How batteries work Lab 3 GITT

Lab handbook · Lab 3

Pulse methods and the galvanostatic intermittent titration technique (GITT)

How do we measure resistance and diffusion?

Figure L3.1 The apparent resistance, voltage change divided by current, read at different times after a constant current is switched on, on a logarithmic time axis from 0.1 ms to 100 s. It starts at the ohmic value, rises as the interfaces charge between about 1 ms and 0.1 s, and keeps rising as the square root of time from diffusion. Green dots give the real part of the impedance at the matching frequency. A marker shows the value at the chosen reading time.
ΔV/I after a current stepreal part of Z at f = 1/(2πt)
The resistance of a cell depends on when you read it. Try this: read the resistance at 10 ms and at 10 s; one is more than half as large again as the other.
SourceInstantaneous drop as the ohmic resistance, later drops from charge transfer and diffusion, dependence on sampling rate and pulse length, and agreement with impedance when timescales match, after Meddings et al. 2020, section 3.1 and Fig. 5D. Computed for an illustrative cell: R0 = 20 mΩ, two R‖C pairs (4 mΩ with 0.25 F, 10 mΩ with 2 F) and a Warburg element with σ = 2 mΩ s−1/2. The step response of the Warburg part, 2σ√(2t/π), is this page’s own working from its impedance; the rest is the standard response of R‖C pairs.

The simplest reading: a current pulse

We begin with the simplest question: how much does the cell resist? Let us switch on a constant current and watch the voltage. It jumps at once; the jump divided by the current, ΔV/ΔI, is the ohmic resistance of electrolyte, active material, current collectors and contacts. Industry calls this the DC internal resistance. After the jump the voltage keeps moving, first as the interfaces charge (charge transfer), then, more slowly, as diffusion sets in.1

So the value we get depends on when we read it, and also on how fast the instrument samples, on the size of the current, on heating and on the change of state of charge during the pulse. That is why test standards specify pulse lengths and currents for “pulse power” tests.1 A pulse of length t probes roughly what an alternating current of frequency 1/(2πt) probes: values from the two methods approximately agree when the timescales match.1

Worked example. The cell in the figure, pulsed with 2 A. read at 0.1 ms: R≈20.5 mΩ, so ΔV≈41 mV read at 10 ms: 28 mΩ; at 1 s: 37 mΩ; at 10 s: 44 mΩ, so 88 mV Same cell, same current: more than a factor of two depending on the reading time.

A resistance quoted without its timescale is half a number.

Figure L3.2 One GITT step on a 2 micrometre film. Left: the lithium content across the film, flat at first, depleted near the surface during a 10 minute current pulse, then flattening again during the rest. Right: the cell voltage and the current against time over 80 minutes, with the four voltages E1 to E4 and the two voltage changes, the transient change during the pulse and the steady-state change after the rest.
lithium content and cell voltagecurrent pulseΔEtΔEsour ion
GITT: one pulse, one rest, two voltage changes. Try this: pause just before the current switches off and look at the profile: the surface is far ahead of the back of the film.
SourceProcedure, E1 to E4, ΔEs = E4 − E1 and ΔEt = E3 − E2, after Kim et al. 2022, section 2 and Figs. 1 and 2; the formula after Weppner and Huggins 1977 as given by Kim et al., eq. 16. The film (L = 2 µm, D = 10−11 cm2/s, a 10 min pulse) is solved numerically from the diffusion equation with a constant flux at the surface and none at the back (Kim et al., eqs. 3 to 6; Crank–Nicolson, this page’s method). The IR step (15 mV) and the voltage scale are illustrative.

GITT: a diffusion coefficient from a voltage

A pulse tells us how much the cell resists, but the slow, diffusive part of its answer is mixed in with everything else. If we keep the pulse short, let the cell rest afterwards and repeat, the voltage curve becomes a diffusion measurement: this is GITT. It starts from equilibrium, with the same lithium content everywhere. A constant current pulse of length τ removes (or adds) a known amount of lithium through the surface; a rest follows until the electrode is in equilibrium again; and the pair is repeated across the whole charge.2

During the pulse, lithium is taken from the surface faster than diffusion can refill it from inside, so the surface composition runs ahead and the voltage climbs: the transient change ΔEt=E3−E2, measured after the immediate IR jump. After the rest the electrode has settled at a slightly different composition: the steady-state change ΔEs=E4−E1, a step along the equilibrium curve. The slower the diffusion, the larger ΔEt compared with ΔEs. Weppner and Huggins turned the ratio into the chemical diffusion coefficient:2,3

D=4πτ(mBVMMBS)2(ΔEsΔEt)2

Here mB, MB and VM are the mass, molar mass and molar volume of the electrode material and S its area in contact with the electrolyte; the bracket mBVM/(MBS) is volume over area, the thickness of a film. For spherical particles of radius r it becomes r/3.2,4 The IR jump is left out of ΔEt because it is not diffusion: it holds the ohmic and the charge-transfer drops.4,5

Worked example. Particles of radius 5 µm, a 30 min pulse, ΔEs = 10 mV and ΔEt = 30 mV. D=4π×1800 s(5 μm3)2(1030)2=2.2×10−16 m2/s = 2.2 × 10−12 cm2/s check: Dτ/r2=2.2×10−16×1800/(5×10−6)2=0.016 The check, explained with figure L3.3, says whether the pulse was short enough for the formula; for a sphere, 0.016 just passes.6
Figure L3.3 Left: the diffusion part of the voltage during a GITT pulse plotted against the square root of time, with the ideal straight line; for long pulses the curve bends away from the line. Right: the diffusion coefficient returned by the Weppner-Huggins formula divided by the true value, against the dimensionless pulse length D tau over L squared on a log axis, for a planar film and for a sphere, with the recommended limits 0.25 and 0.025 marked.
diffusion part of the voltageideal √t linefilmsphere
When is a GITT pulse short enough? Try this: switch to the sphere and lengthen the pulse until the formula is 20 % low; read Dτ/L2 there.
SourceThe two linear assumptions after Kim et al. 2022, section 2.2 and Fig. 2; the dimensionless pulse τ^=Dτ/L2, the recommended limits (below 0.25 for planar samples, one order of magnitude smaller for spheres and cylinders) and the observation that most published GITT studies exceed 0.25, after Kang and Chueh 2021, eq. 5, Fig. 5 and their recommended procedure. Surface concentrations from the exact series solutions (Kang and Chueh eq. A.21 for the film; Nickol et al. 2020, eqs. 3 to 5, for the sphere). The ratio plotted, the Weppner–Huggins value computed with the exact surface change over the true D, is this page’s own calculation. Sample: L = 2 µm, D = 10−11 cm2/s.

Before we trust such a number, we should ask what the formula assumes. It rests on two straight lines. First, the steady-state step must be small, so that the equilibrium curve is straight over it. Second, during the pulse the voltage must grow as t, which is true only while the disturbed layer near the surface is thin compared with the sample: the short-time solution of the diffusion equation.2

What decides “short” is the pulse length in units of the time diffusion needs to cross the sample, τ^=Dτ/L2. The recommended limit is τ^<0.25 for flat samples and about ten times less for spheres and cylinders, and one survey found that most published GITT studies used longer pulses.6 Since D is what we are measuring, we make the check afterwards, with the value just obtained. For spheres a second criterion applies: the t law is within 5 % of the exact solution only for Dt/r2<0.0032.5

Particle size is the other trap. The formula needs the diffusion length, and a porous electrode has secondary particles several micrometres across made of primary grains a few hundred nanometres across. Because D scales with r2, choosing 5 µm instead of 0.25 µm gives a value 400 times larger.5 A published diffusion coefficient means little without the radius it was referred to.

Short pulse, small step, known size: without all three, the GITT formula returns a number, not a diffusion coefficient.

Figure L3.4 Top: one simulated GITT pulse on spherical particles, the potential above its starting value against the square root of time, with the slow double-layer charging at the start, a single-line fit over the first 360 seconds and a two-line fit. Bottom: bars for the six calculation procedures P1 to P6, each showing the diffusion coefficient it returns divided by the true one on a logarithmic axis.
potential during the pulseone-line fit (P3)two-line fit (P4)
Six recipes, one pulse, different answers. Try this: slide τdl from 1 s to 100 s, as when the cell is cooled, and watch which bars leave the line at 1.
SourceProcedures P1 to P6 (eqs. 10 to 12, single-line, two-line and full fits, E1 and E3 read 5 s after switching), the transition time τdl = RctCdl, the factor of 400 between 5 µm and 0.25 µm radii, and the effect of a charge-transfer resistance that changes during the pulse, after Nickol et al. 2020; note that they number the potentials from E0, one lower than figure L3.2. The pulse (r = 5 µm, D = 10−11 cm2/s, 30 min) is simulated with their spherical solution plus an ohmic step of 5 mV and a charge-transfer step of 20 mV that arrives with time constant τdl; the “falls” case lowers it by 40 % over the pulse. Values illustrative; the fits are this page’s.

Even with a short enough pulse, the answer depends on how we read the voltage. In one study the same GITT data on an NCM523 positive electrode were analysed by six procedures: two formulas that need the IR drop read off the curve (P1, P2), a straight-line fit of E against t (P3), a two-line fit that leaves out the start (P4), and fits of the whole pulse to the spherical solution, with and without the start (P5, P6). At 40 °C the results differed by a factor of 3; on cooling, by more than an order of magnitude.5

The reason is the start of the pulse. The ohmic drop is instant, but the charge-transfer drop arrives only as the double layer charges, with time constant τdl=RctCdl: below 1 s above 0 °C at medium lithium content, far longer in the cold.5 A recipe that reads the IR drop at a fixed 5 s, or fits a line through the start, mistakes double-layer charging for diffusion. Procedures that skip the transition (P4, P6) are expected to be more reliable; but if Rct itself changes during the pulse, the full fit P6 is thrown off most.5

In practice this means: measure τdl by impedance before each pulse; use a three-electrode cell, so that the lithium counter electrode’s own overvoltage, large at low temperature, is not mistaken for slow diffusion; keep the current small (0.1C agreed with 0.05C); and check that two currents give the same answer.5

Figure L3.5 Left: the voltage during a pulse against the square root of time, with a straight-line fit. Right: the voltage during the following rest, relative to its final value, against the square root of t plus tau minus the square root of t, which is a straight line; the long-time end of the rest, near zero on this axis, is shaded as the fitting region.
voltagepulse fitrest fit
Read the rest, not the pulse. Try this: tick “resistance falls 17 %” and compare the two estimates; then lengthen the pulse and watch the straight part of the rest plot shrink.
SourceThe relaxation variable √(t + τ) − √t, the 17 % resistance change that halves the pulse slope and overestimates D four times, the straight region lasting up to about ten pulse lengths for Dτ/L2 = 0.02 and the separation of early non-diffusion transients, and the recommended procedure (large dense single-phase samples, at least three pulse magnitudes), after Kang and Chueh 2021, eqs. 4 and 7, Figs. 2, 3 and 6 and the section “The recommended GITT implementation”. Planar sample, exact series solution; the fast surface process is an illustrative exponential with a time constant of τ/40.

The pulse itself is the weak point, so a more robust route reads diffusion from the rest after the pulse. During the pulse the voltage carries the IR drop on top of the diffusion signal, and if the total resistance drifts, as charge-transfer resistance does when the composition changes, the t slope is wrong. In one worked example, a 17 % fall in resistance during the pulse halves the slope and makes D four times too large. During the rest no current flows, so no IR drop can drift.6

The rest can be solved exactly: plotted against t+τ−t, where t is the time since the current stopped, the voltage is a straight line whose slope gives D, without needing the final equilibrium voltage. Fast processes that are not bulk diffusion, such as a surface layer, appear at the start of the rest and can be left out of the fit; the finite size of the sample bends the curve near the end, so the straight part in between is used, which for a short pulse lasts up to about ten pulse lengths of rest. The recommended procedure: large, dense, single-phase samples; at least three pulses of different size; and the τ^ check afterwards.6

The rest must also be long enough. In one study an NMC622 electrode needed about 7 to 9 h to relax below 3.8 V, and above 3.8 V the voltage was still drifting by 0.1 to 0.6 mV per hour after 9 to 12 h; published studies use fixed rests from 40 min to a day.4 The same study showed that ignoring diffusion in the electrolyte inside the pores, as the simple formula does, made its GITT value about four times smaller than a transmission-line analysis of impedance (figure L4.4).4

GITT is easy to run and easy to misread: check the pulse length, the reading of the IR drop, the rest and the size.

Figure L3.6 Top: a GITT run of 16 pulses with rests across a charge, with the voltage at the end of each pulse and of each rest marked. Bottom, switchable: the end-of-rest voltages forming the quasi-equilibrium curve with the end-of-pulse voltages above it; or the overpotential between them against lithium removed; or the diffusion coefficient from each step on a log axis against the value in the model.
cell voltageend of pulse (CCV)end of rest (QOCV)model value
A whole GITT run: three results from one experiment. Try this: open the Diffusion panel and untick “4 h rests”; find where the 1 h rest was not enough.
SourceQuasi-open-circuit voltage, closed-circuit voltage, overpotential η = |CCV − QOCV| and internal resistance η/I, and D at each step, after Kim et al. 2022, eqs. 16 to 19 and section 3; Weppner–Huggins in its sphere form after Abbas et al. 2025, eq. 3. The electrode (r = 2 µm, 10 min pulses at 0.5 mA, D varying fivefold with composition and every pulse below Dτ/r2 = 0.025, an IR drop largest at the start of charge) is illustrative, simulated with the spherical solution of Nickol et al. 2020. Rests are drawn compressed.

So far we have looked at one step at a time. A whole GITT run gives more than a diffusion coefficient. The voltage at the end of each rest is a quasi-open-circuit voltage (QOCV); joined up, these trace the equilibrium curve of the electrode. The voltage at the end of each pulse is the closed-circuit voltage (CCV). Their difference is the overpotential at that state of charge, and dividing by the current gives an internal resistance. With D from each step, the run yields three curves against composition.2

The price is time: sixteen steps of 10 min with 4 h rests take nearly three days, and where relaxation is slow even 4 h may not be enough.4

running and analysing a GITT experiment
  1. Build a cell with the electrode against lithium, preferably with a third, reference electrode, so that the counter electrode’s own overvoltage, large at low temperature, is not read as slow diffusion.5 Before each pulse, measure the double-layer time constant by impedance.5
  2. Start from equilibrium, with the same lithium content everywhere in the material.2
  3. Apply a small constant current (0.1C gave the same result as 0.05C in one study) for a pulse of length τ, then switch it off.5
  4. Rest at open circuit until the voltage stops moving. Fixed rests of 40 min to a day are published; one NMC622 electrode needed 7 to 9 h below 3.8 V, and above 3.8 V was still drifting after 9 to 12 h.4
  5. Repeat pulse and rest across the whole composition range, recording the full voltage transient; the analysis uses the voltage before the pulse, at its start, at its end and after the rest, and the shape of the rest.2,6
  6. Analyse each step with the Weppner–Huggins formula, using r/3 for spherical particles and leaving the IR jump out of ΔEt; or fit the rest with √(t + τ) − √t, which avoids the drifting IR drop.2,6
  7. Check afterwards that Dτ/L2 was below 0.25 for a film, about ten times less for spheres, and repeat with at least two, better three, pulse sizes.5,6 State the particle radius you used: taking 5 µm instead of 0.25 µm changes D by a factor of 400.5
Planning the time: 16 steps of a 10 min pulse and a 4 h rest take 16 × 4.17 h = 67 h, nearly three days.4 The quasi-open-circuit voltages at the ends of the rests trace the equilibrium curve as a by-product.2

References for this page

Numbers in the text refer to this list. All references of the course, with the chapters that use each one.

  1. 1 N. Meddings, M. Heinrich, F. Overney, J.-S. Lee, V. Ruiz, E. Napolitano, S. Seitz, G. Hinds, R. Raccichini, M. Gaberšček, J. Park, "Application of electrochemical impedance spectroscopy to commercial Li-ion cells: A review", Journal of Power Sources 480, 2020, 228742. doi:10.1016/j.jpowsour.2020.228742
  2. 2 J. Kim, S. Park, S. Hwang, W.-S. Yoon, "Principles and Applications of Galvanostatic Intermittent Titration Technique for Lithium-ion Batteries", Journal of Electrochemical Science and Technology 13, 2022, 19–31. doi:10.33961/jecst.2021.00836
  3. 3 W. Weppner, R. A. Huggins, "Electrochemical Investigation of the Chemical Diffusion, Partial Ionic Conductivities, and Other Kinetic Parameters in Li3Sb and Li3Bi", Journal of Solid State Chemistry 22, 1977, 297-308. doi:10.1016/0022-4596(77)90006-8
  4. 4 I. Abbas, H. T. Tran, T. T. N. Tran, T. L. Pham, E.-C. Shin, C.-W. Park, S.-B. Yu, O. J. Lee, A.-G. Nguyen, D. Jeong, B. H. Ka, H.-H. Cho, J. Lim, N. Shin, M. Gaberšček, S.-M. Hur, C.-J. Park, J. Kim, J.-S. Lee, "GITT Limitations and EIS Insights into Kinetics of NMC622", Batteries 11, 2025, 234. doi:10.3390/batteries11060234
  5. 5 A. Nickol, T. Schied, C. Heubner, M. Schneider, A. Michaelis, M. Bobeth, G. Cuniberti, "GITT Analysis of Lithium Insertion Cathodes for Determining the Lithium Diffusion Coefficient at Low Temperature: Challenges and Pitfalls", Journal of The Electrochemical Society 167, 2020, 090546. doi:10.1149/1945-7111/ab9404
  6. 6 S. D. Kang, W. C. Chueh, "Galvanostatic Intermittent Titration Technique Reinvented: Part I. A Critical Review", Journal of The Electrochemical Society 168, 2021, 120504. doi:10.1149/1945-7111/ac3940

Cite this page

Using this page in teaching, a thesis or an article? Cite it as follows; the date is the last update of the course.

Shyma Sajeevan, A. (2026). Pulse methods and the galvanostatic intermittent titration technique (GITT). How batteries work. https://asajeevan.github.io/batteries/lab/gitt/

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