Thermal Transport in Ag8TS6 (T= Si, Ge, Sn) Argyrodites: An Integrated Experimental, Quantum-Chemical, and Computational Modelling Study

Technical Summary: Thermal Transport in Ag8TS6 (T= Si, Ge, Sn) Argyrodites

Problem Statement
Thermoelectric materials require low lattice thermal conductivity ($\kappa_L$) to maximize efficiency, yet many high-performance candidates suffer from a correlation between low $\kappa_L$ and high ionic conductivity, which can compromise device stability. While Ag-based argyrodites (general formula $A_{(11-n)/m}^{m+}T_n^+Q_6^{2-}$) are known for exceptionally low $\kappa_L$ and high ionic conductivity, the specific mechanisms governing thermal transport in the sulfide variants $Ag_8TS_6$ ($T = Si, Ge, Sn$) remain incompletely understood. Existing computational models for predicting $\kappa_L$ face a trade-off: traditional models (e.g., Slack, Cahill) often lack accuracy across the full temperature range or overestimate values, while rigorous ab initio methods are computationally prohibitive for high-throughput screening. Furthermore, the interplay between chemical bonding, anharmonicity, and the independence of thermal versus ionic conductivity in these specific sulfides requires a comprehensive investigation combining experimental data with advanced modeling.

Methodology
The study employs an integrated approach combining experimental synthesis and characterization with multi-scale computational modeling:

1. Experimental Characterization:

   • Synthesis: $Ag_8TS_6$ ($T = Si, Ge, Sn$) samples were synthesized via high-temperature solid-state reactions.
   • Structural Analysis: Powder X-ray diffraction (XRD) was performed from 100 K to 400 K to confirm phase purity and investigate potential phase transitions.
   • Transport Measurements: Thermal diffusivity was measured using laser flash analysis (173–500 K), and ionic conductivity was determined via electrochemical impedance spectroscopy (233–303 K) using electron-blocking electrodes to isolate ionic contributions. Electronic conductivity was verified to be negligible.
   • Elastic Properties: Ultrasonic pulse-echo methods were used to measure sound velocities.

2. Computational Modeling:

   • Quantum Chemistry: Density Functional Theory (DFT) calculations (VASP) were used to optimize structures and compute electronic properties. Bonding analysis was performed using Crystal Orbital Hamilton Populations (COHP) and Crystal Orbital Bond Indices (COBI) via the LOBSTER code to quantify bond strengths, covalency, and multi-center interactions.
   • Phonon Properties: Harmonic phonon band structures, group velocities, and Debye temperatures were calculated. Mode-dependent Grüneisen parameters were derived using the Quasi-Harmonic Approximation (QHA) to quantify anharmonicity.
   • Thermal Conductivity Prediction: Two distinct modeling approaches were developed and compared:
     • Grüneisen-Based Two-Channel Model: A modified approach combining Xia's two-channel model (phonon + diffuson contributions) with Bjerg's method for estimating phonon lifetimes based on Grüneisen parameters and Slack's theory. This avoids expensive anharmonic force constant calculations.
     • Machine-Learned Interatomic Potentials (MLIP): A foundational MLIP (MACE-MP-03b) was utilized to compute thermal conductivity via the full two-channel lattice dynamics approach (Simoncelli et al.), solving the Wigner transport equation.

Key Contributions and Results

• Bonding and Anharmonicity: Chemical bonding analysis reveals that while $T-S$ bonds are strong and covalent, the $Ag-S$ interactions are weak, characterized by occupied antibonding states below the Fermi level. This leads to distorted $Ag^+$ coordination environments and "rattler-like" behavior. The study identifies significant bond heterogeneity, including weak $Ag-Ag$ interactions and hypervalent multi-center bonds ($S-Ag-S$), which drive strong anharmonicity.
• Phonon Properties: All three compounds exhibit dynamically stable structures with no imaginary phonon modes. The low-frequency acoustic modes are dominated by $Ag^+$ vibrations, resulting in low sound velocities (approx. 1000–1500 m/s) and low Debye temperatures. Large Grüneisen parameters are observed for these low-energy modes, confirming high anharmonicity.
• Thermal Conductivity Modeling:
  • Both the Grüneisen-based model and the MLIP-based approach successfully predict the ultra-low lattice thermal conductivity of $Ag_8TS_6$ compounds, showing good agreement with experimental data, particularly at temperatures above 200 K.
  • The results confirm that heat transport is dominated by the diffuson channel (non-propagating vibrational modes), consistent with previous findings in selenide argyrodites.
  • Discrepancies at low temperatures (0–50 K) in experimental data compared to idealized models were attributed to point-defect scattering and boundary scattering (grain boundaries). An analytical model incorporating these scattering mechanisms successfully reproduced the low-temperature behavior.
• Decoupling of Conductivities: Experimental measurements demonstrate that thermal and ionic conductivities are independent in these materials. While ionic conductivity increases by over an order of magnitude between 233 K and 303 K, thermal conductivity remains nearly constant. This suggests that ionic and thermal conductivities can be tuned independently, a crucial finding for thermoelectric applications.
• Isovalent Substitution: Replacing the tetrel atom ($Si, Ge, Sn$) results in minimal differences in bonding character, sound velocities, Grüneisen parameters, and thermal conductivity, indicating that the thermal transport properties are robust across this family.

Significance and Claims
The paper claims to establish a robust framework for predicting the thermal conductivity of complex inorganic materials by integrating bonding analysis with efficient computational models. The primary significance lies in demonstrating that:

1. Bonding Analysis as a Predictor: The specific bonding environment (weak $Ag-S$ bonds, antibonding states, and multi-center interactions) is sufficient to predict the low thermal conductivity and high anharmonicity of these materials.
2. Efficient High-Throughput Screening: The proposed Grüneisen-based two-channel model and the foundational MLIP approach offer computationally inexpensive alternatives to full ab initio anharmonic calculations. These methods are suitable for high-throughput screening of thermal conductivity, provided that scattering effects (defects, boundaries) are accounted for in the interpretation of low-temperature data.
3. Independent Tuning: The study reinforces the finding that in Ag-based argyrodites, thermal and ionic conductivities are decoupled, allowing for the potential optimization of thermoelectric performance without compromising ionic stability.

The authors modestly note that while the MLIP and Grüneisen models show strong agreement with experiments, further verification is needed to define the limits of foundational ML potentials for complex systems and to refine automated training procedures for specific composition spaces.