Cd_xNi_0.5−xCu_0.2Zn_0.3Fe₂O₄ (0 ≤ x ≤ 0.50) ferrite with a spinel structure was prepared using the sol–gel self-propagation method. The effects of Cd²⁺ doping on the structure, morphology, dielectric, and magnetic properties of Ni–Cu–Zn ferrite were examined using XRD, SEM, EDX, FTIR, MPMS, and dielectric tests. The cubic spinel structure was verified by XRD and FTIR analyses. The crystallite size and particle size information of the samples were obtained with XRD and SEM analysis. The sample particle size belonged to a class of nanoscale materials with a particle size range of 1–100 nm. The minor difference between the grain size and particle size indicated that the sample nanoparticles were composed of numerous microcrystals. The EDX spectra indicated that the samples contained all stoichiometric elements. MPMS was used to measure the hysteresis lines of the samples. According to the hysteresis line, the saturation magnetization intensity (M_s), coercivity (H_c), and magnetic moment (μ_B) of the sample increased and then decreased with the increase in cadmium concentration. The magnetization strength (M_s) is between 4–67 emu/g, and the coercivity (H_c) is between 9–46 Oe. The curves of the real part of the dielectric constant (ε′), the imaginary part of the dielectric constant (ε″), and the loss factor (tanδ) with frequency were measured in the frequency range 100 Hz–100 kHz by means of an impedance analyzer. The complex modulus spectrum was analyzed to understand the dynamics of the conduction process.

Perovskite is the largest mineral on earth and has a variety of excellent physical and chemical properties. La_1−xR_xFeO₃ (R = Co, Al, Nd, Sm) were synthesized using the sol-gel method and analyzed by XRD, TG-DTA, and VSM. With the increase in the Co²⁺ doping content, the diffraction peak drifted in the direction of a larger angle. The grain size of La_1−xR_xFeO₃(R = Co) is mainly concentrated between 50.7 and 133.5 nm. As the concentration of Co²⁺ increased, the magnetic loop area and magnetization increased. La_1−xR_xFeO₃(R = Al) is an orthorhombic perovskite structure, the grain size decreased with the increase in Al³⁺ doping concentration, and the minimum crystallite is 17.9 nm. The magnetic loop area and magnetization increased with the increase in Al³⁺ ion concentration. The enclosed area of the M-H curve of the sample decreased, and the ferromagnetic order gradually weakened and tended to be antiferromagnetic, which may be due to the increase in sintering temperature, decrease in the iron oxide composition, and changes in the magnetic properties. Proper doping can improve the magnetization of La_1−xR_xFeO₃(R = Nd), refine the particles, and obtain better magnetic performance. As the Nd³⁺ ion concentration increased, the magnetic properties of the samples increased. Ms of La_0.85Co_0.15FeO₃ prepared by different calcination time increases with the increase in calcination time. As the Sm³⁺ ion concentration increased, the magnetic properties of the samples increased. Proper doping can improve the magnetization of La_1−xR_xFeO₃(R = Sm), refine the particles, and generate better magnetic performance.

A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) ferrite powders have been synthesized by the sol-gel combustion route. The X-ray diffraction of the CoHo_xFe_2−xO₄ (x = 0~0.08) results indicated the compositions of single-phase cubic ferrites. The saturation magnetisation of CoHo_xFe_2−xO₄ decreased by the Ho³⁺ ions, and the coercivity increased initially and then decreased with the increase of the calcination temperature. The Mössbauer spectra indicated that CoHo_xFe_2−xO₄ displays a ferrimagnetic behaviour with two normal split Zeeman sextets. The magnetic hyperfine field tends to decrease by Ho³⁺ substitution owing to the decrease of the A–B super-exchange by the paramagnetic rare earth Ho³⁺ ions. The value of the quadrupole shift was very small in the CoHo_xFe_2−xO₄ specimens, indicating that the symmetry of the electric field around the nucleus is good in the cobalt ferrites. The absorption area of the Mössbauer spectra changed with increasing Ho³⁺ substitution, indicating that the substitution influences the fraction of iron ions at tetrahedral A and octahedral B sites. The X-ray diffraction of Mg_0.5Zn_0.5C_xFe_2−xO₄(C=Gd,Al) results confirmed the compositions of single-phase cubic ferrites. The variation of the average crystalline size and lattice constant are related to the doping of gadolinium ions and aluminum ions. With increasing gadolinium ions and aluminum ions, the coercivity increased and the saturation magnetization underwent a significant change. The saturation magnetization of AlMg_0.5Zn_0.5FeO₄ ferrite reached a minimum value (M_S= 1.94 mu/g). The sample exhibited ferrimagnetic and paramagnetic character with the replacement with Gd³⁺ ions, that sample exhibited paramagnetic character with the replacement with Al³⁺ ions, and the isomer shift values indicated that iron is in the form of Fe³⁺ ions.

Olivine-type LiFePO₄ is a promising cathode candidate for lithium-ion batteries. In this study, undoped and a series of Co-substituted Li_xCoᵧFePO₄ (x = 0.85–1.00, y = 0–0.15) nanocomposites were synthesised by sol–gel auto-combustion using organic–inorganic hybrid xerogel precursors. The effects of sol pH, calcination temperature, calcination holding time and Co²⁺-doping content on crystal structure, phase composition, crystallinity, particle morphology, magnetic-hysteresis performance and Fe valence-state distribution were systematically explored using TG-DTA, XRD, FT-IR, SEM, VSM and Mössbauer spectroscopy. XRD analyses reveal that intermediate-pH conditions (pH 6.5–7.5) readily produce crystalline impurities including LiFeO₂ and Fe₂O₃, whereas high-pH environments (pH 8.5–9.5) facilitate the formation of pure-phase olivine-structured products. Diffraction-peak sharpness increases with rising calcination temperature, indicating improved crystallinity, and the samples treated at 800 °C exhibit the sharpest diffraction signals. As the doping level increases, the (311) diffraction peak first shifts toward lower and then higher angles; correspondingly, the unit-cell volume first increases to a maximum and then declines, whereas the crystallite size varies non-monotonically, confirming that Co doping predominantly modifies the lattice geometry. For the heavily doped Li_0.85Co_0.15FePO₄, carbothermal reduction induced by excessive thermal treatment (T > 700 °C or extended holding) yields a secondary phosphide phase that is tentatively indexed as Co₂P from two weak reflections. Within the Co-substituted series, the 700 °C—10 h condition gives a single-phase product with the highest saturation magnetisation (Ms = 3.45 emu·g⁻¹), which decreases to 2.07 emu·g⁻¹ at 800 °C. VSM results demonstrate a decoupling between the saturation magnetisation (Ms) and the coercivity (Hc); the weak ferromagnetic hysteresis observed in all samples signals trace ferromagnetic secondary phases—most plausibly amorphous or nanoscale products of xerogel thermal decomposition that lie below the XRD detection limit—rather than indicating phase purity; this attribution is indirect and is critically assessed below. Mössbauer spectroscopy validates the coexistence of dominant high-spin Fe²⁺ and minor Fe³⁺ species within the samples. High-level Co substitution (y = 0.15) lowers the relative proportion of the Fe³⁺ impurity species to 7.2% and alters the local Fe coordination environments without generating magnetically ordered sextet components. This work demonstrates that the sol–gel-derived hybrid xerogel is a tunable platform for fabricating phosphate-based battery nanocomposites and provides insights for the gel-precursor-directed design of energy-storage functional materials.