Research on the performance of nickel ferrite ceramics is significant for the practical application. This study prepared Ni_1-xNb_xFe₂O₄ ceramics (x = 0, 0.02, 0.05, 0.07, 0.10, 0.20) via a solid state reaction, and analyzed how Nb doping affected phase compositions, grain sizes, relative densities as well as DC conductivities was investigated. The results showed that the Ni_1-xNb_xFe₂O₄ ceramics contained both NiFe₂O₄ and NiO phases when the Nb doping amount x was less than 0.20. The grain sizes of the Ni_1-xNb_xFe₂O₄ ceramics slowly elevated as the Nb doping amount elevated. The mean grain size of around 50 μm was obtained at the doping amount x of 0.20, 2.5 times higher than that of undoped NiFe₂O₄ ceramics. The relative densities and DC conductivities of the Ni_1-xNb_xFe₂O₄ ceramics first increased and then decreased gradually with the increase of Nb doping amount. When the Nb doping amount x was 0.05, the relative densities and DC conductivities reached the maximum, which were 99.35% and 36.37 S/cm (960 ℃), respectively. The factors affecting the microstructure and DC electrical conductivities of the Ni_1-xNb_xFe₂O₄ ceramics were also discussed in detail.

Keywords: Microstructure, Electrical conductivity, Nickel ferrite, Ceramics.

Nickel ferrite is considered a very attractive material because of its unique properties and practical applications [1, 2]. It is widely used in various areas, like supercapacitor [3], data storage [4], catalysts [5], H₂O decomposition [6], ferrofluids [7], gas sensors [8], inert anodes [9], magnetic drug delivery [10], glycan analysis [11] and microwave absorbers [12]. The microstructure and electrical conductivity of nickel ferrite ceramics is significant for the applications. Therefore, numerous researchers have carried out extensive research and discussion on this issue. Hassan et al. prepared Al substituted Ni ferrites successfully as energy storage devices [13]. They found that the Al substituted Ni ferrites had increased DC electrical resistivity as Al content elevated within the samples, making the material suitable for high frequency applications. Kamar, et al. synthesized four nickel ferrite powder samples of diverse nanoparticle sizes and morphologies, and studied how particle size and morphology affected electrical performances of NiFe₂O₄ nanoparticles [14]. Anu et al. analyzed how Zn doping affected electrical property of NiFe₂O₄ nanoparticles. The results showed that the nanoparticles with critical dopant concentration exhibited higher values of electrical conductivity because of the increased Fe³⁺ ion hopping at octahedral sites [15]. In our previous research, we found that the relative density and DC conductivity of nickel ferrite ceramics sintered under the nitrogen atmosphere dramatically elevated in comparison with those sintered in air [16]. Doping can effectively enhance the relative density and electrical conductivity of nickel ferrite ceramics. Given the facts that the radius of Nb⁵⁺ is relatively closer to that of Ni²⁺, it could be deduced that Nb atoms could intercalate into the crystal lattice of NiFe₂O₄ ceramics by partial replacement of Ni atoms [17]. In this work, Ni_1-xNb_xFe₂O₄ ceramics (x = 0, 0.02, 0.05, 0.07, 0.10, 0.20) were prepared via traditional powder metallurgy process and sintered under nitrogen at the initial oxygen partial pressure being ~100 ppm, so as to analyze how Nbdoping affected the microstructure and DC electrical conductivities of nickel ferrite.

Ni_1-xNb_xFe₂O₄ ceramics (x = 0, 0.02, 0.05, 0.07, 0.10, 0.20) were prepared via a solid state reaction according to the stoichiometry ratio.The high-purity NiO (99.8%, Jinchuan, China), Nb₂O₅ (99.5%, Shanghai, China) and Fe₂O₃ (99.8%, Qidong, China) were used to be raw materials. After weighing, the powder underwent 4 h of wet ball-milling within distilled water with WC-8Co cemented carbide balls, at the ball-to-powder mass ratio of 3:1, with polyvinyl alcohol (PVA) being the binder. This resultant mixed sample was heated for 24 hours under 100 ^oC, followed by 6 h of calcination under 1200 ℃ within a muffle furnace. The calcined powder was later subjected to uniaxial compaction at 120 MPa for forming the cylindrical blocks, and later 4 h of sintering under 1300 ℃ under nitrogen, and the initial oxygen partial pressure was ~100 ppm. After firing, the samples underwent cooling at 0.5 ℃/min for avoiding thermal shock-induced cracking.
The phase compositions of Ni_1-xNb_xFe₂O₄ ceramics were detected by X-ray diffraction (Dmax/2550VB+, Tokyo, Japan) under Cu-Kα radiation. The Ni_1-xNb_xFe₂O₄ ceramics microstructures were analyzed with the use of scanning electron microscopy (Hitachi S-4800, Tokyo, Japan). Archimedes approach was adopted for measuring bulk densities. Also, DC electrical conductivity was calculated at 300-960 ℃ through the four-point probe approach. Among them, two probes were applied in supplying current, whereas the other two were adopted for measuring voltage.

Phase composition
Fig. 1 displays X-ray diffraction patterns for samples
with compositions of Ni_0.98Nb_0.02Fe₂O₄ and Ni_0.80Nb_0.20Fe₂O₄ sintered at 1300 °C under nitrogen atmosphere. It could be observed that at low doping concentrations of Nb₂O₅, the samples predominantly exhibited two phases: NiFe₂O₄ and NiO, with no detectable diffraction peaks corresponding to Nb-containing compounds. However, at a doping concentration of x = 0.20, weaker intensity diffraction peaks of FeNbO₄ emerged in the samples, while the diffraction peaks associated with the NiO phase were no longer present.
Fig. 2 shows the SEM morphology of Ni_1-xNb_xFe₂O₄ ceramics sintered at 1300 °C under nitrogen atmosphere after polishing. It was evident that the number of holes in the doped samples was significantly reduced, resulting in increased density. As the concentration of Nb₂O₅ doping increased, the NiO phase in the samples diminished until it was no longer detectable. At x = 0.20, a white, speckled FeNbO₄ phase emerged in the samples, which aligned with the analytical results obtained from X-ray diffraction (XRD) presented in Fig. 1. Table 1 presents EDX analysis of spinel phase of Ni_1-xNb_xFe₂O₄ ceramics. It was evident that as the Nb content increased, the Ni content within the NiFe₂O₄ ceramic spinel phase continued to rise, even though the Ni content in the sample's composition ratio decreased. This showed that Nb₂O₅ doping could inhibit the dissociation of NiFe₂O₄ ceramics to NiO in nitrogen atmosphere. The ionic radii of Nb⁵⁺ and Ni²⁺ were comparable, both measuring 0.69 Å. However, Nb⁵⁺ possessed a higher cationic valence, resulting in a more tremendous bonding energy for Nb-O ionic bonds compared to Ni-O ionic bonds. Consequently, Nb-O bonds exhibited greater strength than Ni-O bonds. When Nb⁵⁺ partially substituted Ni²⁺ within the lattice of NiFe₂O₄ ceramics, it could effectively reduce the oxygen ion vacancy concentration within the lattice. This reduction enhanced the stability of the spinel structure of NiFe₂O₄ ceramics, thereby inhibiting the dissociation of NiFe₂O₄ [18].
Grain sizes
Fig. 3 displays SEM morphology of Ni_0.95Nb_0.05Fe₂O₄ and Ni_0.90Nb_0.10Fe₂O₄ ceramic powders obtained by calcination at 1200 °C in air. It could be seen that the doped NiFe₂O₄ ceramic powders were well crystallized, with a slight agglomeration phenomenon between the particles and the mean power grain size of about 2.5 μm.
Fig. 4 shows the SEM morphology of Ni_1-xNb_xFe₂O₄ (x = 0, 0.02, 0.05, 0.07, 0.10, 0.20) ceramic fracture sintered at 1300 °C under nitrogen atmosphere. It could be found that NiFe₂O₄ ceramics had gradually increased grain size as Nb₂O₅ doping elevated. The mean grain size of the undoped samples was about 20 μm, and when the doping amount x = 0.20, grain size reached about 50 μm. This phenomenon could be explained by the following reasons. First of all, Nb⁵⁺ ions possessed a higher cationic valence as compared to Ni²⁺ ions. when Nb⁵⁺ replaced Ni²⁺ into the lattice of NiFe₂O₄ ceramics, the cationic vacancies of Ni²⁺ and Fe³⁺ were formed in the lattice in order to maintain the balance of valences. The concentration of these cationic vacancies increased as doping amount elevated. The increasing cation vacancy concentration accelerated the migration rate of grain boundaries and pores, resulting in continuous grain growth. In addition, the previous analysis indicated that the NiO phase in the NiFe₂O₄ ceramic samples decreased continuously with the increase of Nb₂O₅ doping amount. The NiO phase as the second phase hindered the migration of grain boundaries. Therefore, the reduction in the number of NiO phase was also an important reason for promoting the continuous growth of grains with the increase of doping amount.
Relative densities
It could be seen from Fig. 2 that the pores of NiFe₂O₄ ceramics were reduced after doping Nb₂O₅, and the samples became very dense. For investigating how Nb₂O₅ doping affected sintering properties of NiFe₂O₄ ceramics, relative densities and porosities of the samples with different doping amounts were computed (Table 2). Clearly, the lattice constants of NiFe₂O₄ ceramics exhibited minimal variation after Nb₂O₅ doping, primarily due to the same ionic radius between Nb⁵⁺ and Ni²⁺ [19-21]. The relative densities of NiFe₂O₄ ceramics increased and then decreased as Nb₂O₅ doping increased, and relative densities peaked at 99.35% when Nb Nbdoping amount x was 0.05. According to the sintering mechanism, ceramic sample sintering was mainly attained through cation and anion diffusion, and their diffusion rates together decided the sample sintering properties [22]. NiFe₂O₄ was classified as the inverse spinel structure wherein the lattice was densely packed with oxygen ions, and the metal cations were filled in the in the tetrahedral and octahedral interstices. The diffusion rate of each ion was closely related to its vacancy concentration. The higher the ion vacancy concentration, the greater the diffusion rate [23, 24]. For the Ni_1-xNbₓFe₂O₄ series ceramics, all samples were sintered under nitrogen atmosphere. The effect of vacancy concentration and the diffusion rate of oxygen ions on the sample relative densities was basically the same. The primary reason for the difference in relative densities was the vacancy concentration and the diffusion rate of metal cations. Compared to Ni²⁺ ions, Nb⁵⁺ ions had higher cation valence. When Nb⁵⁺ replaced Ni²⁺ into the lattice of NiFe₂O₄ ceramics, cation vacancies of Ni²⁺ and Fe³⁺ were formed in order to maintain charge balance, and the concentration of these cation vacancies increased with higher doping. According to the sintering mechanism [22], the increase of the cation vacancy concentration of Ni²⁺ and Fe³⁺ was conducive to improving the diffusion rate of the corresponding ions, and the sample relative densities eventually elevated with the increase of the doping amount of Nb₂O₅. However, as Nb₂O₅ doping further increased, the increasing cation vacancy concentration increased the moving speed of the grain boundaries, resulting in the growth rate of grains too fast so that the pores could not be eliminated in time and remained in the grains, as shown in Fig. 4(f). As a result, the relative densities of the materials showed a downward trend.
Electrical conductivity
Fig. 5 displays the changes in electrical conductivities at the Ni_1-xNb_xFe₂O₄ ceramics sintering temperature of 1300 °C under nitrogen atmosphere. It could be seen that the sample electrical conductivities elevated with rising temperature, showing the conduction law of semiconductor. The DC conductivities of the
Ni_1-xNb_xFe₂O₄ ceramics first elevated and later declined as Nbdoping amount increased. The x = 0.05 composition showed the highest conductivity of the series with a value of 36.37 S/cm at 960 ℃, which increased by 60.5% compared to undoped NiFe₂O₄ceramics. In order to analyze the concentration of Fe²⁺ at the octahedral and and the valence of the Nb in NiFe₂O₄ ceramics doped with Nb₂O₅, XPS tests were performed on the samples with compositions of NiFe₂O₄ and Ni_0.95Nb_0.05Fe₂O₄. Fig. 6 shows the XPS spectras of the Fe₂p peaks of the two samples. Fe³⁺_A represents Fe³⁺ at the A position of the spinel tetrahedron, Fe³⁺_B and Fe²⁺_B represent Fe³⁺ and Fe²⁺ at the B position of the octahedron, and S1 and S2 are satellite peaks, respectively. It could be seen that the element Fe in both samples presented two valence states of +3 and +2. The corresponding peak positions, peak areas, and the ratios of octahedral Fe²⁺/Fe³⁺ for each peak were shown in Table 3. It could be observed that the ratios of Fe²⁺/Fe³⁺ at octahedral positions in the doped samples increased by 3.9% compared with undoped samples. After Nb⁵⁺ replaced Ni²⁺ into the lattice of NiFe₂O₄ ceramics, some Fe³⁺ were reduced to Fe²⁺ for maintaining the valence balance, and the generated Fe²⁺ preferentially occupied the B-position of the octahedron [25, 26], resulting in the increase of Fe²⁺_B/Fe³⁺_B in the B-position of the octahedron (see Table 3).
The electrical conductivity of NiFe₂O₄ ceramics depended on the concentration of Fe²⁺ at octahedral sites [27, 28]. The higher concentration of Fe²⁺ led to the superior material electrical conductivity. Thus, the increase of Fe²⁺/Fe³⁺ ratio after doping made NiFe₂O₄ ceramics exhibit more excellent electrical conductivity. The Nb⁵⁺ ions into the lattice also resulted in octahedral B-site Fe³⁺ vacancies, and the concentration of these vacancies increased as Nb₂O₅ doping amount increased. The increasing Fe³⁺ vacancy concentration reduced the probability of electron hopping between octahedral Fe²⁺ and Fe³⁺ ions. Therefore, the NiFe₂O₄ ceramics conductivities showed a decreasing trend when the doping amount exceeded 0.05. In addition, the relative densities of doped NiFe₂O₄ ceramics exhibited the similar trend to that of the electrical conductivity, both increasing initially and then decreasing, peaking at x = 0.05. The increasing relative density could reduce the electron transport resistance [29], so the effect of the relative densities of doped NiFe₂O₄ ceramics on the electrical conductivity could not be overlooked.
Fig. 7 shows the plots of lnσ vs. 1000/T for Ni_1-xNb_xFe₂O₄ ceramics sintered at 1300 ℃. Solid lines were fitted to the data according to the Arrhenius equation. The activation energy DE and the R² value were obtained in Table 4 from the slopes of the fitted lines. It could be seen that for all the prepared samples, there was basically a linear relationship between lnσ and 1000/T, indicating that the relationship between the electrical conductivity and temperature in the doped samples remained consistent with σ = σ₀ exp[-(∆E/kT)]. In addition, as shown in Table 4, the doping concentration (x = 0.05) corresponded to the lowest conductive activation energy in the doped samples. The observed inverse correlation between activation energy and electrical conductivity was in good agreement with the fundamental semiconductor theory, where lower activation energies typically correspond to higher charge carrier mobility and improved conductivity performance.

In this work, the microstructures, phase compositions, grain sizes, relative densities as well as electrical conductivities of Nb doped nickel ferrite ceramics were studied. According to our obtained experimental analysis, we could draw three conclusions below.
(1) When the Nb doping amount x was less than 0.20, only diffraction peaks of NiFe₂O₄ and NiO could be detected in Ni_1-xNb_xFe₂O₄ ceramics. On the contrary, when the Nb doping amount x was 0.20, the diffraction peak of FeNbO₄ appeared while the diffraction peak of NiO phase gradually disappeared.
(2) The grain sizes of the Ni_1-xNb_xFe₂O₄ ceramics slowly elevated as Nbdoping amount elevated. At the doping amount x of 0.20, the mean grain size reached around 50 μm, 2.5 times higher than that of undoped NiFe₂O₄ceramics. This was associated with the increasing speed of grain boundary movement and the increase of the pore mobility.
(3) when the Nb doping amount x was 0.05, the relative densities reached the maximum value of 99.35%, which increased by 2.73% compared to pure NiFe₂O₄ samples, attributing to the increase of Ni²⁺ and Fe³⁺ vacancy concentration.
(4) The DC conductivities of the Ni_1-xNb_xFe₂O₄ ceramics first elevated and later declined as the Nbdoping amount elevated. The x = 0.05 composition showed the highest conductivity of the series with a value of 36.37 S/cm at 960 ℃, which increased by 60.5% compared to undoped NiFe₂O₄ceramics. It was because that Fe²⁺ ion concentration elevated at the octahedral sites after Nb doping and the porosity decreased.

This study was funded by the Scientific Research Fund of Hunan Provincial Education Department (23A0614), the Hunan Provincial Natural Science Foundation of China (2024JJ7262) and the Double First-Class Discipline Construction Program of Hunan Province.