[Paper Review] Electrochemical Modeling of GITT Measurements for Improved Solid-State Diffusion Coefficient Evaluation

Jeffrey Horner, Grace Whang+6 more|arXiv (Cornell University)|Jul 13, 2021

Advancements in Battery Materials33 references99 citations

TL;DR

This paper proposes a direct-pulse fitting method using a one-dimensional electrochemical model with non-ideal transport to improve solid-state diffusion coefficient evaluation from GITT data. By numerically fitting the entire GITT transient response—accounting for non-ideal solution behavior and particle radius scaling—it reduces prediction errors by two orders of magnitude compared to conventional square root or exponential fits, demonstrating superior accuracy in discharge profile predictions for FeS2 and NCM523 materials.

ABSTRACT

Galvanostatic Intermittent Titration Technique (GITT) is widely used to evaluate solid-state diffusion coefficients in electrochemical systems. However, the existing analysis methods for GITT data require numerous assumptions, and the derived diffusion coefficients typically are not independently validated. To investigate the validity of the assumptions and derived diffusion coefficients, we employ a direct pulse fitting method for interpreting GITT data that involves numerically fitting an electrochemical pulse and subsequent relaxation to a one-dimensional, single-particle, electrochemical model coupled with non-ideal transport to directly evaluate diffusion coefficients that are independently verified through cycling predictions. Extracted from GITT measurements of the intercalation regime of FeS2 and used to predict the discharge behavior, our non-ideal diffusion coefficients prove to be two orders of magnitude more accurate than ideal diffusion coefficients extracted using conventional methods. We further extend our model to a polydisperse set of particles to show the validity of a single-particle approach when the modeled radius is proportional to the total volume-to-surface-area ratio of the system.

Motivation & Objective

• To address the significant discrepancies in reported solid-state diffusion coefficients for battery materials, which often vary by orders of magnitude due to flawed GITT analysis methods.
• To investigate the validity of common assumptions in conventional GITT analysis, particularly regarding active surface area, ideal vs. non-ideal diffusion, and data selection criteria.
• To develop and validate a more accurate method for extracting diffusion coefficients from GITT data using full-pulse numerical fitting.
• To demonstrate that non-ideal solution theory yields more accurate diffusion coefficients than ideal Fickian diffusion in intercalation materials.
• To show that a single-particle model with a radius proportional to the system’s total volume-to-surface-area ratio accurately represents polydisperse particle systems.

Proposed method

• Numerically fit the entire GITT voltage transient (including both current pulse and relaxation phases) to a one-dimensional, single-particle electrochemical model with non-ideal transport.
• Use the Butler-Volmer equation to model interfacial charge transfer kinetics, with exchange current density dependent on local lithium concentration gradients.
• Implement non-ideal diffusion via concentrated solution theory, where flux is driven by electrochemical potential gradients rather than concentration gradients alone.
• Calibrate the model by minimizing the residual error between simulated and experimental GITT voltage responses using a least-squares fitting approach.
• Validate the derived diffusion coefficients by comparing predicted discharge profiles at multiple C-rates with experimental data.
• Extend the model to polydisperse particle systems by using a single-particle radius scaled to the total system volume-to-surface-area ratio.

Experimental results

Research questions

• RQ1 How do conventional GITT analysis methods (e.g., square root or exponential fits) affect the accuracy of extracted diffusion coefficients?
• RQ2 To what extent does assuming ideal versus non-ideal solution behavior impact the derived diffusion coefficients and prediction accuracy?
• RQ3 Can a single-particle model with an effective radius represent the GITT response of a polydisperse particle system?
• RQ4 How does direct-pulse fitting with a full electrochemical model compare to algebraic fitting methods in predicting discharge behavior?
• RQ5 What is the impact of active surface area estimation errors on the reliability of GITT-derived diffusion coefficients?

Key findings

• Non-ideal diffusion coefficients derived via direct-pulse fitting are two orders of magnitude more accurate than those from conventional square root or exponential fits.
• The direct-pulse fitting method reduces the discrepancy between experimental GITT data and model predictions by nearly two orders of magnitude.
• Non-ideal solution theory requires diffusion coefficients that are more than an order of magnitude lower than those from ideal Fickian models, and these non-ideal values yield significantly better agreement with experimental discharge profiles.
• The single-particle model with a radius proportional to the total system volume-to-surface-area ratio accurately predicts the behavior of polydisperse particle systems.
• Discharge predictions based on non-ideal diffusion coefficients from the direct-pulse fitting method match experimental data across multiple C-rates (C/10, C/20, C/50) with high fidelity.
• The study demonstrates that conventional GITT analysis methods are fundamentally flawed due to unverifiable assumptions about data selection and idealized transport models.