# 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) 1. **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 2. **W. Weppner & R. A. Huggins, *J. Electrochem. Soc.* 124, 1569 (1977).** The original GITT paper. 3. Y. Zhu & C. Wang, "Strain accommodation and potential hysteresis of LiFePO₄…" and related PITT analyses — for the two-phase transient shape. 4. **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. 5. **A. J. Bard & L. R. Faulkner, *Electrochemical Methods*, 2nd/3rd ed.** — Cottrell equation and diffusion fundamentals behind both techniques. 6. **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. 7. K. J. Griffith, C. P. Grey et al., *Nature* 559, 556 (2018) — a clean example of measuring and interpreting fast solid-state diffusion. 8. **BioLogic Application Note 70** — practical setup of EIS / PITT / GITT on a potentiostat.