Microscopic Origin of the Ultralow Lattice Thermal Conductivity in Vacancy-Ordered Halide Double Perovskites Cs$_2BX_6$ ($B$ = Zr, Pd, Sn, Te, Hf, and Pt; $X$= Cl, Br, and I)

TL;DR

This work investigates the microscopic origin of ultralow lattice thermal conductivity in vacancy-ordered Cs2BX6 halide double perovskites using state-of-the-art first-principles calculations within the unified theory of thermal transport. By combining self-consistent phonon renormalization with three- and four-phonon scattering and coherent transport, it reveals that low phonon group velocities, driven by inherently weak bonding, primarily suppress heat conduction across Cs2BX6, with Cs2SnI6 showing additional enhancement of scattering. The study also demonstrates that machine-learning approaches (notably SISSO) can predict $κ_{L}$ from a small set of descriptors, highlighting the role of bond stiffness and vibrational amplitudes in determining thermal transport. These results provide a microscopic framework and design rules for engineering halide-based materials with tailored lattice thermal conductivity for thermoelectric and thermal-insulation applications.

Abstract

Vacancy-ordered halide double perovskites Cs$_2BX_6$ have recently attracted significant attention due to their intrinsically ultralow lattice thermal conductivity ($κ_{\mathrm{L}}$), which is highly desirable for thermal insulation and thermoelectric applications. In this work, we systematically investigate the anharmonic lattice dynamics and thermal transport properties of Cs$_2BX_6$ ($B$ = Zr, Pd, Sn, Te, Hf, and Pt; $X$ = Cl, Br, and I) using state-of-the-art first-principles calculations, based on a unified theory of thermal transport for crystals and glasses. All studied compounds are found to exhibit ultralow $κ_{\mathrm{L}}$ below 1.0~W\,m$^{-1}$\,K$^{-1}$ at room temperature and large derivation from the conventional $T^{-1}$ temperature dependence. Our analysis combining with machine-learning approach show that low sound velocities (1100 -- 1600~m\,s$^{-1}$), which originates from the intrinsically weak chemical bonding, play a crucial role in suppressing heat transport of the most compounds, instead of the strong scattering of rattling phonon modes expected from the large void in the structure. Furthermore, the influence of $B$ and $X$-site elements on phonon dispersion, anharmonicity, and scattering phase space is clarified. Our results provide microscopic insights into the origin of ultralow $κ_{\mathrm{L}}$ in Cs$_2BX_6$ and offer guiding principles for the rational design of halide-based materials with tailored thermal transport properties.

Figures (10)

• Figure 1: Crystal structure of the vacancy-ordered perovskite Cs$_2BX_6$. The 12-fold coordinated Cs atoms and the octahedrally coordinated $B$ atoms are highlighted using polyhedra.
• Figure 2: (a) Calculated lattice thermal conductivity $\kappa_{\mathrm{L}}$ at 300 K, including three- and four-phonon scattering processes ($\kappa_{\mathrm{3,4ph}}^{\mathrm{SCPH}}$) and the coherent contribution ($\kappa_{\mathrm{3,4ph}}^{\mathrm{C}}$), obtained using renormalized second-order force constants within the SCPH framework. (b) Contribution of three-phonon scattering processes ($\kappa_{\mathrm{3ph}}^{\mathrm{SCPH}}$) to $\kappa_{\mathrm{L}}$. (c) Contribution of the coherent term ($\kappa_{\mathrm{3,4ph}}^{\mathrm{C}}$) to the total $\kappa_{\mathrm{L}}$.
• Figure 3: Phonon band structures and phonon density of states (PhDOS) of Cs$_2BX_6$ ($B$ = Zr, Pd, Sn, and Te; $X$ = Cl, Br, and I) calculated at 300 K. Panels (a)–(d) show the phonon band structures and PhDOS of Cs$_2B$Cl$_6$ with $B$ = Zr, Sn, Pd, and Te, respectively. Panels (e)–(h) present the corresponding results for Cs$_2B$Br$_6$, and panels (i)–(l) for Cs$_2B$I$_6$, with the same ordering of $B$ cations.
• Figure 4: Three- and four-phonon scattering rates of Cs$_2BX_6$ ($B$ = Zr, Pd, Sn, and Te; $X$ = Cl, Br, and I) calculated at 300 K. Panels (a)–(d) show the phonon scattering rates of Cs$_2B$Cl$_6$ with $B$ = Zr, Sn, Pd, and Te, respectively. Panels (e)–(h) present the corresponding results for Cs$_2B$Br$_6$, and panels (i)–(l) for Cs$_2B$I$_6$, with the same ordering of $B$ cations.
• Figure 5: Comparison between the DFT-calculated $\kappa_{\mathrm{L}}$ and the predicted $\kappa_{\mathrm{L}}$ of Cs$_2BX_6$ ($B$ = Zr, Pd, Sn, Te, Hf, and Pt; $X$ = Cl, Br, and I) obtained using different models. Panels (a)–(c) correspond to the Slack, modified Slack, and SISSO-constructed models, respectively.