Journal of Solid State Electrochemistry

, Volume 10, Issue 5, pp 293–319 | Cite as

Stress generation and fracture in lithium insertion materials

  • John Christensen
  • John Newman
Original Paper


A mathematical model that calculates volume expansion and contraction and concentration and stress profiles during lithium insertion into and extraction from a spherical particle of electrode material has been developed. The maximum stress in the particle has been determined as a function of dimensionless current, which includes the charge rate, particle size, and diffusion coefficient. The effects of pressure-driven diffusion and nonideal interactions between the lithium and host material have also been described. The model predicts that carbonaceous particles will fracture in high-power applications such as hybrid-electric vehicle batteries.


Lithium Radial Stress Partial Molar Volume Lithium Concentration Exchange Current Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of FreedomCAR and Vehicle Technologies of the US Department of Energy under Contract No. DE-AC02-05CH11231.


  1. 1.
    Beaulieu LY, Eberman KW, Turner RL, Krause LJ, Dahn JR (2001) Electrochem Solid State Lett 4:A137CrossRefGoogle Scholar
  2. 2.
    Thomas KE (2002) Dissertation. University of California, BerkeleyGoogle Scholar
  3. 3.
    Ohzuku T, Tomura H, Sawai K (1997) J Electrochem Soc 144:3496CrossRefGoogle Scholar
  4. 4.
    Sawai K, Yoshikawa K, Tomura H, Ohzuku T (1998) Prog Batteries Battery Mater 17:201Google Scholar
  5. 5.
    Kostecki R, McLarnon F (2003) J Power Sources 119:550CrossRefGoogle Scholar
  6. 6.
    Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular theory of gases and liquids. Wiley, New York, p 714 (corrected printing with notes added, 1964)Google Scholar
  7. 7.
    Curtiss CF, Bird RB (1999) Ind Eng Chem Res 38:2515CrossRefGoogle Scholar
  8. 8.
    Battaglia VS (1993) Dissertation. University of California, BerkeleyGoogle Scholar
  9. 9.
    Kröger FA, Vink HJ (1956) In: Seitz F, Turnbull D (eds) Solid state physics: advances in research and applications, vol 3. Academic, New York, p 310Google Scholar
  10. 10.
    Kröger FA, Vink HJ (1958) J Phys Chem Solids 5:208CrossRefGoogle Scholar
  11. 11.
    Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Cliffs, p 159Google Scholar
  12. 12.
    Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena. Wiley, New York, p 19Google Scholar
  13. 13.
    Timoshenko S (1934) Theory of elasticity. McGraw-Hill, New York, p 203Google Scholar
  14. 14.
    Garcia RE, Chiang YM, Carter WC, Limthongkul P, Bishop CM (2005) J Electrochem Soc 152:A255CrossRefGoogle Scholar
  15. 15.
    Boresi AP (1965) Elasticity in engineering materials. Prentice-Hall, Englewood Cliffs, p 71Google Scholar
  16. 16.
    Ogumi Z, Inaba M (2002) In: van Schalkwijk WA, Scrosati B (eds) Advances in lithium-ion batteries, vol. Kluwer/Plenum, New York, p 79CrossRefGoogle Scholar
  17. 17.
    Inagaki M (2000) New carbons: control of structure and functions. Elsevier, New York, p 199Google Scholar
  18. 18.
    Billaud D, McRae E, Hérold A (1979) Mater Res Bull 14:857CrossRefGoogle Scholar
  19. 19.
    Kganyago KR, Ngoepe PE (2003) Phys Rev B 68:205111CrossRefGoogle Scholar
  20. 20.
    Nicklow R, Smith HG, Wakabaya N (1972) Phys Rev B 5:4951CrossRefGoogle Scholar
  21. 21.
    Hertzberg RW (1996) Deformation and fracture mechanics of engineering materials. Wiley, New York, p 526Google Scholar
  22. 22.
    Winter M, Besenhard JO, Albering JH, Yang J, Wachtler M (1998) Prog Batteries Battery Mater 17:208Google Scholar
  23. 23.
    Zaghib K, Nadeau G, Kinoshita K (2000) J Electrochem Soc 147:2110CrossRefGoogle Scholar
  24. 24.
    Winter M, Novák P, Monnier A (1998) J Electrochem Soc 145:428CrossRefGoogle Scholar
  25. 25.
    Fuller TF, Newman J (1993) Int J Heat Mass Transfer 36:347CrossRefGoogle Scholar
  26. 26.
    Fuller TF (1992) Dissertation. University of California, BerkeleyGoogle Scholar
  27. 27.
    Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  28. 28.
    Sengers JV (1972) Ber Bunsen Ges 76:234Google Scholar
  29. 29.
    Cussler EL (1976) Multicomponent diffusion. Elsevier, New YorkGoogle Scholar
  30. 30.
    Krichevsky IR, Tshekhanskaya YV (1956) Zhurnal Fizicheskoi Khimii 30:2315Google Scholar
  31. 31.
    Vitagliano V, Sartorio R, Chiaravalle E, Ortona O (1980) J Chem Eng Data 25:121CrossRefGoogle Scholar
  32. 32.
    Darling RM (1998) Dissertation. University of California, BerkeleyGoogle Scholar
  33. 33.
    Verbrugge MW, Koch BJ (1996) J Electrochem Soc 143:600CrossRefGoogle Scholar
  34. 34.
    Newman J, Thomas-Alyea KE (2004) Electrochemical systems. Wiley-Interscience, Hoboken, p 142Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of CaliforniaBerkeleyUSA

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