Microsized single-crystal La0.47Sr0.53MnO3 (LSMO), were synthesized by a conventional solid-state reaction at high temperature. The X-ray diffraction patterns showed the presence of a single phase perovskite. Different structural models have been used but the best rietveld fits have been found using a rhombohedral \(R\overline{3 }c \left({C}_{3v}^{6}\right), a=b\approx \sqrt{2}{a}_{p}, c\approx 2\sqrt{3}{a}_{p} , Z=6\) . The rhombohedral structure is characterized by multicomponent octahedral tilt about a threefold axis \({a}^{-}{a}^{-}{a}^{-}\) according to Glazer’s classification scheme and \({\phi }_{x}^{-}{\phi }_{y}^{-}{\phi }_{z}^{-}\) in Aleksandrov tilt systems. We explored various techniques to determine the size of the crystallites. These techniques included the Monshi-Scherrer method (MSM), Williamson-Hall Method (WHM), Size-Strain Plot (SSP), and Halder-Wagner Method (HWM). Among all these methods, Williamson-Hall was considered the most effective as it facilitates the assessment of the energy density, lattice stress, lattice strain, and crystallite size within the synthesized crystal. We compared the results obtained from each model to analyze the variations in the data. The findings confirmed a relationship between the particle sizes in the Size Strain Plot and the Williamson-Hall method.
