Structural stability and mechanical properties of TiB6: A CALYPSO-guided exploration for superhard applications

doi:10.1088/1674-1056/adfb59

中国物理B ›› 2026, Vol. 35 ›› Issue (5): 56105-056105.doi: 10.1088/1674-1056/adfb59

所属专题： SPECIAL TOPIC — John Tse: Pioneer in high-pressure materials science

Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications

Bo Sun(孙博)¹, Yutong Zou(邹雨桐)¹, Tao Wang(王淘)¹, Yujia Wang(王雨佳)¹, Jinyu Liu(刘金禹)¹, Lili Gao(高丽丽)¹, Meiguang Zhang(张美光)^2,†, and Miao Zhang(张淼)^1,‡

1 Department of Physics, School of Sciences, Beihua University, Jilin 132013, China;
2 College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721016, China

收稿日期:2025-06-15 修回日期:2025-07-20 接受日期:2025-08-14 出版日期:2026-04-24 发布日期:2026-04-29
通讯作者: Meiguang Zhang, Miao Zhang E-mail:zhmgbj@126.com;zhangmiaolmc@126.com
基金资助:
This work was supported by the Scientific and Technological Research Project of the Jilin Provincial Education Department (Grant No. JJKH20240077KJ) and the Jilin Provincial Science and Technology Development Joint Fund Project (Grant No. YDZJ202201ZYTS581).

Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications

Bo Sun(孙博)¹, Yutong Zou(邹雨桐)¹, Tao Wang(王淘)¹, Yujia Wang(王雨佳)¹, Jinyu Liu(刘金禹)¹, Lili Gao(高丽丽)¹, Meiguang Zhang(张美光)^2,†, and Miao Zhang(张淼)^1,‡

1 Department of Physics, School of Sciences, Beihua University, Jilin 132013, China;
2 College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721016, China

Received:2025-06-15 Revised:2025-07-20 Accepted:2025-08-14 Online:2026-04-24 Published:2026-04-29
Contact: Meiguang Zhang, Miao Zhang E-mail:zhmgbj@126.com;zhangmiaolmc@126.com
Supported by:
This work was supported by the Scientific and Technological Research Project of the Jilin Provincial Education Department (Grant No. JJKH20240077KJ) and the Jilin Provincial Science and Technology Development Joint Fund Project (Grant No. YDZJ202201ZYTS581).

1. 2026-056105-SI.pdf(631KB)

摘要/Abstract

摘要： Titanium-boron (Ti-B) compounds exhibit great promise as superhard materials due to titanium's low atomic mass and abundant valence electrons. In this work, we systematically investigated the crystal structures of TiB$_{6}$ under pressures ranging from 0-100 GPa using the CALYPSO algorithm combined with first-principles calculations. Phonon dispersion analysis and elastic-constant evaluations confirm the dynamic and mechanical stability of five predicted TiB$_{6}$ structures. Notably, the $\alpha $-Amm2-TiB$_{6}$ structure was predicted to have a remarkable Vickers hardness of 56 GPa, as estimated by Chen's empirical model. All five structures are thermodynamically stable under ambient conditions, suggesting viable synthetic pathways. Their outstanding bulk moduli and ultrahigh hardness further classify them as potential incompressible and superhard materials. These theoretical insights lay a robust foundation for future experimental synthesis efforts.

关键词: superhard materials, transition metal borides, Vickers hardness, first-principles calculations, CALYPSO method

Abstract: Titanium-boron (Ti-B) compounds exhibit great promise as superhard materials due to titanium's low atomic mass and abundant valence electrons. In this work, we systematically investigated the crystal structures of TiB$_{6}$ under pressures ranging from 0-100 GPa using the CALYPSO algorithm combined with first-principles calculations. Phonon dispersion analysis and elastic-constant evaluations confirm the dynamic and mechanical stability of five predicted TiB$_{6}$ structures. Notably, the $\alpha $-Amm2-TiB$_{6}$ structure was predicted to have a remarkable Vickers hardness of 56 GPa, as estimated by Chen's empirical model. All five structures are thermodynamically stable under ambient conditions, suggesting viable synthetic pathways. Their outstanding bulk moduli and ultrahigh hardness further classify them as potential incompressible and superhard materials. These theoretical insights lay a robust foundation for future experimental synthesis efforts.

Key words: superhard materials, transition metal borides, Vickers hardness, first-principles calculations, CALYPSO method

中图分类号: (Theory of crystal structure, crystal symmetry; calculations and modeling)

61.50.Ah

61.50.Ks (Crystallographic aspects of phase transformations; pressure effects) 61.66.Fn (Inorganic compounds)

Bo Sun(孙博), Yutong Zou(邹雨桐), Tao Wang(王淘), Yujia Wang(王雨佳), Jinyu Liu(刘金禹), Lili Gao(高丽丽), Meiguang Zhang(张美光), and Miao Zhang(张淼). Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications[J]. 中国物理B, 2026, 35(5): 56105-056105.

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Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications

Structural stability and mechanical properties of TiB₆: A CALYPSO-guided exploration for superhard applications

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