Nanocrystalline Spinel Mn$_{x}$Cu$_{1 - x}$Fe$_{2}$O $_{4}$ Ferrites—Synthesis and Structural Elucidation Using X-Ray Diffraction and Positron Annihilation Techniques

We have synthesized a series of nanocrystalline ferrite samples with the composition Mn
_x
Cu
_1-x
Fe
₂
O
₄
(x=0.2, 0.4, 0.6, 0.8) by an advanced sol-gel auto-combustion method. The X-ray diffraction patterns confirm the existence of single-phase cubic spinel crystal structure of ferrites with lattice parameter ranges from 8.395 ¿ to 8.45 ¿. We report the equilibrium radii for tetrahedral and octahedral sites in the unit cells and the estimated cation distribution over the two sites of nanocrystalline Mn
_x
Cu
_1-x
Fe
₂
O
₄
. We also estimate the oxygen positional parameter as 0.389. The positron annihilation life time spectroscopic studies were carried out for all the samples and analyzed the variation of life time parameters ¿
₁
; I
₁
, ¿
₂
; I
₂
and the mean life time ¿
_m
to elucidate the defect structure of the nanocrystalline Mn
_x
Cu
_1-x
Fe
₂
O
₄
. We found that the overall vacant type defects fill up as the Mn
²⁺
ion concentration, x, increases. The value of ¿
₁
varies from 150 ps to 170 ps and that of ¿
₂
varies from 295 ps to 335 ps, which are the characteristic values for nanocrystalline samples, indicating the presence of intergranular as well as surface-diffused vacancies in the crystal structure.