Revisiting thermal transport in CuCl: First-principles calculations and machine learning force fields

TL;DR

This work provides a robust first-principles framework for predicting lattice thermal conductivity in strongly anharmonic materials by incorporating temperature-dependent IFC renormalization, four-phonon scattering, and full mode-coupled transport within the TDEP approach. By validating a machine-learning force field for pressure-dependent calculations, the authors reproduce the monotonic decrease of κ_l with pressure and reveal that TA four-phonon scattering and reduced TA group velocity are primary drivers of the ultralow κ_l in CuCl. The study demonstrates the critical roles of higher-order phonon processes and harmonic renormalization, and establishes a practical methodology for accurate thermal transport modeling in similar materials. The findings have implications for thermoelectric and thermal barrier coating design where low κ_l and pressure response are key considerations.

Abstract

Accurate prediction of lattice thermal conductivity ($κ_l$) in strongly anharmonic materials requires renormalized interatomic force constants (IFCs) and appropriate incorporation of diagonal and off-diagonal contributions and higher-order scattering. We investigate CuCl, a highly anharmonic system with a simple zincblende structure and ultralow $κ_l$. Our calculations, including IFC renormalization and four-phonon scattering, show excellent agreement with the experiment, underscoring the critical role of both effects in the accurate estimation of $κ_l$. Furthermore, the unusual pressure dependence of $κ_l$ is explored using a rigorously validated machine-learned force field, with the predicted values showing good agreement with the experimentally observed trend of monotonic decrease. This behavior is primarily driven by a significant increase in four-phonon scattering and a reduction in the group velocity of transverse acoustic modes. Overall, this study establishes a robust framework for modeling thermal transport in strongly anharmonic materials.

Figures (9)

• Figure 1: Calculated phonon dispersion and phonon density of states (PDOS) of CuCl: (a) Phonon dispersion at 0K calculated using different exchange-correlation functionals, compared with experimental data measured at 4.2K (Ref. Prevot_JPCSSP77). (b) Phonon dispersion at 300K without and with thermal expansion (TE), showing its minimal effect. The dispersion obtained using IFCs at 0 K is also shown for direct comparison. (c) Phonon dispersion at different temperatures, showing mode hardening with increasing temperature. The results in panels (b) and (c) were obtained using the PBEsol functional.
• Figure 2: Calculated lattice thermal conductivity of CuCl as a function of temperature using IFCs obtained at selected temperatures and fully temperature-dependent IFCs. Results are presented for (a) three-phonon (3ph) interactions only, and (b) combined three- and four-phonon (3ph + 4ph) interactions. Experimental $\kappa_{l}$ data are taken from Slack et al. Slack_PRB82, where the ambient-pressure values are obtained by extrapolating measurements in the range 0.5-2.8 GPa.
• Figure 3: Comparison of CuCl lattice thermal conductivity for different exchange-correlation functionals and computational methods. In all our cases, IFC renormalization and four-phonon scattering are included. 'TE' denotes the correction for lattice thermal expansion. Literature data are also presented, including experimental results Slack_PRB82, BTE calculations without IFC renormalization and four-phonon scattering Togo_PRB15Mukhopadhyay_PRB17, calculations with IFC renormalization on second-order terms only (without four-phonon scattering) Yang_SCPMA23, and MD simulations Knoop_PRL23.
• Figure 4: (a) Calculated three-phonon (3ph) and four-phonon (4ph) scattering rates for acoustic modes at 300 K. (b) Spectral thermal conductivity and its cumulative sum, with percentage contributions of each mode to the total thermal conductivity.
• Figure 5: Comparison of total energies and atomic forces predicted by DFT and MLFF. The accuracy of the MLFF is quantified using RMSE, MAE, and $R^2$ metrics, as given in the plot.