Ab initio study of lattice thermal conductivity in layered borides M<sub>3</sub>AlB<sub>4</sub> (M = Ti, Zr, Hf).

Abstract

<h4>Context</h4>Efficient heat removal limits the performance of microelectronics, plasma-facing components, and high-temperature structures. Metals exhibit good thermal conductivity but weaken above approximately 1000 K, while ceramics are strong yet brittle. Ultrahigh-temperature M₃AlB₄ compounds (M = Ti, Zr, Hf) maintain metallic conductivity while displaying unusually low lattice thermal conductivity. The origin of the ultralow κ_l in Hf₃AlB₄ was previously unknown, hindering the design of derivatives with even lower κ_l. First-principles simulations reveal that the heavy Hf atom doubles the Grüneisen parameter (γ ≈ twice that of Ti₃AlB₄), which shortens phonon lifetimes and triples the three-phonon scattering phase space, offsetting the velocity increase from softened Hf-B bonds. By combining direction-resolved lattice thermal conductivity and estimated electronic contributions, the calculated total thermal conductivity of M₃AlB₄ ranges from 0.76 to 40.6 W/(m·K), enabling composition-tunable thermal management from thermal insulation to heat conduction applications. Selective substitution with heavy atoms thus tunes κ_l by an order of magnitude without compromising metallic transport, providing a superior platform for thermal barrier coatings, heat spreaders, and thermoelectric elements at higher temperatures.<h4>Methods</h4>Density functional theory (DFT) calculations were performed using VASP with a plane-wave energy cutoff of 700 eV and a 13 × 13 × 13 Monkhorst-Pack k-point mesh. Structural relaxations were carried out until the energy and force convergence criteria were below 1 × 10^-8 eV and 1 × 10^-7 eV/Å, respectively. Crystal orbital Hamiltonian population (COHP) analysis was performed using the LOBSTER package. Harmonic interatomic force constants (IFCs) were obtained using density functional perturbation theory (DFPT) implemented in VASP-Phonopy on a 2 × 2 × 2 supercell. The Thirdorder utility was employed to compute third-order IFCs. The resulting harmonic and third-order IFCs were then input into ShengBTE to calculate the κ_l.