Abstract
Metastable solid electrolytes exhibit superior conductivity compared to stable ones, making them a subject of considerable interest. However, synthesis of the metastable phase is affected by multiple thermodynamic and kinetic parameters, leading to ambiguity in the organization of stability and metastability. In this study, we organized remnant and intermediate metastability based on temperature. The intermediate metastable phase, which is less stable than the temperature-independent stable phase, typically transforms into the stable phase(s) at high temperatures. In contrast, the remnant metastable phase is formed by first obtaining most stable phase at specific temperatures and then “trapping” it by rapidly changing the temperature. By investigating Li+ conducting chlorides, Li3MCl6 (M = Y and Ho), we demonstrated that heating starting materials to approximately 600 K produced low-temperature Li3MCl6 phase with one formula unit while further heating resulted in high-temperature Li3MCl6 phase with three formula units. Annealing quenched Li3MCl6 at 573 K resulted in a phase transition from the high-temperature to low-temperature phase, indicating that the high-temperature phase was remnant metastable at low temperatures.
1. Introduction
Metastability provides a broad range of crystal and electronic structures and properties, leading to the fabrication of numerous functional solid-state materials, including superconductors,1,2 catalysts,3–5 superionic materials,6–8 and electronic materials.9,10 However, the synthesis of such metastable compounds often necessitates rigorous trial and error because the synthesis should be controlled not only thermodynamically but also kinetically. Studies on the prediction of the energy of inorganic solid-state synthesis using density functional theory (DFT) are in progress.11–13 In situ analysis of the synthesis reactions provides another way to comprehend the existence and roles of intermediates before the formation of thermodynamically stable compounds.13–22 Despite these developments, realizing a mechanism-based approach to the synthesis of predesigned inorganic metastable solids remains challenging.23,24
Because both kinetics and thermodynamics affect the solid-state reactions, determining the metastability of polymorphs requires comparing the free energy under different conditions. Martinolich and Neilson previously proposed the use of reaction coordinate diagrams, also known as “kinetic control” and “kinetic trapping”25 as a necessary approach to stabilize metastable phases.
The metastable phase can be easily understood within a thermodynamic framework at a specific thermodynamic condition. However, when the thermodynamic condition changes, metastable phases can be categorized as intermediate or remnant metastable phases. Energy diagrams of the intermediate and remnant metastable phases are presented in Figure 1. In Figure 1a, the intermediate metastable phase has higher energies than the temperature-independent most stable phase at any temperature. This metastability is not the most stable phase during synthesis, and therefore the starting materials play a critical role in designing the reaction.26 For example, an amorphous precursor with less-stable starting materials leads to the thermodynamically metastable polymorphs of Pb-Nb-Se27 and Na3N.28 In contrast, remnant metastable phases, a term introduced by Sun et al.29 are remnants of phases that were once the most stable at different thermodynamic conditions and are obtained by rapidly changing conditions, which kinetically circumvents the phase transition to the stable phase at the changed conditions. Thus, this metastable phase once becomes the most stable phase, in contrast to intermediate metastability. Examples of remnant metastable materials include traditional silica-based glasses,30,31 metallic glasses,32 the recently developed high-entropy alloys,5,33 and exotic electron states such as spin glasses.10 Figure 1b illustrates the energy diagrams of the low-temperature phase, high-temperature phase, and remnant metastable phase. Low-temperature and high-temperature phases are defined as stabilized phases at each thermodynamic condition. If the transition of the high-temperature phase to the low-temperature phase is circumvented through rapid cooling, the resulting polymorph may be considered a remnant metastable phase. Thus, the type of metastability of polymorphs in a given system cannot be determined solely by the first heating.
Energy diagrams depicting intermediate metastability and remnant metastability. (a) Intermediate metastable system in which the intermediate metastable product is located at an intermediate position. (b) Remnant metastable system in which the remnant metastable product is stabilized by high temperature.
The thermodynamic stability can be examined via thermal analysis. However, when the energies of these thermodynamically competing phases are similar, the heat signal may not be detectable. In such cases, annealing at a lower temperature for an extended period is necessary to distinguish them. The decision tree to determine the type of (meta)stability is shown in Figure 2. The intermediate metastable phase cannot be formed from the stable phase, whereas the low-temperature phase can be obtained by annealing the remnant metastable phase. Therefore, we can distinguish between the pair of temperature-dependent stable and intermediate metastable phases or the remnant metastable and low-temperature phases. Notably, the metastable phase appears at a low temperature in the former pair and a high-temperature is the latter pair.
Decision tree to determine the type of metastability. The system with intermediate metastable and stable phases does not exhibit a transition before or after the annealing of the quenched sample. However, a low-temperature phase can be formed by heating the remnant metastable phase obtained through rapid cooling.
Superionic conductors, which have been intensively studied for their potential application in all-solid-state batteries, constitute a class of materials that are particularly relevant for the study of metastable phases. Among these materials, the Li-ion conducting Li3MCl634 (M: Sc,35 Y,36–39 In,38,40 Dy,41 Ho,41,42 and Er41,43) is a noteworthy motif for investigating new structures and the nature of metastability (Table S1). Li3MCl6 can adopt diverse cation arrangements in the relatively simple hexagonal close-packed structure of Cl, indicating the possibility of various metastable states. The synthetic route employed for their preparation affects their structure.36,37,39 Ball milling and subsequent heating produces crystallized samples of Li3YCl6 with low crystallinity.36 Furthermore, cooling after heat treatment resulted in structural diversity, which is attributed to the formation of stacking faults and local structural changes.37,39 In a previous study, we demonstrated that kinetically stabilized Li3YCl6 with disordered Y could be obtained by low-temperature heating at 595 K.14 The calculated energy difference between these phases was small and negligible exothermic/endothermic signals was detected by differential thermal analysis. The increase in temperature brought about uncommon disorder-order transition of Y arrangement. However, we did not discuss the type of metastability.
In this study, we organized the type of metastability by the relative stabilities of polymorphs of Li3YCl6 and discussed the structure–metastability–property relationship. The type of metastability of Li3HoCl6, in which Ho3+ has a similar ionic radii and electronegativity to Y3+, was also investigated.
2. Experimental
Li3YCl6 and Li3HoCl6 were synthesized by heating a mixture of the anhydrous reagents LiCl, YCl3, and HoCl3 in a molar ratio of 3:1. LiCl, YCl3, and HoCl3 were procured from Kojyundo Chemical, Wako, and Aldrich, respectively. In situ synchrotron X-ray diffraction patterns were collected at the BL02B2 beamline of SPring-8 with a temperature sweep rate of 30 K/min (Proposal numbers: 2019B1195, 2021B1175, 2022B0559, 2022A1698). Near-phase pure samples of the two polymorphs of Li3YCl6 were synthesized based on a previous study.15 The samples were first heated at 700 K for 3–4 h and then rapidly cooled to 300 K by removing them from the furnace. Subsequently, they were subjected to further heating at 573–595 K for 50 h in a sealed quartz tube. XRD patterns were recorded at 300 K using CuKα radiation (Miniflex 600, RIGAKU) at the BL02B2 beamline of SPring-8. The crystal structures were refined using the RIETAN-FP44 program and visualized using the VESTA45 program.
X-ray absorption near edge structure (XANES) measurements of the Y, K, and Ho L3 edges were performed at the Aichi Synchrotron Radiation Center BL5S1 (Proposal number: 2022D3006) and Spring-8BL14B2 (Proposal number: 2022A1736). The local structures surrounding Y and Ho were refined using Artemis.46 Solid-state nuclear magnetic resonance (NMR) spectra of 7Li were recorded on a 500 MHz Bruker NMR spectrometer with a magic angle spinning at 15 kHz. AC impedance measurements were performed using an Sl1260 impedance analyzer. The sample powders were uniaxially pressed at approximately 150 MPa, and the cold-pressed pellets were placed between stainless steel plugs. The potential amplitude was set to 30 mV, and the frequency was swept from 10 to 100 Hz. The conductivity was determined as the total resistivity, which includes both bulk and interface resistances.
3. Results and Discussion
Figure 3 displays the in situ XRD patterns of the mixture of LiCl and MCl3 at different temperatures. Both sets of the LiCl-YCl3 and LiCl-HoCl3 mixtures formed different superstructures through a similar two-step reaction. LiCl and MCl3 were designated as the starting materials. Peaks that can be indexed to Li3MCl6 (M = Y, Ho) with a simple structure were observed from 600 K onwards (Figure 3c). Upon heating, the 2|$\bar{1}$|0 peak was observed, suggesting the formation of Li3MCl6 with a superlattice structure (Figure 3c, top). Henceforth, we shall refer to a simple Li3MCl6 structure with Z = 1 (where Z represents the number of formula units in the cell) as S-Li3MCl6 and a superlattice Li3MCl6 structure with Z = 3 as T-Li3MCl6. The 101 peaks were only observed for the T-phase because the corner of the unit cell was periodically occupied by the M cations. The stoichiometry of M:Cl in the S- and T-phases remained constant, as observed by Rietveld refinement; Li3YCl6 can be referred to in a previous study14 and Li3HoCl6 result is summarized in Table S2–3. Rietveld profiles for S- and T-Li3HoCl6 with minor peaks of LiCl and HoOCl and unknown phase(s) were shown in Figures S1 and S2.
Two-step synthesis of S-Li3MCl6 and T-Li3MCl6 monitored by in situ synchrotron XRD. (a, b) In situ XRD patterns for the reaction of LiCl and MCl3 to produce Li3MCl6. Miller indices of T-Li3MCl6 are shown at the top. Products transformed from S-Li3MCl6 to T-Li3MCl6. (c) Average structural models of S- and T-phases; proposed unit cells are denoted using black lines. (d) Temperature profile and fractions of T-phase acquired from the Rietveld refinement of in situ XRD patterns. Diffraction data of Li3YCl6 are reproduced using a previous study.14
To classify the type of metastability, the reversibility of the phase transition of Li3MCl6 was investigated. Figures 4a and 4b display the XRD patterns of T-Li3YCl6 and T-Li3HoCl6 before and after low-temperature annealing at 573 K. Before annealing, all the peaks were indexed to the T-phases and residual LiCl. The relative intensities of the 101 peaks against the 2|$\bar{1}$|0 peaks of Li3YCl6 and Li3HoCl6 decreased after annealing at 573 K, indicating that T-Li3MCl6 transformed to S-Li3MCl6.
Reversibility of phase transition from T-Li3MCl6 to S-Li3MCl6. XRD patterns of (a) T-Li3YCl6 and (b) T-Li3HoCl6 before and after annealing at 595 and 573 K for 50 h. A decrease in the intensity of the 101 peaks of T-Li3HoCl6 upon annealing indicated the formation of the S-phase. Arrows indicate the broad peaks, which are possibly the stacking faults along the c-axis.
The reversible phase transition from S-Li3MCl6 to T-Li3MCl6 is stable at temperatures below 600 K, while T-Li3MCl6 is a remnant metastable phase at temperatures ranging from 300 to 600 K, and becomes stable at higher temperatures. Notably, the type of metastability in ionic Li3MCl6 was observed to be the same owing to the similar ionic radii and electronegativities47 of Y3+ and Ho3+.
The broad peaks at 5.3, 5.8, and 7.3° that appeared only for S-Li3MCl6, can be assigned as 101, 102, and 104 for the supercell, of which the a axis is the same but the c-axis is 3.5 times larger. Thus, these broad peaks can be attributed to the stacking faults along the c-axis,39 although the Rietveld refinement of this large cell is difficult because these peaks are broad. Therefore, we represent simple structure model of S-Li3YCl6 hereafter. The change was observed in the peak widths of similar broad peaks after the heat treatment of ball-milled samples.36
To gain further insights into the underlying causes of the observed metastability, the extended X-ray absorption fine structure (EXAFS) spectra of Y and Ho and the NMR spectra of Li7 were recorded. The XAFS measurements revealed that the local structures of Y and Ho were not affected by the Li3YCl6 or Li3HoCl6 polymorph. However, the NMR data suggested a slight difference in the local structure of Li+ between the two polymorphs.
The Y K-edge and Ho L3-edge of both S- and T-Li3HoCl6 were also analyzed (Figures S3 and 4). The obtained EXAFS spectra of S- and T-Li3YCl6 were found to be comparable (Figure 5a), as were the profiles of S- and T-Li3HoCl6. The Fourier-transformed EXAFS data of S-Li3YCl6 were well-fitted with the simulated data based on the model without the nearest-neighboring Y–Y, as illustrated in the inset of Figure 5b. The refinement of Li3HoCl6 also suggested that the nearest neighboring Ho–Ho did not exist in the structure (see Supporting Information). Accordingly, a structural model comprising 1D atomic chains with alternate Y and Ho species was proposed (Figure 5c). The structural models derived based on the EXAFS and XRD measurements are shown in Figure 5d. The difference between S- and T-Li3YCl6 is reflected in the periodicity of the different lattices. Y is located at the lattice corner in the T-phase, but loses this periodicity in the S-phase, Y loses this periodicity. This periodicity was observed as the 101 diffraction peak in the XRD pattern, as described earlier.
Local structure of Y or Ho in Li3MCl6. (a) EXAFS spectra of Li3MCl6. (b) Fourier transform of EXAFS analysis of T-Li3YCl6; inset shows the structural model obtained from XANES derived from XRD. (c) Schematic image of the MCl6-VMCl6-MCl6 chain along the c-axis. VM denotes the vacancy at the M site. (d) Schematic image of the arrangement of chains in S- and T-Li3MCl6. (d) Local structural models determined by our EXAFS results, where M atoms and vacancies appear alternatively along the c-direction. To ensure the consistency with the model determined by XRD, random occupation of M atoms at 2d (T-phase) or 2b (S-phase) cites of the same c-plane is considered.
The 7Li NMR spectra of different Li3MCl6 polymorphs suggest distinct differences between them, which contrasts with the findings of the X-ray absorption spectra (Figure 6 and Figure S5 (for a longer range)). The peak positions of S- and T-Li3YCl6 were nearly comparable, though the Li signal of S-phase becomes slightly broad. A broad peak indicates a variety of Li local positions and/or Li diffusion through Li local position. The peaks for S- and T-Li3HoCl6 became significantly broader than those for S- and T-Li3YCl6 because strong interactions between unpaired electron spins in the Ho f orbitals and the Li nuclear spins lead to a broadening of the 7Li resonances, which made it difficult to discuss a more detailed local structure.48
Deviation of the local structure surrounding Li in Li3MCl6 and Li-ion conductivity of S- and T-Li3MCl6. (a) Solid-state 7Li NMR spectra of S- and T-Li3MCl6 measured at room temperature. (b) Arrhenius plot of Li+ conductivity of S- and T-Li3MCl6 determined using AC impedance measurements. The conductivities of S- and T-Li3YCl6 are reproduced from a previous study.14
To gain insights into the change in the Li environment, the conductivity of Li+ was evaluated via AC impedance measurements. The ionic conductivities of the metastable T- and stable S-Li3HoCl6 phases, represented by filled and non-filled circles, respectively, were determined and compared with these of T- and stable S-Li3YCl6 phase.14 The ion conductivities were estimated by the total resistivity of bulk and interface resistivity; the corresponding Nyquist plots are shown in Figures S6 and S7. The slope is not exactly linear at lower temperatures, which may be related to the change in transportation mechanism of either bulk or interface conductivities. The ionic conductivity and activation energy of Li+ conduction for T-Li3HoCl6 were estimated to be 0.14 mS·cm−1 and 18 kJ/mol, respectively. These values were observed to be higher and lower than those for S-Li3HoCl6, which were 0.092 mS·cm−1 and 14 kJ/mol, respectively. The ionic conductivities of Li3MCl6 at room temperature are summarized in Table 1.
Properties of Li3YCl6 and Li3HoCl6
| S-Li3YCl614 | T-Li3YCl614 | S-Li3HoCl6 | T-Li3HoCl6 | |
|---|---|---|---|---|
| Stability at ambient temperature and pressure | Low-temperature stable | Remnant metastable | Low-temperature stable | Remnant metastable |
| Synthesis method | Heating at 595 K | Quenching from 700 K | Heating at 700 K and annealing at 500 K | Quenching from 700 K |
| Lattice Volume per formula unit/Å3·Li3MCl6 | 217.962(7) | 217.638(5) | 218.278(9) | 218.434(7) |
| Local Structure of M | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 |
| Li+ Conductivity (mS·cm−1) | 0.12 | 0.014 | 0.092 | 0.14 |
| S-Li3YCl614 | T-Li3YCl614 | S-Li3HoCl6 | T-Li3HoCl6 | |
|---|---|---|---|---|
| Stability at ambient temperature and pressure | Low-temperature stable | Remnant metastable | Low-temperature stable | Remnant metastable |
| Synthesis method | Heating at 595 K | Quenching from 700 K | Heating at 700 K and annealing at 500 K | Quenching from 700 K |
| Lattice Volume per formula unit/Å3·Li3MCl6 | 217.962(7) | 217.638(5) | 218.278(9) | 218.434(7) |
| Local Structure of M | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 |
| Li+ Conductivity (mS·cm−1) | 0.12 | 0.014 | 0.092 | 0.14 |
Properties of Li3YCl6 and Li3HoCl6
| S-Li3YCl614 | T-Li3YCl614 | S-Li3HoCl6 | T-Li3HoCl6 | |
|---|---|---|---|---|
| Stability at ambient temperature and pressure | Low-temperature stable | Remnant metastable | Low-temperature stable | Remnant metastable |
| Synthesis method | Heating at 595 K | Quenching from 700 K | Heating at 700 K and annealing at 500 K | Quenching from 700 K |
| Lattice Volume per formula unit/Å3·Li3MCl6 | 217.962(7) | 217.638(5) | 218.278(9) | 218.434(7) |
| Local Structure of M | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 |
| Li+ Conductivity (mS·cm−1) | 0.12 | 0.014 | 0.092 | 0.14 |
| S-Li3YCl614 | T-Li3YCl614 | S-Li3HoCl6 | T-Li3HoCl6 | |
|---|---|---|---|---|
| Stability at ambient temperature and pressure | Low-temperature stable | Remnant metastable | Low-temperature stable | Remnant metastable |
| Synthesis method | Heating at 595 K | Quenching from 700 K | Heating at 700 K and annealing at 500 K | Quenching from 700 K |
| Lattice Volume per formula unit/Å3·Li3MCl6 | 217.962(7) | 217.638(5) | 218.278(9) | 218.434(7) |
| Local Structure of M | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 | MCl6-VMCl6-MCl6 |
| Li+ Conductivity (mS·cm−1) | 0.12 | 0.014 | 0.092 | 0.14 |
The formation of remnant metastable T-Li3MCl6 and low-temperature stable S-Li3MCl6 suggests a reversible behavior. A summary of the properties of these phases is presented in Table 1. Although the M position exhibits ordered and disordered behavior in the T-phase and S-phase, respectively, the local ordering of vacancies of the M site is similar. In contrast to our observation of the phase transition from S- to T-Li3MCl6 with increasing temperature, this disorder-order transition with an increase temperature is uncommon because a disorder phase usually has higher entropy and is thermodynamically favorable at high temperatures. An explanation is that entropy becomes higher not only by Y disordering but also Li disordering. Thus, we can hypothesize the disorder of Li in T-Li3YCl6 is higher than that in S-Li3YCl6 at high temperatures.
When comparing the phase transformation of Li3YCl6 and Li3HoCl6 and their lattice parameters, their stability cannot be explained simply by the lattice parameters based on ion interactions. While the lattice volume per formula unit of S-Li3YCl6 was larger than that of T-Li3YCl6, the lattice volume of S-Li3HoCl6 was smaller than that of T-Li3HoCl6. In both cases, larger lattice parameters may account for higher ion conductivity through weak interaction between Li+ and Cl−. In the simple ionic model that is generally suitable for ionic chlorides with relatively simple structures, larger lattice parameters indicate a metastable nature because of weak ionic bonding in Li3MCl6. However, the energy estimated by the small lattice volume of metastable T-Li3HoCl6 cannot explain its metastable nature, in contrast to the case of T-Li3YCl6 with a large volume. Therefore, additional parameters that may affect stability need to be further examined, including the examination of Li and possible stacking faults in the wide temperature range through neutron diffraction, 2D-NMR, Pulsed-filed Gradient Spin-Echo NMR, and TEM.
4. Conclusion
Although the concepts of intermediate and remnant metastability had been proposed, the term “metastability” had been often used for both, which could confuse metastable nature and make difficult understanding the synthesis pathway. In this study, remnant and intermediate metastability were organized and a decision tree was proposed to determine these metastabilities. Through the annealing process of Li3MCl6, the phase transition was established to be reversible. The high-temperature stable phase of Li3MCl6, referred to as T-Li3MCl6, was observed to be a remnant metastable phase at low temperatures (below 573 K). Furthermore, annealing produced low-temperature stable S-Li3MCl6, which contained several defects in the crystal structure.
As a general conclusion, the importance of defining metastability should be emphasized. While the terms “high-temperature” and “low-temperature” phases are commonly used, they lack a clear definition of thermodynamic stability. By defining temperature (range) of stable phase, either intermediate or remnant metastable phase is decided. Notably, thermodynamic parameters other than temperature, including pressure and magnetic field, can be used to understand intermediate and remnant metastability. In cases where the energy differences of thermodynamically competing phases are small, local structures and stacking faults can be critical factors in determining thermodynamic stability. However, despite the discovery of stacking faults in several systems, the thermodynamic stability of complicated, layered structures is not yet fully understood. To fully comprehend the thermodynamic stability of such structures, establishing clear definitions and utilizing accurate and quantitative structure analysis related to thermodynamic parameters is essential. This will enable the rational design of metastable polymorphs.
Acknowledgment
A. Miura and H. Ito thank Dr. Shogo Kawaguchi, Dr. Shintaro Kobayashi, and Dr. Yuki Mori (JASRI) for their support in synchrotron XRD measurement in SPring-8, Dr. Naoya Nakagawa for support with solid-state NMR, and Prof. Tomoki Erata for helpful discussion about NMR spectra. This research was partially supported by KAKENHI (Grant No. JP20KK0124), JST PRESTO (Grant Nos. JPMJPR21Q2 and JPMJPR21Q8), and Grant-in-Aid for JSPS Fellows (21J11152).
Supporting Information
Crystallographic data and details of EXAFS, NMR and impedance measurements. These materials are available on https://doi.org/10.1246/bcsj.20230132.
References
J. E. Shelby, M. Lopes, Introduction to Glass Science and Technology, The Royal Society of Chemistry, 2005.
Akira Miura
Akira Miura received a Ph.D. in Engineering from Hokkaido University in 2007 and carried out postdoctoral research in the Department of Chemistry & Biochemistry at Cornell University and at the Institut für Anorganische Chemie at RWTH Aachen University in 2008–2010. I subsequently moved to the Faculty of Engineering at Hokkaido University in 2014. Now, I am an associate professor at Hokkaido University. My research interests include the synthesis and characterization of oxides, hydroxides, oxynitrides, nitrides, sulfides, and chlorides for use in novel semiconductors, catalysts, superconductors, and all-solid-state batteries.
