[Paper Review] Validity of solid-state Li$^+$ diffusion coefficient estimation by electrochemical approaches for lithium-ion batteries

Zeyang Geng, Yu‐Chuan Chien+3 more|arXiv (Cornell University)|Oct 14, 2021

Advancements in Battery Materials4 citations

TL;DR

This study validates the galvanostatic intermittent titration technique (GITT) and intermittent current interruption (ICI) for estimating solid-state Li+ diffusion coefficients in NMC811 lithium-ion battery electrodes using a Doyle-Fuller-Newman (DFN) model. Despite theoretical assumptions not fully holding for porous electrodes, both methods accurately estimate the diffusion coefficient, with ICI offering 85% faster measurement and comparable accuracy, though estimation remains sensitive to electrode thickness, current rate, and electrolyte diffusion properties.

ABSTRACT

The solid-state diffusion coefficient of the electrode active material is one of the key parameters in lithium-ion battery modelling. Conventionally, this diffusion coefficient is estimated through the galvanostatic intermittent titration technique (GITT). In this work, the validity of GITT and a faster alternative technique, intermittent current interruption (ICI), are investigated regarding their effectiveness through a black-box testing approach. A Doyle-Fuller-Newman model with parameters for a LiNi$_{0.8}$Mn$_{0.1}$Co$_{0.1}$O$_2$ electrode is used as a fairly faithful representation as a real battery system, and the GITT and ICI experiments are simulated to extract the diffusion coefficient. With the parameters used in this work, the results show that both the GITT and ICI methods can identify the solid-state diffusion coefficient very well compared to the value used as input into the simulation model. The ICI method allows more frequent measurement but the experiment time is 85% less than what takes to perform a GITT test. Different fitting approaches and fitting length affected the estimation accuracy, however not significantly. Moreover, a thinner electrode, a higher C-rate and a greater electrolyte diffusion coefficient will lead to an estimation of a higher solid-state diffusion coefficient, generally closer to the target value.

Motivation & Objective

• To assess the validity of electrochemical techniques—specifically GITT and ICI—for estimating solid-state Li+ diffusion coefficients in porous NMC811 electrodes.
• To determine whether widely used electrochemical methods yield reliable diffusion coefficient values when applied to realistic battery models.
• To evaluate the impact of experimental parameters such as fitting length, current magnitude, electrode thickness, and electrolyte diffusion coefficient on estimation accuracy.
• To compare the performance and efficiency of GITT and ICI in terms of accuracy and time consumption.
• To provide theoretical validation of these methods using a DFN model as a proxy for real battery systems.

Proposed method

• A Doyle-Fuller-Newman (DFN) model with NMC811 electrode parameters was used as a virtual battery system to simulate GITT and ICI experiments.
• Voltage responses during current pulses were simulated under various conditions, including different electrode thicknesses, current rates, and electrolyte diffusion coefficients.
• The GITT and ICI methods were applied to extract the solid-state diffusion coefficient $ D_s $ using analytical solutions based on Fick’s second law and $ \sqrt{t} $-dependent voltage response.
• Fitting procedures used the $ \tau \ll 1 $ approximation and varied fitting window lengths (e.g., 1–900 s) to assess sensitivity.
• The estimated $ D_s $ values were compared against the true $ D_s $ value used in the simulation to evaluate accuracy and bias.
• Sensitivity analysis was performed by systematically varying electrode thickness, current magnitude, and electrolyte diffusion coefficient $ D_l $.

Experimental results

Research questions

• RQ1 Can the GITT and ICI methods accurately estimate the solid-state Li+ diffusion coefficient in a porous NMC811 electrode when applied to a validated DFN model?
• RQ2 How do fitting approach and fitting window length affect the accuracy of $ D_s $ estimation in GITT and ICI?
• RQ3 To what extent do electrode thickness, current magnitude, and electrolyte diffusion coefficient influence the estimated $ D_s $ value?
• RQ4 Does the ICI method provide a reliable and faster alternative to GITT for $ D_s $ estimation in lithium-ion batteries?
• RQ5 Why do reported $ D_s $ values across literature vary by several orders of magnitude despite similar materials?

Key findings

• Both GITT and ICI methods can estimate the solid-state Li+ diffusion coefficient with high accuracy, showing maximum underestimation of only 66% compared to the true value in the simulation.
• The ICI method reduces test time by 85% compared to GITT while maintaining comparable estimation accuracy, making it significantly more time-efficient.
• A thinner electrode and higher current magnitude lead to higher estimated $ D_s $ values, bringing them closer to the true value, with a 32% underestimation at 40 μm thickness and C/10 rate.
• Increasing the electrolyte diffusion coefficient $ D_l $ by 10 times results in a 5% lower underestimation of $ D_s $, suggesting that electrolyte degradation can contribute to apparent $ D_s $ decline in aging studies.
• Fitting approach and fitting length had only minor effects on estimation accuracy, though longer fitting windows improved GITT results slightly.
• The study confirms that despite theoretical assumptions not fully holding in porous electrodes, both methods remain valid for practical $ D_s $ estimation when used within appropriate experimental conditions.