaging of a straight-milled trench (Fig. S4†). In ceramics, porosity acts as an internal defect providing a crack launch site,⁴⁴ and can be a major contributor to premature failure in compression. During compression, almost all cracking occurs parallel to the force applied, regardless of slip plane orientation. Additionally, both intra- and intergranular cracking is apparent after pillar fracture has occurred, as shown in Fig. S5.† The failure modes observed here present a major risk for through-cracking and short circuiting of the SE, given a crack-propagation-based model of lithium intrusion.⁴⁵

Effective microscale porosity model

Identifying specific causes of premature failure for ceramics in compression is notoriously difficult, as evidenced by the multiplicity of LLZO failure modes observed in pillar compression experiments (Fig. 5). Eqn (2) has been presented in the literature to provide an estimate of Young's modulus reduction as a function of material porosity, x:

E = E0e−bx	(2)

where E₀ is the nonporous Young's modulus and b is an empirical fitting parameter.⁴⁶ This equation, fit to our experimental data, provides an estimate of the effective porosity, i.e. effective loss of LLZO material strength, required to produce the wide range of Young's modulus and compressive strength measurements observed. In the case of microscale pillar compression measurements, it is not possible to experimentally measure localized LLZO porosity at each compression site. Instead, we rely on MD simulations to predict E as a function of effective porosity, x, and estimate an appropriate fitting parameter b. MD simulations were chosen to capture the surface effects of nanovoids that would be left undetected by continuum-scale computational approaches. In the absence of the ability to effectively simulate multiple types of defects that may be present in a single pillar, effective porosity is used to represent the general loss of material strength that occurs with reduced cross-sectional area and the introduction of stress concentrations, thus modeling general effects similar to those caused by types of defects other than pores. In addition to porosity, there could be other factors contributing to reduced Young's modulus, such as grain boundaries and impurities. However, porosity is likely dominant, especially considering the >50% reduction in Young's modulus and compressive strength demonstrated in Fig. 4c.

Porosity in MD simulations was represented as a spherical void in the center of a material model periodic in x, y, and z directions (Fig. 6a), with the void volume vs. total volume set to match the target effective porosity. Since the models are periodic in all directions, they stand for bulk material with the same volume percentage of unconnected voids. Stress–strain curves were generated by uniaxially compressing the simulation volume in one direction and relaxing the other two directions to achieve a stress-free state (Fig. 6b). From stress–strain curves, we calculated Young's modulus (E) and compressive strength (σ) for models with porosity and normalized their values with simulated pristine LLZO Young's modulus (E₀) and compressive strength (σ₀), respectively. Fitting these data to eqn (2) yields a value for b of 1.919 as listed in Table 1.

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Simulated values of normalized Young's modulus and compressive strength can be compared with experimental values given experimental estimates of E₀ and σ₀. We obtain the former from nanoindentation, a surface measurement less sensitive to defects and voids, providing an E₀ ∼ 145 GPa. This value aligns well with the largest Young's modulus measured by pillar compression (E₀ = 150.97 GPa), as well as literature values provided in Table S1.† We take the compressive strength of this same pillar, 2.63 GPa (the largest compressive strength measured), to be an estimated lower bound for σ₀. A plot of normalized Young's modulus vs. normalized compressive strength shows good agreement between simulation and experiment (Fig. 6c).

Fig. 6d plots simulation and experimental values of E/E₀ vs. effective porosity, x. Plotted simulation values were obtained directly from MD results; plotted experimental values come from fitting measured Young's modulus values to the porosity model (eqn (2)) using b = 1.919 and an E₀ = 150.97 GPa to determine an effective localized porosity value (x) for each value. Plotting each pillar's effective porosity with its compressive strength, we obtain Fig. 6e. The results of both analyses show good agreement between computational and experimental data, indicating that microscale porosity and other defects that may produce effects similar to those described by eqn (2) are the cause of the wide range of Young's modulus and compressive strength values in LLZO.

The strength of such an analysis lies in the ability to relate a localized LLZO effective porosity change to a predicted change in mechanical properties. For example, our computational model indicates an effective porosity of 10% results in a 17.5% decrease in Young's modulus. Sandt et al. reported a similar result for LLZO Young's modulus using ab initio simulations, concluding that a porosity of 10% results in a 27% decrease in Young's modulus.⁴⁷ Fitting our experimental results to the porosity model derived from MD simulations enables the large range of experimental Young's modulus (150.97–72.1 GPa) being accounted for by a localized (i.e. microscale) porosity range of 0–38.5%. It is important to note that our results consider localized variations in material strength. While porosity values up to 38.5% are unlikely for bulk LLZO, such material strength reductions are conceivable in localized regions at μm scale and when other defects that contribute to increased effective porosity are considered. It is important to recognize limitations in porosity-based simulations in the limit of high porosity (e.g. >25%).⁴⁶ In such cases, pore geometry and pore–pore interactions can have significant effects on the results. To examine the extent of pore–pore interactions in LLZO pellets used in this work, we obtained a cross-sectional SEM image of a polished pellet (Fig. S6†). Microscale voids present in the cross-sectional view show well-dispersed porosity, suggesting limited pore–pore interactions in experimental LLZO samples. The nature of the porosity inclusion on MD simulation results was briefly explored, where it was observed that one void region or multiple void regions had an insignificant effect on the mechanical response as long as the same porosity volume was used. In cases where high porosities are required to account for large reductions in Young's modulus or compressive strength, further modeling of the effects of other types of defects (e.g. cracks, impurities, etc.) on the mechanical response of LLZO may be needed to account for the observed property changes.

Conclusions

Experimental measurements of LLZO compressive strength and Young's modulus by pillar compression indicate surprising variability in the mechanical properties of SE pellets across micrometer length scales. Highest measured values of Young's modulus by pillar compression agree well with literature reports for bulk LLZO, as well as our own measurements of the same SE pellet by nanoindentation. The results indicate that a pristine LLZO pillar, with no defects present, has a compressive strength of ∼2.63 GPa. As defect density increases, however, the compressive strength of LLZO will decrease. A reduction in compressive strength of nearly 65%, to 0.93 GPa, was observed, with a corresponding decrease in Young's modulus from 150.97 to 72.1 GPa.

The wide range of localized mechanical properties in LLZO may explain the non-uniform plating and stripping in LLZO-based solid-state batteries. We presume that the least resilient pillars correlate with preferential sites for mechanical degradation or Li intrusion. Therefore, complete characterization of LLZO SE should include pillar compression or other microscale techniques to assess the weakest local areas in a bulk specimen. Conventional techniques that measure average mechanical properties are insufficient to capture the local variation that likely dictates ultimate robustness of LLZO in a battery. An initial theory explaining the high variance of experimentally measured mechanical properties based on microscale variations in each pillar (i.e. defects) – represented quantitatively by an effective porosity value – produces good agreement with experimental data. Additionally, our experimental results reveal a nearly constant failure strain across different areas in different LLZO SE samples, even though their compressive strengths varied significantly. Larger porosity means larger surface areas, which provide more opportunities for cracks to initiate and further leads to fracture. Therefore, porosity induces two deformation mechanisms within LLZO: one is the densification process which can lead to a larger strain compared to void-free LLZO; the other is the crack initiation process making the failure happen earlier compared to void-free LLZO. The competition between the two mechanisms appears to reach a balance at a consistent value of uniaxial strain. Future experimental and computational work would do well to study LLZO in complex loading conditions to better understand the consistent failure strain observed here and simulate polycrystalline LLZO in compression with different grain sizes. The current interatomic potential for LLZO makes such simulations prohibitively expensive. Therefore, we leave it to future MD simulation work to computationally elucidate the interactions among porosities, defects, grain boundaries, and fracture.

Disclaimer

This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

Data availability

The raw data required to reproduce these findings can be made available upon request to the author.

Author contributions

Jaron V. Moon – conceptualization, data curation, formal analysis, investigation, project administration, visualization, supervision writing – original draft, review, and editing. Md Takmil Sakir – investigation, data curation, formal analysis, methodology, software, visualization, writing – review and editing. Wooseok Go – investigation, data curation, formal analysis, resources, visualization, writing – review and editing. Rui Xie – investigation, software, formal analysis. Michael C. Tucker – funding acquisition, resources, supervision, writing – review and editing. Marca Doeff – funding acquisition, resources, supervision, writing – review and editing. Haoran Wang – funding acquisition, software, resources, supervision, writing – review and editing. Roseanne Warren – conceptualization, funding acquisition, supervision, writing – review and editing.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Science Foundation under Award #2152561 and Award #2152562, and the Assistant Secretary for Energy, Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This work made use of the University of Utah Nanofab EMSAL shared facilities of the Micron Technology Foundation Inc. Microscopy Suite sponsored by the John and Marcia Price College of Engineering, Health Sciences Center, Office of the Vice President for Research. The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged.

References

1. K. J. Kim, M. Balaish, M. Wadaguchi, L. Kong and J. L. M. Rupp, ‘Solid-State Li–Metal Batteries: Challenges and Horizons of Oxide and Sulfide Solid Electrolytes and Their Interfaces’, Adv. Energy Mater., 2021, 11(1), 1–63,  DOI:10.1002/aenm.202002689 .
2. F. Aguesse, et al., ‘Investigating the dendritic growth during full cell cycling of garnet electrolyte in direct contact with Li metal’, ACS Appl. Mater. Interfaces, 2017, 9, 3808–3816,  DOI:10.1021/acsami.6b13925 .
3. L. C. De Jonghe, L. Feldman and A. Buechele, ‘Failure Modes Of Na-Beta Alumina’, Solid State Ionics, 1981, 5, 267–269 CrossRef CAS  , [Online]. Available: https://escholarship.org/uc/item/2jp514j2.
4. E. J. Cheng, A. Sharafi and J. Sakamoto, ‘Intergranular Li metal propagation through polycrystalline Li6.25Al0.25La3Zr2O12 ceramic electrolyte’, Electrochim. Acta, 2017, 223, 85–91,  DOI:10.1016/j.electacta.2016.12.018 .
5. X. Liu, et al., ‘Local electronic structure variation resulting in Li “filament” formation within solid electrolytes’, Nat. Mater., 2021, 20(11), 1485–1490,  DOI:10.1038/s41563-021-01019-x .
6. S. Kalnaus, N. J. Dudney, A. S. Westover, E. Herbert and S. Hackney, ‘Solid-state batteries: The critical role of mechanics’, Science, 2023, 381, eabg5998,  DOI:10.1126/science.abg5998 .
7. J. Hu, et al., ‘3D stress mapping reveals the origin of lithium-deposition heterogeneity in solid-state lithium-metal batteries’, Cell Rep. Phys. Sci., 2022, 3, 100938,  DOI:10.1016/j.xcrp.2022.100938 .
8. F. Zhang, et al., ‘A review of the effect of external pressure on all-solid-state batteries’, eTransportation, 2023, 15, 100220,  DOI:10.1016/j.etran.2022.100220 .
9. W. Zaman, et al., ‘Temperature and Pressure Effects on Unrecoverable Voids in Li Metal Solid-State Batteries’, ACS Appl. Mater. Interfaces, 2023, 15, 37401–37409,  DOI:10.1021/acsami.3c05886 .
10. X. Ke, Y. Wang, G. Ren and C. Yuan, ‘Towards rational mechanical design of inorganic solid electrolytes for all-solid-state lithium ion batteries’, Energy Storage Mater., 2020, 26, 313–324,  DOI:10.1016/j.ensm.2019.08.029 .
11. S. Yu, et al., ‘Elastic Properties of the Solid Electrolyte Li7La3Zr2O12 (LLZO)’, Chem. Mater., 2016, 12, 197–206,  DOI:10.1021/acs.chemmater.5b03854 .
12. J. E. Ni, E. D. Case, J. S. Sakamoto, E. Rangasamy and J. B. Wolfenstine, ‘Room temperature elastic moduli and Vickers hardness of hot-pressed LLZO cubic garnet’, J. Mater. Sci., 2012, 47, 7978–7985,  DOI:10.1007/s10853-012-6687-5 .
13. A. Wang, J. F. Nonemacher, G. Yan, M. Finsterbusch, J. Malzbender and M. Krüger, ‘Mechanical properties of the solid electrolyte Al-substituted Li7La3Zr2O12(LLZO) by utilizing micro-pillar indentation splitting test’, J. Eur. Ceram. Soc., 2018, 38, 3201–3209,  DOI:10.1016/j.jeurceramsoc.2018.02.032 .
14. Y. Kim, H. Jo, J. L. Allen, H. Choe, J. Wolfenstine and J. Sakamoto, ‘The Effect of Relative Density on the Mechanical Properties of Hot-Pressed Cubic Li 7 la 3 Zr 2 O 12’, J. Am. Ceram. Soc., 2016, 99(4), 1367–1374,  DOI:10.1111/jace.14084 .
15. X. L. Phuah, J. Cho, T. Tsakalakos, A. K. Mukherjee, H. Wang and X. Zhang, ‘Defects in flash-sintered ceramics and their effects on mechanical properties’, MRS Bull., 2021, 46, 44–51,  DOI:10.1557/s43577-020-00014-y .
16. J. D. Hogan, L. Farbaniec, T. Sano, M. Shaeffer and K. T. Ramesh, ‘The effects of defects on the uniaxial compressive strength and failure of an advanced ceramic’, Acta Mater., 2016, 102, 263–272,  DOI:10.1016/j.actamat.2015.09.028 .
17. G. McConohy, et al., ‘Mechanical regulation of lithium intrusion probability in garnet solid electrolytes’, Nat. Energy, 2023, 8, 423,  DOI:10.1038/s41560-022-01186-4 .
18. S. Hu, P. Xu, L. S. De Vasconcelos, L. Stanciu, H. Ni and K. Zhao, ‘Elastic Modulus, Hardness, and Fracture Toughness of Li6.4La3Zr1.4Ta0.6O12Solid Electrolyte’, Chin. Phys. Lett., 2021, 38(9), 098401,  DOI:10.1088/0256-307X/38/9/098401 .
19. S. Mukhopadhyay, et al., ‘Structure and stoichiometry in supervalent doped Li7La3Zr2O12’, Chem. Mater., 2015, 27, 3658–3665,  DOI:10.1021/acs.chemmater.5b00362 .
20. H. Guo, et al., ‘Achieving high critical current density in Ta-doped Li7La3Zr2O12/MgO composite electrolytes’, J. Alloys Compd., 2021, 856, 157222,  DOI:10.1016/j.jallcom.2020.157222 .
21. R. A. Jonson, E. Yi, F. Shen and M. C. Tucker, ‘Optimization of Tape Casting for Fabrication of Li6.25Al0.25La3Zr2O12Sheets’, Energy Fuel., 2021, 35, 8982–8990,  DOI:10.1021/acs.energyfuels.1c00566 .
22. M. D. Uchic and D. M. Dimiduk, ‘A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing’, Mater. Sci. Eng. A, 2005, 400–401, 268–278,  DOI:10.1016/j.msea.2005.03.082 .
23. E. Camposilvan and M. Anglada, ‘Size and plasticity effects in zirconia micropillars compression’, Acta Mater., 2016, 103, 882–892,  DOI:10.1016/j.actamat.2015.10.047 .
24. H. Fei, A. Abraham, N. Chawla and H. Jiang, ‘Evaluation of micro-pillar compression tests for accurate determination of elastic-plastic constitutive relations’, J. Appl. Mech., 2012, 79(6), 1–9,  DOI:10.1115/1.4006767 .
25. R. Xu, H. Sun, L. S. de Vasconcelos and K. Zhao, ‘Mechanical and Structural Degradation of LiNi x Mn y Co z O 2 Cathode in Li-Ion Batteries: An Experimental Study’, J. Electrochem. Soc., 2017, 164(13), A3333–A3341,  DOI:10.1149/2.1751713jes .
26. A. P. Thompson, et al., ‘LAMMPS – a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales’, Comput. Phys. Commun., 2022, 271, 108171,  DOI:10.1016/j.cpc.2021.108171 .
27. G. Kresse and J. Hafner, ‘Ab initio molecular dynamics for liquid metals’, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47(1), 558–561,  DOI:10.1103/PhysRevB.47.558 .
28. G. Kresse and J. Furthmüller, ‘Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set’, J. Phys. Chem. A, 1996, 54(16), 169–186,  DOI:10.1021/acs.jpca.0c01375 .
29. G. Kresse and D. Joubert, ‘From ultrasoft pseudopotentials to the projector augmented-wave method’, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59(3), 1758–1775,  DOI:10.1103/PhysRevB.59.1758 .
30. G. Kresse and J. Furthmüller, ‘Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set’, Comput. Mater. Sci., 1996, 6, 15–50,  DOI:10.1016/0927-0256(96)00008-0 .
31. A. Stukowski, ‘Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool’, Modell. Simul. Mater. Sci. Eng., 2010, 18, 015012,  DOI:10.1088/0965-0393/18/1/015012 .
32. K. Meier, T. Laino and A. Curioni, ‘Solid-state electrolytes: Revealing the mechanisms of Li-Ion conduction in tetragonal and cubic LLZO by first-principles calculations’, J. Phys. Chem. C, 2014, 118, 6668–6679,  DOI:10.1021/jp5002463 .
33. E. Rangasamy, J. Wolfenstine, J. Allen and J. Sakamoto, ‘The effect of 24c-site (A) cation substitution on the tetragonal-cubic phase transition in Li7-xLa3-xAxZr 2O12 garnet-based ceramic electrolyte’, J. Power Sources, 2013, 230, 261–266,  DOI:10.1016/j.jpowsour.2012.12.076 .
34. F. Langer, J. Glenneberg, I. Bardenhagen and R. Kun, ‘Synthesis of single phase cubic Al-substituted Li7La3Zr2O12 by solid state lithiation of mixed hydroxides’, J. Alloys Compd., 2015, 645, 64–69,  DOI:10.1016/j.jallcom.2015.03.209 .
35. J. Awaka, A. Takashima, K. Kataoka, N. Kijima, Y. Idemoto and J. Akimoto, ‘Crystal structure of fast lithium-ion-conducting cubic Li 7La3Zr2O12’, Chem. Lett., 2011, 40, 60–62,  DOI:10.1246/cl.2011.60 .
36. J. F. Ziegler, M. D. Ziegler and J. P. Biersack, ‘SRIM – The stopping and range of ions in matter (2010)’, Nucl. Instrum. Methods Phys. Res., Sect. B, 2010, 268, 1818–1823,  DOI:10.1016/j.nimb.2010.02.091 .
37. J. A. El-Awady, C. Woodward, D. M. Dimiduk and N. M. Ghoniem, ‘Effects of focused ion beam induced damage on the plasticity of micropillars’, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 104104,  DOI:10.1103/PhysRevB.80.104104 .
38. P. Zhu, Y. Zhao, S. Agarwal, J. Henry and S. J. Zinkle, ‘Toward accurate evaluation of bulk hardness from nanoindentation testing at low indent depths’, Mater. Des., 2022, 213, 110317,  DOI:10.1016/j.matdes.2021.110317 .
39. C. P. Frick, B. G. Clark, S. Orso, A. S. Schneider and E. Arzt, ‘Size effect on strength and strain hardening of small-scale [1 1 1] nickel compression pillars’, Mater. Sci. Eng. A, 2008, 489, 319–329,  DOI:10.1016/j.msea.2007.12.038 .
40. Y. Yang, J. C. Ye, J. Lu, F. X. Liu and P. K. Liaw, ‘Effects of specimen geometry and base material on the mechanical behavior of focused-ion-beam-fabricated metallic-glass micropillars’, Acta Mater., 2009, 57, 1613–1623,  DOI:10.1016/j.actamat.2008.11.043 .
41. M. Iskander and N. Shrive, ‘The effect of the shape and size of initial flaws on crack propagation in uniaxially compressed linear brittle materials’, Theor. Appl. Fract. Mech., 2020, 109, 102742,  DOI:10.1016/j.tafmec.2020.102742 .
42. P. R. Howie, S. Korte and W. J. Clegg, ‘Fracture modes in micropillar compression of brittle crystals’, J. Mater. Res., 2012, 27(1), 141–151,  DOI:10.1557/jmr.2011.256 .
43. R. Shahrin and C. P. Bobko, ‘Micropillar compression investigation of size effect on microscale strength and failure mechanism of Calcium-Silicate-Hydrates (C-S-H) in cement paste’, Cem. Concr. Res., 2019, 125, 105863,  DOI:10.1016/j.cemconres.2019.105863 .
44. A. A. Griffith, ‘The phenomena of rupture and flow in solids’, Philos. Trans. R. Soc. London, 1921, 221, 163–198,  DOI:10.1098/rsta.1921.0006 .
45. C. D. Fincher, et al., ‘Controlling dendrite propagation in solid-state batteries with engineered stress’, Joule, 2022, 6, 2794–2809,  DOI:10.1016/j.joule.2022.10.011 .
46. J. Luo and R. Stevens, ‘Porosity-dependence of elastic moduli and hardness of 3Y-TZP ceramics’, Ceram. Int., 1999, 25, 281–286,  DOI:10.1016/S0272-8842(98)00037-6 .
47. R. Sandt, Y. Wang and R. Spatschek, ‘Investigation of mechanical properties of garnet structured Li7La3Zr2O12 under Al3+ and Ta5+ co-substitutions’, Solid State Ionics, 2023, 402, 116364,  DOI:10.1016/j.ssi.2023.116364 .

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta03596h

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