Entropymetry for detecting microcracks in high-nickel layered oxide cathodes

Significance

Monitoring the health of lithium-ion batteries (LIBs) is the first step toward warranting the operating quality of a battery throughout its lifetime. Nonetheless, diagnosing the state of health of a battery cell without disassembly is nontrivial. In conventional thermodynamics, entropy refers to the directionality of a system related to the degree of freedom or the configurational change when targeting the crystal structure. In this study, this thermodynamic principle is introduced to describe and monitor the structural heterogeneity of the LIB cathode, particularly focusing on microcracks that are known to degrade the performance of high-nickel layered cathodes. Entropymetry is demonstrated as a nondestructive diagnostic tool for examining the cathode, with the ultimate goal of improving the safety and reliability of LIBs.

Abstract

Electric vehicles (EVs) are imposing ever-challenging standards on the lifetime and safety of lithium-ion batteries (LIBs); consequently, real-time nondestructive monitoring of battery cell degradation is highly desired. Unfortunately, high-nickel (Ni) layered oxides, the preferred LIB cathodes for EVs, undergo performance degradation originating from microcrack formation during cycling. Entropymetry is introduced as a real-time analytic tool for monitoring the evolution of microcracks in these cathodes along the state of charge. The entropy change of the layered cathode is associated with the lattice configuration and reflects the structural heterogeneity relevant to the evolution of these microcracks. The structural heterogeneity was correlated with peak broadening in in-situ X-ray diffractometry while varying the experimental conditions that affect crack formation such as the upper cutoff voltage during charging and the Ni-content of the active material. Entropymetry, proposed here as a nondestructive diagnostic tool, can contribute greatly to the safe and reliable operation of LIBs for EVs.

As electric vehicles (EVs) are increasingly finding their way into our everyday lives, the demand for monitoring the battery state with focus on safety and performance has strengthened (1–3). Even if a battery cell is manufactured without defects, it tends to degrade with cycling and time. More challenging is that the degradation behavior is difficult to predict because the available parameters (i.e., the current, voltage, capacity, and temperature) and combinations thereof do not accurately reflect the state of the cell. For example, cells that repeatedly undergo fast charging or are exposed to high temperatures usually exhibit shorter lifetimes (4, 5), but it is nontrivial to forecast when and how the capacity decay starts and evolves. Thus, from the outside, it is difficult to diagnose the health and safety of a cell and this is the very limitation of current battery management systems (BMSs) (3). By contrast, examination of the interior of a cell at the material level is a well-known approach to identify the degradation mechanism. For example, high-nickel (Ni) layered cathode materials, the most popular family of cathode materials for EV applications, are known to degrade by parasitic side reactions on their surface involving transition metal (TM) dissolution in conjunction with Li–Ni cation mixing. However, methods capable of capturing the degradation states of these materials and interfaces in a nondestructive manner are presently unavailable.

The aforementioned degradation of layered oxide cathodes engages in the structural destruction. The details of crystallographic changes during such destruction have been studied in detail using diverse analytical tools including X-ray diffraction (XRD) and transmission electron microscopy (TEM) (6–8). However, these methods are destructive; cycling needs to be terminated to allow the cell to be opened. Therefore, the development of nondestructive ways for analyzing the structure of layered cathode materials during cycling is desirable. Along this direction, entropy could be an appropriate parameter because it relates to the crystallographic ordering of the given layered oxide structure (9, 10).

Entropy is the state function associated with the degree of randomness of a system (11). With respect to inorganic materials, the entropy represents the disordering of atoms in the corresponding crystal lattice. Thus, the arrangement of Li ions in the layered host structure could be correlated to the entropy in such a way that configurational entropy refers to the number of possible arrangements of Li ion occupancies and vacancies in the lattice structure (12, 13). In this regard, Boltzmann’s entropy is described by the following formula:

$$S=k_{\mathit{B}}·\ln W,$$ [1]

where k_B is the Boltzmann constant, and W is the number of possible microstates. In the case of the layered cathode material, W corresponds to the number of arrangements of Li ion occupancies and vacancies.

Applying this logic, if the entropy change (∆S) of a layered cathode material could be measured during cycling, the structural change responsible for inducing performance degradation could be nondestructively monitored. For a battery cell, ∆S could be assessed by measuring the change in the open-circuit voltage (OCV) with respect to the temperature change based on the following series of equations. The derivation of ΔS starts with the following relation involving the Gibbs free energy (ΔG):

$$\mathit{∆}G\mathit{\left(}\mathit{x}\mathit{\right)}=-nFE\left(x\right),$$ [2]

where n is the charge number of the carrier ion (n = 1 for the Li ion), F is the Faraday constant, and E is the OCV. The Gibbs free energy and OCV are both functions of x, the stoichiometry of the Li ion in the formula of the cathode material. The free energy relates to the enthalpy change (∆H) and entropy change (∆S):

$$∆G\left(x\right)=\mathit{∆}H\left(x\right)-T∆S\left(x\right).$$ [3]

Combining Eqs. 2 and 3 yields the following relation between the entropy change and OCV:

$$∆S\mathit{\left(}x\mathit{\right)}=F\left(\frac{\mathrm{d}E\mathit{\left(}\mathit{x}\mathit{\right)}}{\mathrm{d}T}\right).$$ [4]

This equation indicates that ΔS can be obtained by measuring the OCV upon sweeping the temperatures at each state of charge (SOC) of the cell (14–16).

The usefulness of entropymetry was demonstrated for LiCoO₂ by monitoring the structural configuration at different SOCs over cycling, and the effect of adding Ni as a dopant was elucidated in the same context (9). In the present work, we further expand the territory of entropymetry to cover popular high-Ni layered cathode materials, particularly focusing on their structural destruction as represented by the formation of microcracks. The family of high-Ni layered cathodes has played a pivotal role in increasing the energy density of a cell and thus extending the mileage of EVs (17, 18). However, the high Ni content leads to anisotropic elongation along the c-axis (8), which creates microcracks. The formation of these cracks has a fatal effect on the cycle life because the electrolyte can penetrate the cracks and trigger side reactions that increase the interfacial resistance (19). Importantly, the formation of these cracks and the resulting structural heterogeneity would change ΔS (20, 21), indicating that entropymetry could be an appropriate nondestructive tool to monitor the formation of cracks in high-Ni cathode materials and therefore assess the health of the corresponding cell. By employing various cycling conditions as well as in-situ XRD, we indeed verify that entropymetry can mirror the structural degradation of high-Ni layered oxide cathodes.

Results and Discussion

Interpretation of ∆S Profiles.

Among the family of high-Ni layered cathodes, we evaluated LiNi_0.8Co_0.1Mn_0.1O₂ (NCM811) of which the Ni content is sufficiently large to induce microcracks (8). We first note that the entropy change experienced by layered cathode materials is mainly related to configurational entropy rather than vibrational or electronic entropy. This is in accordance with Fultz and Yazami’s earlier report that the vibrational and electronic entropy contribute insubstantially during the operation of LiCoO₂ (22). Fig. 1A shows the ∆S and dQ dV⁻¹ profiles of precycled NCM811 as a function of the OCV while charging during its first cycle. Interestingly, in the regions shaded pale green where the dQ dV⁻¹ profile exhibits peaks, the ∆S profile declines monotonically with a slope reversal in between the shaded colored regions. This correlation seems reasonable because the peaks of the dQ dV⁻¹ profile usually are associated with electrochemical reactions accompanied by structural changes that alter the lattice arrangements significantly (23).

Fig. 1.

Entropy (change) profiles of NCM811 and their correlation with phase behavior. (A) ΔS (black) and dQ dV⁻¹ (blue) profiles of NCM811 along the OCV landscape. (B) Schematic diagrams of entropy (S) and entropy change (ΔS) with different degrees of energy state separation in the OCV landscape.

To understand the profile shape by particularly focusing on the region demarcated by the orange box in Fig. 1A, three different S profiles were simulated with respect to the energy state (Fig. 1B): no separation (black), mild separation (green), and discrete separation (gray). The “no separation” behavior corresponds to the monotonic Li (de)intercalation in the absence of drastic entropy change, whereas the two split convex profiles (mild and discrete separations) indicate the presence of a restricted phase at the mid-point, dividing the S landscape into front and rear parts (12, 13, 24). The degree of separation between the two states depends on the extent to which the mid-phase condition is restricted. For example, if the mid-phase is completely restricted (S_mid = 0), the front and rear states are discretely separated (see “discrete separation” in Fig. 1B). Each Li site has its own energy state at which a Li ion can be (de)intercalated, and the energy of this site is determined based on the lattice environment offered by the host structure. In this regard, each peak on the dQ dV⁻¹ profile (blue curve in Fig. 1A) can be considered to be the potential at which Li ions are stored at sites with the equivalent energy states. Because the profile of S typically becomes convex when Li ions fill sites of the equivalent energy state, the apex of the convex profile of S corresponds with each peak on the dQ dV⁻¹ profile. In this way, the two pale green regions in Fig. 1B represent two different energy states, which manifest themselves as independent convex parabolas on the S profile. These two convex parabolas are then converted into two separate monotonically declining curves on the ∆S profile. At the same time, the midpoint between the two parabolas in the S profile translates into a slope reversal around the midpoint of the ∆S profile. Thus, the slope reversal on the ∆S profile, in turn, can be correlated with the presence of a restricted phase in the S landscape. Moreover, the more entropically restricted the midphase is, the steeper the reversed slope becomes near the midpoint (gray curve in Fig. 1B). With this logic, the relatively gentle slope reversal in the middle region in Fig. 1A (red arrow in the orange box) indicates mild separation with respect to S. In addition, we calculated the ∆S profile of NCM811 along the SOC by assuming that each peak on the dQ dV⁻¹ profile corresponds to an equivalent energy state of Li sites (see details in SI Appendix, Fig. S1). The calculated ∆S profile corresponds well with the measured ∆S profile, which validates our reasoning above. This interpretation of ∆S in relation to changes in the cathode structure is well aligned with that of previous studies on LiMn₂O₄ (13, 24).

Structural Changes of NCM811 along with the SOC.

We conducted in-situ XRD analysis to observe the structural change of NCM811 during charging with the aim of correlating these changes with its entropy change. Fig. 2A shows the evolution of in-situ XRD peaks corresponding to the c-lattice (003) and a-lattice (110) during charging (8). The changes in these lattice parameters were calculated from the XRD results and are presented in the upper part of Fig. 2B. The c-lattice parameter increases gradually as the potential scans to around 4 V, but decreases abruptly at around 4.2 V. By contrast, the a-lattice parameter decreases continuously in the same potential range. When charging commences, the distance between the oxygen layers increases as Li ions are extracted because of the diminished screening effect of Li ions. As charging progresses, however, the negative charges on the oxygen atoms decrease because the TM 3d and O 2p orbitals overlap to a certain extent, thereby lowering the interslab repulsion and causing the oxygen layers to collapse at high SOC levels (23). Apart from the changes in the lattice parameters, peak broadening also provides information related to the crystalline size and microstrain of the material (25). The broadening of the (003) peak also changes drastically near 4.2 V and this is discussed in detail in the following section.

Fig. 2.

In-situ XRD analysis for tracking the lattice changes of NCM811 during charging. (A) Evolution of the in-situ XRD profiles around the (003) and (110) peaks during the first charging of NCM811 after precycling. The red profiles were obtained at the voltages noted on the left. (B) Changes (Top) in the c- and a-lattice parameters along with the OCV and their derivatives (Bottom). D represents d-spacing.

In fact, the lattice parameters of most Ni-rich NCM layered cathodes undergo similar changes (8, 26); particularly, with increasing nickel content (notably ≥ 0.8), the H2 → H3 phase transition occurs more dominantly near 4.2 V and the corresponding decrease in the intensity of the c-lattice peak becomes more prominent (23), introducing local strain at the grain boundaries (27). Notably, the scale of the c-lattice change (~0.6 Å) is much larger than that of the a-lattice (~0.06 Å), as is evident from the differential d-spacing curves with respect to the voltage (dD dV ⁻¹, D = d-spacing) in Fig. 2B. Therefore, consistent with the literature (19, 26, 28, 29), the anisotropic expansion/contraction near 4.2 V and the resulting abrupt change in the c-lattice parameter must be the main culprit responsible for the formation of cracks between and within Ni-rich NCM particles.

Structural Heterogeneity by Microcrack Formation.

Fig. 3 A–C shows cross-sectional images of secondary particles of the NCM811 cathode at different cycling states. Here, the precycle refers to the state after two formation cycles, whereas the other two images show the cathode after 100 cycles at 60 °C with upper cut-off potentials of 4.1 V and 4.3 V, respectively. The cycling performance and voltage profiles of these different conditions are presented in SI Appendix, Fig. S2. After the precycle, the particle did not appear to contain any microcracks at all (Fig. 3A) whereas after 100 cycles with upper cut-off voltages of 4.1 V and 4.3 V, the particles displayed cracks of various magnitudes (Fig. 3 B and C ). A comparison of the two particles after 100 cycles revealed that crack formation at the microscale was more severe when the cathode was charged to 4.3 V (Fig. 3C), reconfirming that cracks are dominantly formed at higher voltages (30, 31).

Fig. 3.

Characterizing microcrack formation by SEM and XRD analyses. Cross-sectional SEM images of NCM811 particles (A) after precycle and at 101^th cycle at 60 °C with upper cutoff of (B) 4.1 V and (C) 4.3 V. The scale of the white bar is 5 μm. Magnified in-situ XRD profiles near (003) peaks at OCVs of (D) 4.15 V, (E) 4.2 V, and (F) 4.25 V.

For high-Ni NCM cathodes, heterogenous lithiation is a well-accepted phenomenon as lithiation takes place throughout many primary particles with different sizes and levels of contact with the electrolyte. Doeff et al. (32) confirmed the occurrence of heterogenous lithiation in polycrystalline cathode materials by observing the distribution of the oxidation states of Ni in a secondary particle using X-ray absorption near-edge structure analysis to create a 2D map. In contrast to the intuition that heterogenous lithiation in a secondary particle could occur mainly because of the kinetic limitation of Li ion diffusion through the secondary particle, the heterogenous SOC in a secondary particle remains even after an extended period of rest. Chueh et al. (21) explained that the heterogenous SOC across primary particles (even after a long rest) could arise to relieve the heterogeneous stress field among the primary particles in a polycrystalline secondary particle. In the same context, Liu et al. (20) revealed the occurrence of inhomogeneities between the surface and bulk with respect to the oxidation state during cycling. In particular, high-voltage operation is known to play a role in inducing local disorder and strain from which microcracks evolve.

Within a primary particle, intragranular cracks could also be generated in relation to heterogeneous (de)lithiation along the c-lattice (33). These intragranular cracks can be triggered by the formation of dislocations or transition to the rock salt phase, both of which give rise to tensile stress and consequently uneven (de)intercalation of Li ions. A crack usually evolves from the premature stage to the more discrete, permanent stage as tensile stress is accumulated, and it also tends to propagate through a granule (6, 34). Scanning transmission electron microscopy and electron energy loss spectroscopy analyses portray a consistent scenario with regard to microstructural evolution (SI Appendix, Fig. S3). Upon scanning from the bulk region to an intragranular crack (white arrow in SI Appendix, Fig. S3A), the oxidation state of Ni decreases (SI Appendix, Fig. S3B), which is indicative of the formation of the rock salt phase in the vicinity of the crack. Hence, an intragranular phase transition constitutes evidence of the atomic heterogeneity of a cycled NCM811 particle involving crack formation (6).

Fig. 3 D–F show the magnified in-situ XRD peaks of NCM811 after the precycle and at the 101^th cycle at 60 °C with upper cut-off potentials of 4.1 V and 4.3 V, respectively. The reason for focusing on the profiles when the potential passed through 4.2 V in each case is the drastic phase transition known to occur around this potential. Peak broadening or separation at 4.2 V could occur via the following mechanisms. First, the NCM family undergoes an H2 → H3 phase transition at ~4.2 V although the degree of the phase transition is known to vary depending on the Ni content (8). Second, multiple peaks could appear in reflection of a heterogenous SOC within a secondary particle (35). In these particles, rapid and anisotropic contraction of randomly oriented primary particles also causes the strain and extent of lithiation to vary (21). In this manner, the formation of intra- and intergranular cracks would accelerate heterogenous (de)lithiation accompanied with peak broadening around ~4.2 V during charging. Doeff and Liu et al. (36) also reported that cracks hinder the facile diffusion of Li ions into particles such that the local difference in ionic diffusivity among primary particles causes different SOCs in a secondary particle.

The peak broadening was evaluated quantitatively by measuring the integral breadth, defined as the integral area of the peaks over the intensity of the highest peak, at OCVs of 4.15, 4.2, and 4.25 V to compare the peak broadening for different cycling conditions during charging. For the precycled electrode, the (003) peak shifts to a higher 2-theta value without peak separation (Fig. 3D), which means that the phase separation between H2 and H3 is impeded (33, 37). Nonetheless, owing to the presence of the energy barrier between the two phases, the integral breadth slightly increases at 4.2 V (the potential at which the H2 → H3 phase transition is known to occur), as compared with that at 4.15 V and 4.25 V. However, the cycled NCM811 electrodes showed peak separations and broader peaks at 4.2 V (Fig. 3 E and F). Between the two different cutoff conditions, the electrode with the cutoff of 4.3 V had broader peaks (Fig. 3F) than that with the cutoff of 4.1 V (Fig. 3E). This observation can be understood in a way that the phase separation between H2 and H3 becomes more significant during cycling with the higher cutoff voltage in the microscopic environment in which crack formation accelerates uneven (de)lithiation along the c-lattice layers. Additionally, intergranular cracks themselves give rise to a heterogenous SOC between primary particles. In the same vein, the degree of shift with respect to the c-lattice parameter from 4.15 V to 4.25 V increases from Fig. 3D to Fig. 3F: 0.36 Å after the precycle, 0.45 Å after 100 cycles with a cutoff of 4.1 V, and 0.52 Å after 100 cycles with a cutoff of 4.3 V. These results imply that the broader distribution of d-spacing of the c-lattice layers directly stems from the layers splitting into lithiated and delithiated ones, which results in the emergence of dual XRD peaks for the (003) plane. Overall, the microcracks would affect the lithiation heterogeneity throughout all the particles, and this property can be captured by measuring the peak broadening using in-situ XRD at ~4.2 V.

Detection of Microcracks from ∆S Profiles.

Fig. 4A displays the cycling performance of four cells operated for different cycling periods or under different conditions: 50 or 100 cycles at 60 °C with cutoff potentials of 4.1 or 4.3 V. These series of data verify that the cyclability of NCM811 is highly sensitive to the cutoff voltage when cycled at high temperatures. To correlate the cycling performance with the degree of crack formation, we plotted the integral breadths for these cells after 50 or 100 cycles (Fig. 4B). The integral breadths of all the cells remain in the narrow range when the operating potential is below 4.1 V. However, the integral breadth profiles increased rapidly around 4.2 V for all of the cells, but they increased distinctly with that of the cell operated for 100 cycles with a cutoff of 4.3 V having increased most significantly. In the same line as the aforementioned description, the increase in the integral breadth is attributed to the H2 → H3 phase transition. The increase is thus associated with heterogenous lithiation induced by microcracks, suggesting that the cell with a cutoff of 4.3 V experienced crack formation most considerably for 100 cycles. Importantly, the changing trend observed for the integral breadth profiles bears a remarkable resemblance to that of the ∆S profiles (Fig. 4C), particularly near 4.2 V. The cell operated for 100 cycles with a cutoff of 4.3 V exhibited the greatest decrease in ∆S. This correlation between the integral breadth and ∆S can be understood on the basis of the rationale that heterogeneous lithiation over different particles to broaden the (003) peak is directly linked to the behavior of ∆S, as the heterogeneity represents the complexity in the atomic configuration in the lattice. Specifically, as the microstructures of particles become heterogeneous, the number of available microstates at the given SOC decreases, with the result that ∆S is lowered accordingly. The ∆S measurements were quite reproducible over multiple cells for identical cycling conditions (SI Appendix, Fig. S4). For accurate measurement of entropymetry, the potentiometric method was adopted with 3.5 h rest time at each SOC point. The lattice distortion accompanying the phase transition above 4.2 V hinders Li diffusion between primary particles, which further accelerates the heterogenous (de)lithiation. The rapid decline in the Li ion diffusivity above 4.2 V was confirmed by analyses using the galvanostatic intermittent titration technique (SI Appendix, Fig. S5) (38).

Fig. 4.

Cycle life, integral breadth of XRD peaks, and entropy changes of NCM811 with different cycling conditions. (A) Cycling performance of four NCM811 cells for 50 or 100 cycles at 60 °C with cutoff potentials of 4.1 or 4.3 V, respectively. (B) Changes in the integral breadth (integrated intensity / maximum intensity of the highest peak) based on analyses of the in-situ XRD peaks. (C) Entropy changes vs. OCV. The error bars at 4.2 V correspond to the range of minimum and maximum values obtained from four different cells measured under the same conditions.

As depicted in Fig. 5, the energy states of the Li sites are more or less equivalent in the original state as the local lattice environments of the Li sites are largely identical. However, the formation of cracks perturbs the original uniform energy states of the Li sites such that, at a given SOC, the number of possible microstates decreases; that is, the configurational entropy is lowered. Projecting the impact of the local lattice environment on individual Li ions in the process of diffusion, those Li ions in the original state have equivalent energy barriers for diffusion to homogeneously lithiate a particle. In contrast, in the case of a cracked particle, Li ions experience different energy barriers for diffusion at a given state of charging, whereupon heterogeneous lithiation is promoted. All in all, as a result of the increasing formation of cracks, heterogeneous environments constitute the core of uneven lithiation and could explain why entropymetry can serve as a tool for detecting cracks in Ni-rich layered oxide cathodes.

Fig. 5.

Schematic comparison between homogeneous and heterogeneous lithiation of an NCM811 particle before and after degradation. As the number of microcracks and extent of surface degradation increase, heterogeneous lithiation preferably occurs, which causes the configurational entropy to decrease.

Generalization across the Family of High-Ni Layered Oxides.

Other than the NCM811 cathodes, entropymetry was applied to NCM622 and LiNiO₂ (Fig. 6 A–D) to see the versatility of this technique with respect to the detection of crack formation arising from high-Ni compositions. For this test, half-cells containing both NCM622 and LiNiO₂ were cycled at 60 °C with the cutoff potential of 4.3 V. As displayed in Fig. 6C, the capacity of the NCM622 cell gradually decreased for 100 cycles, whereas that of the LiNiO₂ cell steeply declined even within 25 cycles. The more severe capacity fading of the LiNiO₂ cell is ascribed to the aforementioned mechanism that, the higher the Ni content of the NCM cathode, the greater is the amount of shrinkage along the c-axis above 4.1 V (8). This axial strain induces severe crack propagation and a rapid decline in capacity. A SEM analysis visualized the lesser extent of crack formation in secondary particles of NCM622 after 100 cycles than those of LiNiO₂ after only 25 cycles (Fig. 6 A and B). To confirm the correlation between the degree of crack formation and the change in the entropymetry profile, the entropy changes of NCM622 and LiNiO₂ were measured before and after cycling. Precycled LiNiO₂ exhibited the signature trough at 4.2 V (the pale green region in Fig. 6D), which downshifted after 25 cycles, and is consistent with the trend observed for NCM811 in Fig. 4C. By contrast, the change in the entropy of NCM622 after 100 cycles with a cutoff of 4.3 V was far less prominent in the signature region compared to both LiNiO₂ after 25 cycles and NCM811 after 100 cycles, indicating that the heterogeneity in its structure was less advanced. The comparative results between these two cathodes with their different Ni contents reconfirm that entropymetry is a useful tool for evaluating the extent to which microcracks have developed.

Fig. 6.

Degree of microcrack formation, cycle life, and entropy changes of NCM622 and LiNiO₂. Cross-sectional SEM images of (A) NCM622 and (B) LiNiO₂ particles after 100 cycles at 60 °C with upper cutoff of 4.3 V. The scale of the white bar is 5 μm. (C) Cycling performance of half-cells with NCM622 and LiNiO₂ cathodes at 60 °C with cutoff potential of 4.3 V. (D) Entropy changes along OCV for the NCM622 and LiNiO₂ cells before and after cycling.

Conclusions

In summary, we demonstrated the effectiveness of entropymetry as a nondestructive analytical tool for diagnosing the formation and evolution of microcracks in high-Ni layered cathodes, which is closely related to their cycle life. Entropymetry detects microcracks by utilizing the structural heterogeneity as the main parameter because the formation and propagation of microcracks change the number of microstates of Li ion occupancy/vacancy and thus the configurational entropy. We foresee the advancement of BMS technology by taking into consideration the key chemical reactions in a cell and the structural changes in the electrodes, and expect entropymetry to play a critical role in the development of this technology.

Materials and Methods

Detailed information of the materials and methods used in this work is provided in SI Appendix, including electrochemical tests, characterization of materials, and entropy measurements.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix.