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Chin. Phys. B, 2026, Vol. 35(5): 056105    DOI: 10.1088/1674-1056/adfb59
SPECIAL TOPIC — John Tse: Pioneer in high-pressure materials science Prev   Next  

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
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 TiB6 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 TiB6 structures. Notably, the α-Amm2-TiB6 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.
Keywords:  superhard materials      transition metal borides      Vickers hardness      first-principles calculations      CALYPSO method  
Received:  15 June 2025      Revised:  20 July 2025      Accepted manuscript online:  14 August 2025
PACS:  61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling)  
  61.50.Ks (Crystallographic aspects of phase transformations; pressure effects)  
  61.66.Fn (Inorganic compounds)  
Fund: 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).
Corresponding Authors:  Meiguang Zhang,E-mail:zhmgbj@126.com;Miao Zhang,E-mail:zhangmiaolmc@126.com     E-mail:  zhmgbj@126.com;zhangmiaolmc@126.com

Cite this article: 

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 2026 Chin. Phys. B 35 056105

[1] Sung C M and Sung M 1996 Mater. Chem. Phys. 431
[2] Haines J, Leger J and Bocquillon G 2001 Annu. Rev. Mater. Res. 311
[3] Kaner R B, Gilman J J and Tolbert S H 2005 Science 3081268
[4] Dong J, Yao Z, Yao M, Li R, Hu K, Zhu L, Wang Y, Sun H, Sundqvist B, Yang K and Liu B 2020 Phys. Rev. Lett. 124065701
[5] Liu H, Li Q, Zhu L and Ma Y 2011 Phys. Lett. A 375771
[6] Zhang M, Liu H, Li Q, Gao B, Wang Y, Li H, Chen C and Ma Y 2015 Phys. Rev. Lett. 114015502
[7] Wentorf R H 1957 J. Chem. Phys. 26956
[8] Du J and Li X 2020 J. Alloys Compd. 815152324
[9] Akopov G, Pangilinan L E, Mohammadi R and Kaner R B 2018 APL Mater. 6070901
[10] Yeung M T, Mohammadi R and Kaner R B 2016 Annu. Rev. Mater. Res. 46465
[11] Chung H Y, Weinberger M B, Levine J B, Kavner A, Yang J M, Tolbert S H and Kaner R B 2007 Science 316436
[12] Niu H, Wang J, Chen X Q, Li D, Li Y, Lazar P, Podloucky R and Kolmogorov A N 2012 Phys. Rev. B 85144116
[13] Li X and Peng F 2019 Phys. Chem. Chem. Phys. 2115609
[14] Lin H S, Wang C Y, Djouadi M A, Kuang T C and Dong H F 2023 J. Mater. Sci. 581139
[15] Zhang G, Bai T, Feng G and He J 2024 Mater. Today Commun. 41110318
[16] Mohn P 1988 J. Phys. C Solid State Phys. 212841
[17] Ding L P, Tiandong Y H, Shao P, Tang Y, Zhao Z L and Lu H 2021 J. Phys. Chem. Lett. 125423
[18] Xie C, Zhang Q, Zakaryan H A, Wan H, Liu N, Kvashnin A G and Oganov A R 2019 J. Appl. Phys. 125205109
[19] Huang L H, Zhao Y R, Zhang G T, Zhang M G, Li P Y and Hu Y F 2019 Mol. Phys. 117547
[20] Wei S, Li D, Lv Y, Liu Z, Tian F, Duan D, Liu B and Cui T 2016 J. Alloys Compd. 6881101
[21] Ji Z W, Hu C H, Wang D H, Zhong Y, Yang J, Zhang W Q and Zhou H Y 2012 Acta Mater. 604208
[22] Zhang X, Zhao E and Wu Z 2015 J. Alloys Compd. 63237
[23] Zhang M, Wang H, Wang H, Zhang X, Iitaka T and Ma Y 2010 Inorg. Chem. 496859
[24] Ding L P, Shao P, Zhang F H, Lu C, Ding L, Ning S Y and Huang X F 2016 Inorg. Chem. 557033
[25] Zhang M, Lu M, Du Y, Gao L, Lu C and Liu H 2014 J. Chem. Phys. 140174505
[26] Knappschneider A, Litterscheid C, Dzivenko D, Kurzman J A, Seshadri R, Wagner N, Beck J, Riedel R and Albert B 2013 Inorg. Chem. 52540
[27] Li X, Tao Y and Peng F 2016 J. Alloys Compd. 687579
[28] Li Q, Zhou D, Zheng W, Ma Y and Chen C 2015 Phys. Rev. Lett. 115185502
[29] Decker B F and Kasper J S 1954 Acta Crystallogr. 777
[30] Norton J T, Blumenthal H and Sindeband S J 1949 JOM 1749
[31] Cao K, Shi G Y, Liu T T, Li X, Li J F, Wang X L, Su Y H, Zhang C and Jiang H 2023 Vacuum 217112582
[32] Li P, Zhou R and Zeng X C 2015 ACS Appl. Mater. Interfaces 715607
[33] Chen M R, Dou X L, Song T, Yan Z P and Sun X W 2024 Results Phys. 61107779
[34] Pan Y 2023 Phys. Chem. Chem. Phys. 2524417
[35] Pan Y and Jia Y 2019 J. Mater. Res. 343554
[36] Zhang G, Song Y, Bai T, Zhang M and Liu T 2023 Comput. Mater. Sci. 228112379
[37] Kresse G and Furthmuller J 1996 Phys. Rev. B 5411169
[38] Kohn W and Sham L J 1965 Phys. Rev. 140 A1133
[39] Wang Y, Lv J, Zhu L and Ma Y 2010 Phys. Rev. B 82094116
[40] Wang Y, Lv J, Zhu L and Ma Y 2012 Comput. Phys. Commun. 1832063
[41] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 773865
[42] Perdew J P and Wang Y 1992 Phys. Rev. B 4513244
[43] Kresse G and Joubert D 1999 Phys. Rev. B 591758
[44] Blochl P E 1994 Phys. Rev. B 5017953
[45] Monkhorst H J and Pack J D 1976 Phys. Rev. B 135188
[46] Togo A, Oba F and Tanaka I 2008 Phys. Rev. B 78134106
[47] Chen X Q, Niu H, Li D and Li Y 2011 Intermetallics 191275
[48] Tian Y, Xu B and Zhao Z 2012 Int. J. Refract. Metals Hard Mater. 3393
[49] Simunek A · 2009 Phys. Rev. B 80060103
[50] Deligoz E, Colakoglu K and Ciftci Y O 2009 Solid State Commun. 1491843
[51] Liu A, Cheng X, Wang X, Zou Y and Zhang M 2023 Phys. Chem. Chem. Phys. 2520837
[52] Liu J, Liu A, Wang Y, Gao L, Luo X and Zhang M 2025 Chin. Phys. B 34046201
[53] Wang X F, Wang Y X, Wang Z, Zhang Y X and Gu J B 2024 Chin. Phys. B 33126103
[54] Oganov A R, Chen J, Gatti C, Ma Y, Ma Y, Glass C W, Liu Z, Yu T, Kurakevych O O and Solozhenko V L 2009 Nature 457863
[55] Ivanovskii A L 2012 Prog. Mater. Sci. 57184
[56] Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J and Meng J 2007 Phys. Rev. B 76059904
[57] Yan H, Zhang W, Chen L, Zhang Y, Wang H, Zhang M and Wei Q 2025 Phys. Chem. Chem. Phys. 276134
[58] Liao M, Liu Y, Cui P, Qu N, Zhou F, Yang D, Han T, Lai Z and Zhu J 2020 Comput. Mater. Sci. 172109289
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