Determine elastic parameters and nanocrystalline size of spinel ferrites MFe2O4 (M = Co, Fe, Mn, Zn) through X-ray diffraction and infrared spectrum: Comparative approach

MFe2O4 (M = Co, Fe, Mn, Zn) nanoparticles were successfully synthesized by coprecipitation. Analyzing the X-ray diffraction by the Rietveld method confirmed the spinel ferrite structure of the samples. Rietveld refinement results show that Co, Mn and Zn occupy both the tetrahedral and octahedral sites. Variation in elastic parameters was determined by Fourier transform infrared spectroscopy, and cation distribution was deduced from X-ray diffraction. X-ray diffraction peak expansion was analyzed by employing a variety of calculating methods such as modified Scherrer, Williamson–Hall, size–strain, and Halder–Wagner to determine the crystallite size and elastic parameters of the cubic-structured MFe2O4 nanoparticles, including intrinsic strain, stress, and energy density. Comparison of the results obtained from these different methods revealed that they are ideally suited to each other. Moreover, the transmission electron microscopy image confirmed that the average size of MFe2O4 (M = Co, Fe, Mn, Zn) nanoparticles ranges from 10 to 14nm, consistent with the dimensions obtained from the preceding methods.