Abstract

Powder X-ray diffraction was used to validate the crystal structure of iron metal powder and to demonstrate a transparent workflow for extracting crystallographic and microstructural information from a simple laboratory dataset. The diffraction profile collected over the angular range of approximately 36° to 95° contains three dominant reflections located at 2θ = 44.850°, 65.218°, and 82.540°. Conversion of the peak positions into d-spacings using Bragg’s law gives values of approximately 2.020 Å, 1.430 Å, and 1.170 Å. The squared-sine ratios, when referenced to the first reflection, follow the sequence of 1:2:3, which is characteristic of the allowed reflections of a body-centered cubic lattice when multiplied by the first allowed value of N = h2 + k2 + l2 = 2. Therefore, the peaks are assigned to the (110), (200), and (211) reflections of α-Fe. The extracted lattice constants are 2.853, 2.860, and 2.865 Å, yielding an average value of 2.859 Å, which is close to the accepted room-temperature value of approximately 2.866 Å for α-Fe. Peak-width calculations based on the observed, instrument-uncorrected FWHM values are included only as illustrative apparent line-broadening indicators. Because an external instrumental standard was not measured under identical conditions, no quantitative coherent-domain size or microstrain is claimed. The Williamson–Hall treatment is therefore used only to demonstrate the sensitivity of size-strain interpretation to peak breadth, profile selection, and the limited number of available reflections. The intensity hierarchy was analyzed using the body-centered cubic-structure factor, reflection multiplicity, Fe atomic form factor, and Lorentz polarization correction. The comparison between calculated and experimental intensities shows stronger disagreement than the lattice-parameter analysis, illustrating the greater sensitivity of intensity analysis to preferred orientation, specimen preparation, peak-profile selection, and background treatment. The work provides a publication-style reconstruction of an iron powder XRD experiment, connecting peak fitting, indexing, lattice-parameter determination, crystallite size estimation, size-strain analysis, and intensity interpretation in a single critical framework.

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