Regularization-Based Crystallite Size Distribution Analysis of Pt/C Catalysts from X-Ray Diffraction
Abstract
Accurate determination of the platinum crystallite size distribution in carbon-supported platinum (Pt/C) catalysts is critical for evaluating both the initial performance and long-term durability of proton exchange membrane fuel cells (PEMFCs). Conventional characterization approaches—including transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and the Scherrer equation—are limited by restricted statistical sampling, sensitivity to support interference, or the inability to resolve the full breadth of the size distribution. In this work, we present a regularization-based inversion framework that extracts the volume-weighted crystallite size distribution directly from X-ray diffraction (XRD) line profiles, without requiring any a priori assumption regarding the functional form of the distribution. The observed diffraction intensities at three high-angle Pt reflections—(220), (311), and (222)—can be expressed as a linear combination of pre-computed Pearson VII single-crystallite profiles organized in a dictionary matrix, and the unknown size distribution is recovered by solving a non-negative Tikhonov-regularized least-squares problem with automatic L-curve parameter selection. Multi-peak joint inversion substantially improves numerical stability and provides an internal self-consistency check across all three reflections. Validation against TEM particle size statistics on a series of commercial Pt/C catalysts with Pt loadings of 40 wt% – 60 wt% demonstrates good quantitative agreement between the XRD-derived and TEM-measured distributions. Applied to intact aged catalyst-coated membranes (CCMs) after removal of both carbon papers, the method successfully resolves a bimodal degradation signature comprising a ~ 5 nm population attributable to electrochemical Ostwald ripening, and a ~25 nm population consistent with particle migration and coalescence, in agreement with post-mortem TEM analysis. The proposed framework offers a non-destructive, statistically representative, and computationally efficient alternative to existing size characterization techniques, with broad applicability to nanocrystalline materials beyond fuel cell catalysts. An open-source Python implementation is publicly available at https://github.com/dragonMaLong/xrd-analyzer.
Graphical Abstract
Keywords
Carbon-supported platinum catalyst, Crystallite size distribution, X-ray diffraction, Tikhonov regularization, Proton exchange membrane fuel cell
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Date
2026-10-28
Online Available Date
2026-07-13
Revised Date
2025-07-02
Received Date
2026-05-18
Recommended Citation
Cheng-Long Ma, Wei-Yu Shi, Zhong-Jun Hou.
Regularization-Based Crystallite Size Distribution Analysis of Pt/C Catalysts from X-Ray Diffraction[J]. Journal of Electrochemistry,
2026,
32(10): 2605181.
DOI: 10.61558/2993-074X.3622
Available at:
https://jelectrochem.xmu.edu.cn/journal/vol32/iss10/3
