Properties of materials greatly differ in nanoparticle form compared to their bulk counterpart. Strain mechanism, elastic properties and cation distribution play a major role as particle size decreased to nanoscale level and therefore it is necessary to evaluate these properties precisely through reliable methodology. In the present work, a detailed investigation has been carried out on nanocrystalline particles of Mg–Mn co-substituted CdFe₂O₄ to estimate intrinsic strain through Williamson-Hall (W–H) analysis. The results were compared with those obtained from Scherrer equation and Rietveld refinement. Bertuat method was used to estimate the cation distribution of spinel ferrite. Elastic properties such as, stiffness constant, Young's modulus, bulk modulus, rigidity modulus, Poisson's ratio and Debye temperature were studied by using the band positions of tetrahedral – A and octahedral – B sites observed through infrared spectra. The obtained results were discussed in the light of strain mechanism, elastic constants and substitution of Mg–Mn ions in the CdFe₂O₄.

与它们的本体相比，材料的性质在纳米颗粒形式上有很大不同。随着粒径减小至纳米级，应变机制，弹性性质和阳离子分布起主要作用，因此有必要通过可靠的方法精确评估这些性质。在目前的工作中，已经对Mg-Mn共取代的CdFe ₂ O _4的纳米晶体颗粒进行了详细的研究。通过Williamson-Hall（W–H）分析来估计固有应变。将结果与从Scherrer方程和Rietveld精炼获得的结果进行比较。用Bertuat方法估算尖晶石铁素体的阳离子分布。通过使用红外光谱观察到的四面体– A和八面体– B位的能带位置，研究了诸如刚度常数，杨氏模量，体积模量，刚度模量，泊松比和德拜温度等弹性性能。根据应变机理，弹性常数和CdFe ₂ O ₄中Mg-Mn离子的取代对所得结果进行了讨论。