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Adaptive Genetic Algorithm for Structure Prediction and Application to Magnetic Materials

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Handbook of Materials Modeling

Abstract

We present an adaptive genetic algorithm which can be used to predict the atomistic structures of crystals, interfaces, and nanoparticles based on the chemical composition of the materials. The method combines the speed of structure exploration by classical potentials with the accuracy of total energy calculations using first-principles density functional theory (DFT). This method increases the efficiency of structure prediction based on DFT calculations by several orders of magnitude and allows considerable increase in size and complexity of systems that can be studied. The performance of the method is demonstrated by successful structure identifications of complex binary and ternary intermetallic compounds with the number of atoms in the unit cell as large as 150 atoms. Applications of the method to discovery of novel magnetic materials are discussed.

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References

  • Artrith N, Urban A, Ceder G (2017) Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species. Phys Rev B 96:014112

    Article  ADS  Google Scholar 

  • Balasubramanian B, Zhao X, Valloppilly SR, Beniwal S, Skomski R, Sarella A, Jin Y, Li X, Xu X, Cao H, Wang H, Enders A, Wang C-Z, Ho K-M, Sellmyer DJ (2018) Magnetism of new metastable magnetic nitride compounds. Nanoscale 10:13011

    Article  Google Scholar 

  • Bauer D, Diamond D, Li J, Sandalow D, Telleen P, Wanner B (2011) Critical materials strategy. US Department of Energy. http://energy.gov/sites/prod/files/DOE_CMS2011_FINAL_Full.pdf

  • Behler J (2017) First principles neural network potentials for reactive simulations of large molecular and condensed systems. Angew Chem Int Ed 56:2–15

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Blochl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953

    Article  ADS  Google Scholar 

  • Brommer P, Gahler F (2006) Effective potentials for quasicrystals from ab-initio data. Philos Mag 86:753

    Article  ADS  Google Scholar 

  • Brommer P, Gahler F (2007) Potfit: effective potentials from ab initio data. Model Simul Mater Sci Eng 15:295

    Article  ADS  Google Scholar 

  • Buschow KHJ, Wernick JH, Chin GY (1978) Note on the Hf-Co phase diagram. J Less-Common Met 59:61–67

    Article  Google Scholar 

  • Ci PH et al (2017) Quantifying van der Waals interactions in layered transition metal dichalcogenides from pressure-enhanced valence band splitting. Nano Lett 17:4982

    Article  ADS  Google Scholar 

  • Daw MS, Baskes MI (1984) Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B 29:6443

    Article  ADS  Google Scholar 

  • Deaven DM, Ho KM (1995) Molecular geometry optimization with a genetic algorithm. Phys Rev Lett 75:288–291

    Article  ADS  Google Scholar 

  • Demczyk BG, Cheng SF (1991) Structures of Zr2Co11 and HfCo7 intermetallic compounds. J Appl Crystallogr 24:1023

    Article  Google Scholar 

  • Doll K, Schön JC, Jansen M (2007) Global exploration of the energy landscape of solids on the ab initio level. Phys Chem Chem Phys 9:6128–6133

    Article  Google Scholar 

  • Dong YH, Lu WC, Xu X, Zhao X, Ho KM, Wang CZ (2017) Theoretical search for possible Au-Si crystal structures using a genetic algorithm. Phys Rev B 95:134109

    Article  ADS  Google Scholar 

  • Eberhart ME, Clougherty DP (2004) Looking for design in materials design. Nat Mater 3:659–661

    Article  ADS  Google Scholar 

  • Gabay AM, Zhang Y, Hadjipanayis GC (2001) Cobalt-rich magnetic phases in Zr–Co alloys. J Magn Magn Mater 236:37

    Article  ADS  Google Scholar 

  • Goedecker S (2004) Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J Chem Phys 120:9911–9917

    Article  ADS  Google Scholar 

  • Gupta R, Pandey N, Tayal A, Gupta M (2015) Phase formation, thermal stability and magnetic moment of cobalt nitride thin films. AIP Adv 5:097131

    Article  ADS  Google Scholar 

  • Harris KDM, Johnston RL, Kariuki BM (1998) Acta Crystallogr. The genetic algorithm: foundations and applications in structure solution from powder diffraction data. Acta Crystallogr A54:632–645

    Article  Google Scholar 

  • Ivanova GV, Shchegoleva NN (2009) The microstructure of a magnetically hard Zr2Co11 alloy. Phys Met Metallogr 107:270

    Article  ADS  Google Scholar 

  • Ivanova GV, Shchegoleva NN, Gabay AM (2007) Crystal structure of Zr2Co11 hard magnetic compound. J Alloys Compd 432:135

    Article  Google Scholar 

  • Ji M, Umemoto K, Wang CZ, Ho KM, Wentzcovitch RM (2011) Ultrahigh-pressure phases of H2O ice predicted using an adaptive genetic algorithm. Phys Rev B 220105(R):84

    Google Scholar 

  • Kim TK, Takahashi M (1972) New magnetic material having ultrahigh magnetic moment. Appl Phys Lett 20:492

    Article  ADS  Google Scholar 

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  ADS  MathSciNet  Google Scholar 

  • Kresse G, Furthmüller J (1996a) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6:15

    Article  Google Scholar 

  • Kresse G, Furthmüller J (1996b) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169

    Article  ADS  Google Scholar 

  • Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758

    Article  ADS  Google Scholar 

  • Lv XB, Zhao X, Wu SQ, Wu P, Sun Y, Nguyen MC, Shi YL, Lin ZJ, Wang CZ, Ho KM (2017) A scheme for the generation of Fe-P networks to search for low-energy LiFePO4 crystal structures. J Mater Chem A 5:14611–14618

    Article  Google Scholar 

  • Lyakhov AO, Oganov AR, Stokes H, Zhu Q (2013) New developments in evolutionary structure prediction algorithm USPEX. Comp Phys Comm 184:1172–1182

    Article  ADS  Google Scholar 

  • Maddox J (1988) Crystals from first principles. Nature 335:201

    Article  ADS  Google Scholar 

  • Nguyen MC, Choi JH, Zhao X, Wang CZ, Zhang Z, Ho KM (2013) New layered structures of cuprous chalcogenides as thin film solar cell materials: Cu2Te and Cu2Se. Phys Rev Lett 111:165502

    Article  ADS  Google Scholar 

  • Nguyen MC, Chen C, Zhao X, Liu J, Wang CZ, Ho KM (2018) Prediction of novel stable Fe-V-Si ternary phase. J Alloys Comp 732:567–572

    Article  Google Scholar 

  • Oganov AR, Glass CW (2008) Evolutionary crystal structure prediction as a tool in materials design. J Phys Condens Matter 20:064210

    Article  ADS  Google Scholar 

  • Onat B, Cubuk ED, Malone BD, Kaxiras E (2018) Implanted neural network potentials: application to Li-Si alloys. Phys Rev B 97:094106

    Article  ADS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865 Phys. Rev. Lett. 78, 1396 (1997)(E)

    Article  ADS  Google Scholar 

  • Pickard CJ, Needs RJ (2011) Ab initio random structure searching. J Phys Condens Matter 23:053201

    Article  ADS  Google Scholar 

  • Skomski R, Sellmyer DJ (2009) Anisotropy of rare-earth magnets. J Rare Earth 27:675

    Article  Google Scholar 

  • Sugita Y, Mitsuoka K, Komuro M, Hoshiya H, Kozono Y, Hanazono M (1991) Giant magnetic moment and other magnetic properties of epitaxially grown Fe16N2 single-crystal films. J Appl Phys 70:5977

    Article  ADS  Google Scholar 

  • Tkachenko et al Handbook of materials modeling. Springer International Publishing, 2nd edn, vol~1

    Google Scholar 

  • Voroshilov YV, Krypyakevych PI, Kuz’ma YB (1971) Crystal structures of ZrCo3B2 and HfCo3B2. Sov Phys–Crystallogr 15:813–816

    Google Scholar 

  • Wales D, Doye J (1997) Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116

    Article  Google Scholar 

  • Wang Y, Lv J, Zhu L, Ma Y (2010) Crystal structure prediction via particle-swarm optimization. Phys Rev B 82:094116

    Article  ADS  Google Scholar 

  • Wang Y, Lv J, Zhu L, Ma Y (2012) CALYPSO: a method for crystal structure prediction. Comp Phys Commun 183:2063–2070

    Article  ADS  Google Scholar 

  • Wille LT (1986) Searching potential energy surfaces by simulated annealing. Nature 324:46–48

    Article  ADS  Google Scholar 

  • Woodley SM (2004) Prediction of crystal structures using evolutionary algorithms and related techniques. Struct Bond 110:95–132

    Article  Google Scholar 

  • Woodley SM, Catlow R (2008) Crystal structure prediction from first principles. Nature Mater 7:937–946

    Article  ADS  Google Scholar 

  • Woodley SM, Battle PD, Gale JD, Catlow CRA (1999) The prediction of inorganic crystal structures using a genetic algorithm and energy minimization. Phys Chem Chem Phys 1:2535–2342

    Article  Google Scholar 

  • Wu SQ, Umemoto K, Ji M, Wang CZ, Ho KM, Wentzcovitch RM (2011) Identification of post-pyrite phase transitions in SiO2 by a genetic algorithm. Phys Rev B 83:184102

    Article  ADS  Google Scholar 

  • Wu SQ, Ji M, Wang CZ, Nguyen MC, Zhao X, Umemoto K, Wentzcovitch RM, Ho KM (2014) Adaptive genetic algorithm for crystal structure prediction. J Phys Condens Matter 26:035402

    Article  Google Scholar 

  • Wu S, Balamurugan B, Zhao X, Yu S, Nguyen MC, Sun Y, Valloppilly SR, Sellmyer DJ, Ho KM, Wang CZ (2017) Exploring new phases of Fe3-xCoxC for rare-earth free magnets. J Phys D Appl Phys 50:215005

    Article  ADS  Google Scholar 

  • Zhang WY, Li XZ, Valloppilly S, Skomski R, Shield JE, Sellmyer DJ (2013) Magnetism of rapidly quenched rhombohedral Zr2Co11-based nanocomposites. J Phys D 46:135004

    Article  ADS  Google Scholar 

  • Zhang L, Han J, Wang H, Car R, E W (2018) Deep potential molecular dynamics: a scalable model with accuracy of quantum mechanics. Phys Rev Lett 120:143001

    Article  ADS  Google Scholar 

  • Zhao X, Shu Q, Nguyen MC, Wang Y, Ji M, Xiang H, Ho KM, Gong X, Wang CZ (2014a) Interface structure prediction from first-principles. J Phys Chem C 118:9524–9530

    Article  Google Scholar 

  • Zhao X, Nguyen MC, Wang CZ, Ho KM (2014b) New stable Re-B phases for ultra-hard materials. J Phys Condens Matter 26:455401

    Article  Google Scholar 

  • Zhao X, Nguyen MC, Zhang WY, Wang CZ, Kramer MJ, Sellmyer DJ, Li XZ, Zhang F, Ke LQ, Antropov VP, Ho KM (2014c) Exploring the structural complexity of intermetallic compounds by an adaptive genetic algorithm. Phys Rev Lett 112:045502

    Article  ADS  Google Scholar 

  • Zhao X, Ke L, Nguyen MC, Wang CZ, Ho KM (2015a) Structures and magnetic properties of Co-Zr-B magnets studied by first-principles calculations. J Appl Phys 117:243902

    Article  ADS  Google Scholar 

  • Zhao X, Wu SQ, Lv XB, Nguyen MC, Wang CZ, Lin ZJ, Zhu ZZ, Ho KM (2015b) Exploration of tetrahedral structures in silicate cathodes using a motif-network scheme. Sci Rep 5:15555

    Article  ADS  Google Scholar 

  • Zhao X, Ke L, Wang CZ, Ho KM (2016a) Metastable cobalt nitride structures with high magnetic anisotropy for rare-earth free magnets. Phys Chem Chem Phys 18:31680–31690

    Article  Google Scholar 

  • Zhao X, Wang CZ, Yao Y, Ho KM (2016b) Large magnetic anisotropy predicted for rare-earth-free Fe16-xCoxN2 alloys. Phys Rev B 94:224424

    Article  ADS  Google Scholar 

  • Zhao X, Yu S, Wu S, Nguyen MC, Wang CZ, Ho KM (2017a) Structures, phase transitions, and magnetic properties of Co3Si from first-principles calculations. Phys Rev B 96:024422

    Article  ADS  Google Scholar 

  • Zhao X, Wang CZ, Kim M, Ho KM (2017b) Fe-cluster compounds of chalcogenides: candidates for rare-earth-free permanent magnet and magnetic nodal-line topological material. Inorg Chem 56:14577–14583

    Article  Google Scholar 

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Acknowledgments

We are grateful to Dr. David Sellmyer, Dr. B. Balamurugan, and Dr. J. R. Chelikowsky for useful discussion and collaboration on magnetic structure prediction and discovery. We would like to acknowledge US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering, who supported the development of adaptive genetic algorithm for crystal structure prediction. We also would like to acknowledge the support from the National Science Foundation (NSF), Division of Materials Research (DMR) under Award DMREF: SusChEM 1436386 and DMREF: SusChEM 1729677 to support the research on discovery of novel magnetic materials. Ames Laboratory is operated for the U.S. DOE by Iowa State University under contract # DE-AC02-07CH11358.

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Correspondence to Cai-Zhuang Wang .

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Zhao, X., Wu, S., Nguyen, M.C., Ho, KM., Wang, CZ. (2019). Adaptive Genetic Algorithm for Structure Prediction and Application to Magnetic Materials. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_73-1

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