Glass-like thermal transport in polycrystalline perovskite lithium-ion conductor Li_3/8Sr_7/16Hf_1/4Ta_3/4O₃

Abstract

Understanding the thermal properties of lithium-ion conductors is vital for optimizing heat dissipation and enhancing the overall performance, reliability, and safety of all-solid-state batteries. Here, we investigate the specific heat and thermal conductivity of Li_3/8Sr_7/16Hf_1/4Ta_3/4O₃ (LSHT), a promising perovskite-type lithium-ion conductor. We found that LSHT exhibits glass-like thermal behavior with a low thermal conductivity of 1.7 ± 0.5 W m⁻¹ K⁻¹ at room temperature, comparable to some amorphous materials yet distinct from typical crystalline perovskites. Our theoretical analysis indicates that diffusons contribute significantly to heat transfer within this highly disordered material. These findings provide crucial insights into thermal transport in LSHT, which are essential for effective thermal management in all-solid-state batteries utilizing this material.

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All-solid-state batteries (ASSBs) are increasingly recognized as promising alternatives to conventional lithium-ion batteries, offering superior safety, enhanced energy density, and extended cycle life due to the elimination of flammable liquid electrolytes.¹ Among the diverse classes of solid electrolytes, oxide-based systems stand out for their high thermal stability, mechanical integrity, and electrochemical compatibility.^2–4

Perovskite-type Li_3xLa_{2/3 − x}TiO₃ (LLTO) is one of the most promising oxide-based solid electrolytes due to its high bulk lithium-ion conductivity, which can reach up to 1 × 10⁻³ S cm⁻¹ at room temperature.^5,6 It also offers excellent thermal stability, good mechanical strength, and low electronic conductivity, making it attractive for safe and durable solid-state battery applications. Despite these advantages, LLTO suffers from poor chemical stability against lithium metal, which limits its compatibility with lithium metal anodes, and exhibits high grain boundary resistance, which significantly reduces its overall ionic conductivity to about 2 × 10⁻⁵ S cm⁻¹ at room temperature.⁶ To address these issues, researchers developed multiple modified perovskite compositions such as (Li_0.45La_0.85)ScO₃,⁷ Li_2x − ySr_{1 − x − y}La_yTiO₃,⁸ and Li_3/8Sr_7/16Ta_3/4Zr_1/4O₃ (LSTZ).⁹ Building on LSTZ, substitution of Zr with Hf led to the optimized composition Li_3/8Sr_7/16Hf_1/4Ta_3/4O₃ (LSHT), which achieves a high ionic conductivity of 3.8 × 10⁻⁴ S cm⁻¹ and a low activation energy of 0.36 eV.¹⁰

While considerable progress has been made in understanding the electrochemical properties of LSHT, its thermal properties remain largely unexplored. Thermal management is critical in battery systems to mitigate temperature (T) gradients, enhance operational safety, and ensure long-term reliability.¹¹ Inadequate heat dissipation can result in localized overheating and thermal runaway, which compromises both safety and performance.¹² Recently, there has been increased interest in the thermal transport behavior of solid electrolytes.^13–16 Therefore, a detailed understanding of the thermal behavior of solid electrolytes like LSHT is essential for the rational design of next-generation ASSBs.

In this work, we investigate the thermal properties of LSHT, including its specific heat (C_p) and thermal conductivity (κ) over a broad temperature range. We found that LSHT exhibits glass-like thermal transport with a low κ of 1.7 ± 0.5 W m⁻¹ K⁻¹ at room temperature. This thermal behavior can be attributed to the combination of boundary scattering, structural disorder and vacancy-driven phonon scattering. These results yield valuable understanding of the thermal transport mechanisms in LSHT.

Fig. 1a shows the crystal structure of LSHT with Pm3̄m symmetry. In this perovskite crystal structure, Li ions occupy the midpoints of the cube edges, Sr ions occupy the A-sites, while Hf and Ta ions are located at the B-sites, each surrounded by oxygen octahedra. The perovskite framework is important because it supports efficient Li-ion migration, contributing to both high ionic conductivity and stability.¹⁰ Recent structural analysis¹⁷ indicates that Li ions may reside on different crystallographic sites. Specifically, Li ions are found at the (24 k) site at the unit cell edge, whereas oxygen atoms deviate from typical face-centered locations. This configuration forms a “zig–zag” migration pathway for Li ions, rather than a straight path. The zig–zag pathway may facilitate Li transport by providing accessible vacancies, although ordering effects at low temperatures could reduce conductivity.

Fig. 1 (a) Cubic perovskite structure of LSHT. (b) XRD patterns of LSHT pellets measured along different orientations together with a powder sample, indicated by schematic diagrams. Standard XRD pattern calculated from reported structure¹⁷ is shown for comparison.

The X-ray diffraction (XRD) patterns of LSHT pellets measured along different orientations are shown in Fig. 1b. The diffraction peaks are indexed to the cubic perovskite structure, confirming the formation of LSHT. The lattice parameter was refined to be 3.98 Å, consistent with the previous reports on LSHT.^10,17 A minor LiTaO₃ impurity phase was detected, similar to a previous study.¹⁷ The XRD patterns also reveal a discernible texture effect in the LSHT pellets, with the (100) plane being the most preferred orientation on the press surface and the (211) plane being the preferred orientation on the cross-section surface. The orientation factors along the (100) direction were calculated as 0.13 for the press surface sample. The (211) direction has an orientation factor of 0.05 for the cross-section surface sample. Details of the calculation are provided in SI. These values indicate a moderate degree of crystallographic alignment in the LSHT pellets.

Scanning electron microscopy (SEM) images of LSHT, shown in Fig. 2a and b, reveal a dense, homogeneous microstructure with an average grain size of about 3 μm. The grains are tightly packed with well-defined intergranular connectivity and minimal porosity. Some layer-like structures are shown in Fig. 2b. The energy-dispersive X-ray spectroscopy (EDS) shows peaks corresponding to O, Ta, Hf, and Sr, with measured atomic percentages of 68%, 15%, 5%, and 12%, respectively, in good agreement with the expected composition. EDS elemental mapping also confirms a uniform distribution of all elements throughout the sample.

Fig. 2 SEM micrographs of the fracture surfaces of LSHT pellet showing (a) low-magnification and (b) high-magnification views. (c) Corresponding EDS spectrum illustrating elemental peaks for O, Ta, Hf, and Sr. (d) Elemental distribution maps of O, Ta, Hf, and Sr within the LSHT pellet.

The temperature-dependent C_p of LSHT was measured using both Quantum Design physical property measurement system (PPMS) for low temperatures and differential scanning calorimetry (DSC) for high temperatures, as presented in Fig. 3a. The details on the measurements are provided in the SI. The C_p converges toward the Dulong–Petit limit¹⁸ at high temperatures (0.45 J g⁻¹ K⁻¹), indicative of classical lattice vibrations dominating thermal energy storage at elevated temperatures.

Fig. 3 (a) Temperature dependence of C_p of LSHT measured via PPMS and DSC. (b) Low-temperature C_p/T versus T² plot of LSHT with linear fit analysis.

Fig. 3b shows a linear dependence of C_p/T against T² at low temperatures. This trend can be fitted with the Debye model,¹⁹ as detailed in SI. The fitting yields a Debye temperature θ_D = 437 ± 7 K. Using the obtained Debye temperature, the average sound velocity v_s was calculated to be v_s = 3472 ± 55 m s⁻¹. The room temperature physical properties of LSHT are summarized in SI. The value of the Debye temperature and derived sound velocity are similar to other oxide lithium-ion conductors, such as Li_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZTO).¹⁶

Fig. 4a presents the κ of polycrystalline LSHT measured along different directions in comparison with the single crystal of prototypical perovskite KTaO₃ (KTO)²⁰ and amorphous SiO₂.²¹ LSHT exhibits a remarkably lower κ than KTO across the entire temperature range, comparable to amorphous SiO₂. The pronounced reduction in κ can be attributed to several factors. First, the increased boundary-scattering in the polycrystalline sample can suppress κ. Second, the doping of multiple cations introduces substantial atomic mass and force-constant disorder, which strengthens phonon scattering and suppresses thermal transport. Third, the significant concentration of Li vacancies intrinsic to the LSHT structure further enhances phonon scattering by introducing additional mass and bonding disorder. The recently reported structure of LSHT suggests a higher concentration of Li vacancies than previously assumed.¹⁷ Such atomic-scale disorder is necessary to facilitate high ionic conductivity but is also causing low, glass-like κ.¹³ In addition to these factors, strong phonon anharmonicity—previously observed in other complex solid electrolytes—likely^14–16 plays a key role in limiting κ in LSHT. Anharmonicity increases phonon–phonon scattering rates, particularly at elevated temperatures, further reducing the mean free path (MFP) and impeding heat transport. Together, these effects result in the low glass-like κ of LSHT.

Fig. 4 (a) Temperature dependence of the κ of LSHT measured for in-plane and for cross-plane directions. High-temperature κ was determined by the laser flash analysis (LFA) method. For comparison, the data of single-crystal KTO²⁰ and amorphous SiO₂²¹ are included. (b) Porosity-corrected solid thermal conductivity (κ_s) of LSHT with the dashed line as the estimated minimum thermal conductivity (κ_min) based on the Cahill model.²² (c) Decomposition of κ_s into propagon and diffuson contributions. (d) Temperature-dependent phonon mean free path extracted from low-temperature data.

The κ of LSHT was corrected for porosity to obtain the solid thermal conductivity (κ_s), as shown in Fig. 4b. Details of the porosity correction can be found in the SI. Anisotropic κ is clearly manifested in the LSHT samples, with the in-plane (κ_‖) component consistently exceeding the cross-plane (κ_⊥) counterpart. This anisotropy can be rationalized by the crystallographic texture revealed by XRD analysis. The ratio of κ_‖ to κ_⊥ is about 1.2 : 1 at 100 K, consistent with the moderate texture observed by XRD. It was reported that even for cubic structure, the orientation can cause anisotropy in κ.²³ The preferred crystallographic orientation and possible alignment of grains during densification contribute to anisotropic phonon transport.²⁴ Additionally, the layer-like microstructure observed in SEM images may decrease κ_‖ by introducing more grain boundaries and interfaces that scatter phonons, further enhancing the anisotropic behavior. The dashed line in Fig. 4b indicates the estimated minimum thermal conductivity (κ_min) based on the Cahill model,²² which serves as a reference for showcasing the low κ of LSHT.

To account for the texture effect, we calculated the average solid thermal conductivity κ_avg, as shown in Fig. 4c. Calculation details are provided in the SI. The obtained room temperature κ_avg value is 1.7 ± 0.5 W m⁻¹ K⁻¹. The temperature dependence of κ_avg shows a weak increase with increasing temperature. This behavior is common in amorphous materials²⁵ but is unusual for crystalline materials, which typically exhibit an apparent κ peak at intermediate temperatures. The weak temperature dependence of κ is consistent with the glass-like thermal transport behavior observed in materials with complex or highly defective crystal structures.^16,26 Additionally, two minor anomalies appear in the low-temperature regime ∼40 K and ∼130 K. However, comparison with specific heat data indicates that these features are not associated with typical phase transitions. Possible explanations may involve Li-ion activation processes or a broadened, smeared phase transition. Further investigation is needed to fully understand their origins.

To elucidate the underlying thermal transport mechanisms in LSHT, an analytical two-channel model²⁷ was applied to fit the experimental thermal conductivity (κ_exp) data (Fig. 4c). Details of the fitting are shown in SI. In this framework, heat conduction is decomposed into contributions from two distinct channels: propagons and diffusons.²⁸ Propagons are phonons with well-defined group velocities under the harmonic approximation, behaving independently in a gas-like manner. On the other hand, diffusons mediate thermal transport through coupling between different phonon modes that are close in energy and momentum, which should be independent under the harmonic assumption. This mechanism becomes prominent in complex or disordered crystals where anharmonicity and structural complexity hinder propagons.¹⁵

Based on the two-channel model, the thermal conductivity of LSHT is given by: κ_avg = κ_pr + κ_diff, where κ_pr is the contribution from propagons and κ_diff is the contribution from diffusons. The κ_pr component exhibits a peak near 58 K, arising from the competition between the increasing specific heat and the reduction of phonon MFP due to increased phonon scattering. The peak temperature in LSHT falls within the range reported for other solid electrolytes, such as LLZTO (22 K)¹⁶ and NaZr₂P₃O₁₂ (NZP) (45 K).¹⁵ In contrast, κ_diff increases monotonically with temperature due to enhanced mode coupling in the disordered structure. The interplay between the decreasing κ_pr and increasing κ_diff results in the overall weak temperature dependence of κ observed in LSHT. At room temperature, diffusons contribute 34% of the κ_s, indicating that diffuson-mediated transport plays a significant role in the κ of LSHT. Similar behavior was observed in other ionic conductors, such as LLZTO,¹⁶ NZP,¹⁵ and NaSbS₂.²⁹

The average phonon MFP of LSHT at low temperatures can be calculated based on the Debye–Callaway model.³⁰ As shown in Fig. 4d, the MFP exhibits a steep decrease from ∼2 μm at 3 K to ∼4 nm at 50 K. This rapid reduction with increasing temperature highlights the strong temperature dependence of phonon scattering processes in LSHT. The upper limit of MFP is comparable to the average grain size of 3 μm determined by SEM, as expected at low temperatures where phonon scattering is dominated by grain boundaries.

In conclusion, we investigated the thermal properties of perovskite lithium-ion conductor LSHT. The C_p measurements yielded a Debye temperature of 437 ± 7 K and a sound velocity of 3472 ± 55 m s⁻¹. The κ of LSHT was measured to be 1.7 ± 0.5 W m⁻¹ K⁻¹ at room temperature, exhibiting glass-like thermal transport behavior, comparable to amorphous materials. Two-channel modeling of the κ data indicated that diffusons play an important role in heat conduction. These findings provide valuable insights into the underlying mechanisms governing thermal transport in this lithium-ion conductor.

Y. W.: conceptualization, investigation, formal analysis, writing – original draft. Q. J.: investigation, writing – review & editing. S. L.: validation. L. S.: supervision, project administration, writing – review & editing. Y. L.: investigation, resources, writing – review & editing. X. C.: conceptualization, supervision, project administration, funding acquisition, writing – review & editing.

This work was supported by the National Science Foundation (NSF) under Grant no. 2144328. The high-T κ measurements were supported by NSF Grant no. 2321302.

Conflicts of interest

There are no conflicts to declare.

Data availability

Data for this article, including XRD, EDS, specific heat, and thermal conductivity data, are available at Zenodo at https://doi.org/10.5281/zenodo.16839157.

Supplementary information (SI): details of experiments, orientation factor, bulk sound velocity calculation, and two-channel fitting. See DOI: https://doi.org/10.1039/d5cc04693a.

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Footnotes

† Current address: Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Texas, 76019, USA.

‡ Current address: Beijing Frontier Research Center on Clean Energy, Huairou Division, Institute of Physics, Chinese Academy of Sciences, Beijing, 101400, P. R. China.

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