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First-principles database for fitting a machine-learning silicon interatomic force field

MRS Advances volume 7, pages 39–47 (2022)Cite this article

Abstract

Data-driven machine learning has emerged to address the limitations of traditional methods when modeling interatomic interactions in materials, such as electronic density functional theory (DFT) and semi-empirical potentials. These machine-learning frameworks involve mathematical models coupled to quantum mechanical data. In the present article, we focus on the moment tensor potential (MTP) machine-learning framework. More specifically, we provide an account of the development of a preliminary MTP for silicon, including details pertaining to the construction of a DFT database.

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References

  1. G. Hautier, C. Fischer, V. Ehrlacher, A. Jain, G. Ceder, Data mined ionic substitutions for the discovery of new compounds. Inorg. Chem. 50(2), 656–663 (2011)

    CAS  Google Scholar 

  2. Y. Liu, T. Zhao, J. Wangwei, S. Shi, Materials discovery and design using machine learning. J. Materiomics 3(3), 159–177 (2017)

    Google Scholar 

  3. E.V. Podryabinkin, E.V. Tikhonov, A.V. Shapeev, A.R. Oganov, Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning. Phys. Rev. B 99(6), 064114 (2019)

    CAS  Google Scholar 

  4. Y.X. Zuo, C. Chen, X.G. Li, Z. Deng, Y.M. Chen, J. Behler, G. Csanyi, A.V. Shapeev, A.P. Thompson, M.A. Wood, Performance and cost assessment of machine learning interatomic potentials. J. Phys. Chem. A 124(4), 731–745 (2020)

    CAS  Google Scholar 

  5. J. Behler, M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98(14), 146401 (2007)

    Google Scholar 

  6. T. Mueller, A.G. Kusne, R. Ramprasad, Machine learning in materials science: Recent progress and emerging applications. Rev. Comput. Chem. 29, 186–273 (2016)

    CAS  Google Scholar 

  7. M. Mohri, A. Rostamizadeh, A. Talwalkar, Foundations of Machine Learning (MIT Press, Cambridge, 2018)

    Google Scholar 

  8. V. Botu, R. Batra, J. Chapman, R. Ramprasad, Machine learning force fields: construction, validation, and outlook. J. Phys. Chem. C 121(1), 511–522 (2017)

    CAS  Google Scholar 

  9. V.L. Deringer, M.A. Caro, G. Csányi, Machine learning interatomic potentials as emerging tools for materials science. Adv. Mater. 31(46), 1902765 (2019)

    CAS  Google Scholar 

  10. A.V. Shapeev, Moment tensor potentials: A class of systematically improvable interatomic potentials. Multiscale Model. Simul. 14(3), 1153–1173 (2016)

    Google Scholar 

  11. R. Ramprasad, R. Batra, G. Pilania, A. Mannodi-Kanakkithodi, C. Kim, Machine learning in materials informatics: Recent applications and prospects. npj Comput. Mater. 3(1), 1–13 (2017)

    Google Scholar 

  12. K. Gubaev, E.V. Podryabinkin, A.V. Shapeev, Machine learning of molecular properties: Locality and active learning. J. Chem. Phys. 148(24), 241727 (2018)

    Google Scholar 

  13. S. Zhao, E.N. Hahn, B. Kad, B.A. Remington, C.E. Wehrenberg, E.M. Bringa, M.A. Meyers, Amorphization and nanocrystallization of silicon under shock compression. Acta Mater. 103, 519–533 (2016)

    CAS  Google Scholar 

  14. K. Persson, Materials data on sio2 (sg:15) by materials project, 11 2014. An optional note

  15. M.J. Mehl, D. Hicks, C. Toher, O. Levy, R.M. Hanson, G. Hart, S. Curtarolo, The aflow library of crystallographic prototypes: Part 1. Comput. Mater. Sci. 136, S1–S828 (2017)

    CAS  Google Scholar 

  16. D. Hicks, M.J. Mehl, E. Gossett, C. Toher, O. Levy, R.M. Hanson, G. Hart, S. Curtarolo, The aflow library of crystallographic prototypes: Part 2. Comput. Mater. Sci. 161, S1–S1011 (2019)

    CAS  Google Scholar 

  17. O.B. Gadzhiev, S.K. Ignatov, M.Y. Kulikov, A.M. Feigin, A.G. Razuvaev, P.G. Sennikov, O. Schrems, Structure, energy, and vibrational frequencies of oxygen allotropes o n (n 6) in the covalently bound and van der waals forms: Ab initio study at the ccsd (t) level. J. Chem. Theory Comput. 9(1), 247–262 (2013)

    CAS  Google Scholar 

  18. R.T. Downs, M. Hall-Wallace, The American mineralogist crystal structure database. Am. Miner. 88(1), 247–250 (2003)

    CAS  Google Scholar 

  19. H. Zheng, X.-G. Li, R. Tran, C. Chen, M. Horton, D. Winston, K.A. Persson, S.P. Ong, Grain boundary properties of elemental metals. Acta Mater. 186, 40–49 (2020)

    CAS  Google Scholar 

  20. R. Tran, X. Zihan, B. Radhakrishnan, D. Winston, W. Sun, K.A. Persson, S.P. Ong, Surface energies of elemental crystals. Sci. Data 3(1), 1–13 (2016)

    Google Scholar 

  21. B.-J. Lee, A modified embedded atom method interatomic potential for silicon. Calphad 31(1), 95–104 (2007)

    CAS  Google Scholar 

  22. C. Li, C. Wang, J. Han, L. Yan, B. Deng, X. Liu, A comprehensive study of the high-pressure-temperature phase diagram of silicon. J. Mater. Sci. 53(10), 7475–7485 (2018)

    CAS  Google Scholar 

  23. J. Crain, S.J. Clark, G.J. Ackland, M.C. Payne, V. Milman, P.D. Hatton, B.J. Reid, Theoretical study of high-density phases of covalent semiconductors. i. ab initio treatment. Phys. Rev. B 49(8), 5329 (1994)

    CAS  Google Scholar 

  24. M. De Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Sluiter, C.K. Ande, S.V. Der Zwaag, J.J. Plata, Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data 2(1), 1–13 (2015)

    Google Scholar 

  25. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, C.G. Van de Walle, First-principles calculations for point defects in solids. Rev. Mod. Phys. 86(1), 253 (2014)

    Google Scholar 

  26. E. Clouet, Ab initio models of dislocations. Handbook of Materials Modeling: Methods: Theory and Modeling, pp. 1503–1524 (2020)

  27. A. Goyal, Y. Li, A. Chernatynskiy, J.S. Jayashankar, M.C. Kautzky, S.B. Sinnott, S.R. Phillpot, The influence of alloying on the stacking fault energy of gold from density functional theory calculations. Comput. Mater. Sci. 188, 110236 (2021)

    CAS  Google Scholar 

  28. P.J.H. Denteneer, W. Van Haeringen, Stacking-fault energies in semiconductors from first-principles calculations. J. Phys. C 20(32), L883 (1987)

    Google Scholar 

  29. F.-Y. Tian, N.-X. Chen, L. Delczeg, L. Vitos, Interlayer potentials for fcc (1 1 1) planes of Pd–Ag random alloys. Comput. Mater. Sci. 63, 20–27 (2012)

    CAS  Google Scholar 

  30. W. Li, L. Song, H. Qing-Miao, S.K. Kwon, B. Johansson, L. Vitos, Generalized stacking fault energies of alloys. J. Phys. 26(26), 265005 (2014)

    Google Scholar 

  31. Y.-M. Juan, E. Kaxiras, Generalized stacking fault energy surfaces and dislocation properties of silicon: A first-principles theoretical study. Philos. Mag. A 74(6), 1367–1384 (1996)

    CAS  Google Scholar 

  32. W. Sun, G. Ceder, Efficient creation and convergence of surface slabs. Surf. Sci. 617, 53–59 (2013)

    CAS  Google Scholar 

  33. D. Sholl, J.A. Steckel, Density Functional Theory: A Practical Introduction (Wiley, Hoboken, 2011)

    Google Scholar 

  34. A. Ghoufi, P. Malfreyt, D.J. Tildesley, Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface. Chem. Soc. Rev. 45(5), 1387–1409 (2016)

    CAS  Google Scholar 

  35. J.-C. Neyt, A. Wender, V. Lachet, P. Malfreyt, Prediction of the temperature dependence of the surface tension of so2, n2, o2, and ar by Monte Carlo molecular simulations. J. Phys. Chem. B 115(30), 9421–9430 (2011)

    CAS  Google Scholar 

  36. P. Geysermans, D. Gorse, V. Pontikis, Molecular dynamics study of the solid–liquid interface. J. Chem. Phys. 113(15), 6382–6389 (2000)

    CAS  Google Scholar 

  37. R. Šolc, M.H. Gerzabek, H. Lischka, D. Tunega, Wettability of kaolinite (001) surfaces-molecular dynamic study. Geoderma 169, 47–54 (2011)

    Google Scholar 

  38. G. Ulian, D. Moro, G. Valdrè, Dft simulation of the water molecule interaction with the (00l) surface of montmorillonite. Minerals 11(5), 501 (2021)

    CAS  Google Scholar 

  39. Z. Liang, W. Evans, P. Keblinski, Equilibrium and nonequilibrium molecular dynamics simulations of thermal conductance at solid–gas interfaces. Phys. Rev. E 87(2), 022119 (2013)

    Google Scholar 

  40. F.H. Stillinger, T.A. Weber, Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31(8), 5262 (1985)

    CAS  Google Scholar 

  41. J. Tersoff, New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37(12), 6991 (1988)

    CAS  Google Scholar 

  42. G.T. Barkema, N. Mousseau, High-quality continuous random networks. Phys. Rev. B 62(8), 4985 (2000)

    CAS  Google Scholar 

  43. V.L. Deringer, N. Bernstein, A.P. Bartók, M.J. Cliffe, R.N. Kerber, L.E. Marbella, C.P. Grey, S.R. Elliott, G. Csányi, Realistic atomistic structure of amorphous silicon from machine-learning-driven molecular dynamics. J Phys Chem Lett 9(11), 2879–2885 (2018)

    CAS  Google Scholar 

  44. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, Quantum espresso: A modular and open-source software project for quantum simulations of materials. J. Phys. 21(39), 395502 (2009)

    Google Scholar 

  45. P.E. Blöchl, Projector augmented-wave method. Phys. Rev. B 50(24), 17953 (1994)

    Google Scholar 

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

    CAS  Google Scholar 

  47. H.J. Monkhorst, J.D. Pack, Special points for brillouin-zone integrations. Phys. Rev. B 13(12), 5188 (1976)

    Google Scholar 

  48. I.S. Novikov, K. Gubaev, E. Podryabinkin, A.V. Shapeev, The MLIP package: Moment tensor potentials with MPI and active learning. Mach. Learn. 2, 025002 (2020)

    Google Scholar 

  49. B. Mortazavi, E.V. Podryabinkin, S. Roche, T. Rabczuk, X. Zhuang, A.V. Shapeev, Machine-learning interatomic potentials enable first-principles multiscale modeling of lattice thermal conductivity in graphene/borophene heterostructures. Mater. Horiz. 7(9), 2359–2367 (2020)

    Google Scholar 

  50. A. Lomaka, T. Tamm, Linearization of moment tensor potentials for multicomponent systems with a preliminary assessment for short-range interaction energy in water dimer and trimer. J. Chem. Phys. 152(16), 164115 (2020)

    CAS  Google Scholar 

  51. I.S. Novikov, Y.V. Suleimanov, A.V. Shapeev, Automated calculation of thermal rate coefficients using ring polymer molecular dynamics and machine-learning interatomic potentials with active learning. Phys. Chem. Chem. Phys. 20(46), 29503–29512 (2018)

    CAS  Google Scholar 

  52. K. Gubaev, E.V. Podryabinkin, G.L.W. Hart, A.V. Shapeev, Accelerating high-throughput searches for new alloys with active learning of interatomic potentials. Comput. Mater. Sci. 156, 148–156 (2019)

    CAS  Google Scholar 

  53. I.I. Novoselov, A.V. Yanilkin, A.V. Shapeev, E.V. Podryabinkin, Moment tensor potentials as a promising tool to study diffusion processes. Comput. Mater. Sci. 164, 46–56 (2019)

    CAS  Google Scholar 

  54. K.T. Butler, D.W. Davies, H. Cartwright, O. Isayev, A. Walsh, Machine learning for molecular and materials science. Nature 559(7715), 547–555 (2018)

    CAS  Google Scholar 

  55. J.F. Cannon, Behavior of the elements at high pressures. J. Phys. Chem. Ref. Data 3(3), 781–824 (1974)

    CAS  Google Scholar 

  56. H. Jing Zhu, L.D. Merkle, C.S. Menoni, I.L. Spain, Crystal data for high-pressure phases of silicon. Phys. Rev. B 34(7), 4679 (1986)

    Google Scholar 

  57. K. Zongo, L. K Béland, C. Ouellet-Plamondon, Improving atom-scale models of clay minerals using machine learning. Can. Nuclear Soc. (2021)

  58. A.P. Bartók, J. Kermode, N. Bernstein, G. Csányi, Machine learning a general-purpose interatomic potential for silicon. Phys. Rev. X 8(4), 041048 (2018)

    Google Scholar 

  59. G. Henkelman, B.P. Uberuaga, H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113(22), 9901–9904 (2000)

    CAS  Google Scholar 

  60. G.S. Hwang, W.A. Goddard III., Diffusion and dissociation of neutral divacancies in crystalline silicon. Phys. Rev. B 65(23), 233205 (2002)

    Google Scholar 

  61. D. YaojunA, S.A. Barr, K.R.A. Hazzard, T.J. Lenosky, R.G. Hennig, J.W. Wilkins, Fast diffusion mechanism of silicon tri-interstitial defects. Phys. Rev. B 72(24), 241306 (2005)

    Google Scholar 

  62. F. El-Mellouhi, N. Mousseau, P. Ordejón, Sampling the diffusion paths of a neutral vacancy in silicon with quantum mechanical calculations. Phys. Rev. B 70(20), 205202 (2004)

    Google Scholar 

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Acknowledgments

We thank Dr. Yaoting Zhang for insightful discussions. The authors wish to thank Compute Canada for generous allocation of computer resources, the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Nuclear Waste Management Organization (NWMO) for financial support. There is no conflict of interest. Data will be made available upon request.

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Authors and Affiliations

  1. Ecole de Technologie Supérieure, Université du Québec, Montreal, QC, Canada

    K. Zongo & C. Ouellet-Plamondon

  2. Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada

    L. K. Béland

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  1. K. Zongo
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  2. L. K. Béland
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  3. C. Ouellet-Plamondon
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Correspondence to C. Ouellet-Plamondon.

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Zongo, K., Béland, L.K. & Ouellet-Plamondon, C. First-principles database for fitting a machine-learning silicon interatomic force field. MRS Advances 7, 39–47 (2022). https://doi.org/10.1557/s43580-022-00228-z

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  • DOI: https://doi.org/10.1557/s43580-022-00228-z