How to read a Nyquist plot — and see a cell age in real time
Electrochemical impedance spectroscopy compresses a cell's entire frequency response into one curve. Read it correctly and you can watch resistance grow as the cell degrades; read it carelessly and the axes alone will trip you.
A Nyquist plot graphs the negative imaginary impedance (−Z″) against the real impedance (Z′) as frequency sweeps from high to low. The high-frequency intercept on the real axis is the series resistance Rs; the semicircle's diameter is the charge-transfer resistance Rct; and the ~45° tail at low frequency is the Warburg (diffusion) impedance. As a cell ages, the semicircle grows — rising Rct is impedance growth you can read directly off the curve.
What the axes actually are
Impedance is complex: every frequency gives a real part (Z′, in phase with the current) and an imaginary part (Z″, 90° out of phase). The Nyquist plot puts Z′ on the x-axis and −Z″ on the y-axis (negated so capacitive behavior points up), with equal scaling on both axes — a semicircle has to look like a semicircle. Frequency is not an axis; it is implicit, running high-to-low as you move left-to-right along the curve.
How to read it well
1 · The left intercept is Rs
Where the curve meets the real axis at high frequency is the ohmic series resistance — electrolyte, contacts, current collectors. It shifts the whole curve right; a sudden jump in Rs across a series usually means a connection or electrolyte problem, not the electrode.
2 · The semicircle diameter is Rct
The semicircle is the parallel combination of double-layer capacitance and charge-transfer resistance. Its diameter equals Rct; its apex frequency sets the RC time constant. A semicircle that grows over cycles is the cleanest visual of interfacial resistance rising as the cell ages.
3 · The 45° tail is diffusion
At low frequency the curve breaks into a roughly 45° line — the Warburg impedance of solid-state diffusion. A steeper-than-45° rise toward vertical signals blocking or finite-length diffusion.
4 · Map it to the Randles circuit
The whole curve is the response of a Randles circuit: Rs in series with (double-layer capacitance in parallel with Rct plus Warburg). Each feature maps to one element — Rs to the left intercept, Rct to the semicircle diameter, the capacitance to the apex frequency, Warburg to the tail. Fitting the circuit turns the shape into numbers.
Common ways a Nyquist plot misleads you
- Unequal axis scaling squashes the semicircle into an ellipse and makes you misjudge Rct. Always plot with a 1:1 aspect ratio.
- Depressed semicircles (centre below the axis) are normal — real electrodes need a constant-phase element, not an ideal capacitor. Don't force an ideal fit.
- Overlapping arcs from two processes can read as one fat semicircle. A companion Bode plot separates the time constants the Nyquist hides.
- Drift during a slow sweep — if the cell relaxes or warms while you measure low frequencies, the curve distorts. Confirm the system is at steady state.
Where this gets slow by hand
One spectrum is quick to fit. A cycle-life study is hundreds of spectra across states of charge and ages, each needing equivalent-circuit fitting, Rs/Rct extraction, and trend-tracking to see the semicircle creep. Doing that by hand, file by file, is where the aging signal gets lost in the bookkeeping.
From raw EIS files to a tracked aging trend
Niobia ingests the raw impedance sweeps, fits the Randles equivalent circuit, and extracts Rs, Rct and the Warburg coefficient for every spectrum in the study — then tracks how each evolves across state of charge and cycle number, so the growing semicircle becomes a quantified aging trend rather than a stack of plots. It cross-checks the diffusion coefficient against the values from cyclic voltammetry and GITT, and flags spectra that drifted during acquisition. The output is the diagnosis — what's growing, where, and how fast — not another curve to fit.
Frequently asked
What does a Nyquist plot show in EIS?
It plots the negative imaginary impedance (−Z″) against the real impedance (Z′) as frequency sweeps from high to low. The high-frequency real-axis intercept is the series resistance Rs, the semicircle diameter is the charge-transfer resistance Rct, and the 45-degree low-frequency tail is the Warburg diffusion impedance.
What does the semicircle on a Nyquist plot represent?
The semicircle represents the charge-transfer process at the electrode interface — the double-layer capacitance in parallel with the charge-transfer resistance. Its diameter equals Rct, and it grows as the cell ages and interfacial resistance rises.
What is the Warburg tail?
The roughly 45-degree line at low frequency is the Warburg impedance, the signature of semi-infinite solid-state diffusion of ions into the electrode. A rise toward vertical indicates finite-length or blocked diffusion.