Solid-state synthesis of heterogeneous Ni_0.5Cu_0.5-xZn_xFe₂O₄ spinel oxides with controlled morphology and tunable dielectric properties

Heterogeneous Ni_0.5Cu_0.5−xZn_xFe₂O₄ (0.0 ≤ x ≤ 0.5) nanoparticles are prepared via a green, solventless and additive-free, soft mechanochemical process at room temperature. This solid-state synthetic procedure yields ternary and quaternary oxide nanoparticles with uniform morphology (average particle size: 104–136 nm). X-ray diffraction analyses of Ni_0.5Cu_0.5−xZn_xFe₂O₄ nanoparticles reveal a cubic spinel structure with crystallite size in the range of 24–31 nm. The lattice parameter (a) and hopping length for tetrahedral (L_A) and octahedral (L_B) lattice sites are found to increase with the increase in Zn²⁺ content, while X-ray (ρ_xrd) and bulk (ρ_bulk) densities decrease slightly due to increasing lattice volume. Ni_0.5Cu_0.5−xZn_xFe₂O₄ nanoparticles with (x = 0.2, 0.3, 0.4) exhibit excellent dielectric performance with high permittivity (ε̍ = 92–111) and suppressed dielectric loss (ε̎ = 1.8–2.8) at high frequency (~ 10⁶ Hz). The polarization mechanism is discussed, involving major contributions from the electron hopping (Fe²⁺  ↔ Fe³⁺) at the octahedral sites. The influence of Cu²⁺ and Zn²⁺ concentration on the cationic distribution and dielectric performance is analyzed. The electrical conductivity is found to follow the power law (σ_ac = Aωⁿ) with n = 0.7, which confirms the ac conduction phenomenon driven by the electron hopping mechanism. The dielectric behavior of Ni_0.5Cu_0.5−xZn_xFe₂O₄ nanoparticles reveals their potential for applications in high-frequency microwave devices.