Critical Crystallographic Interpretation of NaCl Powder XRD: From FCC Indexing to Coherence-Length Uncertainty

Powder X-ray diffraction (XRD) was used to determine the crystal structure of sodium chloride (NaCl) powder and to evaluate the accuracy with which a simple laboratory diffraction dataset can recover the crystallographic parameters of a well-known ionic solid. The diffraction profile collected over the angular interval 20° ≤ 2θ ≤ 90° contains nine indexed reflections at approximately 27.4°, 31.7°, 45.5°, 53.9°, 56.5°, 66.3°, 73.1°, 75.4°, and 84.1°. The sequence of squared-sine ratios, when referenced to the first reflection, is consistent with the allowed reflections of a face-centered cubic lattice. The observed indexing sequence is assigned to the (111), (200), (220), (311), (222), (400), (331), (420), and (422) reflections of the rock-salt structure. From Bragg analysis and the cubic interplanar-spacing relation, the average lattice parameter was determined as a = 5.642 ± 0.004 Å, in excellent agreement with the accepted value of approximately 5.640 Å for NaCl at ambient conditions. Peak broadening was further used to estimate an apparent Scherrer crystallite size of about 41.6 nm. This value should be interpreted as an XRD coherence length rather than as a direct particle size, because instrumental broadening and microstrain were not independently deconvoluted. A structure-factor and Lorentz–polarization analysis was used to rationalize the intensity hierarchy of the diffraction peaks and to explain why odd allowed reflections are weak but observable in NaCl owing to the difference between the Na+ and Cl− scattering factors. The contribution of this work is methodological and educational: it reconstructs a transparent workflow connecting peak fitting, indexing, lattice-constant evaluation, crystallite-size estimation, and intensity interpretation within one coherent analysis. The incorporation of data-driven whole-pattern analysis significantly enhances structural validation, providing improved accuracy in lattice-parameter determination and a more reliable interpretation of crystallite size and microstrain effects.