Unique Hierarchical Rotational Dynamics Induces Ultralow Lattice Thermal Conductivity in Cyanide-bridged Framework Materials

TL;DR

This work addresses the challenge of achieving ultralow lattice thermal conductivity in lightweight materials by integrating hierarchical vibrational architectures with rotational dynamics in cyanide-bridged framework materials (CFMs). Using a first-principles and machine-learning-assisted approach alongside unified phonon transport theory, it shows that multiple negative Grüneisen peaks and a large four-phonon scattering phase space, coupled with strong quartic anharmonicity from rotation modes, suppress $κ_{\mathrm{L}}$ by 1–2 orders of magnitude compared with perovskite-like counterparts of similar mass. Specific CFMs such as Cd(CN)$_{2}$, NaB(CN)$_{4}$, LiIn(CN)$_{4}$, and AgX(CN)$_{4}$ exhibit ultralow room-temperature $κ_{\mathrm{L}}$ values ranging from 0.35 to 0.81 W/mK. The study establishes CFMs as a new platform for extreme phonon anharmonicity and offers a design paradigm for achieving ultralow thermal conductivity in lightweight materials by harnessing hierarchical and rotational lattice dynamics.

Abstract

The pursuit of materials combining light constituent elements with ultralow lattice thermal conductivity ($κ_{\mathrm{L}}$) is crucial to advancing technologies like thermoelectrics and thermal barrier coatings, yet it remains a formidable challenge to date. Herein, we achieve ultralow $κ_{\mathrm{L}}$ in lightweight cyanide-bridged framework materials (CFMs) through the rational integration of properties such as the hierarchical vibrations exhibited in superatomic structures and rotational dynamics exhibited in perovskites. Unique hierarchical rotation behavior leads to multiple negative peaks in Grüneisen parameters across a wide frequency range, thereby inducing pronounced negative thermal expansion and strong cubic anharmonicity in CFMs. Meanwhile, the synergistic effect between large four-phonon scattering phase space (induced by phonon quasi-flat bands and wide bandgaps) and strong quartic anharmonicity (associated with rotation modes) leads to giant quartic anharmonic scattering rates in these materials. Consequently, the $κ_{\mathrm{L}}$ of these CFMs decreases by one to two orders of magnitude compared to the known perovskites or perovskite-like materials with equivalent average atomic masses. For instance, the Cd(CN)$_{2}$, NaB(CN)$_{4}$, LiIn(CN)$_{4}$, and AgX(CN)$_{4}$ (X = B, Al, Ga, In) exhibit ultralow room-temperature $κ_{\mathrm{L}}$ values ranging from 0.35 to 0.81 W/mK. This work not only establishes CFMs as a novel and rich platform for studying extreme phonon anharmonicity, but also provides a new paradigm for achieving ultralow thermal conductivity in lightweight materials via the conscious integration of hierarchical and rotational dynamics.

Figures (6)

• Figure 1: (a) A simplified model of cubic crystal structure, with each sphere consisting of a tetrahedral superatom cluster. Scheme of unit cell structure of (b) Zn(CN)$_{2}$ and Cd(CN)$_{2}$, (c) LiB(CN)$_{4}$, CuB(CN)$_{4}$, and AgB(CN)$_{4}$, (d) and NaB(CN)$_{4}$. (e-g) Calculated finite-temperature phonon dispersion, accounting for thermal expansion effects, for Zn(CN)$_{2}$, AgB(CN)$_{4}$, and NaB(CN)$_{4}$, respectively. The middle and right panels of (e-g) present the mode $\gamma$ and SRs (including three- and four-phonon processes) at room temperature, respectively.
• Figure 2: The potential well for different rotation modes. The quadratic and quartic fitting curves are represented by gray dashed lines and yellow solid lines, respectively. The insets label the vibration eigenvectors for different rotation modes
• Figure 3: The temperature-dependent $\kappa_{\mathrm{L}}$ of (a) Zn(CN)$_{2}$, (b) AgB(CN)$_{4}$, and (c) NaB(CN)$_{4}$ is calculated based on different models are compared with molecular dynamics simulations.
• Figure 4: The temperature-dependent $\kappa_{\mathrm{L}}$ calculated using the HNEMD method for (a) Zn(CN)$_{2}$ and Cd(CN)$_{2}$, (b) AgX(CN)$_{4}$, (c) CuX(CN)$_{4}$, and (d) LiX(CN)$_{4}$ (X=B, Al, Ga, In).
• Figure 5: (a) The ELF, (b) RMSD of N and C atoms, (c) $\gamma$, and (d) phonon SRs for AgX(CN)$_{4}$ (X=B, Al, Ga, In). The inset of (b) shows the –iCOHP for different atomic bonds.