Picture 1
The crowd
Inside are two stores for lithium, with a liquid between them. One is graphite: sheets of carbon, stacked like pages, that lithium can slip between. The other is iron phosphate, a crystal with rooms for it. The electrolyte carries lithium across as an ion, Li⁺, but no electrons: they have to go round the outside.
Charging pulls lithium out of the phosphate, sends it across, and packs it into the graphite. For every lithium ion that crosses inside, one electron makes the same trip outside, through the charger. Using the battery runs it all backwards. The same lithium sloshes from one side to the other, for hundreds or thousands of cycles, losing a little each time to a thin film that slowly grows on the graphite.
Now watch the graphite while it charges fast. Lithium arrives at its surface faster than it can soak inwards, so it piles up there, filling the ends of the sheets nearest the liquid while the far ends stay nearly empty.
Shows
What moves, and where it goes. The pile-up at the surface when you charge fast.
Hides
Why lithium flows back on its own, where 3.3 volts comes from, and why a pile-up would matter.
Picture 2
Two shelves
Here is what the crowd doesn't show: lithium has an energy, and it's different in each place. Physicists call it the chemical potential, μLi. It's the free energy it takes to add one more atom, so it counts how crowded the place already is as well as how strongly the place holds on.
In the phosphate, lithium sits low, 3.4 eV below where it would sit as a lump of pure . In the graphite it sits high, just below the metal. Charging lifts every lithium atom from the low shelf to the high one. That's where a battery keeps its energy, and the height of the jump, divided by the electron's charge, is the battery's voltage: about 3.3 eV per atom makes about 3.3 volts.
Each shelf rises as its host fills: the fuller it gets, the harder it is to squeeze in more. That's why a battery's voltage creeps up as it charges and sags as it empties.
Charge fast and the pile-up shows here as a shelf that bends up at the graphite's surface. The open circle, lithium arriving at the surface, rides above that, pushed up by the effort of crossing in. And there's a ceiling: the line. Going in is still downhill, but push the arriving lithium above that line and turning into metal is downhill too, so some of it can plate out on the surface instead: lithium plating. Much of the plated lithium is lost to the battery for good, and in rare worst cases it grows spikes through the separator that short the battery out.
There's a gap in the middle, too. In the electrolyte lithium has no shelf, because there it's never whole: the ion crosses through the liquid while its electron goes the long way, round the wire. To see the crossing itself, you need to follow the two halves separately. That's picture 4.
Shows
Where the energy is kept, why the voltage is 3.3 volts and why it drifts as the battery fills, and how close the graphite is to plating.
Hides
The trip between the shelves, which is where the energy is lost. It also doesn't say what a charger can actually see.
Picture 3
The charging curve
A charger can't see inside the battery. It sees two numbers, the voltage across the terminals and the current it's pushing, and it can track how much charge has gone in. This is the picture an engineer looks at first.
Charging, the voltage runs above the dashed line; discharging, below it. The gap is the extra push the current costs, and the energy it represents ends up as heat. The faster you go, the wider the gap. Charge fast with the voltage limit alone, and the curve looks fine: the current holds at full speed until the voltage reaches its ceiling, then tapers. But tick watch for plating and run it again. The current starts easing off well before half full, long before the voltage limit, because the charger is now holding the graphite's surface just under the plating line. A real charger can't watch that, of course. It follows a schedule of current against charge and temperature, worked out in advance with models and tests like this one.
The voltage ceiling has a job of its own: in this iron phosphate battery it marks where the phosphate runs out of lithium and the voltage shoots up (in a phone's oxide battery, it also keeps the oxide and the liquid from being overcharged). It's what slows the very end of every charge, careful or not.
Shows
What a charger can measure, the losses as a gap, and the taper.
Hides
Where inside the battery the losses happen, and so why the taper has to start so early.
Picture 4
Every species
The last picture follows lithium's two halves separately. Give each charged species a line: its free energy per charge, a voltage, Vi = μ̄i/ziF. The electrons' line is the familiar Fermi level, in volts (so drawn upside down), and it's what a voltmeter reads. The lithium ions' line runs right across the battery, liquid included.
A current flows down the slope of its own species' line, so every slope and step is a place where some of the push is spent. Where both lines exist, in each host, the gap between them is picture 2's shelf. So the two pictures agree, and this one fills in the gap.
Charging hard, look where the volts go. Each surface takes a step: the price of an ion crossing in or out. The liquid takes a slope too, partly resistance and partly salt running low next to the graphite and piling up next to the phosphate; it's gentle here, because this battery's liquid layer is thin. In a real battery's thick, porous electrodes it's one of the main limits on charging fast. Inside each host, lithium's crowding adds a slope of its own.
The salt's other half, PF₆⁻, gets a line too, in the liquid only. At rest it lies right on top of Li⁺'s. That's partly a choice of zero, made at the salt's standard strength of 1 M; the physical part is the gap between the two lines, which opens wherever the salt is weaker or stronger than that. Under current PF₆⁻'s line stays flat, because PF₆⁻ can't enter either host, so once things settle it carries no current at all.
Then look at the graphite's surface. Plating is decided in one place: where Li⁺ in the liquid meets an electron in the graphite. If the red line just outside rises above the blue line just inside, lithium metal can form. Fast charging pushes red up there in two ways at once: the surface step, and the pile-up behind it, which lifts the graphite's shelf.
Shows
Each species' push, and exactly where each loss happens. How pictures 2 and 3 fit together.
Hides
The lithium itself: a crowd you can't see, made of two species with opposite charges. And it takes practice to read.
So
Why it slows down near full
Two things slow a charge down as the battery fills. The last stretch belongs to the voltage ceiling: the fuller the battery, the higher its resting voltage, so the less push the charger has to spare under the ceiling, and the current falls whatever else happens (picture 3). The easing that starts much earlier is about plating. Put the pictures together. Charging fast piles lithium up at the graphite's surface (picture 1). That lifts the graphite's shelf toward the line (2), and the surface step lifts arriving lithium higher still (4). The fuller the graphite, the higher its shelf already sits, so the closer the line and the less room there is for the pile-up. A charger that won't plate has to slow down, and keep slowing, as the battery fills (3).
Race two chargers from empty at the speed in the bar: one that only watches the voltage, and one that watches for plating too.
Voltage limit only
- time
- 0 min
- past the plating line
- 0 min
Watching for plating
- time
- 0 min
- past the plating line
- 0 min
In this battery, at 4C, the careful charger finishes about three minutes later and never crosses the line. The other spends minutes past it. Real phone chargers juggle more limits than this, temperature above all. In a real battery's thick, porous electrodes, the salt running short in the liquid between the grains adds to the pile-up too, where this one slows its graphite on purpose to show it. And a phone's other electrode is a different metal oxide that runs nearer 3.8 volts. But the graphite side, where this story happens, is the same, and so is the shape: fast while the graphite has room, then gentler.
And while we're here
Other questions the pictures answer
Why can a phone die with charge still in it?
Fill the battery, then press Use at full speed. Lithium is pulled out of the graphite's surface faster than it can come up from inside, so the surface runs dry, the shelf there drops, and the voltage sags to the cut-off with plenty of lithium still in the battery. Press Rest and the voltage climbs back as the inside catches up. In a real phone the sag usually comes more from the battery's resistance than from one surface running dry, and cold and age both add to it. But the story is the same: the voltage hits the cut-off before the lithium runs out. That's the phone that dies at 20% on a ski slope and comes back to life indoors.
Why does a battery warm up when it charges fast?
Every slope and step in picture 4 is energy turned into heat, at a rate of current × voltage spent. Double the current and each of those drops roughly doubles too, so heat is made about four times as fast. The charge also takes half as long, so the heat per charge only about doubles.
Why do batteries hate the cold?
Cold slows everything that picture 4 charges for: the crossing at each surface most of all, and the soaking in as well. The pile-up comes sooner and taller, and the plating line arrives at a much lower charge. That's why phones and cars charge slowly, or refuse to, when they're cold.
Four pictures
Which one, when?
| Picture | Makes easy | Hides |
|---|---|---|
| The crowd | What moves where; the pile-up. | Energy, and why anything moves. |
| Two shelves | Where the energy is kept; the voltage; the plating line. | The trip between, where the losses are. |
| The curve | What a charger sees; losses as a gap; the taper. | Where the losses happen. |
| Every species | Each loss in its place; how the others fit together. | The lithium itself; it takes practice. |
None of them is the picture of a battery. They're one set of physics in four notations, and the questions get easy when you can move between them.
Under the hood
How a battery is simulated
A chemistry course meets batteries as electrochemistry: two half-reactions, a table of standard potentials, the Nernst equation. That gets you the voltage of a battery at rest. Almost everything on this page is something else: lithium having to move, through solids and through a liquid, over micrometres and minutes. The pile-up, the plating line, the sag and the heat all come from that motion. So the programs that design real batteries (the Doyle–Fuller–Newman model, in tools like PyBaMM and COMSOL) are transport simulations first.
At heart, in their simplest form, they follow one rule, the one picture 4 draws: each species is pushed down its own electrochemical potential, μ̄, so each one's current runs down its own line. Its flux is proportional to how steeply its μ̄ falls:
flux = −(D c / RT) · slope of μ̄ = −(D c F / RT) · z · slope of Vi
Write μ̄ out, as a concentration part and an electrical part, μ̄ = μ° + RT ln c + zFφ, and the one push becomes two familiar ones:
flux = −D · slope of c − (z F D c / RT) · slope of φ
diffusion, down the concentration · drift, pushed by the electric field
That pair is called drift–diffusion (the Nernst–Planck equation, to electrochemists), and it sits at the heart of these simulations. Add bookkeeping (lithium and charge are conserved: whatever flows into a slice either stays there or flows out) and a rule for each surface, how fast ions cross it for a given push, and you have the whole machine. The simulator chops the battery into thin slices, and steps forward in time solving all of it at once.
The real battery models carry more detail than this page: electrodes made of porous layers of particles, so lithium soaks into each particle while also travelling through the layer (that's the "pseudo-two-dimensional" in the Doyle–Fuller–Newman model); measured open-circuit curves with graphite's real steps; a concentrated electrolyte; full Butler–Volmer kinetics; heat. This one, built on driftlet, keeps one dimension, simple materials and a linear surface law, so it can solve a few hundred time steps a second in your browser. The things that decide the answers here are all in it: lithium and charge conserved, every species pushed down its own μ̄, and the surfaces taking their toll.