Can we refine X-ray analysis for more precise material characterization? This paper introduces a novel convolution approach to X-ray powder line-profile fitting, synthesizing line shapes from the Cu Kα emission profile, diffractometer dimensions, and specimen physical variables. This method allows for fitting parameters such as receiving-slit width, length, X-ray-source size, incident beam divergence, specimen X-ray attenuation coefficient, and crystallite size. This self-consistent approach uses usually known instrumental parameters, refined by simultaneously fitting profiles at high and low 2θ values to minimize correlation. The Cu Kα emission profile, based on recent measurements, identifies a doublet structure in both Kα1 and Kα2 components. Researchers developed fast and accurate convolution procedures and use multilinear regression and Gauss–Newton non-linear least squares with numerical differentials for fitting the profiles. The method is evaluated using powder diffraction data from well crystallized MgO and Y3Al5O12 (YAG) specimens and instrumental parameter alterations. This approach improves the accuracy of X-ray analysis, proving instrumental in **crystallography** research, **materials** science, and quality control where precise **X-ray line-profile fitting** is critical.
Appearing in the Journal of Applied Crystallography, which publishes articles focused on the technique of crystallography and its applications, this paper fits squarely within the journal's scope. By presenting a novel approach to X-ray line-profile fitting, the research offers valuable insights and tools for crystallographers and materials scientists. The article is highly relevant and significant to the journal's audience.