NMC / graphite lithium-ion cell 1 / 3
Scene 1 of 3

How a lithium-ion cell works

Cross-section · discharge, pause, charge
motor
liquid
−
+
Graphite (−)
NMC (+)
Li⁺ ion — only inside the cell electron e⁻ — only in the external circuit
Charge (SoC)0% — lithium in NMC · 100% — in graphite
Charge 62 %
At the terminals 3.80 V
Equilibrium OCV 3.80 V
Current 0 A

No current flows: ions sit in lattice positions, and the terminal voltage equals the equilibrium value.

Li⁺ in graphite: 10 / 16 · OCV rises monotonically from 3.0 V at 0% to 4.2 V at 100%, nominal 3.6–3.7 V. The slope is a property of NMC; for LFP the curve would be flat.

The voltage sag arrives in three steps

V = OCV − I·Ri on discharge
V = OCV + I·Ri on charge

R₀ — ohmic: foil, electrolyte, contacts 0.000 V
instant, fractions of a second
R_ct — charge transfer at the particle boundary 0.000 V
over a second or two
R_diff — lithium diffusion inside the particles 0.000 V
over tens of seconds
Total I·Ri 0.000 V

At a 1C current, the total sag is roughly 0.15 V. During a pause each step relaxes on its own timescale — so the voltage does not return to OCV right away.

What is deliberately different here from popular illustrations

01

The ion does not glide down a wide corridor. Inside the lattice it hops from site to site over an energy barrier. The value 4.7 Å is the interlayer spacing plus the thickness of the oxide slab, not the width of a free passage: the free gallery is only about 2.6 Å.

02

There is no metallic lithium layer inside charged graphite. There, the ions are Li⁺, and their electrons are smeared across the conduction band of the carbon.

03

Li⁺ is a lithium ion, not a proton. It is not the same as H⁺.

04

Inside the cell, only ions carry current; outside, only electrons do. So there is not a single electron in the electrolyte, and not a single ion in the wire.

05

On discharge, ions and electrons move in the same direction — from anode to cathode, each by its own path. There is no counter-flow in this scene.
Scene 2 of 3 · nanometer scale

The path of a single lithium ion

From graphite into the liquid, through the liquid inside a shell, shedding the shell at the boundary, then hops inside the NMC.

liquid
graphite
NMC
Li⁺ ion, diameter 1.52 Å EC and DMC molecules attached to the ion — the solvation shell free solvent molecules in the LiPF₆ electrolyte metallic lithium on the graphite surface graphene layers, interlayer spacing 0.352 nm NMC oxide slabs, interlayer 4.7 Å · gallery 2.6 Å
Temperature+22 °C
Current0.5C

Pause. The ion sits at a lattice site: a hop requires energy, and without current there is none.

Step 1 of 12 · graphite

Cold mode: metallic lithium plating

At +5 °C and below, at currents above 0.3–0.5C, there is not enough energy to shed the shell and hop: ions pile up at the graphite surface and, instead of entering between the layers, plate onto it as metal.

— Degradation accelerates by 3–5×.

— The risk of thermal runaway does not appear right away, but days or weeks after the event.

— Detected from the shape of the voltage-relaxation curve after charging.

When the temperature rises back above +5 °C, or the current drops, the mode stops, but metal already plated does not disappear.

Plated this session: 0 %

The numbers behind this scene

Graphite

Interlayer spacing 0.335 nm when empty and 0.370 nm when full — an expansion of about 10%. The full anode has the composition LiC₆: one lithium ion per six carbon atoms. There is no metallic lithium inside — there are Li⁺ ions, and their electrons are smeared across the carbon's conduction band.

Electrolyte

LiPF₆ salt in a mixture of EC and DMC carbonates. A bare lithium ion weighs 7 amu; an EC molecule — 88, DMC — 90. A complex of the ion and 4–6 molecules weighs 359–535 amu — 50–75× heavier than the bare ion. That is why it moves slowly.

NMC

Interlayer spacing 4.7 Å — this is the spacing plus the thickness of the oxide slab, not the width of the passage. The free gallery between the oxygen planes is about 2.6 Å, and the lithium ion diameter is 1.52 Å. The hop follows the route octahedral site → tetrahedral → octahedral, with a barrier of 0.3–0.5 eV.

Shedding the shell

This happens at both boundaries, twice per cycle: an ion only enters a lattice bare. This is the main contributor to the charge-transfer resistance R_ct.

Scene 3 of 3

Where the voltage comes from

Electron energy is height. Cell voltage is the drop between two heights.

Panel A

A lithium atom gives up exactly one electron

The height axis here is the electron's binding energy in the atom, measured from the free state: the lower the step, the more tightly the electron is held. This panel has its own scale, not shared with Panel B.

free electron · 0 eV
scale break
2s¹ — outer shell
5.39 eV
1s² — inner shell
75.6 eV
1s² shell
sealed
Li⁺ · inert carrier
1s² 2s¹

The outer electron is removed for 5.39 eV. The next one costs 75.6 eV — 14 times more. That is why lithium gives up exactly one electron and never more.

Below is a different scale: potential measured from a metallic lithium electrode
Panel B

Two electrodes filled with electrons to different heights

The fill level is the Fermi level — the boundary of electron-state occupation. It is a height on the energy axis, not a layer inside the material. The drop between the two levels is the cell voltage.

energy ↑
potential ↓
graphite
0.08 V
NMC
3.88 V
3.80 V
electrons filling the electrode's states Fermi level E_F — the fill boundary the drop between the levels — the cell voltage
Cell charge62 %
Voltage 3.80 V

The circuit is open. The levels sit at their own heights, and the drop between them is the voltage.

V = −E_F/e = −ΔG/(n·F)

A deep-lying Fermi level means the material accepts an electron eagerly — that is, a high potential. A level raised high means the material tends to push an electron out — that is, a low potential.

Graphite: 0.05–0.2 V relative to metallic lithium. NMC over the working charge range: 3.6–4.2 V — it drops lower only on deep discharge, outside the working window. Cell voltage is their difference: about 4.0 V when charged, 3.0 V when discharged. It is set by the pair of materials and does not depend on the cell's size — size sets the capacity.

Who gives up electrons in NMC

Ni³⁺

Nickel gives up electrons, moving sequentially through the states Ni²⁺ → Ni³⁺ → Ni⁴⁺. It is the source of charge on the cathode side.

Mn⁴⁺

Manganese stays Mn⁴⁺ and gives up no electrons: the Mn⁴⁺/Mn⁵⁺ redox couple lies outside the 0–4.2 V working potential window.

Co³⁺

Cobalt stays Co³⁺ and stabilizes the structure.

Four words about bands

Valence band — the energies of electrons locked in fixed chemical bonds.

Conduction band — energies at which an electron is free and can move through the crystal.

Band gap — a range where an electron cannot exist, because electron waves cancel each other out in the lattice's periodic field.

Fermi level — the boundary of electron-state occupation.

Three scenes · NMC/graphite cell · 31.07.2026