Cerium (Ce³⁺)-substituted cobalt–nickel (Co–Ni) ferrite nanostructures of spinel cubic phase with space group Fd\(\bar{3}\)m had been successfully engineered by solution combustion route. The effect of Ce³⁺ substitution on the structural, morphological, dielectric, and impedance spectroscopic investigations are probed by using X-ray diffraction (XRD), scanning electron microscope (SEM), and impedance analysis, respectively. Rietveld refinement of XRD data reveal that samples exhibit well-crystalline nature with single phase. The microstructural realm with various Ce³⁺ doping levels has been identified from SEM micrographs. The replacement of Fe³⁺ by Ce³⁺ cations has been confirmed by using energy-dispersive analysis of the ferrite samples. The dielectric constant (ε′), dielectric loss (tanδ), ac conductivity (σ_ac), and impedance (Z′ and Z″) at room temperature is investigated as a function of frequency, respectively. The variation of dielectric properties ε′, tanδ, σ_ac with frequency are explained by Maxwell–Wagner type of interfacial polarization and the hopping of charge between Fe²⁺ and Fe³⁺ as well as the dopant ions at B-sites. The decrease in dielectric constant and dielectric loss tangent with frequency follows the phenomenon of Debye’s relaxation. The enhancement in AC conductivity with frequency is proportional to Ce³⁺ concentration which follows Jonscher law. The complex impedance plots (Z′ vs. Z″) allows to determine the contribution for conductivity either from grain or grain boundary. Complex electric modulus plot (M′ vs. M″) provides the validation to the result drawn from the complex impedance plots. The results indicate the existence of non-Debye type of relaxation in these ferrites. Impedance spectroscopy allows the ferrite materials to estimate electrical properties which arise due to hopping and relaxation phenomena.

中文翻译：

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Ce 3+取代对汽车用Co-Ni铁氧体的结构，形态，介电和阻抗谱研究的影响

通过溶液燃烧途径成功地设计了空间群为Fd \（\ bar {3} \）m的尖晶石立方相的铈（Ce ³⁺）取代的钴镍镍（Co-Ni）铁氧体纳米结构。分别使用X射线衍射（XRD），扫描电子显微镜（SEM）和阻抗分析来探讨Ce ³⁺取代对结构，形态，介电和阻抗谱研究的影响。XRD数据的Rietveld改进表明，样品具有单相良好的结晶性质。从SEM显微照片已经鉴定出具有各种Ce ³⁺掺杂水平的微观结构领域。更换的Fe ³⁺被Ce ³⁺通过使用铁氧体样品的能量色散分析已确认了阳离子。介电常数（ε'），介电损耗（tanδ δ），交流电导率（σ_交流分别在室温下），和阻抗（Z'和Z“）进行了研究作为频率的函数，。介电性能ε'，tanδ的变化δ，σ_交流与频率由麦克斯韦-瓦格纳型界面极化的解释和Fe之间的电荷的跳频²⁺和Fe ³⁺以及B位置的掺杂离子。介电常数和介电损耗正切随频率的降低遵循德拜弛豫现象。交流电导率随频率的增加与遵循琼斯定律的Ce ³⁺浓度成正比。复数阻抗图（Z'与Z''）可以确定晶界或晶界对电导率的贡献。复数模量图（M'与M''）为从复数阻抗图得出的结果提供了验证。结果表明在这些铁氧体中存在非德拜弛豫类型。阻抗谱使铁氧体材料能够估计由于跳变和张弛现象而产生的电性能。