How batteries work Chapter 16 Degradation

Chapter 16

Degradation: loss of lithium inventory, loss of active material and resistance rise

Why does my battery hold less after a few years?

Where we are. In chapter 15 we pushed both electrodes beyond today’s materials, towards lithium metal, nickel-rich oxides and organic molecules, and met materials that fail fast and loudly. A well-made lithium-ion cell fails slowly and quietly: a little capacity gone each week, whether it is used or not. In this module we ask where that capacity goes: we name the thieves and see how each one works.

Figure 16.1 Capacity against cycle number with the loss split into three stacked shaded parts: lithium lost to side reactions, growing as the square root of cycles; active material lost, growing steadily; and capacity hidden by rising resistance, which comes back when the cell is measured at a low rate. A dashed line marks 80 percent, the end of cycle life.
Capacity fade, taken apart into three thieves. Try this: switch off the lithium loss and see how much longer the cell lives; then press Measure at a low rate.
SourceCategories after Goodenough and Park 2013 (reversible loss at high rate; irreversible loss from volume changes, electrode-electrolyte reactions and decomposition; cycle life to 80 %) and Tarascon and Armand 2001 (side reactions at the electrode-electrolyte interface; particles that disintegrate and lose contact). The lithium-loss band follows the square-root law of figure 16.3; the sizes of all three bands and the cycle axis are schematic, not data for any cell.

Let us start from the symptom: the cell holds less than it did. Capacity is lost in two ways. Some is only hidden: at a high current the cell reaches its cut-off early, and the capacity comes back at a gentler rate. The rest is gone for good, to changes in the volume of the electrodes, to reactions between electrodes and electrolyte, and to decomposition of the electrodes; the cycle life ends when the capacity has faded to 80 % of its initial value.1 In lithium-ion cells, poor lifetimes are rooted mainly in side reactions at the electrode-electrolyte interface.2

Sorted by what they take, these causes are the three thieves of figure 16.1. Side reactions lock up lithium that could have carried charge. Cracking, contact loss and dissolution remove active material, the room the lithium needs. And thicker interfaces raise the resistance, so that at a given current the cell runs out of voltage before it runs out of charge.

Mechanical abuse adds to these thieves. In electric vehicles, vibration and impact shock reduce capacity and raise the internal resistance, and the fade has been traced to loss of active material and loss of lithium inventory; they can also bruise the active material and deform the separator, the start of an internal short circuit.3

A battery rarely dies of one cause; diagnosing it means separating the causes.

Figure 16.2 Capacity kept against cycle number up to 1000 cycles if a fixed fraction of the charge is lost on every cycle, for the chosen Coulombic efficiency and for reference values of 99.5, 99.9 and 99.99 percent, with the 80 percent end-of-life line and the 300-cycle commercial requirement.
your efficiencyreferences: 99.5, 99.9, 99.99 %
Why 99.9 % per cycle is not good enough. Try this: find the lowest efficiency at which the blue line still crosses the 300-cycle line above 80 %.
SourceCoulombic efficiency (eq. 4) and cycle life to 80 % of the initial capacity after Goodenough and Park 2013; the 300-cycle requirement after Winter and Brodd 2004, section 2.6. Retention =CEN is arithmetic for the idealized case in which all the charge missing on each cycle is lost for good; it is an idealization, not a model of a real cell.

Ageing leads to a practical question: how long does a cell last? Two numbers summarize a cell’s life. The Coulombic efficiency is the charge returned on discharge divided by the charge put in on charge, as a percentage; the cycle life is the number of cycles until the capacity has faded to 80 % of its initial value.1

CE=100×QdisQch %

In 2004 a commercial rechargeable cell was expected to survive at least 300 full cycles with less than 20 % loss; most needed three to eight hours to charge while users wanted a quarter of an hour, and fast charging shortens cycle life.4 LiFePO4, with a much longer cycle life and calendar life than most NMC cells, is now used for grid storage and shorter-range electric vehicles.5 The fast-charging goal is 80 % of the charge in under 15 minutes.6

Not every loss is permanent. Capacity hidden by a high rate comes back at a low one; what does not come back is lost to changes in the electrodes’ volume, to reactions between electrodes and electrolyte, and to decomposition of the electrodes.1 The first charge of a lithium-ion cell is a special case, a loss paid once (chapter 10).1

Worked example. Let us see what the 300-cycle benchmark asks of each cycle. How good must the Coulombic efficiency be for a cell to keep 80 % of its capacity after 300 cycles? Take the simplest case, in which every bit of charge that does not come back is lost for good. after 1 cycle: CE; after 2 cycles: CE×CE=CE2; after N cycles: CEN the goal: CE300=0.80 take the 300th root: CE=0.801/300=0.99926, that is 99.93 % the other way round, at 99.9 %: 0.999N=0.80⇒N=ln0.80ln0.999=−0.223−0.001=223 cycles So losing just one coulomb in a thousand on every cycle uses up the 20 % allowance after 223 cycles, well short of 300.

Lifetime is set by tiny losses repeated hundreds of times.

Figure 16.3 The SEI on graphite thickening with time, beside a plot of thickness against time for three growth regimes: proportional to the square root of time when diffusion through the layer limits it, proportional to time when the reaction or migration during charging limits it, and not growing when migration during discharge limits it; a bar shows the interfacial resistance rising with the thickness.
graphiteSEIinterfacial resistance
The SEI keeps growing, and the exponent tells you why. Try this: both laws start from the same loss after the first month; compare where b = 1/2 and b = 1 end, then imagine the cell stored full and warm.
SourceGrowth law LSEI ∝ tb and capacity loss ΔQ ∝ tb, with b = 0.5 (diffusion limitation, the literature standard), b = 1 (reaction limitation, or migration limitation while charging) and b = 0 (migration limitation while discharging), after von Kolzenberg, Latz and Horstmann 2020, eqs. 36 and 37; fastest growth at high state of charge and high charging rate, also theirs. That the SEI adds interfacial impedance and evolves with cycling after Goodenough and Park 2013. Axes and the resistance bar are schematic.

Let us follow the first thief, the one that takes lithium. The SEI of chapter 10 does not stop at the first charge. It keeps growing, more slowly, adding to the interfacial impedance as it evolves.1 Its thickness follows a power law in time, L ∝ tb, and so does the capacity lost to it: b = 1/2 when the supply through the layer is limited by diffusion, the usual assumption; b = 1 when the reaction itself, or migration during charging, is the bottleneck; b = 0 for migration during discharge. It grows fastest when the cell sits at a high state of charge and is charged fast.7 Too thick a layer means lost capacity and higher impedance at once.8

How much does it matter? In storage, most of the capacity a lithium-ion cell loses goes into the SEI, and in a well-engineered cell more than half of all capacity loss can be traced to its growth.9,10 The layer grows while the graphite is being filled, not while it is being emptied,9 and in a charged cell it keeps growing at rest, more slowly; in the standard models only a fully discharged cell stops feeding it.11 On silicon the picture changes: the large volume change keeps cracking the SEI, and the growth becomes linear in time.9

Worked example. What does the square-root law mean over the years of a cell’s life? Take an illustrative start: suppose the SEI costs 2 % of the capacity in the first month. after 4 months: 2 % × √4 = 4 % after 1 year: 2 % × √12 = 6.9 %; after 4 years: 2 % × √48 = 13.9 % The loss slows down, but it never stops. With b = 1 the same start would have cost 24 % in a year.7
Figure 16.4 Manganese ions leave a LiMn2O4 spinel positive electrode, cross the electrolyte and lodge in the SEI on the graphite negative electrode, which then protects less well.
Mn(II)SEI (darker once poisoned)spinelelectrolyte
Manganese on the move: one electrode’s loss becomes the other’s problem. Try this: count how many manganese ions it takes before the SEI is marked as working worse; the threshold is a drawing choice, not a value from the cited work.
SourceSequence after Goodenough and Park 2013: Mn(II) dissolves from the spinel and poisons the SEI of the negative electrode. Numbers of ions and the moment the layer is marked as poisoned are schematic.

So far we have watched one thief at a time. They can also work together. In a cell with a spinel LiMn2O4 positive electrode, manganese dissolves as Mn(II), crosses the electrolyte and poisons the SEI on the negative electrode.1 The positive electrode loses active material; the negative electrode’s protection weakens, and with it more lithium is lost. Particles that crack and lose contact, as alloys do (figure 7.3), are the other route to losing active material.2

Figure 16.5 Two points on a logarithmic shelf-time axis: a lithium-MnO2 primary cell keeps 90 percent of its charge after 8 years, while a nickel-metal hydride cell can lose up to 30 percent in a month.
On the shelf: self-discharge differs by orders of magnitude between chemistries. Try this: count the decades on the axis between the two dots.
SourceValues after Winter and Brodd 2004, section 2.6: Li-MnO2 primary cells keep 90 % of their capacity after 8 years; Ni-MH can lose up to 30 % per month; self-discharge rises with temperature. Only these two points are drawn, since the source gives no curves.

Cells also age when nothing is connected, on the shelf. Self-discharge, the slow loss of charge with nothing connected, differs enormously between chemistries: a nickel-metal hydride cell can lose up to 30 % a month, while a lithium-MnO2 primary cell keeps 90 % after eight years. It rises with temperature.4 Overcharging or overdischarging a cell is another way to age it fast: both drive irreversible reactions that form new compounds and cost capacity.4

For lithium-ion cells, one textbook gives about 5 % lost in the first four hours after charging and then only 1 to 2 % per month, half the self-discharge of a nickel-cadmium cell.12

You can now explain the difference between capacity that is hidden and capacity that is lost, the three thieves and how they cooperate, why the SEI keeps costing lithium and how fast, and why a cell ages on the shelf as well as in use.

To catch a thief we need a witness. Next we see how these losses are measured, and how the measurements tell one thief from another.

Go deeper: how sure is the square-root law?

The square-root law is the usual reading of storage data, and it is what a growth limited by something diffusing through the layer predicts.7,9 Which something is still debated: solvent through the pores, electrons through the compact inner layer, or neutral lithium atoms; storage tests at different states of charge favour the last.9 A recent comparison adds two cautions: few of the √t fits in the literature are statistically justified, and none of the standard models reproduces how much larger the loss in the first cycle is than in the later ones.11 The shape of a fade curve alone cannot prove a mechanism.9

Go deeper: paying back the first-charge loss

The lithium a new cell locks into its SEI on the first charge is gone before the cell is ever used, and in conversion electrodes the first-cycle loss reaches about 30 %. Can we pay it back? One remedy, proposed by Armand, is sacrificial salts: lithium salts with an oxidizable anion mixed into the positive electrode. On the first charge the anion is oxidized and gives up its lithium, which pays for the SEI; what is left of the salt leaves pores behind that help the electrolyte wet the electrode. The salt is chosen by its oxidation potential to suit the cell, and the idea extends to sodium and potassium cells.8

The mathematics of this chapter

LSEI ∝ tb, ΔQ ∝ tb, b ∈ {0, 1/2, 1}SEI growth and the capacity it costs; b = 1/2 diffusion-limited, 1 reaction-limited or migration-limited on charge, 0 migration-limited on discharge

ΔQ(t2) = ΔQ(t1) (t2/t1)bscaling a measured loss forward in time (worked example)

Qlow rate − Qhigh rate = capacity hidden, not lostthe reversible part of figure 16.1, recovered by measuring slowly

References for this chapter

Numbers in the text refer to this list. All references of the course, with the chapters that use each one.

  1. 1 J. B. Goodenough, K.-S. Park, "The Li-Ion Rechargeable Battery: A Perspective", Journal of the American Chemical Society 135, 2013, 1167-1176. doi:10.1021/ja3091438
  2. 2 J.-M. Tarascon, M. Armand, "Issues and challenges facing rechargeable lithium batteries", Nature 414, 2001, 359-367. doi:10.1038/35104644
  3. 3 O. Faruque, M. J. Isalm, O. Faruq, M. M. Alam, "A comprehensive review of past and present developments of Li-ion batteries", Discover Sustainability 7, 2026, 881. doi:10.1007/s43621-026-02920-8
  4. 4 M. Winter, R. J. Brodd, "What Are Batteries, Fuel Cells, and Supercapacitors?", Chemical Reviews 104, 2004, 4245-4269. doi:10.1021/cr020730k
  5. 5 J.-J. Marie, S. Gifford, "Developments in lithium-ion battery cathodes", Faraday Insights, Issue 18 (The Faraday Institution), 2023, September 2023. link
  6. 6 M. M. Rahman, U. Nisar, A. Abouimrane, I. Belharouak, R. Amin, "Valuation of Anode Materials for High-Performance Lithium Batteries: From Graphite to Lithium Metal and Beyond", Electrochemical Energy Reviews 8, 2025, 14. doi:10.1007/s41918-025-00249-w
  7. 7 L. von Kolzenberg, A. Latz, B. Horstmann, "Solid-Electrolyte Interphase During Battery Cycling: Theory of Growth Regimes", ChemSusChem 13, 2020, 3901-3910. doi:10.1002/cssc.202000867
  8. 8 D. Shanmukaraj, P. Ranque, H. Ben Youcef, T. Rojo, P. Poizot, S. Grugeon, S. Laruelle, D. Guyomard, "Review—Towards Efficient Energy Storage Materials: Lithium Intercalation/Organic Electrodes to Polymer Electrolytes—A Road Map (Tribute to Michel Armand)", Journal of The Electrochemical Society 167, 2020, 070530. doi:10.1149/1945-7111/ab787a
  9. 9 B. Horstmann, F. Single, A. Latz, "Review on multi-scale models of solid-electrolyte interphase formation", Current Opinion in Electrochemistry 13, 2019, 61-69. doi:10.1016/j.coelec.2018.10.013
  10. 10 A. Wang, S. Kadam, H. Li, S. Shi, Y. Qi, "Review on modeling of the anode solid electrolyte interphase (SEI) for lithium-ion batteries", npj Computational Materials 4, 2018, 15. doi:10.1038/s41524-018-0064-0
  11. 11 K. Manmi, M. Tuchel, E. Kendrick, F. Brosa Planella, "A Comparison of Standard SEI Growth Models in the Context of Battery Formation", Journal of The Electrochemical Society 171, 2024, 100530. doi:10.1149/1945-7111/ad8548
  12. 12 S. A. Arote, "Fundamentals and perspectives of lithium-ion batteries", chapter 1 of Lithium-ion and Lithium–Sulfur Batteries: Fundamentals to Performance, IOP Publishing, 2022, pp. 1-1 to 1-26. doi:10.1088/978-0-7503-4881-2ch1

Cite this page

Using this page in teaching, a thesis or an article? Cite it as follows; the date is the last update of the course.

Shyma Sajeevan, A. (2026). Degradation: loss of lithium inventory, loss of active material and resistance rise. How batteries work. https://asajeevan.github.io/batteries/degradation/

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