Comment on the Halder–Wagner Approach to Size–Strain Separation

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Abstract
The Halder–Wagner (H–W) method is widely used to separate crystallite size and microstrain contributions from X-ray diffraction (XRD) peak broadening. However, different forms of the H–W equation exist in the literature, including simplified expressions based on the full width at half maximum (FWHM). Here, we examine the dimensional consistency of a commonly used FWHM-based formulation. Our analysis shows that this form violates the requirement of dimensional homogeneity, potentially leading to physically questionable estimates of crystallite size (D) and microstrain (ε). Representative data from published studies are reanalyzed, revealing discrepancies between reported and recalculated values, with crystallite sizes differing by up to one order of magnitude in some cases. We then revisit the original H–W formulation, based on the integral breadth and a Voigt-type description of peak broadening, which preserves dimensional consistency. This approach provides a physically meaningful framework for size–strain analysis. This Comment highlights the importance of using dimensionally consistent formulations to improve the reliability and reproducibility of XRD-based microstructural characterization.

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