Complete Micro‐Structural Analysis and Elastic Properties of Sm3+‐Doped Ni‐Mn‐Zn Mixed Spinel Ferrite Nanoparticles

AbstractA series of Ni‐Mn‐Zn mixed spinel ferrite doped with Sm3+ ions is prepared by using sol‐gel auto‐combustion technique. Single phase cubic spinel structure of all the samples is confirmed by using XRD analysis. Incorporation of Sm3+ ions in Ni‐Mn‐Zn ferrites increases the lattice parameter from 8.4105 to 8.4134 Å. Williamson – Hall (W‐H) and strain size plot (SSP) analysis confirms the tensile‐type strain induced in the crystal lattice, which increases with the addition of Sm3+ ions. Average crystallite size estimated from Scherrer equation is found in the range 21.7–24.9 nm, which in good agreement with the results obtained from W‐H and SSP analysis. Infrared spectra recorded in the range 350–800 cm−1 reveals the characteristic features of spinel ferrites. Higher frequency band ν1 is observed near 580 cm−1 and lower frequency band ν2 is observed near 380 cm−1. By using the IR data, elastic constant (stiffness constant) and elastic moduli (Young's modulus, bulk modulus, and rigidity modulus) are estimated. Debye temperature obtained from Anderson formula ranging from 535 to 562 K and from Waldron equation ranging from 676 to 713 K with the substitution of Sm3+ ions.