GITT & PITT — what they measure, how to run them, how to calculate

Two intermittent titration techniques for intercalation / insertion electrodes. Both step the cell a little, then wait, across the whole state of charge (SOC), and from the response they give you the chemical (apparent) diffusion coefficient of the working ion in the solid, plus the equilibrium (OCV) curve and the resistance/overpotential as a function of SOC.

Read the caveats at the end first if you only read one part: the number you get is an apparent diffusion coefficient. Its absolute value can be wrong by orders of magnitude because it depends on an area and a diffusion length you rarely know well. Use these techniques to compare samples measured the same way, and report every assumption.

What each one answers

Question	GITT	PITT
Chemical diffusion coefficient D vs SOC	✔	✔
Equilibrium potential / OCV vs SOC (thermodynamics)	✔ (rest voltage)	✔ (from step charges)
Overpotential & internal resistance vs SOC	✔	— (indirect)
Distinguish solid-solution vs two-phase reaction	partly (D dip)	✔ (current-transient shape)
Fine resolution near a phase transition / plateau	coarse	✔
Time to run	very long (hours–weeks)	long, often faster than GITT

Both also reveal kinetic hysteresis between charge and discharge (run both directions).

GITT — galvanostatic intermittent titration technique

How to run it (design)

A series of constant-current pulses, each followed by a rest (relaxation) to equilibrium.
Typical conditions (from the literature): current C/20–C/10 (or ~20 mA g⁻¹), pulse 5–30 min, rest 1–10 h — long enough that the voltage is flat (dV/dt below a set threshold) at the end.
Keep the current small and the pulse short so the step is near-equilibrium and the transient voltage is linear in √t.
Run in both charge and discharge, over the full voltage window.

One step, four voltages

E1 equilibrium before → E2 after the instant IR jump → E3 end of the pulse → (IR drop) → E4 new equilibrium after rest.

ΔE_s = E4 − E1 — the steady-state (equilibrium/OCV) change caused by the step.
ΔE_τ = E3 − E2 — the transient change during the pulse (i.e. with the IR drop removed).

How to calculate D (Weppner–Huggins)

When the current is small, the pulse short, and E is linear in √t (so dE/d√t ≈ ΔE_τ/√τ):

        4      ( m_B · V_M )²   ( ΔE_s )²
  D  =  ───  · (───────────)  · (──────)          valid for   τ ≪ L² / D
        π·τ    (  M_B · S  )     ( ΔE_τ )

τ = pulse duration (s)
m_B, M_B = mass (g) and molar mass (g mol⁻¹) of the active material
V_M = molar volume of the active material (cm³ mol⁻¹)
S = electrode–electrolyte contact area (cm²) — see caveats
ΔE_s, ΔE_τ from the step, as defined above

Also get, per step:

OCV(SOC) = E4 (the rested voltage) — the equilibrium/thermodynamic curve.
Overpotential η = E_meas − E_eq (close-circuit minus rested voltage).
Internal resistance R = η / I_applied.

Worked example (do this per step, then plot D vs SOC)

Electrode: m_B = 1.5 mg, M_B = 96 g/mol, density 4.8 g/cm³ → V_M = M_B/ρ = 20 cm³/mol, S = 1.13 cm² (a 12 mm disk), pulse τ = 600 s. One step gives ΔE_s = 8 mV, ΔE_τ = 40 mV.

m_B·V_M / (M_B·S) = (1.5e-3 · 20) / (96 · 1.13) = 2.77e-4 cm

D = (4 / (π·600)) · (2.77e-4)² · (8/40)²  ≈  6.5 × 10⁻¹²  cm² s⁻¹

Units check: (cm)² · (dimensionless)² / s = cm²/s. ✔ Watch the mg→g and the area (say whether S is geometric or BET — BET can shift D by orders of magnitude).

Do not do this by hand for 50 steps. Use gitt_pitt.py (in the Resources downloads): it finds each pulse, extracts E1–E4, computes D vs SOC, and plots it; run python gitt_pitt.py for a demo.

PITT — potentiostatic intermittent titration technique

How to run it (design)

A staircase of small potential steps; hold each step until the current decays to a small cut-off, then step again. Integrate the current over a step to get the charge ΔQ (→ incremental capacity dQ/dE and the OCV curve).
Keep steps small — ΔE ≪ RT/F ≈ 25 mV (commonly 5–20 mV) — so the response is linear and D can be read almost continuously vs potential.
Run charge and discharge over the full window.

How to calculate D (current transient of each step)

The current after a step decays; fit one of the two limits (you need the diffusion length L):

  Long time  (t ≳ L²/D):   ln I(t) = const − (π² D / 4L²) · t
                           → plot ln I vs t, take the linear-tail slope s
                           →  D = −(4 L² / π²) · s

  Short time (t ≪ L²/D):   I(t) ∝ t^(−1/2)      (Cottrell)
                           → plot I vs t^(−1/2); slope with ΔQ and L gives D

L = characteristic diffusion length (e.g. particle radius, or film thickness) — see caveats.

Bonus: reaction mechanism from the transient shape

Solid-solution insertion → current decays monotonically (Cottrell-like).
Two-phase reaction → current rises then falls (a bell), as a phase boundary sweeps through. PITT resolves this far better than GITT, which is why it is preferred around plateaus.

What to report (both)

Technique, pulse/step size, pulse/step duration, rest criterion (the dV/dt or current cut-off you used), temperature, and direction (charge/discharge).
Every quantity in the equation: m_B, M_B, V_M, S (GITT) or L (PITT) — and how you got S / L (geometric area? BET? particle radius from SEM/PSD?).
A representative single step (E–t, and E–√t for GITT / ln I–t for PITT) to justify the linear-fit assumption.
D vs SOC for charge and discharge (log scale), not a single headline number.
Call D an apparent / chemical diffusion coefficient, and state the range, not one value.
Follow the general battery reporting checklist (loading, n cells, etc.) as well.

Caveats — read these

The absolute D is not trustworthy. A porous composite electrode has a particle-size distribution and an unknown true active area S; using geometric vs BET area shifts D by orders of magnitude. The value is meaningful mainly for relative comparison of samples run under identical conditions.
Phase-transition and conversion materials violate the assumptions (single phase, small volume change). Near a two-phase plateau the Weppner–Huggins D is unreliable — PITT’s transient shape is more informative there.
τ ≪ L²/D must actually hold; if the pulse is too long the √t linearity fails.
Equilibrium must really be reached during rest, or ΔE_s (and the OCV) is wrong. Conversion electrodes can need days.
GITT and PITT should agree if the physics is right; large disagreement means an assumption is broken.

References to read (start with the first two)

J. Kim, S. Park, S. Hwang, W.-S. Yoon, “Principles and Applications of the Galvanostatic Intermittent Titration Technique for Lithium-ion Batteries,” J. Electrochem. Sci. Technol. 13, 19–31 (2022). Open access, beginner-friendly, full derivation. https://doi.org/10.33961/jecst.2021.00836
W. Weppner & R. A. Huggins, J. Electrochem. Soc. 124, 1569 (1977). The original GITT paper.
Y. Zhu & C. Wang, “Strain accommodation and potential hysteresis of LiFePO₄…” and related PITT analyses — for the two-phase transient shape.
J. Xie / X. Li et al., “Apparent diffusion coefficient of intercalated species measured with PITT: a simple formulation,” Electrochim. Acta 51, 1039 (2005). Practical PITT formulas.
A. J. Bard & L. R. Faulkner, Electrochemical Methods, 2nd/3rd ed. — Cottrell equation and diffusion fundamentals behind both techniques.
Cautionary reading: papers titled “Spurious chemical diffusion coefficients of Li⁺… GITT” (Electrochim. Acta, 2004) and “Spurious potential dependence… PITT” (Electrochim. Acta, 2002) — why the absolute numbers can be wrong.
K. J. Griffith, C. P. Grey et al., Nature 559, 556 (2018) — a clean example of measuring and interpreting fast solid-state diffusion.
BioLogic Application Note 70 — practical setup of EIS / PITT / GITT on a potentiostat.