J. Semicond. > 2018, Volume 39 > Issue 7 > 071004
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SPECIAL TOPIC ON SEMICONDUCTOR MATERIALS GENOME INITIATIVE: NEW CONCEPTS AND DISCOVERIES

Crystal structure prediction in the context of inverse materials design

G. Trimarchi

+ Author Affiliations

 Corresponding author: G. Trimarchi, g-trimarchi@northwestern.edu

DOI: 10.1088/1674-4926/39/7/071004

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Abstract: Inverse materials design tackles the challenge of finding materials with desired properties, tailored to specific applications, by combining atomistic simulations and optimization methods. The search for optimal materials requires one to survey large spaces of candidate solids. These spaces of materials can encompass both known and hypothetical compounds. When hypothetical compounds are explored, it becomes crucial to determine which ones are stable (and can be synthesized) and which are not. Crystal structure prediction is a necessary step for assessing theoretically the stability of a hypothetical material and, therefore, is a crucial step in inverse materials design protocols. Here, we describe how biologically-inspired global optimization methods can efficiently predict the stable crystal structure of solids. Specifically, we discuss the application of genetic algorithms to search for optimal atom configurations in systems in which the underlying lattice is given, and of evolutionary algorithms to address the general lattice-type prediction problem.

Key words: crystal structure prediction, evolutionary algorithm optimization, inverse design



[1]
Martin R M. Electronic structure: basic theory and practical methods. Cambridge University Press, 2004
[2]
Martin R M, Reining L, Ceperley D M. Interacting electrons. Cambridge University Press, 2016
[3]
Franceschetti A, Zunger A. The inverse band-structure problem of finding an atomic configuration with given electronic properties. Nature, 1911, 402: 60
[4]
Inorganic Chemistry Structure Database (ICSD). Fachinformationszentrum, Karlsruhe, Karlsruhe, Germany, 2015
[5]
Trimarchi G, Zhang X, DeVries Vermeer M J, et al. Emergence of a few distinct structures from a single formal structure type during high-throughput screening for stable compounds: the case of RbCuS and RbCuSe. Phys Rev B, 2015, 92: 165103 doi: 10.1103/PhysRevB.92.165103
[6]
Zhang X, Yu L, Zakutayev A, et al. Sorting stable versus unstable hypothetical compounds: the case of multi-functional abx half-heusler filled tetrahedral structures. Adv Funct Mater, 2012, 22: 1425 doi: 10.1002/adfm.v22.7
[7]
Zhang X, Stevanović V, d’Avezac M, et al. Prediction of A2BX4 metal-chalcogenide compounds via first-principles thermodynamics. Phys Rev B, 2012, 86: 014109 doi: 10.1103/PhysRevB.86.014109
[8]
Woodley S M, Catlow R. Crystal structure prediction from first principles. Nat Mater, 2008, 7: 937 doi: 10.1038/nmat2321
[9]
Oganov A R. Modern methods of crystal structure prediction. 1st ed. Wiley-VCH, 2011
[10]
Goldberg D E. Genetic algorithms in search,optimization and machine learning. Addison-Wesley, Reading, MA, 1989
[11]
Eiben A E, Smith J E. Introduction to evolutionary computing. Berlin Heidelberg: Springer, 2003
[12]
Wells A F. Structural inorganic chemistry. 5th ed. Oxford University Press, 1984
[13]
Strukturbericht. Akademische Verlagsgesellschaft M. B. H, Leipzig, 1931, 1: 7
[14]
Trimarchi G, Graf P, Zunger A. Exploring the configurational space of binary alloys: Different sampling for different cell shapes. Phys Rev B, 2006, 74: 014204 doi: 10.1103/PhysRevB.74.014204
[15]
Ferreira L G, Wei S H, Zunger A. Stability, electronic structure, and phase diagrams of novel inter-semiconductor compounds. Int J Supercomput Appl, 1991, 5: 34 doi: 10.1177/109434209100500103
[16]
Barabash S V, Blum V, Müller S, et al. Prediction of unusual stable ordered structures of Au–Pd alloys via a first-principles cluster expansion. Phys Rev B, 2006, 74: 35108 doi: 10.1103/PhysRevB.74.035108
[17]
Zunger A. Statistics and dynamics of alloys phase transformations. New York: Plenum Press, 1994: 361
[18]
Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated annealing. Readings in Computer Vision, 1983, 220: 671 doi: 10.1142/9789812799371_0035
[19]
Kim K, Graf P A, Jones W B. A genetic algorithm based inverse band structure method for semiconductor alloys. J Comput Phys, 2005, 208: 735 doi: 10.1016/j.jcp.2005.03.005
[20]
Ihm J, Zunger A, Cohen M L. Momentum-space formalism for the total energy of solids. J Phys C, 1979, 12: 4409 doi: 10.1088/0022-3719/12/21/009
[21]
Doll K, Schön J C, Jansen M. Structure prediction based on ab initio simulated annealing for boron nitride. Phys Rev B, 2008, 78: 144110 doi: 10.1103/PhysRevB.78.144110
[22]
Martoňák R, Laio A, Parrinello M. predicting crystal structures: the parrinello-rahman method revisited. Phys Rev Lett, 2003, 90: 075503 doi: 10.1103/PhysRevLett.90.075503
[23]
Laio A, Parrinello M. Escaping free-energy minima. Proce Natl Acad Scie, 2002, 99: 12562 doi: 10.1073/pnas.202427399
[24]
Wales D J, Doye J P K. Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. J Phys Chem A, 1997, 101: 5111 doi: 10.1021/jp970984n
[25]
Wales D J, Scheraga H A. Global optimization of clusters, crystals, and biomolecules. Science, 1999, 285: 1368 doi: 10.1126/science.285.5432.1368
[26]
Goedecker S. Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J Chem Phys, 2004, 120: 9911 doi: 10.1063/1.1724816
[27]
Amsler M, Goedecker S. Crystal structure prediction using the minima hopping method. J Chem Phys, 2010, 133: 224104 doi: 10.1063/1.3512900
[28]
Pickard C J, Needs R J. High-pressure phases of silane. Phys Rev Lett, 2006, 97: 045504 doi: 10.1103/PhysRevLett.97.045504
[29]
Pickard C J, Needs R J. Ab initio random structure searching. J Phys: Conden Matter, 2011, 23: 053201 doi: 10.1088/0953-8984/23/5/053201
[30]
Needs R J, Pickard C J. Perspective: role of structure prediction in materials discovery and design. APL Mater, 2016, 4: 053210 doi: 10.1063/1.4949361
[31]
Woodley S M, Battle P D, Gale J D, et al. The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation. Phys Chem Chem Phys, 1999, 1: 2535 doi: 10.1039/a901227c
[32]
Zhao X, Nguyen M C, Zhang W Y, et al. Exploring the structural complexity of intermetallic compounds by an adaptive genetic algorithm. Phys Rev Lett, 2014, 112: 045502 doi: 10.1103/PhysRevLett.112.045502
[33]
Oganov A R, Glass C W. Crystal structure prediction using ab initio evolutionary techniques: Principles and applications. J Chem Phys, 2006, 124: 244704 doi: 10.1063/1.2210932
[34]
Oganov A R, Glass C W, Ono S. High-pressure phases of CaCO3: Crystal structure prediction and experiment. Earth Planet Sci Lett, 2006, 241: 95 doi: 10.1016/j.jpgl.2005.10.014
[35]
Abraham N L, Probert M I J. Improved real-space genetic algorithm for crystal structure and polymorph prediction. Phys Rev B, 2008, 77: 134117 doi: 10.1103/PhysRevB.77.134117
[36]
Abraham N L, Probert M I J. A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction. Phys Rev B, 2006, 73: 224104 doi: 10.1103/PhysRevB.73.224104
[37]
Lyakhov A O, Oganov A R, Stokes H T, et al. New developments in evolutionary structure prediction algorithm USPEX. Comput Phys Commun, 2013, 184: 1172 doi: 10.1016/j.cpc.2012.12.009
[38]
Lonie D C, Zurek E. XtalOpt: An open-source evolutionary algorithm for crystal structure prediction. Comput Phys Commun, 2011, 182: 372 doi: 10.1016/j.cpc.2010.07.048
[39]
Tipton W W, Hennig R G. A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials. J Phys: Conden Matter, 2013, 25: 495401 doi: 10.1088/0953-8984/25/49/495401
[40]
Wang Y, Lv J, Zhu L, Ma Y. CALYPSO: a method for crystal structure prediction. Comput Phys Commun, 2012, 183: 2063 doi: 10.1016/j.cpc.2012.05.008
[41]
Wang Y, Lv J, Zhu L, Ma Y. Crystal structure prediction via particle-swarm optimization. Phys Rev B, 2010, 82: 094116 doi: 10.1103/PhysRevB.82.094116
[42]
Trimarchi G, Zunger A. Global space-group optimization problem: Finding the stablest crystal structure without constraints. Phys Rev B, 2007, 75: 104113 doi: 10.1103/PhysRevB.75.104113
[43]
Trimarchi G, Zunger A. Finding the lowest-energy crystal structure starting from randomly selected lattice vectors and atomic positions: first-principles evolutionary study of the Au–Pd, Cd–Pt, Al–Sc, Cu–Pd, Pd–Ti, and Ir–N binary systems. J Phys: Conden Matter, 2008, 20: 295212 doi: 10.1088/0953-8984/20/29/295212
[44]
Glass C W, Oganov A R, Hansen N. USPEX—evolutionary crystal structure prediction. Comput Phys Commun, 2006, 175: 713 doi: 10.1016/j.cpc.2006.07.020
[45]
Deaven D M, Ho K M. Molecular geometry optimization with a genetic algorithm. Phys Rev Lett, 1995, 75: 288 doi: 10.1103/PhysRevLett.75.288
[46]
Trimarchi G, Freeman A J, Zunger A. Predicting stable stoichiometries of compounds via evolutionary global space-group optimization. Phys Rev B, 2009, 80: 092101 doi: 10.1103/PhysRevB.80.092101
[47]
Blum V, Zunger A. Structural complexity in binary bcc ground states: The case of bcc Mo-Ta. Phys Rev B, 2004, 69: 020103 doi: 10.1103/PhysRevB.69.020103
[48]
Blum V, Zunger A. Mixed-basis cluster expansion for thermodynamics of bcc alloys. Phys Rev B, 2004, 70: 155108 doi: 10.1103/PhysRevB.70.155108
[49]
Blum V, Zunger A. Prediction of ordered structures in the bcc binary systems of Mo, Nb, Ta, and W from first-principles search of approximately 3 000 000 possible configurations. Phys Rev B, 2005, 72: 020104 doi: 10.1103/PhysRevB.72.020104
[50]
Sanati M, Wang L G, Zunger A. Adaptive crystal structures: CuAu and NiPt. Phys Rev Lett, 2003, 90: 045502 doi: 10.1103/PhysRevLett.90.045502
[51]
Gautier R, Zhang X, Hu L, et al. Prediction and accelerated laboratory discovery of previously unknown 18-electron ABX compounds. Nat Chem, 2015, 7: 308 doi: 10.1038/nchem.2207
[52]
Massalski T B. Binary alloy phase diagrams. ASM International, 1992
[53]
Villars P, Cenzual K, Daams J L C, et al. Inorganic materials database and design system. ASM International, 2003
[54]
Fujikawa S, Sugaya M, Takei H, et al. Solid solubility and residual resistivity of scandium in aluminum. J Less-Common Met, 1979, 63: 87 doi: 10.1016/0022-5088(79)90211-X
[55]
Curtarolo S, Morgan D, Ceder G. Accuracy of ab initio methods in predicting the crystal structures of metals: a review of 80 binary alloys. Calphad, 2005, 29: 163 doi: 10.1016/j.calphad.2005.01.002
[56]
Raub E, Röschel E. Die Titan-Palladium-Legierungen. Z Metallkd, 1968, 59: 112
Fig. 1.  (Color online) (a) Schematic summarizing which of the series of possible I-I-VI ABX compounds are reported in the ICSD (shown by check marks) and those that are missing from the ICSD and whose existence was unknown. Here, A and B are column I metals, i.e, Li, Na, K, Rb, and the d10 noble metals Cu, Ag, and Au (which predominantly exhibit a monovalent character). The X species are the column VI elements S, Se and Te. (b) Compounds predicted to be stable (denoted by + signs) or unstable (denoted by – signs) in the half-Heusler alloy structure. (c) Compounds predicted to be stable or unstable in Ref. [20] performing DFT total energy calculations of each ABX system using a set of 41 structure types. Adapted with permission from Ref. [5].

DownLoad: Full-Size Img PowerPoint
Fig. 2.  (Color online) (a) The circles indicate the number of inequivalent cell shapes of a system of binary compounds AxB1-x as a function of the number of atoms N per unit cell as obtained applying the exhaustive direct enumeration algorithm of Ref. [21]. The interpolating solid red line shows that the number NICS of ICSs obtained by exhaustive enumeration increases as a function of N following a power law BNα where α ≈ 1.5. (b) The largest number of same-shape structures (SSSs), is a function of the number of sites N per cell was not full sentence. Note that the enumeration algorithm of Ref. [21] applies symmetry checks to discard structures that are symmetry-equivalent to structures previously generated during the enumeration. Even with the symmetry filters applied, the number NSSS ≈ increases as a function of the number of atoms per cell following the exponential law AeγN. Adapted with permission from Ref. [14].

DownLoad: Full-Size Img PowerPoint
Fig. 3.  (Color online) The result of the ground state search performed by the DSDS procedure for the Au–Pd metallic alloy exploring structures with up to 32 atoms per cell: each circle corresponds to the structure of the lowest formation energy found by performing a genetic algorithm search for each of the directly enumerated inequivalent cell shapes. Up to four genetic algorithm runs were performed per ICS starting from independent random populations and the lowest among the optimal structures was retained for the given ICS. Adapted with permission from Ref. [14].

DownLoad: Full-Size Img PowerPoint
Fig. 4.  (Color online) Evolutionary optimization run for Al2Sc6 performed with a population of 20 individuals evolved replacing the 4 highest energy individuals at each generation. The optimal structure is displayed in panel (b) and exhibits the D019 structure type and was found after 76 structures were generated and evaluated by full structural relaxation during the search run. Adapted with permission from Ref. [42].

DownLoad: Full-Size Img PowerPoint
Fig. 5.  (Color online) (a) Evolutionary optimization run for Pd2Ti6 performed with a population of 20 individuals evolved replacing the 5 highest energy individuals at each generation. The optimal structure displayed in panel (b) exhibits the A15 structure type and was found after approximately 100 structures were generated and evaluated by full structural relaxation during the search run. Adapted with permission from Ref. [42].

DownLoad: Full-Size Img PowerPoint
Fig. 6.  (Color online) Central panel: the solid line shows the ground-state convex hull of Al–Sc with the breaking points (shown by the red dots) corresponding to the formation energies of the ground-state structures. The overall ground state convex hull line is determined by combining the convex hull lines obtained by X-GSGO searches run on cells containing 6 and 8 atoms shown respectively by the dash line and the dot-dashed line. Adapted with permission from Ref. [46].

DownLoad: Full-Size Img PowerPoint
[1]
Martin R M. Electronic structure: basic theory and practical methods. Cambridge University Press, 2004
[2]
Martin R M, Reining L, Ceperley D M. Interacting electrons. Cambridge University Press, 2016
[3]
Franceschetti A, Zunger A. The inverse band-structure problem of finding an atomic configuration with given electronic properties. Nature, 1911, 402: 60
[4]
Inorganic Chemistry Structure Database (ICSD). Fachinformationszentrum, Karlsruhe, Karlsruhe, Germany, 2015
[5]
Trimarchi G, Zhang X, DeVries Vermeer M J, et al. Emergence of a few distinct structures from a single formal structure type during high-throughput screening for stable compounds: the case of RbCuS and RbCuSe. Phys Rev B, 2015, 92: 165103 doi: 10.1103/PhysRevB.92.165103
[6]
Zhang X, Yu L, Zakutayev A, et al. Sorting stable versus unstable hypothetical compounds: the case of multi-functional abx half-heusler filled tetrahedral structures. Adv Funct Mater, 2012, 22: 1425 doi: 10.1002/adfm.v22.7
[7]
Zhang X, Stevanović V, d’Avezac M, et al. Prediction of A2BX4 metal-chalcogenide compounds via first-principles thermodynamics. Phys Rev B, 2012, 86: 014109 doi: 10.1103/PhysRevB.86.014109
[8]
Woodley S M, Catlow R. Crystal structure prediction from first principles. Nat Mater, 2008, 7: 937 doi: 10.1038/nmat2321
[9]
Oganov A R. Modern methods of crystal structure prediction. 1st ed. Wiley-VCH, 2011
[10]
Goldberg D E. Genetic algorithms in search,optimization and machine learning. Addison-Wesley, Reading, MA, 1989
[11]
Eiben A E, Smith J E. Introduction to evolutionary computing. Berlin Heidelberg: Springer, 2003
[12]
Wells A F. Structural inorganic chemistry. 5th ed. Oxford University Press, 1984
[13]
Strukturbericht. Akademische Verlagsgesellschaft M. B. H, Leipzig, 1931, 1: 7
[14]
Trimarchi G, Graf P, Zunger A. Exploring the configurational space of binary alloys: Different sampling for different cell shapes. Phys Rev B, 2006, 74: 014204 doi: 10.1103/PhysRevB.74.014204
[15]
Ferreira L G, Wei S H, Zunger A. Stability, electronic structure, and phase diagrams of novel inter-semiconductor compounds. Int J Supercomput Appl, 1991, 5: 34 doi: 10.1177/109434209100500103
[16]
Barabash S V, Blum V, Müller S, et al. Prediction of unusual stable ordered structures of Au–Pd alloys via a first-principles cluster expansion. Phys Rev B, 2006, 74: 35108 doi: 10.1103/PhysRevB.74.035108
[17]
Zunger A. Statistics and dynamics of alloys phase transformations. New York: Plenum Press, 1994: 361
[18]
Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated annealing. Readings in Computer Vision, 1983, 220: 671 doi: 10.1142/9789812799371_0035
[19]
Kim K, Graf P A, Jones W B. A genetic algorithm based inverse band structure method for semiconductor alloys. J Comput Phys, 2005, 208: 735 doi: 10.1016/j.jcp.2005.03.005
[20]
Ihm J, Zunger A, Cohen M L. Momentum-space formalism for the total energy of solids. J Phys C, 1979, 12: 4409 doi: 10.1088/0022-3719/12/21/009
[21]
Doll K, Schön J C, Jansen M. Structure prediction based on ab initio simulated annealing for boron nitride. Phys Rev B, 2008, 78: 144110 doi: 10.1103/PhysRevB.78.144110
[22]
Martoňák R, Laio A, Parrinello M. predicting crystal structures: the parrinello-rahman method revisited. Phys Rev Lett, 2003, 90: 075503 doi: 10.1103/PhysRevLett.90.075503
[23]
Laio A, Parrinello M. Escaping free-energy minima. Proce Natl Acad Scie, 2002, 99: 12562 doi: 10.1073/pnas.202427399
[24]
Wales D J, Doye J P K. Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. J Phys Chem A, 1997, 101: 5111 doi: 10.1021/jp970984n
[25]
Wales D J, Scheraga H A. Global optimization of clusters, crystals, and biomolecules. Science, 1999, 285: 1368 doi: 10.1126/science.285.5432.1368
[26]
Goedecker S. Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J Chem Phys, 2004, 120: 9911 doi: 10.1063/1.1724816
[27]
Amsler M, Goedecker S. Crystal structure prediction using the minima hopping method. J Chem Phys, 2010, 133: 224104 doi: 10.1063/1.3512900
[28]
Pickard C J, Needs R J. High-pressure phases of silane. Phys Rev Lett, 2006, 97: 045504 doi: 10.1103/PhysRevLett.97.045504
[29]
Pickard C J, Needs R J. Ab initio random structure searching. J Phys: Conden Matter, 2011, 23: 053201 doi: 10.1088/0953-8984/23/5/053201
[30]
Needs R J, Pickard C J. Perspective: role of structure prediction in materials discovery and design. APL Mater, 2016, 4: 053210 doi: 10.1063/1.4949361
[31]
Woodley S M, Battle P D, Gale J D, et al. The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation. Phys Chem Chem Phys, 1999, 1: 2535 doi: 10.1039/a901227c
[32]
Zhao X, Nguyen M C, Zhang W Y, et al. Exploring the structural complexity of intermetallic compounds by an adaptive genetic algorithm. Phys Rev Lett, 2014, 112: 045502 doi: 10.1103/PhysRevLett.112.045502
[33]
Oganov A R, Glass C W. Crystal structure prediction using ab initio evolutionary techniques: Principles and applications. J Chem Phys, 2006, 124: 244704 doi: 10.1063/1.2210932
[34]
Oganov A R, Glass C W, Ono S. High-pressure phases of CaCO3: Crystal structure prediction and experiment. Earth Planet Sci Lett, 2006, 241: 95 doi: 10.1016/j.jpgl.2005.10.014
[35]
Abraham N L, Probert M I J. Improved real-space genetic algorithm for crystal structure and polymorph prediction. Phys Rev B, 2008, 77: 134117 doi: 10.1103/PhysRevB.77.134117
[36]
Abraham N L, Probert M I J. A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction. Phys Rev B, 2006, 73: 224104 doi: 10.1103/PhysRevB.73.224104
[37]
Lyakhov A O, Oganov A R, Stokes H T, et al. New developments in evolutionary structure prediction algorithm USPEX. Comput Phys Commun, 2013, 184: 1172 doi: 10.1016/j.cpc.2012.12.009
[38]
Lonie D C, Zurek E. XtalOpt: An open-source evolutionary algorithm for crystal structure prediction. Comput Phys Commun, 2011, 182: 372 doi: 10.1016/j.cpc.2010.07.048
[39]
Tipton W W, Hennig R G. A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials. J Phys: Conden Matter, 2013, 25: 495401 doi: 10.1088/0953-8984/25/49/495401
[40]
Wang Y, Lv J, Zhu L, Ma Y. CALYPSO: a method for crystal structure prediction. Comput Phys Commun, 2012, 183: 2063 doi: 10.1016/j.cpc.2012.05.008
[41]
Wang Y, Lv J, Zhu L, Ma Y. Crystal structure prediction via particle-swarm optimization. Phys Rev B, 2010, 82: 094116 doi: 10.1103/PhysRevB.82.094116
[42]
Trimarchi G, Zunger A. Global space-group optimization problem: Finding the stablest crystal structure without constraints. Phys Rev B, 2007, 75: 104113 doi: 10.1103/PhysRevB.75.104113
[43]
Trimarchi G, Zunger A. Finding the lowest-energy crystal structure starting from randomly selected lattice vectors and atomic positions: first-principles evolutionary study of the Au–Pd, Cd–Pt, Al–Sc, Cu–Pd, Pd–Ti, and Ir–N binary systems. J Phys: Conden Matter, 2008, 20: 295212 doi: 10.1088/0953-8984/20/29/295212
[44]
Glass C W, Oganov A R, Hansen N. USPEX—evolutionary crystal structure prediction. Comput Phys Commun, 2006, 175: 713 doi: 10.1016/j.cpc.2006.07.020
[45]
Deaven D M, Ho K M. Molecular geometry optimization with a genetic algorithm. Phys Rev Lett, 1995, 75: 288 doi: 10.1103/PhysRevLett.75.288
[46]
Trimarchi G, Freeman A J, Zunger A. Predicting stable stoichiometries of compounds via evolutionary global space-group optimization. Phys Rev B, 2009, 80: 092101 doi: 10.1103/PhysRevB.80.092101
[47]
Blum V, Zunger A. Structural complexity in binary bcc ground states: The case of bcc Mo-Ta. Phys Rev B, 2004, 69: 020103 doi: 10.1103/PhysRevB.69.020103
[48]
Blum V, Zunger A. Mixed-basis cluster expansion for thermodynamics of bcc alloys. Phys Rev B, 2004, 70: 155108 doi: 10.1103/PhysRevB.70.155108
[49]
Blum V, Zunger A. Prediction of ordered structures in the bcc binary systems of Mo, Nb, Ta, and W from first-principles search of approximately 3 000 000 possible configurations. Phys Rev B, 2005, 72: 020104 doi: 10.1103/PhysRevB.72.020104
[50]
Sanati M, Wang L G, Zunger A. Adaptive crystal structures: CuAu and NiPt. Phys Rev Lett, 2003, 90: 045502 doi: 10.1103/PhysRevLett.90.045502
[51]
Gautier R, Zhang X, Hu L, et al. Prediction and accelerated laboratory discovery of previously unknown 18-electron ABX compounds. Nat Chem, 2015, 7: 308 doi: 10.1038/nchem.2207
[52]
Massalski T B. Binary alloy phase diagrams. ASM International, 1992
[53]
Villars P, Cenzual K, Daams J L C, et al. Inorganic materials database and design system. ASM International, 2003
[54]
Fujikawa S, Sugaya M, Takei H, et al. Solid solubility and residual resistivity of scandium in aluminum. J Less-Common Met, 1979, 63: 87 doi: 10.1016/0022-5088(79)90211-X
[55]
Curtarolo S, Morgan D, Ceder G. Accuracy of ab initio methods in predicting the crystal structures of metals: a review of 80 binary alloys. Calphad, 2005, 29: 163 doi: 10.1016/j.calphad.2005.01.002
[56]
Raub E, Röschel E. Die Titan-Palladium-Legierungen. Z Metallkd, 1968, 59: 112

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      Article Navigation >  Journal of Semiconductors  > 2018  >  39(7): 071004
      G. Trimarchi. Crystal structure prediction in the context of inverse materials design[J]. Journal of Semiconductors, 2018, 39(7): 071004. doi: 10.1088/1674-4926/39/7/071004 ****G Trimarchi, Crystal structure prediction in the context of inverse materials design[J]. J. Semicond., 2018, 39(7): 071004. doi: 10.1088/1674-4926/39/7/071004.
      Citation:
      G. Trimarchi. Crystal structure prediction in the context of inverse materials design[J]. Journal of Semiconductors, 2018, 39(7): 071004. doi: 10.1088/1674-4926/39/7/071004 ****
      G Trimarchi, Crystal structure prediction in the context of inverse materials design[J]. J. Semicond., 2018, 39(7): 071004. doi: 10.1088/1674-4926/39/7/071004.
      shu

      Crystal structure prediction in the context of inverse materials design

      DOI: 10.1088/1674-4926/39/7/071004

      • Department of Chemistry, Northwestern University, Evanston, Illinois, USA

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