Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes

Journal name:
Nature Materials
Year published:
Published online


Many battery electrodes contain ensembles of nanoparticles that phase-separate on (de)intercalation. In such electrodes, the fraction of actively intercalating particles directly impacts cycle life: a vanishing population concentrates the current in a small number of particles, leading to current hotspots. Reports of the active particle population in the phase-separating electrode ​lithium iron phosphate (​LiFePO4; ​LFP) vary widely, ranging from near 0% (particle-by-particle) to 100% (concurrent intercalation). Using synchrotron-based X-ray microscopy, we probed the individual state-of-charge for over 3,000 ​LFP particles. We observed that the active population depends strongly on the cycling current, exhibiting particle-by-particle-like behaviour at low rates and increasingly concurrent behaviour at high rates, consistent with our phase-field porous electrode simulations. Contrary to intuition, the current density, or current per active internal surface area, is nearly invariant with the global electrode cycling rate. Rather, the electrode accommodates higher current by increasing the active particle population. This behaviour results from thermodynamic transformation barriers in ​LFP, and such a phenomenon probably extends to other phase-separating battery materials. We propose that modifying the transformation barrier and exchange current density can increase the active population and thus the current homogeneity. This could introduce new paradigms to enhance the cycle life of phase-separating battery electrodes.

At a glance


  1. Lithium fraction within each particle of an electrode charged to 50% SoC at a rate of 5.0 C.
    Figure 1: Lithium fraction within each particle of an electrode charged to 50% SoC at a rate of 5.0 C.

    a, Reference X-ray absorption spectra for fully lithiated and delithiated particles. b, The state-of-charge map, which was produced by fitting a linear combination of the references to every single-pixel spectrum. The hue represents the lithium fraction, and the brightness designates the particle thickness. c, TEM image of the same electrode region, which also includes faint features of carbon black and the binder. We used these images to identify the boundary of each particle. We outline actively intercalating particles in b and c. df, Typical particles and their absorption spectra.

  2. Active particle fraction as a function of cycling condition.
    Figure 2: Active particle fraction as a function of cycling condition.

    The fraction of actively intercalating particles varies as a function of rate in both the experiments and the phase-field simulations. The experimental error bars are calculated assuming a binomial distribution (active or not active) taken at three standard deviations. We reanalysed data from our previous work for the 1.0 C charge experiment16.

  3. Schematic of the combined porous electrode and phase-field model.
    Figure 3: Schematic of the combined porous electrode and phase-field model.

    We divide the ​LFP electrode into 10 representative volumes, each containing 10 ​LFP particles immersed in a liquid electrolyte and connected electronically through the carbon network. A one-dimensional Cahn–Hilliard equation (equation (2)) governs the Li diffusional chemical potential along the a axis of each particle. A Butler–Volmer equation (equation (3)) governs the insertion and removal of Li.

  4. Results from combined phase-field and porous electrode simulations of LFP.
    Figure 4: Results from combined phase-field and porous electrode simulations of ​LFP.

    a, The active particle fraction and current density as a function of rate for an electrode discharged to 50% SoC. Simulation results using a phase-separating approximation are also shown. For all rates less than Icrit, higher electrode current, or cycling rate, increases the number of active particles, but the average current density for the active particles remains approximately constant with discharge rate. Once the active particle fraction saturates, the current density increases in regime 2. be, Simulation snapshots of 50% SoC electrodes discharged different rates; the hue represents the lithiation fraction in the snapshots. A preferential lithiation of the small particles results in a larger number of lithiated (red) particles in the simulation; owing to wiring, such preferential lithiation of small particles is not observed experimentally (Supplementary Fig. 13). The size of the particles in the snapshots is proportional to the square root of the size of the simulated particles. We used the experimental particle size distribution (Supplementary Fig. 1) to determine the size of the simulated particles.

  5. Simulated behaviour of a typical LFP particle.
    Figure 5: Simulated behaviour of a typical ​LFP particle.

    a, The diffusional chemical potential of Li as a function of the particle’s lithiation fraction. μLi, LFP contains a transformation barrier (Δμb), defined as the difference between the local maxima and the diffusional chemical potential at the centre of the miscibility gap. b, Plot of a typical particle’s reaction overpotential and current density as a function of discharge rate when the particle’s SoC is 50%. As we assume solid-state diffusion to be fast, the reaction overpotential is entirely consumed by the surface reaction through equation (3). In regime 1, the electrode ensemble potential is approximately equal to the top of the transformation barrier because not all particles are active, so the reaction overpotential η1 for active particles is approximately equal to Δμb/e. In regime 2, the reaction overpotential η2 is above Δμb/e, so all particles lithiate concurrently. The reaction overpotential and current density of the particle increase with discharge rate to accommodate the extra current. We note that the current density here is higher than in Fig. 4a because one typical particle with a SoC of 50% is considered, whereas Fig. 4a averages the current density for all active particles, which have different SoCs.

  6. Schematic representation of the proposed transformation-barrier-limited model against prevailing models.
    Figure 6: Schematic representation of the proposed transformation-barrier-limited model against prevailing models.

    A homogeneous electrode model assumes that the current is distributed evenly to all particles, so the current density increases uniformly with the global cycling rate. An electrode-transport-limited model results in an electrode-level moving front25 and reduced active particle population at high rates, but the current distribution is homogeneous at lower rates. In our transformation-barrier-limited model, the active particle population is small at low rates, indicating a low degree of current homogeneity. At higher rates, the current homogeneity increases, but electrode transport would limit the active particle population at very high rates (blue dashed lines).


  1. Aricò, A. S., Bruce, P., Scrosati, B., Tarascon, J-M. & Van Schalkwijk, W. Nanostructured materials for advanced energy conversion and storage devices. Nature Mater. 4, 366377 (2005).
  2. Ohzuku, T., Iwakoshi, Y. & Sawai, K. Formation of lithium–graphite intercalation compounds in nonaqueous electrolytes and their application as a negative electrode for a lithium ion (shuttlecock) cell. J. Electrochem. Soc. 140, 24902498 (1993).
  3. Padhi, A. K., Nanjundaswamy, K. S. & Goodenough, J. B. Phospho-olivines as positive-electrode materials for rechargeable lithium batteries. J. Electrochem. Soc. 144, 11881194 (1997).
  4. Tang, M., Carter, W. C. & Chiang, Y-M. Electrochemically driven phase transitions in insertion electrodes for lithium-ion batteries: Examples in lithium metal phosphate olivines. Annu. Rev. Mater. Res. 40, 501529 (2010).
  5. Ohzuku, T., Ueda, A. & Yamamoto, N. Zero-strain insertion material of Li[Li1/3Ti5/3]O4 for rechargeable lithium cells. J. Electrochem. Soc. 142, 14311435 (1995).
  6. Ariyoshi, K., Iwakoshi, Y., Nakayama, N. & Ohzuku, T. Topotactic two-phase reactions of Li[Ni1/2Mn3/2]O4(P4332) in nonaqueous lithium cells. J. Electrochem. Soc. 151, A296A303 (2004).
  7. Woodford, W. H., Chiang, Y-M. & Carter, W. C. “Electrochemical shock” of intercalation electrodes: A fracture mechanics analysis. J. Electrochem. Soc. 157, A1052A1059 (2010).
  8. Christensen, J. & Newman, J. Stress generation and fracture in lithium insertion materials. J. Solid State Electrochem. 10, 293319 (2006).
  9. Yamada, A. et al. Room-temperature miscibility gap in LixFePO4. Nature Mater. 5, 357360 (2006).
  10. Meethong, N., Huang, H-Y. S., Carter, W. C. & Chiang, Y-M. Size-dependent lithium miscibility gap in nanoscale Li1−xFePO4. Electrochem. Solid-State Lett. 10, A134A138 (2007).
  11. Wagemaker, M. et al. Dynamic solubility limits in nanosized olivine LiFePO4. J. Am. Chem. Soc. 133, 1022210228 (2011).
  12. Malik, R., Abdellahi, A. & Ceder, G. A critical review of the Li insertion mechanisms in LiFePO4 electrodes. J. Electrochem. Soc. 160, A3179A3197 (2013).
  13. Delmas, C., Maccario, M., Croguennec, L., Le Cras, F. & Weill, F. Lithium deintercalation in LiFePO4 nanoparticles via a domino-cascade model. Nature Mater. 7, 665671 (2008).
  14. Brunetti, G. et al. Confirmation of the domino-cascade model by LiFePO4/FePO4 precession electron diffraction. Chem. Mater. 23, 45154524 (2011).
  15. Sugar, J. D. et al. High-resolution chemical analysis on cycled LiFePO4 battery electrodes using energy-filtered transmission electron microscopy. J. Power Sources 246, 512521 (2014).
  16. Chueh, W. C. et al. Intercalation pathway in many-particle LiFePO4 electrode revealed by nanoscale state-of-charge mapping. Nano Lett. 13, 866872 (2013).
  17. Dreyer, W. et al. The thermodynamic origin of hysteresis in insertion batteries. Nature Mater. 9, 448453 (2010).
  18. Laffont, L. et al. Study of the LiFePO4/FePO4 two-phase system by high-resolution electron energy loss spectroscopy. Chem. Mater. 18, 55205529 (2006).
  19. Badi, S-P. et al. Direct synthesis of nanocrystalline Li0.90FePO4: Observation of phase segregation of anti-site defects on delithiation. J. Mater. Chem. 21, 1008510093 (2011).
  20. Ferguson, T. R. & Bazant, M. Z. Phase transformation dynamics in porous battery electrodes. Electrochim. Acta (in the press)
  21. Srinivasan, V. & Newman, J. Discharge model for the lithium iron–phosphate electrode. J. Electrochem. Soc. 151, A1517A1529 (2004).
  22. Yu, D. Y. W., Donoue, K., Inoue, T., Fujimoto, M. & Fujitani, S. Effect of electrode parameters on LiFePO4 cathodes. J. Electrochem. Soc. 153, A835A839 (2006).
  23. Dargaville, S. & Farrell, T. W. Predicting active material utilization in LiFePO4 electrodes using a multiscale mathematical model. J. Electrochem. Soc. 157, A830A840 (2010).
  24. Prada, E. et al. Simplified electrochemical and thermal model of LiFePO4-graphite Li-ion batteries for fast charge applications. J. Electrochem. Soc. 159, A1508A1519 (2012).
  25. Ferguson, T. R. & Bazant, M. Z. Nonequilibrium thermodynamics of porous electrodes. J. Electrochem. Soc. 159, A1967A1985 (2012).
  26. Bai, P. & Tian, G. Statistical kinetics of phase-transforming nanoparticles in LiFePO4 porous electrodes. Electrochim. Acta 89, 644651 (2013).
  27. Levi, M. D. et al. Collective phase transition dynamics in microarray composite LixFePO4 electrodes tracked by in situ electrochemical quartz crystal admittance. J. Phys. Chem. C 117, 1550515514 (2013).
  28. Bai, P. & Bazant, M. Z. Charge transfer kinetics at the solid–solid interface in porous electrodes. Nature Commun. 5, 517557 (2014).
  29. Orvananos, B. et al. Architecture dependence on the dynamics of nano-LiFePO4 electrodes. Electrochim. Acta 137, 245257 (2014).
  30. Zhang, X. et al. Rate-induced solubility and suppression of the first-order phase transition in olivine LiFePO4. Nano Lett. 14, 22792285 (2014).
  31. Liu, H. et al. Capturing metastable structures during high-rate cycling of LiFePO4 nanoparticle electrodes. Science 344, 1252817 (2014).
  32. Newman, J. & Thomas-Alyea, K. E. Electrochemical Systems 517577 (Wiley, 2004).
  33. Bazant, M. Z. Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics. Acc. Chem. Res. 46, 11441160 (2013).
  34. Bluhm, H. et al. Soft X-ray microscopy and spectroscopy at the molecular environmental science beamline at the advanced light source. J. Electron Spectrosc. Relat. Phenom. 150, 86104 (2006).
  35. Kilcoyne, A.L.D. et al. Interferometer-controlled scanning transmission X-ray microscopes at the advanced light source. J. Synchrotron Radiat. 10, 125136 (2003).
  36. Kilcoyne, D. et al. in 10th Int. Conf. Synchrotron Radiat. Instrum. (eds Garrett, R., Gentle, I., Nugent, K. & Wilkins, S.) 465468 (American Institute of Physics, 2010).
  37. Liu, X. et al. Phase transformation and lithiation effect on electronic structure of LixFePO4: An in-depth study by soft X-ray and simulations. J. Am. Chem. Soc. 134, 1370813715 (2012).
  38. Cogswell, D. A. & Bazant, M. Z. Theory of coherent nucleation in phase-separating nanoparticles. Nano Lett. 13, 30363041 (2013).
  39. Gibot, P. et al. Room-temperature single-phase Li insertion/extraction in nanoscale LixFePO4. Nature Mater. 7, 741747 (2008).
  40. Bai, P., Cogswell, D. A. & Bazant, M. Z. Suppression of phase separation in LiFePO4 nanoparticles during battery discharge. Nano Lett. 11, 48904896 (2011).
  41. Malik, R., Zhou, F. & Ceder, G. Kinetics of non-equilibrium lithium incorporation in LiFePO4. Nature Mater. 10, 587590 (2011).
  42. Yu, X. et al. High rate delithiation behaviour of LiFePO4 studied by quick X-ray absorption spectroscopy. Chem. Commun. 48, 1153711539 (2012).
  43. Cahn, J. W. On spinodal decomposition. Acta Metall. 9, 795801 (1961).
  44. Allen, S. M. & Cahn, J. W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27, 10851095 (1979).
  45. Cogswell, D. A. & Bazant, M. Z. Coherency strain and the kinetics of phase separation in LiFePO4 nanoparticles. ACS Nano 6, 22152225 (2012).
  46. Morgan, D., Van der Ven, A. & Ceder, G. Li conductivity in LixMPO4 (M = Mn, Fe, Co, Ni) olivine materials. Electrochem. Solid-State Lett. 7, A30A32 (2004).
  47. Srinivasan, V. & Newman, J. Existence of path-dependence in the LiFePO4 electrode. Electrochem. Solid-State Lett. 9, A110A114 (2006).
  48. Orvananos, B., Ferguson, T. R., Yu, H-C., Bazant, M. Z. & Thornton, K. Particle-level modeling of the charge-discharge behavior of nanoparticulate phase-separating Li-ion battery electrodes. J. Electrochem. Soc. 161, A535A546 (2014).
  49. Gaberscek, M., Küzma, M. & Jamnik, J. Electrochemical kinetics of porous, carbon-decorated LiFePO4 cathodes: Separation of wiring effects from solid state diffusion. Phys. Chem. Chem. Phys. 9, 18151820 (2007).
  50. Meethong, N., Huang, H-Y. S., Speakman, S. A., Carter, W. C. & Chiang, Y-M. Strain accommodation during phase transformations in olivine-based cathodes as a materials selection criterion for high-power rechargeable batteries. Adv. Funct. Mater. 17, 11151123 (2007).
  51. Omenya, F. et al. Why substitution enhances the reactivity of LiFePO4. Chem. Mater. 25, 8589 (2013).
  52. Ravnsbæk, D. B. et al. Extended solid solutions and coherent transformations in nanoscale olivine cathodes. Nano Lett. 14, 14841491 (2014).
  53. Kang, B. & Ceder, G. Battery materials for ultrafast charging and discharging. Nature 458, 190193 (2009).
  54. Park, K. et al. Enhanced charge-transfer kinetics by anion surface modification of LiFePO4. Chem. Mater. 24, 32123218 (2012).

Download references

Author information


  1. Department of Materials Science & Engineering, Stanford University, Stanford, California 94305, USA

    • Yiyang Li &
    • William C. Chueh
  2. Sandia National Laboratories, Livermore, California 94551, USA

    • Farid El Gabaly,
    • Norman C. Bartelt &
    • Joshua D. Sugar
  3. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Todd R. Ferguson,
    • Raymond B. Smith &
    • Martin Z. Bazant
  4. Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

    • Kyle R. Fenton
  5. Samsung Advanced Institute of Technology America, Cambridge, Massachusetts 02142, USA

    • Daniel A. Cogswell
  6. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • A. L. David Kilcoyne &
    • Tolek Tyliszczak
  7. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Martin Z. Bazant
  8. Stanford Institute of Materials and Energy Science, Menlo Park, California 94025, USA

    • William C. Chueh


W.C.C., F.E.G. and Y.L. conceived the experiments. K.R.F. and F.E.G. prepared the ​LFP samples for imaging. Y.L., T.T. and A.L.D.K. performed the SoC imaging. J.D.S. and Y.L. performed the TEM imaging. Y.L. analysed the active particle population from the images. T.R.F., R.B.S., D.A.C. and M.Z.B. conceived and created the phase-field porous electrode model. W.C.C. and M.Z.B. supervised the project. All authors participated in writing the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (1.91 MB)

    Supplementary Information

Additional data