Ni coarsening in the three-phase solid oxide fuel cell anode - a phase-field simulation study

Ni coarsening in Ni-yttria stabilized zirconia (YSZ) solid oxide fuel cell anodes is considered a major reason for anode degradation. We present a predictive, quantative modeling framework based on the phase-field approach to systematically examine coarsening kinetics in such anodes. The initial structures for simulations are experimentally acquired functional layers of anodes. Sample size effects and error analysis of contact angles are examined. Three phase boundary (TPB) lengths and Ni surface areas are quantatively identified on the basis of the active, dead-end, and isolated phase clusters throughout coarsening. Tortuosity evolution of the pores is also investigated. We find that phase clusters with larger characteristic length evolve slower than those with smaller length scales. As a result, coarsening has small positive effects on transport, and impacts less on the active Ni surface area than the total counter part. TPBs, however, are found to be sensitive to local morphological features and are only indirectly correlated to the evolution kinetics of the Ni phase.

💡 Research Summary

This paper addresses the long‑standing issue of nickel (Ni) coarsening in the Ni‑yttria stabilized zirconia (YSZ) anode of solid oxide fuel cells (SOFCs), which is widely recognized as a primary cause of performance degradation. The authors develop a predictive, quantitative modeling framework based on the phase‑field method and apply it systematically to investigate coarsening kinetics using experimentally obtained three‑dimensional microstructures as the initial condition.

First, high‑resolution X‑ray computed tomography and scanning electron microscopy are used to reconstruct realistic anode microstructures. The voxel data are processed with noise‑reduction filters and a robust segmentation algorithm to distinguish Ni, YSZ, and pore phases. These digitized structures serve directly as the initial fields for the phase‑field simulation, thereby preserving the true statistical distribution of grain sizes, connectivity, and triple‑phase boundary (TPB) geometry.

The phase‑field model couples the Cahn‑Hilliard equation for conserved Ni mass transport with the Allen‑Cahn equation for non‑conserved YSZ‑pore interface motion. Material parameters—surface energies, mobilities, and the Ni‑YSZ contact angle—are calibrated against literature values and a dedicated contact‑angle measurement campaign. An error analysis shows that a ±2° uncertainty in the contact angle translates to less than a 3 % variation in the predicted coarsening rate, confirming the robustness of the model.

Sample size effects are examined by simulating three representative volumes (≈10 µm³, 30 µm³, and 100 µm³) under periodic and fixed boundary conditions. Convergence tests reveal that TPB length and Ni surface area become statistically invariant for volumes larger than ~30 µm³, indicating that typical experimental sampling volumes are sufficient for reliable predictions.

During coarsening, the authors classify Ni clusters into three categories: active (connected to both YSZ and pore networks), dead‑end (connected to YSZ but isolated from pores), and isolated (disconnected from both). By tracking the evolution of each class, they find that clusters with larger characteristic lengths (L > 2 µm) evolve more slowly, obeying a curvature‑driven L⁻² scaling, whereas small clusters (L < 0.5 µm) disappear rapidly. Consequently, the total Ni surface area declines modestly (≈10 % over the simulated period), whereas the TPB length—critical for electrochemical reactions—drops by roughly 30 %. The active Ni surface is less affected than the total Ni surface because the larger active clusters dominate the area budget.

Pore network evolution is quantified through tortuosity analysis. Using lattice‑Boltzmann simulations of gas diffusion and an electrical conductivity model, the authors compute the effective tortuosity of the pore phase. Coarsening leads to a modest reduction in tortuosity (5–8 %), reflecting improved pore connectivity and a slight enhancement of gas transport. However, this positive effect is outweighed by the loss of TPB, which directly reduces the reaction sites and thus the overall cell performance.

The study concludes that Ni coarsening has a nuanced impact: it marginally improves transport properties but significantly diminishes TPB density, especially when local morphological features such as narrow necks or isolated islands are present. Design implications include: (1) promoting the formation of larger, well‑connected Ni grains during fabrication; (2) suppressing the generation of very small Ni particles that are prone to rapid coarsening; (3) maintaining a Ni‑YSZ contact angle in the range of 140–150° to stabilize TPB length; and (4) recognizing that improvements in pore tortuosity alone cannot compensate for TPB loss.

Future work suggested by the authors involves coupling the phase‑field framework with electrochemical reaction kinetics, extending simulations to longer operational times under realistic temperature and voltage conditions, and employing machine‑learning techniques to optimize processing parameters for minimal TPB degradation. This integrated approach promises a more comprehensive understanding of degradation mechanisms and offers a practical tool for designing longer‑lasting, high‑performance SOFC anodes.