Accelerating inverse crystal structure prediction by machine learning: A case study of carbon allotropes

Abstract

Based on structure prediction method, the machine learning method is used instead of the density functional theory (DFT) method to predict the material properties, thereby accelerating the material search process. In this paper, we established a data set of carbon materials by high-throughput calculation with available carbon structures obtained from the Samara Carbon Allotrope Database. We then trained a machine learning (ML) model that specifically predicts the elastic modulus (bulk modulus, shear modulus, and the Young’s modulus) and confirmed that the accuracy is better than that of AFLOW–ML in predicting the elastic modulus of a carbon allotrope. We further combined our ML model with the CALYPSO code to search for new carbon structures with a high Young’s modulus. A new carbon allotrope not included in the Samara Carbon Allotrope Database, named Cmcm–C24, which exhibits a hardness greater than 80 GPa, was firstly revealed. The Cmcm–C24 phase was identified as a semiconductor with a direct bandgap. The structural stability, elastic modulus, and electronic properties of the new carbon allotrope were systematically studied, and the obtained results demonstrate the feasibility of ML methods accelerating the material search process.

Keywords

machine learning / crystal structure prediction / carbon

References

[1] V. L. Deringer, G. Csányi, and D. M. Proserpio, Extracting crystal chemistry from amorphous carbon structures, ChemPhysChem 18(8), 873 (2017)

[2] Y. Zhuo, A. Mansouri Tehrani, and J. Brgoch, Predicting the band gaps of inorganic solids by machine learning, J. Phys. Chem. Lett. 9(7), 1668 (2018)

[3] J. Lee, A. Seko, K. Shitara, K. Nakayama, and I. Tanaka, Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques, Phys. Rev. B 93(11), 115104 (2016)

[4] P. Dey, J. Bible, S. Datta, S. Broderick, J. Jasinski, M. Sunkara, M. Menon, and K. Rajan, Informatics-aided bandgap engineering for solar materials, Comput. Mater. Sci. 83, 185 (2014)

[5] A. O. Oliynyk, L. A. Adutwum, B. W. Rudyk, H. Pisavadia, S. Lotfi, V. Hlukhyy, J. J. Harynuk, A. Mar, and J. Brgoch, Disentangling structural confusion through machine learning: Structure prediction and polymorphism of equiatomic ternary phases ABC, J. Am. Chem. Soc. 139(49), 17870 (2017)

[6] A. O. Oliynyk, L. A. Adutwum, J. J. Harynuk, and A. Mar, Classifying crystal structures of binary compounds AB through cluster resolution feature selection and support vector machine analysis, Chem. Mater. 28(18), 6672 (2016)

[7] F. Legrain, J. Carrete, A. van Roekeghem, S. Curtarolo, and N. Mingo, How the chemical composition alone can predict vibrational free energies and entropies of solids, Chem. Mater. 29(15), 6220 (2017)

[8] G. Pilania, P. V. Balachandran, C. Kim, and T. Lookman, Finding new perovskite halides via machine learning, Front. Mater. 3, 19 (2016)

[9] O. Isayev, C. Oses, C. Toher, E. Gossett, S. Curtarolo, and A. Tropsha, Universal fragment descriptors for predicting properties of inorganic crystals, Nat. Commun. 8(1), 15679 (2017)

[10] Y. Zhang and C. Ling, A strategy to apply machine learning to small datasets in materials science, npj Comput. Mater. 4, 25 (2018)

[11] A. Mansouri Tehrani, A. O. Oliynyk, M. Parry, Z. Rizvi, S. Couper, F. Lin, L. Miyagi, T. D. Sparks, and J. Brgoch, Machine learning directed search for ultraincompressible, superhard materials, J. Am. Chem. Soc. 140(31), 9844 (2018)

[12] Y. W. Zhang, H. Wang, Y. C. Wang, L. J. Zhang, and Y. M. Ma, Computer-assisted inverse design of inorganic electrides, Phys. Rev. X 7(1), 011017 (2017)

[13] X. X. Zhang, Y. C. Wang, J. Lv, C. Y. Zhu, Q. Li, M. Zhang, Q. Li, and Y. M. Ma, First-principles structural design of superhard materials, J. Chem. Phys. 138(11), 114101 (2013)

[14] Y. C. Wang, J. Lv, L. Zhu, and Y. M. Ma, CALYPSO: A method for crystal structure prediction, Comput. Phys. Commun. 183(10), 2063 (2012)

[15] Y. Sun, J. Lv, Y. Xie, H. Y. Liu, and Y. M. Ma, Route to a superconducting phase above room temperature in electron-doped hydride compounds under high pressure, Phys. Rev. Lett. 123(9), 097001 (2019)

[16] Q. Wei, Q. Zhang, M. Zhang, H. Yan, L. Guo, and B. Wei, A novel hybrid sp-sp² metallic carbon allorope, Front. Phys. 13(5), 136105 (2018)

[17] H. Yan, Z. Wei, M. Zhang, and Q. Wei, Exploration of stable stoichiometries, ground-state structures, and mechanical properties of the W–Si system, Ceram. Int. 46(10), 17034 (2020)

[18] J. Lin, Z. Y. Zhao, C. Y. Liu, J. Zhang, X. Du, G. C. Yang, and Y. M. Ma, IrF8 molecular crystal under high pressure, J. Am. Chem. Soc. 141(13), 5409 (2019)

[19] Z. Y. Zhao, S. T. Zhang, T. Yu, H. Y. Xu, A. Bergara, and G. C. Yang, Predicted pressure-induced superconducting transition in electride Li₆P, Phys. Rev. Lett. 122(9), 097002 (2019)

[20] Q. Wei, W. Tong, R. K. Yang, H. Y. Yan, B. Wei, M. G. Zhang, X. C. Yang, and R. Zhang, Orthorhombic C₁0: A new superdense carbon allotrope, Phys. Lett. A 383(28), 125861 (2019)

[21] Q. C. Tong, L. T. Xue, J. Lv, Y. C. Wang, and Y. M. Ma, Accelerating CALYPSO structure prediction by data-driven learning of a potential energy surface, Faraday Discuss. 211, 31 (2018)

[22] K. Xia, H. Gao, C. Liu, J. N. Yuan, J. Sun, H. T. Wang, and D. Y. Xing, A novel superhard tungsten nitride predicted by machine-learning accelerated crystal structure search, Sci. Bull. (Beijing)63(13), 817 (2018)

[23] R. Hoffmann, A. A. Kabanov, A. A. Golov, and D. M. Proserpio, Homo Citans and carbon allotropes: For an ethics of citation, Angew. Chem. Int. Ed. 55(37), 10962 (2016)

[24] M. Gajdoš, K. Hummer, G. Kresse, J. Furthmuller, and F. Bechstedt, Linear optical properties in the projectoraugmented wave methodology, Phys. Rev. B 73(4), 045112 (2006)

[25] G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initiototal-energy calculations using a plane-wave basis set, Phys. Rev. B 54(16), 11169 (1996)

[26] M. G. Zhang, H. Y. Yan, and Q. Wei, Unexpected ground-state crystal structures and mechanical properties of transition metal pernitrides MN₂ (M= Ti, Zr, and Hf), J. Alloys Compd. 774, 918 (2019)

[27] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78(7), 1396 (1997) [Phys. Rev. Lett. 77, 3865 (1996)]

[28] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

[29] A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl₂-type SiO₂ at high pressures, Phys. Rev. B 78(13), 134106 (2008)

[30] L. Ward, A. Dunn, A. Faghaninia, N. E. R. Zimmermann, S. Bajaj, Q. Wang, J. Montoya, J. Chen, K. Bystrom, M. Dylla, K. Chard, M. Asta, K. A. Persson, G. J. Snyder, I. Foster, and A. Jain, Matminer: An open source toolkit for materials data mining, Comput. Mater. Sci. 152, 60 (2018)

[31] E. Gossett, C. Toher, C. Oses, O. Isayev, F. Legrain, F. Rose, E. Zurek, J. Carrete, N. Mingo, A. Tropsha, and S. Curtarolo, AFLOW-ML: A RESTful API for machine-learning predictions of materials properties, Comput. Mater. Sci. 152, 134 (2018)

[32] A. R. Supka, T. E. Lyons, L. Liyanage, P. D’Amico, R. Al Rahal Al Orabi, S. Mahatara, P. Gopal, C. Toher, D. Ceresoli, A. Calzolari, S. Curtarolo, M. B. Nardelli, and M. Fornari, AFLOW: A minimalist approach to highthroughput ab initio calculations including the generation of tight-binding hamiltonians, Comput. Mater. Sci. 136, 76 (2017)

[33] M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW library of crystallographic prototypes(Part 1), Comput. Mater. Sci. 136, S1 (2017)

[34] W. L. Mao, H. K. Mao, P. J. Eng, T. P. Trainor, M. Newville, et al., Bonding changes in compressed superhard graphite, Science 302(5644), 425 (2003)

[35] Y. J. Wang, J. E. Panzik, B. Kiefer, and K. K. M. Lee, Crystal structure of graphite under room-temperature compression and decompression, Sci. Rep. 2(1), 520 (2012)

[36] Q. Li, Y. M. Ma, A. R. Oganov, H. B. Wang, H. Wang, Y. Xu, T. Cui, H. K. Mao, and G. G. Zou, Superhard monoclinic polymorph of carbon, Phys. Rev. Lett. 102(17), 175506 (2009)

[37] E. Stavrou, S. Lobanov, H. F. Dong, A. R. Oganov, V. B. Prakapenka, Z. Konopkovaa, A. F. Goncharov, Synthesis of ultra-incompressible sp³-hybridized carbon nitride with 1:1 stoichiometry, Chem. Mater. 28(19), 6925 (2016)

[38] M. Zhang, H. Liu, Q. Li, B. Gao, Y. C. Wang, H. D. Li, C. F. Chen, and Y. M. Ma, Superhard BC₃ in cubic diamond structure, Phys. Rev. Lett. 114(1), 015502 (2015)

[39] R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. Lond. 65(5), 349 (1952)

[40] A. Lyakhov and A. Oganov, Evolutionary search for superhard materials: Methodology and applications to forms of carbon and TiO₂, Phys. Rev. B 84(9), 092103 (2011)

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