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Thermal transport mechanism of electrons and phonons in pristine and defective HfB2

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Abstract

Hafnium diboride (HfB2) is an important metallic ceramic that works in harsh environments, due to its high strength and thermal conductivity. Although the thermal conductivity of HfB2 has been measured, the experimental results are scattered. Also, the thermal transport mechanism of HfB2 is not well understood. In this work, we study the thermal transport in both pristine and defective HfB2 from first-principles calculations. For the pristine HfB2, the room-temperature thermal conductivities are 175.0 and 157.7 W·m−1·K−1 on a- and c-axes, respectively, where the contributions from electron and phonon are comparable. The Lorenz number is significantly smaller than the Sommerfeld value and shows a temperature dependence, which demonstrates that the Wiedemann–Franz law cannot be used to estimate electronic thermal conductivity. The phonon–isotope and the phonon–electron scattering are non-negligible compared to the phonon–phonon scattering. For the defective HfB2, the grain size effects are negligible with length scales larger than 1 μm. The pore can limit thermal conductivity when its occupancy is larger than 10%. The vacancy is found to induce scattered results in experiments. The phonon thermal conductivity significantly reduces even with only 1% vacancy, while the electronic thermal conductivity is not sensitive to the vacancy. Our study provides an in-depth understanding of the thermal transport in HfB2, and the revealed mechanisms provide important guidance on the design of HfB2-based materials.

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摘要

二硼化铪（HfB2）是一种重要的，可以在恶劣的环境中工作的金属陶瓷。这是因为其拥有高强度和高热导率。 然而尽管已有实验上测得的热导率实验数据，测量的结果数据却是不一致的。另一方面，二硼化铪的热输运机 制也尚未充分理解。在本研究中，我们通过第一原理计算研究了本征的和含缺陷的二硼化铪的热输运。研究表 明，对于本征二硼化铪，室温下a 轴和c 轴上的热导率为 175.0 和 157.7 W·m‒1·K‒1，且电子和声子对导热的贡 献相当。电子导热分析中，发现洛伦兹数明显小于索末菲值且表现出温度依赖性，这表明魏德曼–夫兰兹定理不 适用于估算电子热导率。电子导热分析中，则发现声子-同位素散射，声子-电子散射与声子-声子散射相当，因 而不可忽略。缺陷对热导率影响的研究中发现，当晶粒尺寸大于 1 μm 的情况下，晶界对热导率的影响可以忽 略。宏观的孔隙率高于 10%时，热导率会显著下降。实验上不一致的测量结果则主要是由原子空位所导致的。 即使只有 1%的原子空位，声子热导率也会明显降低；而电子热导率则对原子空位不敏感。本研究深入理解了二 硼化铪中的导热机制，并为二硼化铪相关的材料设计提供了重要指导。

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (NSFC) (No. 52122606). S.-H. Li acknowledges the support by Shanghai Municipal Natural Science Foundation (No. 22YF1400100) and the Fundamental Research Funds for the Central Universities (No. 2232022D-22). Simulations were performed on the π 2.0 cluster supported by the Center for High Performance Computing at Shanghai Jiao Tong University.

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  1. Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ao Wang & Hua Bao

  2. University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, 200240, China

    Ao Wang & Hua Bao

  3. College of Mechanical Engineering, Donghua University, Shanghai, 201620, China

    Shou-Hang Li

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Wang, A., Li, SH. & Bao, H. Thermal transport mechanism of electrons and phonons in pristine and defective HfB2. Rare Met. 42, 3651–3661 (2023). https://doi.org/10.1007/s12598-023-02354-5

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