The Lithium-Ion Battery

A phone that lasted a full day when it was new is often dying by mid-afternoon two or three years later. Nothing inside it has visibly changed: no part has worn through, nothing leaks, the battery still charges to 100%. Yet the same 100% holds less. To see why, we first need to know what a charged battery actually holds, and that turns out to be a surprisingly concrete thing: a few grams of lithium, moved from one material to another and waiting to move back.

Phones use flat cells, and electric cars and power tools often use cylinders, but inside they are built the same way. Here is one of the cylinders, a 21700 cell, 21 mm across and 70 mm long, holding 5 amp-hours (Ah) at about 3.6 volts. Drag to turn it, and slide the cut to open it:

Under the can is one long, thin sandwich, rolled up like a jelly roll. Unrolled, it is about 79 cm long and 6.5 cm wide, and in a real cell it goes round about twenty timesMy estimate: each turn of the roll is about 0.37 mm thick, and the roll fills the space between a 3 mm hole in the middle and the inside of the can.. The dark strip is the negative electrode, called the anode. The pale strip is the positive electrode, the cathode. Between them, on both sides, runs a plastic film thinner than a hair, the separator. The steel can is wired to the anode and the button on top to the cathode.

Cut a small square out of the roll, peel its layers apart, and lay them out one above the other. Pull them apart with the slider and point at a layer to name it:

The two foils are just wires spread flat: copper on the anode side, aluminum on the cathode side. The coatings do the work. The anode coating is a paste of graphite grains, the stuff of pencil leads. The cathode coating is a paste of grains of a metal oxide, here one made of lithium, nickel, manganese, cobalt, and oxygen, called NMC. The whole stack is about a fifth of a millimeter thick, two sheets of paper. Every gap in it, including the pores of the separator, is soaked in a liquid, the electrolyte.

Nothing in this stack moves, and nothing burns. So where, in a few grams of graphite and oxide, is 18 watt-hours of energy hiding? The answer lies in what those two coatings would do if they were allowed to touch.

Two materials, kept apart

Start with two materials. One is lithium metal, whose atoms each hold one outer electron loosely. The other is a cobalt oxide with empty spaces for lithium, the material in the first lithium-ion cells, which pulls hard on electrons. Pull them apart and push them back together with the switch, and watch the boundary:

Where the blocks touch, a lithium atom hands its outer electron to the oxide, and the lithium, now a positive ion, slips in after it. Each one that crosses releases about 4 electronvolts (eV) of energy, the energy an electron picks up crossing 4 volts. Pull the blocks apart and it stops at once: electrons can't jump a gap.

One material losing electrons is called oxidation; the other gaining them is reduction. Together they make a redox reaction, the kind behind rust and fire. Touching, the two halves happen in the same spot, and all the energy turns to heat right there. A battery is a redox reaction with its two halves held apart, so the only way the electrons can cross is a route we choose.

So keep them apart, and give the electrons another way across: a wire through a lamp. In between, the cell can hold an electrolyte or nothing at all. Switch the electrolyte off and on, and watch the current in the wire:

With the cell empty of electrolyte, a burst of electrons flows through the lamp and then stops. Each electron that arrives makes the oxide more negative and leaves the lithium more positive, and within moments that piled-up charge pushes back as hard as the reaction pulls. Fill the space with electrolyte and the current keeps going, because for every electron that goes round the wire, a lithium ion crosses inside, and neither side builds up charge.

The electrolyte is a lithium salt, usually lithium hexafluorophosphate, dissolved in a mix of organic solvents. It carries ions freely and electrons not at all. That is the whole trick of a battery: the same charge has to cross by two roads, ions inside and electrons outside, and the only road open to electrons runs through whatever we want to power.

That is also why the separator matters as much as the electrolyte. It is soaked through, so ions pass, but it keeps the electrodes from touching. Let a sliver of metal bridge it, thin or thick, and watch where the electrons go:

Electrons take the easiest road, and metal is far easier than a lamp. A thin bridge steals most of the current and the lamp dims; a thick one takes nearly all of it, and the lamp goes dark. Either way, the cell's energy now pours into a spot smaller than a pinhead, at about three times the power the lamp was getting. This is an internal short circuit. A short like this sits behind most battery fires. We'll see later how a cell can grow its own bridge.

Why lithium

Some materials hold their electrons loosely and others grab for more. Chemists rank them by a voltage, the standard electrode potential: the more negative it is, the more eagerly the material gives its electrons away. Any two make a cell whose voltage is the gap between them, with electrons flowing from the lower to the higher. Pick a pair:

Zinc and copper, the pair in some of the first batteries, give 1.10 V. Lithium and copper give 3.38 V. Lithium sits at the very bottom, at −3.04 V, so it opens a bigger gap with any partner than anything else on the list. What puts lithium lowest is the ion it leaves behind: it is so small that the molecules around it cling to it unusually hard, and that grip pays back more of the cost of losing the electron than for any other metalThese potentials are measured in water, where lithium metal would fizz away. In a battery's organic electrolyte the numbers shift, but lithium stays at the bottom..

Voltage is only half of what makes a battery good. The other half is weight. Here every metal from the ladder is placed by its potential and by how much charge a gram of it can give. Point at a dot to name it, or pick one:

Lithium is the lightest metal, 6.94 grams per mole, light enough to float on oil. Each atom gives one electron, so a gram of it can deliver 3,860 milliamp-hours (mAh), more than any other metal here, and it does so at the most negative potential. Aluminum comes closest on charge per gram, because each atom gives three electrons, but at about half lithium's voltage, and its triply charged ion is hard to move in and out of solids.

Lithium metal has a dark side, though. Recharged, it doesn't plate back smoothly but grows spikes, and the first rechargeable lithium-metal cells were prone to shorting and catching fire. The answer, the idea behind every lithium-ion cell, was never to let lithium be metal at all: keep it as ions, stored inside two host materials, and move it back and forth between them.

Rooms for lithium

Both electrodes of a lithium-ion cell are hosts: solids full of empty spaces that lithium ions can slip into and out of without the solid falling apart. The anode's host is graphite, a stack of flat sheets of carbon atoms joined in a honeycomb. Turn the stack, and fill it with lithium:

Each lithium slides in from the edge of the sheets, since the honeycomb itself is too tight to pass through, and settles over the middle of a hexagon. At most one lithium fits for every six carbons, a compound written LiC₆, which gives graphite a capacity of 372 mAh per gram: a tenth of lithium metal's, the price of keeping lithium out of its metallic form. A full gap is 0.370 nm wide instead of 0.335 nm, so graphite swells by about a tenth as it fills, and the sheets beside a full gap slide into line. Slipping guests between the layers of a host like this is called intercalation.

Notice that lithium filled the middle gap before touching the outer two. Graphite prefers to fill some gaps completely while leaving others empty. Here is a side view of a whole stack of gaps in a graphite grain, with the electrolyte to its right. Fill it, and watch the potential of the graphite measured against lithium metal:

At first a few lithium scatter through every gap, then gather into every fourth or third gap, then every second, then all of them. These arrangements are called stages. While one stage is turning into the next, the two share the grain and the potential holds steady, which is why the curve has flat steps near 0.21 V, 0.13 V, and 0.09 V. Most of graphite's lithium goes in below 0.2 V, barely above lithium metal itself. So a lithium stored in graphite carries almost as much energy as one in the metal, which keeps the cell's voltage high. It also leaves little margin when we charge too fast.

The cathode is a host of a different kind: a metal oxide built of flat slabs, with lithium in single layers between them. Here is a small piece of it. Take lithium out with the slider, and turn it to look along the layers:

Each slab is a sheet of metal atoms, here mostly nickel with some manganese and cobalt, each at the center of an octahedron of six oxygen atoms. The lithium sits in single layers between the slabs, which repeat about every 0.47 nm. When a lithium ion leaves, its electron leaves too, taken from one of the metal atoms in the slab, whose charge rises by one. Not all of it can leave, though. Strip out too much and the empty layers let the slabs shift and shed oxygen, so a cell is built to stop with about a quarter of the cathode's lithium still in place when it reads 100%.

The rocking chair

Put the two hosts on either side of the separator and we have the whole cell. When it is charged, nearly all the lithium that can move is in the graphite. Connect a lamp and let it run, then switch to a charger:

While the lamp is lit, lithium ions leave the graphite grains, cross the electrolyte and separator, and slip into the oxide grains. For each one, an electron leaves the graphite through the copper foil, goes round through the lamp, and comes back in through the aluminum foil to meet its ion in the oxide. Switch to the charger and both flows reverse: the charger pulls electrons out of the oxide and pushes them into the graphite, and the lithium follows them back. The lithium rocks from one host to the other and back, which is why the first of these were called rocking-chair batteries.

Nothing is used up: no metal dissolves, no gas forms, and the same lithium makes the trip every time. Real cells lose a little on each trip, and the second half of this page is about where it goes.

Where the voltage comes from

Why should lithium in graphite want to move into an oxide at all? Because it has less energy there. Picture each host as a shelf whose height is the energy of a lithium stored in it, measured from lithium metal. A lithium that moves from the graphite shelf down to the oxide shelf gives up the difference, and that drop, per electron, is the cell's voltage. Run the cell down and watch both shelves:

When the cell is full, a lithium falling from graphite to oxide gives up 4.19 electronvolts, so the cell reads 4.19 V. As it drains, the shelves close in from both ends. The oxide fills up, and each newcomer is less welcome in a crowded host, so the oxide's shelf rises. The graphite empties, and the lithium left behind is held more tightly, so its shelf sinks, slowly at first and then fast at the very end. By the time the cell reads empty, the drop is down to 2.5 V.

Plot each shelf against the charge that has flowed out of the cell and we get its discharge curve. Each electrode's potential is measured against lithium metal, so the cell's voltage is the gap between the two curves. Drag along the discharge:

Through most of the discharge the anode sits nearly flat, near 0.1 V, so the slope of the cell's curve comes mostly from the cathode, from 4.3 V down to about 3.6 V. The cliff at the end comes from the anode. When the graphite is almost empty its potential shoots up, and the cell's voltage collapses with it. A battery manager stops the discharge at 2.5 V, so 0% on a phone doesn't mean the cell has run out of lithium. It means the graphite has, while the oxide is still a tenth empty. Averaged over the whole discharge, this cell gives 3.69 V, close to its rated 3.63 V.

Pushing lithium uphill

Charging has to lift every lithium from the oxide shelf back up to the graphite shelf. A charger does it by holding the cell's terminals at a voltage of its own, and the cell pushes back with its own voltage. Here the cell is half charged, so it pushes back with 3.71 V. Set the charger's voltage and watch which way the lithium goes:

Set the charger below the cell and the cell wins: current flows out of it, into the charger, and the lithium keeps falling. Match it and nothing moves. Raise it above and lithium climbs back to the graphite. How fast depends on the margin. The cell has an internal resistance, here 30 milliohms, so every 0.03 V of extra push drives about 1 A. That resistance is the sum of many small obstacles: ions shouldering through the electrolyte, electrons crossing from grain to grain, and the effort of getting each ion across the surface of a grain.

Why not push hard all the way? Because the cell can't safely sit above 4.2 V. Push the cathode higher and it starts to come apart, and the electrolyte starts to break down. So chargers work in two phases: a steady current until the cell reads 4.2 V, then that voltage held steady while the current dies away. Choose the charging current and drag through the charge:

At 5 A, enough to fill this cell in an hour, the voltage climbs with the cell's own voltage (dashed) plus the 0.15 V it takes to push 5 A through its resistance. It reaches 4.2 V after 50 minutes, at about 83%. From then on the charger holds 4.2 V, and as the cell's own voltage creeps up toward it the margin shrinks and the current fades. Double the current to 10 A and 80% comes in 25 minutes instead of 48, but the switch to constant voltage comes at about two-thirds full, and the whole charge takes 49 minutes, not 36. This is why fast chargers quote 0 to 80%: the last fifth runs at the pace of the taper, however strong the charger.

Capacity, energy, and power

A cell's capacity, in amp-hours, counts lithium: 1 Ah is 3,600 coulombs, the charge on about a quarter of a gram of lithium ions. Its energy, in watt-hours, is capacity times voltage, added up along the way, which is the area under the discharge curve. Drag along the curve to see the energy delivered so far, then switch the cathode to lithium iron phosphate:

The NMC cell delivers 18.5 Wh. The iron phosphate cell, with the same 5 Ah and the same graphite, delivers 16.0 Wh, because its cathode holds lithium at a lower, flatter 3.3 V or so. It trades energy for a cheaper, longer-lasting cathode with no nickel or cobalt. The cell in Figure 1 stores 18.2 Wh in 69 g, about 260 Wh per kilogram, roughly ten times what a lead-acid car battery manages.

Capacity and energy say how much a cell holds. Power is how fast it can give it, and here the internal resistance comes back. Every amp pulled through 30 milliohms costs 0.03 V, so the harder we pull, the lower the voltage the device sees, and the sooner the cell hits its 2.5 V cut-off. Raise the current, then cool the cell:

At a gentle 1 A the loaded curve hugs the dashed one and the cell gives nearly all its 18.5 Wh. At 15 A the whole curve drops by 0.45 V: the cell still delivers almost all its charge, but each coulomb arrives with less energy, and 2.2 Wh, an eighth of the total, stays behind in the cell as heat. Cold does the same thing more harshly. Ions move sluggishly through cold electrolyte and across cold surfaces, so the resistance climbs. In the winter preset it is about nine times higher, and the cell hits its cut-off with more than half its lithium still in the graphite. That is why phones die early on a ski slope, and recover indoors.

The power the device gets is current times the voltage it sees, while the heat inside grows with the square of the current. Pull ever harder and there comes a point where more current gives less power. Choose a current:

At 1 A, about what a busy phone draws, less than 1% of the power becomes heat. A power tool's 20 A wastes 16%, 12 W warming the cell from inside. The device's share peaks at 62 A, where exactly half the power is lost and the cell would be heating itself at over 100 W. No one runs a cell there. The same trade shapes cell design: thin coatings give short paths for ions and high power, thick ones give more room for lithium and more energy.

The film that saves and costs

Now the question from the start: why does the same 100% hold less after a few years? Look again at the graphite's potential, below 0.2 V against lithium metal for most of its filling. The electrolyte's solvents are not stable that low. Below about 0.8 V they pick up electrons from the graphite and break down, and the pieces, along with lithium, form a solid film over every graphite grain. It is called the solid electrolyte interphase, or SEI.

The film is what makes the cell possible. It blocks electrons but lets lithium ions through, so once it covers the graphite the breakdown nearly stops. Nearly, not completely: solvent keeps creeping through it, and every bit of new film locks away more lithium for good. The thicker the film, the slower the creep, so the loss grows with the square root of time, and like most chemistry it runs faster when warm. Set the temperature the cell lives at, and point at the curve to read it:

At 25 °C this model cell loses about 2.5% in its first year and under 6% in five. At 40 °C, a phone left on a sunny dashboard, it loses more in one year than the 25 °C cell does in five. The film also grows faster when the cell sits full, because a full cell keeps its graphite at the lowest potential, where the solvent breaks down most readily. Storage tests find the fade climbing in steps with the charge level, matching the graphite's own steps.

Where does the lost lithium leave the cell? The graphite and the oxide are mostly undamaged. There is simply less lithium to shuttle between them, and that shifts how the two electrodes line up. Take lithium away and watch the window between full and empty:

Each amp-hour of lithium lost costs almost exactly an amp-hour of capacity. The cell still charges to 4.2 V, because the top is set by the oxide, which empties to the same point as before. But at the bottom the graphite runs out of lithium early, its potential shoots up, and the cell reads empty while the oxide still has rooms it can't fill. With 1 Ah lost the oxide stops at 78% full instead of 91%. This loss of cyclable lithium is the main way most cells fade. Other wear adds to it: grains of oxide crack as they swell and shrink with every cycle, and fresh cracks grow fresh film.

Plating and spikes

Charging adds a faster way to lose lithium. Pushing current into the graphite takes an extra push at its surface, so during charging the graphite sits below its resting potential by an amount that grows with the current and with the cold. It starts only about 0.09 V above lithium metal. If the push takes it below zero, lithium stops slipping between the sheets and coats the grains as metal instead. Choose a charging rate and a temperature:

At room temperature this model cell can take 3C, a full charge in 20 minutes, without plating. At 4C it plates in the last third of the charge, where the graphite's potential is lowest. Cold is worse: at freezing even a one-hour charge plates from 60% on, and at −10 °C only a trickle is safe. That is why battery managers slow charging in the cold and near full, and why fast chargers taper early. Some plated lithium slips back in later; the rest is cut off, covered in fresh film, and lost.

Plated lithium also doesn't lie flat. It grows where the current is strongest, and the tip of any bump draws more current than the hollow beside it, so bumps become needles. These dendrites are the same spikes that sank the early lithium-metal cells. Given enough cycles, one can push through the 12 µm separator and become the metal bridge from earlier in the page, an internal short.

Back to the phone

So the phone that dies by mid-afternoon has lost lithium, mostly into the film on its graphite: a little more every day it was warm, every night it sat at 100%, and every time it was fast-charged in the cold. Its graphite and oxide still work; there is just less lithium to carry between them. Choose the charge a phone usually sits at and how warm it lives, and compare it with one kept full at room temperature:

In this model a phone that stops at 80% keeps about 2 points more capacity after three years than one kept full, and one that sits full and hot loses more than twice as much. That is why phones offer to pause charging at 80% overnight, slow down charging when hot or cold, and why a battery stored for months is best kept half full and cool.

The same picture explains where batteries are heading. Silicon holds ten times more lithium per gram than graphite but swells and grows new film as it does. Solid electrolytes might let lithium metal back into the anode without growing spikes. Each is a different answer to the same two questions this page started from: how far can lithium fall, and how much of it can we keep from getting lost on the way.

References

1. C.-H. Chen, F. Brosa Planella, K. O’Regan, D. Gastol, W. D. Widanage, and E. Kendrick, “Development of experimental techniques for parameterization of multi-scale lithium-ion battery models,” Journal of The Electrochemical Society 167 (2020), 080534. The teardown of the LG M50 cell, and the electrode curves used throughout this page.
2. X. Feng, M. Ouyang, X. Liu, L. Lu, Y. Xia, and X. He, “Thermal runaway mechanism of lithium ion battery for electric vehicles: A review,” Energy Storage Materials 10 (2018), 246-267.
3. M. S. Whittingham, “Electrical energy storage and intercalation chemistry,” Science 192 (1976), 1126-1127.
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5. The Nobel Prize in Chemistry 2019, awarded to John B. Goodenough, M. Stanley Whittingham, and Akira Yoshino “for the development of lithium-ion batteries.” nobelprize.org.
6. J. R. Dahn, “Phase diagram of Li_xC₆,” Physical Review B 44 (1991), 9170-9177.
7. S. Afshar, K. Morris, and A. Khajepour, “Efficient electrochemical model for lithium-ion cells,” arXiv:1709.03970 (2017). The lithium iron phosphate curve in the energy figure.
8. E. Peled, “The electrochemical behavior of alkali and alkaline earth metals in nonaqueous battery systems: the solid electrolyte interphase model,” Journal of The Electrochemical Society 126 (1979), 2047-2051.
9. H. J. Ploehn, P. Ramadass, and R. E. White, “Solvent diffusion model for aging of lithium-ion battery cells,” Journal of The Electrochemical Society 151 (2004), A456.
10. P. Keil, S. F. Schuster, J. Wilhelm, J. Travi, A. Hauser, R. C. Karl, and A. Jossen, “Calendar aging of lithium-ion batteries,” Journal of The Electrochemical Society 163 (2016), A1872-A1880.
11. C. R. Birkl, M. R. Roberts, E. McTurk, P. G. Bruce, and D. A. Howey, “Degradation diagnostics for lithium ion cells,” Journal of Power Sources 341 (2017), 373-386.
12. T. Waldmann, B.-I. Hogg, and M. Wohlfahrt-Mehrens, “Li plating as unwanted side reaction in commercial Li-ion cells: a review,” Journal of Power Sources 384 (2018), 107-124.

Further reading

• Lithium-ion battery and Graphite intercalation compound on Wikipedia.
• J. B. Goodenough and K.-S. Park, “The Li-ion rechargeable battery: a perspective,” Journal of the American Chemical Society 135 (2013), 1167-1176.