Diffuson-Dominated Thermal Transport Crossover from Ordered to Liquid-like Cu$_3$BiS$_3$:The Negligible Role of Ion Hopping

TL;DR

The paper addresses ultralow lattice thermal conductivity in phase-change Cu3BiS3 across ordered and liquid-like phases. It combines experimental crystal-structure characterization, first-principles self-consistent phonon calculations with bubble corrections (SCPB), the Wigner transport equation (including population and diffuson contributions), and machine-learning-based Green-Kubo molecular dynamics to probe lattice dynamics and heat transport. It finds $\kappa_L \approx 0.34$–$0.36\ \mathrm{W\ m^{-1}\ K^{-1}}$ at 400 K in both phases, with diffuson-like transport dominating and ion hopping playing a negligible role, as confirmed by GK-EMD. The study shows that strong anharmonicity from Cu/Bi vibrations and dense phonon spectra drive the diffuson channel, and that ordered-crystal models can reasonably capture κ in partially occupied/disordered phases, offering a practical approach for evaluating thermal transport in complex materials.

Abstract

Fundamentally understanding lattice dynamics and thermal transport behavior in liquid-like, partially occupied compounds remains a long-standing challenge in condensed matter physics. Here, we investigate the microscopic mechanisms underlying the ultralow thermal conductivity in ordered/liquid-like Cu$_3$BiS$_3$ by combining experimental methods with first-principles calculations. We first experimentally synthesize and characterize the ordered structure and liquid-like, partially Cu-atom occupied Cu$_3$BiS$_3$ structure with increasing temperature. We then combine self-consistent phonon calculations, including bubble-diagram corrections, with the Wigner transport equation, considering both phonon propagation and diffuson contributions, to evaluate the anharmonic lattice dynamics and thermal conductivity in phase-change Cu$_3$BiS$_3$. Our theoretical model predicts an ultralow thermal conductivity of 0.34 W/m/K at 400 K, dominated by diffuson contributions, which accurately reproduces and explains the experimental data. Importantly, the machine-learning-based molecular dynamics (MD) simulations not only reproduced the partially Cu-atom occupied Cu$_3$BiS$_3$ structure with the space group $\mathrm{P2_12_12_1}$ but also successfully replicated the thermal conductivity obtained from experiments and Wigner transport calculations. This observation highlights the negligible impact of ionic mobility arising from partially occupied Cu sites on the thermal conductivity in diffuson-dominated thermal transport compounds. Our work not only sheds light on the minimal impact of ionic mobility on ultralow thermal conductivity in phase-change materials but also demonstrates that the Wigner transport equation accurately describes thermal transport behavior in partially occupied phases with diffuson-dominant thermal transport.

Figures (5)

• Figure 1: Rietveld refinement of the powder X-ray diffraction (PXRD) data recorded at 300 K and 500 K for the Cu$_3$BiS$_3$ sample and representations of the different crystal structures of Cu$_3$BiS$_3$ (space group $P{2_12_12_1}$ and $Pnma$. Purple, blue, and yellow colors represent Bi, Cu, and S, respectively.
• Figure 2: (a) Trajectory sampling plot of ab initio molecular dynamics simulation (AIMD) at 500 K. Inset: Crystal structure characterization with eight-fold coordination of S atom. (b) The comparison of summed crystal orbital Hamilton populations for different Cu–S bonds.
• Figure 3: Finite-temperature phonon dispersions calculated using the SCPH method with bubble digram correction (SCPB method) for (a) $P{2_12_12_1}$ phase and (b) $Pnma$ phase. (c) Calculated temperature dependent averaged lattice thermal conductivity, including contributions from population and coherence conductivities, considering both 3ph and 4ph scattering processes. Illustration: Comparison of the thermal conductivity of the $P{2_12_12_1}$ phase (calculated from 300 to 600 K) and the $Pnma$ phase (calculated from 400 to 600 K) with the $Pnma$ phase obtained using the Green-Kubo method at 400 and 500 K. (d) Comparison of the total thermal conductivity, taking into account various scattering mechanisms such as three-, four-phonon, isotope, boundary, and point defect scattering, with experimental measurements from 2 to 100 K.
• Figure 4: (a) Calculated spectral/cumulative populations’ thermal conductivity $\kappa_P$ using the SCPB+3,4ph models along the three-direction for $P{2_12_12_1}$ phase at 300 K and $Pnma$ phase at 400 K, respectively. (b) Color-coded atomic participation ratio (APR) of Cu atoms projected onto the phonon dispersions for $P{2_12_12_1}$ phase at 300 K. (c) Calculated phonon lifetime as a function of frequency for $P{2_12_12_1}$ phase at 300 K and $Pnma$ phase at 400 K, where the green solid line represents the Wigner limit in time. Inset: Calculated phonon mean free path (MFP) as a function of frequency, where the red solid line represents the Ioffe-Regel limit in space. (d) Calculated spectral/cumulative coherences’ thermal conductivity $\kappa_C$ along the three-direction for $P{2_12_12_1}$ phase at 300 K and $Pnma$ phase at 400 K, respectively.
• Figure 5: (a) Three-dimensional visualizations of the coherences' thermal conductivity $\kappa_C$($\omega_{qj}$,$\omega_{qj'}$) based on the SCPB+3,4ph model along with the $x$-axis for the $P{2_12_12_1}$ phase at 300 K. The diagonal data points ($\omega_{qj}$ = $\omega_{qj'}$) indicate phonon degenerate eigenstates. (b) The same as (a), but for $y$-axis. (c) The same as (a), but for $z$-axis. (d) The same as (a), but for the $Pnma$ phase at 400 K. (e) The same as (d), but for $y$-axis. (f) The same as (e), but for $y$-axis.