How batteries work Chapter 7 Insertion hosts

Chapter 7

Insertion hosts: intercalation, alloying and conversion reactions

When a cell is charged, where is the lithium stored?

Figure 7.1 A ball-and-stick model, drawn to one scale, of seven graphene sheets seen almost edge-on, with buttons for graphite without lithium and for stages 4, 3, 2 (LiC12) and 1 (LiC6): lithium layers fill every fourth, third, second or every gap, entering from the edge. Letters mark the A and B stacking of the sheets; brackets mark empty gaps of 0.335 nanometres and the wider lithium layers. A second view shows LiCoO2: three CoO2 sheets with lithium layers between them and a slider that removes lithium down to about half.
lithiumcarboncobaltoxygen
The two hosts, atom by atom: graphite fills by stages; LiCoO2 gives up half its lithium. Try this: press the stage buttons from Stage 4 to Stage 1 and watch which gaps fill.
SourceGraphite: hexagonal graphene sheets held by van der Waals forces and π–π interactions, ABAB stacking in natural graphite, 0.335 nm between sheets, C–C 0.14 nm, staging from stage 4 to stage 1 (the stage being the number of graphene sheets between lithium layers), LiC12 and LiC6, full lithium layers as in the Rüdorff-Hofmann picture, lithium entering at the edge planes and about 10 % expansion mostly along the stacking axis, after Nagendra et al. 2026; one lithium per six carbons in LiC6 after Goodenough and Park 2013. LiCoO2: lithium between octahedral CoO2 sheets after Zhang et al. 2020; about half used after Tarascon and Armand 2001. Drawn from the standard crystal structures, each view to scale (LiCoO2 magnified 1.3 times relative to graphite): lithium over every third carbon ring, the AA stacking and 0.370 nm width of a filled gap, and the LiCoO2 cell (a = 0.282 nm, 0.468 nm between sheets) are not yet from a source in hand. In the Daumas-Hérold picture the guest forms islands within the layers instead; this figure shows the Rüdorff-Hofmann picture.

Graphite: sheets, and lithium by stages

So far we have described each host in a sentence. Let us now look at them atom by atom, beginning with graphite. Graphite is a stack of graphene sheets: carbon atoms joined in hexagonal rings, the sheets held to one another by weak van der Waals forces and π–π interactions, 0.335 nm apart; in natural graphite they are mostly stacked in the order A, B, A, B.1 The lithium goes into the gaps between the sheets, at most one lithium for every six carbons, LiC6.2 The edges of the sheets are the favourable sites for lithium to go in, and it diffuses faster there; the flat faces, the basal planes, are less reactive.1

The lithium does not fill all the gaps at once. It fills some gaps and leaves the others empty, forming stages: the stage number is the number of graphene sheets between two lithium layers. As the cell charges, the graphite passes from stage 4 through stage 3 to stage 2, LiC12, and finally stage 1, LiC6, with lithium in every gap. Stages 2 and 3 are stable phases that affect the equilibrium potential and the diffusion of lithium. Each change of stage is favoured thermodynamically but held back kinetically, the last one, from LiC12 to LiC6, most of all. In the Rüdorff-Hofmann picture each stage is made of complete lithium layers, as the figure draws them; in the Daumas-Hérold picture the guest forms islands within the layers instead. Full lithiation swells the graphite by about 10 %, mostly by the sheets moving apart, not by the sheets stretching.1

LiCoO2: lithium between oxide sheets

Now we cross to the other side. LiCoO2 is a layered compound too: cobalt surrounded by oxygen in CoO2 sheets, with the lithium in the layer between two of them. The idea came from sodium, which Hagenmuller and co-workers had put between such sheets in the 1970s; in 1979 and 1980 Goodenough’s group made the lithium compound, at twice the voltage of TiS2.3 As we saw, only about half of its lithium is taken out on charge.2,4

In both hosts, then, the sheets are what makes the cell work. Lithium comes and goes; the framework of carbon or of cobalt oxide stays, so the electrodes keep their structure and shape and the reaction can run back and forth many times.5

Two layered solids and one guest: charging moves lithium from between the oxide sheets to between the carbon sheets, and discharging moves it back.

Figure 7.2 Three blocks drawn in perspective. Layered LiCoO2: solid oxide layers with dashed lithium planes between them; arrows show lithium moving in both directions within a plane and a red cross blocks movement from one plane to the next. Spinel LiMn2O4: a three-dimensional grid of paths, with an ion turning in all directions. Olivine LiFePO4: parallel tubes along one direction, an ion going back and forth in one tube and a red cross between tubes.
Three hosts, three kinds of path for the ion. Try this: follow each ion for a few seconds and note which directions it never takes.
SourceDimensionality of the lithium paths after Goodenough and Park 2013: two-dimensional in the layered oxides, three-dimensional in the spinel, one-dimensional in olivine LiFePO4. The blocks are schematic pieces of each structure, not its real polyhedra; the paths show only the dimensionality. Schematic, not to scale.

Our ion is now inside a host, protected by the SEI where it needs one. How does it move once it is in? The host decides. In the layered oxides lithium travels within two-dimensional planes; the spinel LiMn2O4 offers a three-dimensional network; in olivine LiFePO4 the paths are one-dimensional channels.2

Inside the solid the ion moves by diffusion, down its concentration gradient, as Fick’s first law describes; in a time t it typically gets about (2Dt)1/2 from where it started, where D is its diffusion coefficient.6 Turned around, emptying a particle of size L takes a time of order L2/2D: halve the particle and it empties four times faster. We return to this in chapter 11, when the particles shrink to nanometres.

Figure 7.3 Three ways a negative electrode takes up lithium, chosen with buttons: graphite layers that lithium slips between, a silicon particle that swells to nearly four times its volume and cracks, and an iron oxide particle that turns into iron grains in lithium oxide. Beside each, a schematic first-cycle voltage curve with the part of the first charge that is lost shaded, and the return curve.
lithium in (first charge)lithium outlost in the first cycleour ion
Three ways to store lithium. Try this: play each mode and compare the shaded first-cycle loss and the gap between the two curves.
SourceMechanisms, general reactions and the shapes of the first cycles after Rahman et al. 2025, Fig. 2 and section 2; first-cycle losses (about 10 % for graphite, 20 to 40 % for alloys) and hysteresis (10 to 50 mV for graphite, about 1 V for conversion) after their Table 1 and section 2(iii). The curves are schematic, drawn after their Fig. 2, not data; the volume change of silicon is drawn at 280 %.

The families on the map differ in what happens to the material when lithium enters it, and there are three ways for that to go. In intercalation, lithium slips between the layers of a host that keeps its structure, as in graphite, Li+ + e− + xC ⇌ LiCx, or in titanium oxides; that is why these materials last for many cycles. In alloying, lithium forms an alloy with an element such as silicon, germanium or tin, xLi+ + xe− + M ⇌ LixM. In conversion, a compound is taken apart into metal and a lithium compound and rebuilt on the way back. Alloys and conversion materials tend to break into smaller particles as they cycle.7

All three pay a price on the very first charge: they lose a large part of it, mostly to the SEI, which takes lithium from the positive electrode and lowers the first-cycle Coulombic efficiency. Alloys and conversion materials also show a large gap between the voltage at which lithium goes in and the voltage at which it comes out, which lowers the energy a full cell can deliver.7

You can now explain where the lithium sits in graphite and in LiCoO2, why the cell is called a rocking chair, why a new cell loses lithium on its first charge and what it gets in return, how the host shapes the ion’s path, and how the cell came together between 1972 and 1996.

On every trip between the two hosts, our ion had to cross something to get there.

The mathematics of this chapter

LixC6, 0 ≤ x ≤ 1; Li1−yCoO2, y ≤ 0.5 in practicehow much lithium each host holds: up to one per six carbons, and about half the lithium of LiCoO2 used in practice

2 EC + 2 Li+ + 2 e− → Li2EDC + C2H4↑the main SEI-forming reduction of ethylene carbonate, from about 0.8 V vs Li/Li+; the ethylene is among the gases let out during formation

LiCoO2 + C6 ⇌ Li1−xCoO2 + LixC6the cell reaction, charge to the right: the carbon is made empty because LixC6 is very reactive, and LiCoO2 is the only source of lithium

N = Q/e = nNA, n = Q/Fthe number of ions, and of moles, that carry a charge Q (worked example)

J = −D ∂C/∂x, Δ = (2Dt)1/2, t ≈ L2/2DFick’s first law; the diffusion length in a time t; and, turned round, the order of magnitude of the time to cross a particle of size L

eVOC = μA − μC, stable if μA < LUMO and μC > HOMOthe open-circuit voltage from the two electrodes’ electrochemical potentials, and the condition for the electrolyte to survive without a passivating layer

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 K. Nagendra, K. Nikgoftar, A. K. Madikere Raghunatha Reddy, J. Rajpurohit, J. I. G. Dawkins, T. M. Guimaraes Selva, K. Zaghib, "Challenges and Issues in Using Coated and Uncoated Graphitic Anodes in Lithium-Ion Batteries", Batteries 12, 2026, 154. doi:10.3390/batteries12050154
  2. 2 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
  3. 3 H. Zhang, C. Li, G. G. Eshetu, S. Laruelle, S. Grugeon, K. Zaghib, C. Julien, A. Mauger, D. Guyomard, T. Rojo, N. Gisbert-Trejo, S. Passerini, X. Huang, Z. Zhou, P. Johansson, M. Forsyth, "From Solid-Solution Electrodes and the Rocking-Chair Concept to Today's Batteries", Angewandte Chemie International Edition 59, 2020, 534-538. doi:10.1002/anie.201913923
  4. 4 J.-M. Tarascon, M. Armand, "Issues and challenges facing rechargeable lithium batteries", Nature 414, 2001, 359-367. doi:10.1038/35104644
  5. 5 M. Winter, R. J. Brodd, "What Are Batteries, Fuel Cells, and Supercapacitors?", Chemical Reviews 104, 2004, 4245-4269. doi:10.1021/cr020730k
  6. 6 A. J. Bard, L. R. Faulkner, H. S. White, "Electrochemical Methods: Fundamentals and Applications", Wiley, 3rd edition, 2022.
  7. 7 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
  8. 8 J. T. Frith, M. J. Lacey, U. Ulissi, "A non-academic perspective on the future of lithium-based batteries", Nature Communications 14, 2023, 420. doi:10.1038/s41467-023-35933-2
  9. 9 A. Manthiram, "A reflection on lithium-ion battery cathode chemistry", Nature Communications 11, 2020, 1550. doi:10.1038/s41467-020-15355-0
  10. 10 J.-J. Marie, S. Gifford, "Developments in lithium-ion battery cathodes", Faraday Insights, Issue 18 (The Faraday Institution), 2023, September 2023. link
  11. 11 J. B. Goodenough, "How we made the Li-ion rechargeable battery", Nature Electronics 1, 2018, 204. doi:10.1038/s41928-018-0048-6
  12. 12 K. Brandt, "Historical development of secondary lithium batteries", Solid State Ionics 69, 1994, 173-183. doi:10.1016/0167-2738(94)90408-1
  13. 13 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
  14. 14 M. Fichtner, K. Edström, E. Ayerbe, M. Berecibar, A. Bhowmik, I. E. Castelli, S. Clark, R. Dominko, M. Erakca, A. A. Franco, A. Grimaud, B. Horstmann, A. Latz, H. Lorrmann, M. Meeus, R. Narayan, F. Pammer, J. Ruhland, H. Stein, T. Vegge, M. Weil, "Rechargeable Batteries of the Future—The State of the Art from a BATTERY 2030+ Perspective", Advanced Energy Materials 12, 2022, 2102904. doi:10.1002/aenm.202102904
  15. 15 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
  16. 16 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
  17. 17 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
  18. 18 O. Borodin, X. Ren, J. Vatamanu, A. von Wald Cresce, J. Knap, K. Xu, "Modeling Insight into Battery Electrolyte Electrochemical Stability and Interfacial Structure", Accounts of Chemical Research 50, 2017, 2886-2894. doi:10.1021/acs.accounts.7b00486
  19. 19 K. Abe, "Nonaqueous Electrolytes and Advances in Additives", in T. R. Jow, K. Xu, O. Borodin, M. Ue (eds.), Electrolytes for Lithium and Lithium-Ion Batteries, Modern Aspects of Electrochemistry 58, Springer, New York, 2014, 167-207. doi:10.1007/978-1-4939-0302-3_3
  20. 20 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). Insertion hosts: intercalation, alloying and conversion reactions. How batteries work. https://asajeevan.github.io/batteries/insertion-hosts/

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