Journal of Phase Equilibria and Diffusion

, Volume 28, Issue 2, pp 140–149

Evolutionary and Genetic Algorithms Applied to Li+-C System: Calculations Using Differential Evolution and Particle Swarm Algorithm

  • N. Chakraborti
  • R. Jayakanth
  • S. Das
  • E. D. Çalişir
  • Ş. Erkoç
Basic and Applied Research


A set of empirical potentials based upon two and three body interactions were constructed for the Li+-C system and structural optimizations for various assemblages containing Li+ ions and graphene sheets were conducted using some emerging evolutionary and genetic algorithms, differential evolution, and particle swarm optimization in particular. Some limited molecular dynamics calculations were also performed. The results are discussed and analyzed with reference to the lithium ion batteries, where the graphite-Li+ assemblages traditionally constitute the negative electrode, for which the present results are highly pertinent.


optimization ab initio methods binary system calculations computation first principles modeling genetic algorithm 


  1. 1.
    Tersoff J. (1988) New Empirical Approach for the Structure and Energy of Covalent Systems. Phys. Rev. B 37:6991-7000CrossRefADSGoogle Scholar
  2. 2.
    Tersoff J. (1988) Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon. Phys. Rev. Lett. 61:2879-2882CrossRefADSGoogle Scholar
  3. 3.
    Kohn W., Sham L.J. (1965) Self-consistent Equations Including Exchange and Coelation Effects. Phys. Rev. A 140:A1133-A1138CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Becke A.D. (1993) Density-functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 98:5648-5652CrossRefADSGoogle Scholar
  5. 5.
    Lee C., Yang W., Parr R.G. (1993) Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B 37:785-789CrossRefADSGoogle Scholar
  6. 6.
    Krishnan R., Kinkley J.S., Seeger R., Pople J.A. (1980) Self-consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 72:650--654CrossRefADSGoogle Scholar
  7. 7.
    Gaussian-98 Rev. A.7 package. Gaussian Inc., 1998, Pittsburgh, PA 15106, USAGoogle Scholar
  8. 8.
    Michalewicz: Z. (1999) Genetic Algorithms + Data Structures = Evolution Programs (edition 3), Springer, Berlin,Google Scholar
  9. 9.
    Mitchell M. (1998) An Introduction to Genetic Algorithms. Prentice-Hall India, New Delhi,MATHGoogle Scholar
  10. 10.
    Egorov-Yegorov I.N., Dulikravich G.S. (2005) Chemical Composition Design of Superalloys for Maximum Stress, Temperature, and Time-to-rupture Using Self-adapting Response Surface Optimization. Mater. Manuf. Processes 20:569-590CrossRefGoogle Scholar
  11. 11.
    Chakraborti N. (2004) Genetic Algorithms in Materials Design and Processing. Int. Mater. Rev. 49:246-260CrossRefGoogle Scholar
  12. 12.
    Wang C.Z., M Ho K. (1997) Material Simulations with Tight-binding Molecular Dynamics. J. Phase Equilibria 18:516-529MATHGoogle Scholar
  13. 13.
    Hartke B. (1993) Global Geometry Optimization of Clusters Using Genetic Algorithms. J. Phys. Chem. 97:9973CrossRefGoogle Scholar
  14. 14.
    Iwamatsu M. (2000) Global Geometry Optimization of Silicon Clusters Using the Space-fixed Genetic Algorithm. J. Chem. Phys. 112:10976CrossRefADSGoogle Scholar
  15. 15.
    Klimeck G., Bowen R.C., Boykin T.B., Salazar-Lazaro C., Cwik T.A., Stoica A. (2000) Si Tight-binding Parameters from Genetic Algorithm Fitting. Superlattices Microstruct. 27:77-88CrossRefADSGoogle Scholar
  16. 16.
    Niesse J.A., Mayne H.R. (1996) Global Geometry Optimization of Atomic Clusters Using a Modified Genetic Algorithm in Space-fixed Coordinates. J. Chem. Phys. 105:4700-4706CrossRefADSGoogle Scholar
  17. 17.
    Chakraborti N., Mishra P., Erkoç Ş. (2004) A Study of the Cu Clusters Using Gray-coded Genetic Algorithms and Differential Evolution. J. Phase Equilibria Diffusion 25:16-21Google Scholar
  18. 18.
    Chakraborti N., Kumar R. (2003) Re-evaluation of Some Select SinH2m Clusters Using Genetic Algorithms. J. Phase Equilibria 24:132-139CrossRefGoogle Scholar
  19. 19.
    Chakraborti N., Misra K., Bhatt P., Barman N., Prasad R. (2001) Tight-binding Calculations of Si-H Clusters Using Genetic Algorithms and Related Techniques: Studies Using Differential Evolution. J. Phase Equilibria 22:525-530CrossRefGoogle Scholar
  20. 20.
    Chakraborti N., De P.S., Prasad R. (2002) Genetic Algorithms Based Structure Calculations for Hydrogenated Silicon Clusters. Mater. Lett. 55:20-26CrossRefGoogle Scholar
  21. 21.
    Erkoç Ş., Leblebicioğlu K., Halici U. (2003) Application of Genetic Algorithms to Geometry Optimization of Microclusters: A Comparative Study of Empirical Potential Energy Functions for Silicon. Mater. Manuf. Process. 18:329-339CrossRefGoogle Scholar
  22. 22.
    Price K., Storn R. (1997) Differential Evolution. Dr Dobbs J. 22:18+Google Scholar
  23. 23.
    Price K.V., Storn R.M., Lampinen J.A. (2005) Differential Evolution –A Practical Approach to Global Optimization. Springer, BerlinMATHGoogle Scholar
  24. 24.
    Chakraborti N., Kumar A. (2003) The Optimal Scheduling of a Reversing Strip Mill: Studies Using Multipopulation Genetic Algorithms and Differential Evolution. Mater. Manufact. Processes 18:433-445CrossRefGoogle Scholar
  25. 25.
    Rane T.D., Dewri R., Ghosh S., Mitra K., Chakraborti N. (2005) Modeling the Recrystallization Process Using Inverse Cellular Automata and Genetic Algorithms: Studies Using Differential Evolution. J. Phase Equilibria Diffusion 26:311-321Google Scholar
  26. 26.
    Kennedy J.F., Eberhart R.C., Shi Y. (2001) Swarm Intelligence. Morgan Kaufmann Pub., San Francisco,Google Scholar
  27. 27.
    Ghoshal S.P. (2004) Optimizations of PID Gains by Particle Swarm Optimizations in Fuzzy Based Automatic Generation Control. Electric Power Syst. Res. 72:203-212CrossRefGoogle Scholar
  28. 28.
    He S., Wu Q.H., Wen J.Y., Saunders J.R., Paton R.C. (2004) A Particle Swarm Optimizer with Passive Congregation. Biosystems 78:135-147CrossRefGoogle Scholar
  29. 29.
    Heerman D.W. (1986) Computer Simulation Methods in Theoretical Physics. Springer-Verlag, Berlin, HeidelbergGoogle Scholar
  30. 30.
    Basu S. (1999) Early Studies on Anodic Properties of Lithium Intercalated Graphite. J. Power Sources 81:200-206CrossRefGoogle Scholar
  31. 31.
    Janot R., Guerard D. (2005) Ball-milling in Liquid Media – Applications to the Preparation of Anodic Materials for Lithium-ion Batteries. Prog. Mater. Sci. 50:1-92CrossRefGoogle Scholar
  32. 32.
    Udomvech A., Kerdcharoen T., Osotchan T. (2005) First Principles Study of Li and Li+ Adsorbed on Carbon Nanotube: Variation of Tubule Diameter and Length. Chem. Phys. Lett. 406:161-166CrossRefADSGoogle Scholar
  33. 33.
    N. Chakraborti, S. Das, R. Jayakanth, R. Pekoz, and Ş. Erkoç, Genetic Algorithms Applied to Li+ Ions Contained in Carbon Nanotubes: An Investigation Using Particle Swarm Optimization and Differential Evolution along with Molecular Dynamics. Mater. Manuf. Process., 2007, 22, in pressGoogle Scholar
  34. 34.
    Ş. Erkoç, Stability of Carbon Nanostructures: Balls, Tubes, Rods, Toroids. In: N. Chakraborti and U.K. Chatterjee (Eds), Proceedings of the International Conference on Advances in Materials and Materials Processing (ICAMMP-2002). 1-3 February, 2002, IIT-Kharagpur, India. Tata McGraw-Hill Pub. Com. Ltd., New Delhi, 2002, pp. 356-363Google Scholar
  35. 35.
    Garau C., Frontera A., Quiñonero D., Costa A., Ballester P., Deyà P.M. (2004) Ab Initio Investigations of Lithium Diffusion in Single-walled Carbon Nanotubes. Chem. Phys. 297:85-91CrossRefGoogle Scholar
  36. 36.
    Huang Z.G, Guo Z.N, Chen X, Yue T.M, To S, Lee W.B (2006) Molecular Dynamics Simulation for Ultrafine Machining. Mater. Manuf. Process. 21:393-397CrossRefGoogle Scholar

Copyright information

© ASM International 2007

Authors and Affiliations

  • N. Chakraborti
    • 1
  • R. Jayakanth
    • 1
  • S. Das
    • 1
  • E. D. Çalişir
    • 2
  • Ş. Erkoç
    • 2
  1. 1.Department of Metallurgical & Materials EngineeringIndian Institute of TechnologyKharagpurIndia
  2. 2.Department of PhysicsMiddle East Technical UniversityAnkaraTurkey

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