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Electronic structures and strengthening mechanisms of superhard high-entropy diborides

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Abstract

High-entropy diborides (HEBs) have attracted extensive research due to their potential ultra-high hardness. In the present work, the effects of transition metals (TM) on lattice parameters, electron work function (EWF), bonding charge density, and hardness of HEBs are comprehensively investigated by the first-principles calculations, including (TiZrHfNbTa)B2, (TiZrHfNbMo)B2, (TiZrHfTaMo)B2, (TiZrNbTaMo)B2, and (TiHfNbTaMo)B2. It is revealed that the disordered TM atoms result in a severe local lattice distortion and the formation of weak spots. In view of bonding charge density, it is understood that the degree of electron contribution of TM atoms directly affects the bonding strength of the metallic layer, contributing to the optimized hardness of HEBs. Moreover, the proposed power-law-scaled relationship integrating the EWF and the grain size yields an excellent agreement between our predicted results and those reported experimental ones. It is found that the HEBs exhibit relatively high hardness which is higher than those of single transition metal diborides. In particular, the hardness of (TiZrNbTaMo)B2 and (TiHfNbTaMo)B2 can be as high as 29.15 and 28.02 GPa, respectively. This work provides a rapid strategy to discover/design advanced HEBs efficiently, supported by the coupling hardening mechanisms of solid solution and grain refinement based on the atomic and electronic interactions.

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摘要

高熵二硼化物(HEBs)因其潜在的超高硬度而引起了广泛的研究。本文采用第一原理计算方法，以(TiZrHfNbTa)B2、(TiZrHfNbMo)B2、(TiZrHfTaMo)B2、(TiZrNbTaMo)B2和(TiHfNbTaMo)B2五种高熵二硼化物为例，全面研究了过渡金属对高熵二硼化物晶格参数、电子功函数、键合电子密度和硬度的影响。结果表明，不同元素之间的原子大小差异导致了严重的局域晶格畸变和薄弱点的形成。结合键合电子密度可知，金属原子的电子贡献程度直接影响金属层的键合强度，进而优化了高熵二硼化物的硬度。此外，本工作建立了耦合电子功函数和晶粒尺寸预测硬度的三参数幂律模型，预测的硬度值与实验值吻合较好。预测结果表明，高熵二硼化物具有较高的硬度，并且高于单金属二硼化物的硬度。其中，(TiZrNbTaMo)B2和(TiHfNbTaMo)B2的硬度分别高达29.15和28.02 GPa。本工作阐明了高熵二硼化物固溶强化与细晶强化的耦合强化机制，为先进超硬高熵硼化物的设计提供了一种有效的预测方法。

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Acknowledgements

This study was financially supported by the Science Challenge Project (No. TZ 2018002). First-principles calculations were carried out on the clusters at the Northwestern Polytechnical University.

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Authors and Affiliations

  1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an, 710072, China

    Gang Yao, William-Yi Wang, Pei-Xuan Li, Ke Ren, Jia-Qi Lu, Jun Wang & Jin-Shan Li

  2. Innovation Center, NPU Chongqing, Chongqing, 401135, China

    Gang Yao, William-Yi Wang, Pei-Xuan Li, Ke Ren, Jia-Qi Lu, Jun Wang & Jin-Shan Li

  3. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Xing-Yu Gao, De-Ye Lin & Hai-Feng Song

  4. Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081, China

    Yi-Guang Wang

  5. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA, 16802, USA

    Zi-Kui Liu

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  1. Gang Yao
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Yao, G., Wang, WY., Li, PX. et al. Electronic structures and strengthening mechanisms of superhard high-entropy diborides. Rare Met. 42, 614–628 (2023). https://doi.org/10.1007/s12598-022-02152-5

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