| Summary: | The merging of pore designs is a potential strategy for achieving ultra-low lattice thermal conductivity (<i>κ</i>), for which phonon anharmonicity and size effect are indispensable for discovering novel functional materials in thermal applications. In this study, monolayer holey graphyne (HGY) and boron nitride holey graphyne (BN-HGY) were examined for their phonon thermal transport properties through first-principles calculation and phonon Boltzmann function. HGY exhibits an intrinsic lattice thermal conductivity (κ) of 38.01 W/mK at room temperature, which exceeds BN-HGY’s 24.30 W/mK but is much lower than 3550 W/mK for BTE graphene. The phonon–phonon scattering behavior of BN-HGY is obviously increased compared to HGY due to the enhancement of anharmonicity, which leads to a shorter phonon lifetime and lower <i>κ</i>. Additionally, at room temperature, the representative mean free path (rMFP) of BN-HGY is substantially higher than that of HGY, and the <i>κ</i> of BN-HGY decreases faster at a larger rMFP (within a unit nm). This work will be constructive to further the application of HGY and BN-HGY as thermal management materials.
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