Cathode Grain Cracking 2D: Single-Crystal vs Polycrystalline NMC

Cathode Particle

Cycling Protocol

Depth of discharge 100%

Charge/discharge rate 1.0C

Grain count 150

Live Readouts

State of charge

100%

Cycle count

Cracked grains

Capacity retention

100%

How it works

Layered-oxide cathodes (LiNi_xMn_yCo_zO₂, "NMC") change unit-cell shape as lithium leaves and returns. The c-axis expands through most of charge but contracts sharply above ~80% state of charge (the H2→H3 phase transition), while the in-plane a-axis contracts monotonically:

ε_c(SOC) =  ε_c,max · SOC/0.8            SOC ≤ 0.8
ε_c(SOC) =  ε_c,max · (1 − 3.5·(SOC−0.8))  SOC > 0.8
ε_a(SOC) = −ε_a,max · SOC

This 2D cross-section renders a polycrystalline secondary particle as a mosaic of grains packed inside a circular boundary, each with its own random crystallographic axis angle. Because every grain expands/contracts along a different in-plane direction, neighboring grains pull against each other at their shared boundary — a mismatch stress that grows with the misorientation angle θ between their axes:

σ_boundary ≈ E · |ε_c − ε_a| · sin(θ)
dD = k · σ_boundary² · |ΔSOC| · (0.5 + 0.5·C-rate)
grain cracks once accumulated damage D ≥ 1

A single-crystal particle has no internal grain boundaries, so this intergranular mismatch mechanism cannot act on it — the same lattice strain still happens, but there is nothing for it to crack against. This is the real reason single-crystal NMC cathodes are being pursued industrially: they resist the microcracking that lets electrolyte infiltrate a particle's interior, oxidize fresh surface, and cause the capacity fade seen in polycrystalline cells cycled to deep discharge.

Depth of discharge — wider swings mean a larger anisotropic strain excursion every cycle, so damage accumulates faster.
C-rate — faster cycling increases diffusion-limited concentration gradients inside each grain, amplifying the effective boundary stress.
Grain count — more, smaller grains means more boundaries and a finer mosaic; the underlying per-boundary fatigue model is unchanged.
Capacity retention here is illustrative: it falls with the fraction of grains that have cracked, standing in for the isolated active material and parasitic electrolyte reactions a real cracked particle suffers.
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Undamaged grain Accumulating damage Cracked

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