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)

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 1.0W,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 – 1600m,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.

💡 Research Summary

This study provides a comprehensive first‑principles investigation of the lattice thermal conductivity (κ L) in vacancy‑ordered halide double perovskites of the form Cs₂BX₆, where B = Zr, Pd, Sn, Te, Hf, Pt and X = Cl, Br, I. Using density‑functional theory (VASP, PBEsol) the authors fully relaxed the cubic structures and verified the accuracy of lattice constants against experimental data. Harmonic force constants were obtained with Phonopy, while third‑ and fourth‑order force constants were extracted via compressive‑sensing lattice dynamics (CSLD). To capture strong anharmonicity, the self‑consistent phonon (SCPH) method was employed to renormalize the second‑order force constants at finite temperature. Thermal transport was then evaluated by iteratively solving the Peierls‑Boltzmann transport equation with the FourPhonon package, thereby including both three‑phonon and four‑phonon scattering processes. A coherent term, arising from wave‑like phonon transport, was also computed within the unified crystal‑glass theory.

The calculated κ L values at 300 K are all below 1 W m⁻¹ K⁻¹, confirming the ultralow thermal conductivity of this family. The lowest value (0.28 W m⁻¹ K⁻¹) is found for Cs₂SnI₆, in excellent agreement with experimental measurements (0.29 W m⁻¹ K⁻¹). Generally κ L decreases from Cl → Br → I, reflecting the increasing halogen mass and the concomitant weakening of Cs–X and B–X bonds. An exception is the Te series, where Cs₂TeI₆ shows a slightly higher κ L than its Cl and Br counterparts; this anomaly is traced to a larger particle‑like contribution to heat transport and weaker anharmonicity in the Te‑based compounds.

A key insight emerges from a machine‑learning analysis (random‑forest regression) of thirty structural and chemical descriptors (bond lengths, charge distribution, elastic constants, average sound velocity, etc.). Feature‑importance ranking identifies the average sound velocity (ν g) and elastic moduli (bulk and shear) as the dominant predictors of κ L, while bond‑strength descriptors play a secondary role. The average sound velocities, computed from elastic constants, lie in the narrow range 1100–1600 m s⁻¹, markedly lower than in conventional perovskites (≈3000 m s⁻¹). This low ν g originates from intrinsically weak chemical bonding, as confirmed by crystal‑orbital Hamilton population (COHP) analyses showing reduced B–X and Cs–X covalency. Because κ L ∝ C_V ν g² τ, the squared dependence on ν g makes the reduced sound speed the primary factor suppressing heat transport across the entire series.

Three‑phonon scattering alone (κ_SCPH^3ph) already yields low κ L, but inclusion of four‑phonon processes (κ_SCPH^{3,4ph}) further reduces κ L by 10–35 % (average ≈20 %). The largest four‑phonon contribution appears in Cs₂ZrCl₆ (35 % reduction), while the smallest is in Cs₂PdBr₆ (10 %). The coherent term κ_C (both three‑ and four‑phonon) remains modest, contributing roughly 15 % of the total κ L at room temperature, with the highest fraction (≈21 %) for Cs₂SnI₆. This modest coherent contribution correlates with the degree of anharmonicity: compounds with stronger anharmonicity exhibit larger coherent fractions.

The role of the B‑site cation varies with the halogen. For the Cl‑based series, κ L shows a pronounced dependence on the B element, reflecting differences in bond stiffness and phonon dispersion. In contrast, for Br‑ and I‑based series the influence of B is weak, and the halogen species dominates the thermal transport behavior. Notably, only Cs₂SnI₆ displays significant “rattling”‑like low‑frequency optical modes that flatten the phonon branches and enhance three‑phonon scattering; other compounds lack such flat branches, indicating that rattling is not the universal mechanism for ultralow κ L in this family.

In summary, the paper establishes that (i) accurate inclusion of high‑order phonon scattering is essential for quantitative κ L prediction; (ii) the ultralow lattice thermal conductivity of vacancy‑ordered halide double perovskites is primarily driven by weak chemical bonding that yields low sound velocities, rather than by rattling‑induced scattering; (iii) the X‑site halogen controls κ L more strongly than the B‑site cation, especially for heavier halogens; and (iv) machine‑learning analysis corroborates the physical picture, highlighting elastic properties and sound speed as the key design parameters. These insights provide clear guidelines for engineering new halide‑based materials with tailored thermal transport, such as selecting heavier, softer halogens and promoting weak bonding environments to achieve extreme thermal insulation or enhanced thermoelectric performance.