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

Journal name:
Nature Materials
Volume:
13,
Pages:
1149–1156
Year published:
DOI:
doi:10.1038/nmat4084
Received
Accepted
Published online

Abstract

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

Figures

  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).

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Author information

Affiliations

  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

Contributions

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.

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