Method group NG-EIS
Impedance and titration
Impedance separates losses that a capacity curve shows only as one number. Done carelessly it also produces beautiful spectra of a cell that was never at equilibrium, which is why half of this page is about the conditions before the sweep rather than the sweep itself.
Potentiostatic impedance
| Parameter | Default | Note |
|---|---|---|
| Frequency range | 100 kHz → 10 mHz | lower limit on request, 1 mHz costs 2.5 h per spectrum |
| Points per decade | 10 | logarithmic, 7 to 15 accepted |
| Amplitude | 10 mV rms | 5 mV for cells above 2 Ah, linearity checked |
| States of charge | 20, 50, 80 % | any set between 5 and 100 % |
| Rest before sweep | 4 h | extended to 12 h if drift exceeds the limit below |
| Drift limit | 0.2 mV per hour | measured over the last 30 minutes of rest |
| Temperature | 25 °C | −20 to +60 °C, chamber logger quoted |
Every spectrum is checked for consistency before it leaves the building. We compute the residual between measured data and its own transform; spectra whose residual exceeds 1 % over the mid-frequency range are repeated rather than fitted. A spectrum that fails twice is reported as failed, with the drift log attached, because a cell that cannot hold a potential for four hours is itself the finding.
Fitting is optional and priced as analysis time, not instrument time. When it is ordered, three things are always stated in the report: the circuit used, the starting values, and the confidence interval on each fitted element. A fit without the last of those is decoration.
- Default circuit for graphite cells: series resistance, two parallel resistor–capacitance elements with constant-phase behaviour, and a finite-length diffusion element.
- Elements are only reported when the data actually constrains them. If the lowest measured frequency does not reach the diffusion regime, the diffusion element is left out and we say so.
- Distribution-of-relaxation-times analysis is available on request. The regularisation parameter changes the number of visible peaks, so we deliver the result at three settings and never at one.
Intermittent titration for diffusion coefficients
A current pulse followed by a long relaxation, repeated across the state-of-charge window. The apparent diffusion coefficient comes out of the voltage transient during each pulse.
- Pulse
- C/20 for 10 minutes, 25 pulses across the window by default
- Relaxation
- 60 minutes, extended to 120 near phase transitions where relaxation is slow
- Sampling
- 50 ms during the pulse and the first minute of rest, 1 s thereafter
- Duration
- roughly 30 hours of channel time per cell per direction
- Output
- coefficient against state of charge, with the particle radius and active mass used in the calculation stated explicitly
The number produced by this method depends on an assumed particle radius and on the assumption of one-dimensional transport into a sphere. For a polycrystalline secondary particle neither holds exactly. We report the coefficient, the inputs, and the factor by which it would change under a different radius assumption — usually within a factor of four. Treat it as a comparison between your own samples, not as a material constant.
| Quantity | Uncertainty | Dominant contribution |
|---|---|---|
| Impedance modulus, 1 Hz to 10 kHz | 0.4 % | reference resistor and lead compensation |
| Impedance modulus, below 0.1 Hz | 1.6 % | cell drift during the sweep |
| Phase angle | 0.3° | cabling capacitance |
| Series resistance | 0.15 mΩ | contact resistance at the holder |
| Cell temperature | 0.5 K | gradient between holder and chamber sensor |
Figures above 10 kHz are given in the method sheet of the individual job; inductive contributions from the holder and the cell itself dominate there and depend on the format.
Leads are compensated against a short and against a 10 mΩ reference before each session, and the compensation file is delivered with the raw data. The methodology page explains how the uncertainty budget is assembled, and sample requirements covers what we need in the shipment to run this at all.