On the Structure and Some Properties of LaCo Co-substituted NiZn Ferrites Prepared Using the Standard Ceramic Technique

XRD

Figure 1 shows the XRD patterns for the ferrites samples. Samples A and B are single-phase NiZn ferrites with a spinel structure, indicating the absence of any other impurity phases with Co substitution. However, there is a secondary phase (LaFeO₃) in samples C and D. The secondary phase (LaFeO₃) was formed after the substitution of La³⁺ in place of Fe³⁺ in NiZn ferrites [25]. It can be explained that the radius of La³⁺ (1.06Ǻ) is larger than that of Fe³⁺(0.64Ǻ) and a portion of La³⁺ cannot enter into the lattice, so the redundant La³⁺ will form the secondary phase (LaFeO₃) on grain boundaries.

Figure 1:

XRD patterns for the samples.

The calculated values of lattice parameter a are displayed in Table 2. It is observed that the lattice parameter a of sample B increases compared to that of sample A. One possible explanation is that the radius of Co²⁺ (0.72Ǻ) is larger than that of Ni²⁺ (0.69Ǻ) which makes the lattice expand [23]. Compared to that of sample A, the lattice parameter a of sample C decreases, which was expected to increase considering the radius of La³⁺ (1.06Ǻ) is larger than that of Fe³⁺(0.64Ǻ). This can be ascribed to the crystal anisotropy and volume strain that have been changed due to large size mismatch of La³⁺ and Fe³⁺. Hence, lattice parameter a decreases in order to relax the lattice strain [26]. Due to the combined effect of both La³⁺ and Co²⁺, the value of lattice parameter a of sample D is between that of samples B and C.

SEM

Typical SEM micrographs of samples are shown in Figure 2. The average grain size (D) is calculated by the line intercept method and is tabulated in Table 2. It can be seen that the average grain size of the unsubstituted ferrite (Figure 2(A)) displays is about 3.1 μm and other samples (Figure 2(B)–(D)) have a smaller grain size. It is obvious that La³⁺ and Co²⁺ lead to the decrease in grain size. On the one hand, due to the reaction course is slowly and homogeneous with Co substitution, the grain size of sample B (Figure 2(B)) decreases to 2.4 μm [27]. On the other hand, due to the secondary phase (LaFeO₃) on grain boundaries hinder the growth of grains, the grain size of sample C (Figure 2(B)) decreases to 2.8 μm [28]. Meanwhile, the grain size of sample D (Figure 2(D)) is between that of sample B and C, which is probably attributed to the co-substitution of La–Co leading to the growth of grains slowly, the symmetry of the crystal structure and the secondary phase (LaFeO₃).

Figure 2:

Typical SEM micrographs of samples.

The effect of La³⁺ and Co²⁺ substitution on the porosity (P) of the prepared samples is observed in Figure 2. The porosity of samples has been calculated using the following equation [29]:

where d is bulk density (Table 2), D_x is the X-ray density which has been calculated from XRD patterns. From Table 2, we can see the sample D has the lowest porosity. The porosity formed between the grains, which decreased by substituting La³⁺ and Co²⁺ which results in the shrinkage of the crystal lattice, decrease in grain size and formation of secondary phase (LaFeO₃). However, the bulk density and porosity behave inversely. Therefore, it is found that the sample D has the highest bulk density (5.17 g/cm³) and the lowest porosity (3.9%).

VSM

The variation of samples saturation magnetization (M_s) is demonstrated in Table 3. According to Miller’s site preference energies of ion s^–l [30], the cations distribution in the case of NiZn ferrites can be represented by the formula:

where the ionic magnetic moments of Zn²⁺, Ni²⁺, Fe³⁺, Co²⁺ and La³⁺ are 0, 2, 5, 3 and 0μ_B. In AB₂O₄ spinel ferrites structure, the saturation magnetization (M_s) is dominated by the superexchange interactions between A-sites and B-sites. It is calculated by the relation

When the smaller magnetic moments of Ni²⁺ ions (2 μ_B) on B-sites are replaced by the higher magnetic moments of Co²⁺ ions (3 μ_B), the magnetic moments of B-sites (M_B) increases. This induces saturation magnetization of sample B increases (in Table 3). The results are in agreement with the report by Nobuhiro et al. [31]. Compared to Co²⁺ ions, La³⁺ ions’ contribution to the saturation magnetization is inverse. When the non-magnetic La³⁺ ions replaced by Fe³⁺(5 μ_B) on B sites, the magnetic moments of B-sites (M_B) decreased and superexchange interactions weakened. Hence, the saturation magnetization of sample C decreases. As observed from Table 3, the saturation magnetization of sample D decreases. This could be attributed to two factors: (1) It is known that Co²⁺ (3 μ_B) substitutes Ni²⁺ (2 μ_B) and La³⁺ (0 μ_B) substitutes Fe³⁺ (5 μ_B) in sample D. Due to x=y=0.02, the magnetic moments of B-sites (M_B) decrease which also makes saturation magnetization to decrease. (2) We have revealed that the sample D with La–Co substitution has a smaller gain size (from Table 2). Disordered spins increase with the decrease in grain size which causes the saturation magnetization to reduce [32].

All samples exhibit high coercive field (H_c) values compared to sample A in Table 3, meanwhile, the sample D exhibits the highest coercive field. The coercive field is a microstructure property; it mainly depends on the symmetry of crystal and size of grains [33]. On the one hand, CoFe₂O₄ and NiFe₂O₄ have an inverse spinel structure, so the substitution of Co²⁺ results in the increase in K₁. The coercive field can be written as the following relation:

In this relation, K₁ is the magnetocrystalline anisotropy (see Table 3). According to this relation, H_c would increase with the increase in K₁ and decrease with the increase in M_s. When x=0.02, further increase in K₁ than M_s leads to increase in H_c. The similar results have been reported by Li et al. [24]. On the other hand, La³⁺ ions have stronger s-l coupling and weaker crystal field, so the symmetry of crystal is lower, which results in strong magnetocrystalline anisotropy, inducing the H_c to increase. Moreover, the secondary phase (LaFeO₃) has a limit in the grain size (see Figure 2). When the grain size decreases, the grains tend to be multi-domains, the H_c starts to increase [34]. Therefore, the sample D has a higher coercive field (H_c).

Thermal variation of initial permeability (μ_i)

Figure 3 correlates the thermal variation of initial permeability (μ_i) of samples with temperature in the range from –30°C to the Curie temperature (T_c). The initial permeability is expressed as [35]

where M_s is the saturation magnetization, K₁ is the magnetocrystalline anisotropy, λ is the magnetostriction coefficient, σ is the inner stress, a and b are constants.

Figure 3:

Thermal variation of initial permeability (μ_i) for NiZn ferrite samples.

As in Figure 3 (tested at 10kHz), all samples exhibit a ferromagnetic behavior that the initial permeability of samples slowly rise with temperature up to the Curie temperature (T_c) and drop to zero sharply. This is attributed to the K₁ decreases far more quickly than M_s when temperature changes. According to eq. (4), μ_i increases with temperature increases to the Curie temperature [36]. When the temperature over Curie temperature, the samples would exhibit a paramagnetism, so μ_i falls sharply.

With a further observation to Figure 3, it is noticed that, the Curie temperature (T_c) of sample D decreases with La–Co co-substitution. The T_c mainly depends on the A–B superexchange interactions. No-magnetic La³⁺ ions substitutes Fe³⁺ ions on B sites, which results in weakening of the A–B superexchange interactions from Fe_A³⁺–O²–Fe_B³⁺ and decreasing the ferromagnetic region [37]. In addition, Co²⁺ substitutes Ni²⁺ on B sites and the T_c of CoFe₂O₄ (525°C) is less than that of NiFe₂O₄ (585°C) [38]. Hence, the T_c decreases by substituting La³⁺-Co²⁺ ions.

Frequency dependence of initial permeability (μ_i)

Figure 4 presents the variation of initial permeability with frequency in the range from 10 kHz to 1 GHz. It is well known that the initial permeability of NiZn ferrites is related to two different magnetizing mechanisms: domain wall motion and spin rotation [39]. At lower frequency, the value of initial permeability is mainly contributed by domain wall motion. The domain wall motion is dominated by the grain size, and increases with the increase of grain size. Therefore, big grain size has advantage in initial permeability [40]. As increasing frequency, spin rotation makes a major contribution to the initial permeability. The spin rotation is determined by the chemical composition which is related to the magnetic superexchange interactions between A-sites and B-sites. At higher frequency, a higher initial permeability can be attributed to a reinforce of A–B superexchange interactions [41]. From the above parts we have known that the A–B superexchange interactions of sample D is the weakest. Hence, it has been indicated that the initial permeability is decreased for La–Co co-substituted NiZn ferrite (sample D) in the frequency of 10 kHz to 1 GHz.

Figure 4:

Frequency variation of initial permeability (μ_i) for NiZn ferrite samples.

From Figures 3–4 we can observed that the value of initial permeability (μ_i) of unsubstituted ferrite (sample A) is larger than that of other samples. Relying on above analyses, a high initial permeability of sample A depends on chemical composition and microstructural modification such as grain size, magnetocrystalline anisotropy, A–B superexchange interactions, etc.

Resistivity (ρ)

The observed resistivity (ρ) at room temperature is summarized in Table 3. It can be seen that the resistivity increases from 4.5×10⁶ to 9.2×10⁶Ω/cm with Co substitution, to 7.3×10⁶Ω/cm with La substitution and 14.7×10⁶Ω/cm with La–Co co-substitution. This can be explained by the decrease in Fe²⁺ and the formation of secondary phase (LaFeO₃). We have known that the electron exchange between Ni²⁺ and Fe³⁺ can be described as the relation Ni2++Fe3+⇔Ni3++Fe2+ by the Verwey mechanism [42]. According to the relation, the reduction in Fe²⁺ is due to the substitution of Co²⁺ on Ni²⁺ site impedes the Verwey mechanism, thereby increasing resistivity. Meanwhile, the formation of secondary phase (LaFeO₃) on NiZn ferrites grain boundaries hinders the contribution of the electron hopping between Fe³⁺ and Fe²⁺. Finally, smaller grain sizes and abundant grain boundaries are against the flow of electrons [43]. As a result, it is concluded that the resistivity increases with La–Co substitution.

The power loss (P_cv)

As we have known, the power loss (P_cv) usually can be divided into hysteresis loss (P_h), eddy current loss (P_e) and residual loss (P_r) in NiZn ferrites [44]. At low frequency (less than 1 MHz), the hysteresis loss (P_h) is much bigger than eddy current loss (P_e) and residual loss (P_r). So the power loss can be expressed as P_cv ≈ P_h. The hysteresis loss depends on microstructure, magnetocrystalline anisotropy, Saturation magnetization and coercive field, and it has an inverse proportion to initial permeability, i.e. P∝h1/μi3. However, at high frequency (more than 1 MHz) P_h would be neglected, the power loss is mainly attributed to the eddy current loss (P_e) and residual loss (P_r), i.e. P_cv ≈ P_e+P_r. The P_e has been observed to decrease in NiZn ferrites with the increase in resistivity (ρ) and decrease in grain size (D), while the value of P_r to be inversely related to the number of Fe²⁺ ions and the size of grains [45].

The relationship between the power loss and exciting flux density (B_m) at 20 kHz of samples is shown in Figure 5. According to the description in above part, the predominant factor in P_cv is P_h when the samples are excited at 20 kHz. Due to the effect of domain wall movement, the P_h of samples increases as increasing in B_m, which is in agreement with the observation in Figure 5. It also can be seen that the sample D with La–Co substitution has the higher P_cv. This behavior can be related to the fact that sample D has a smaller value of μ_i, which leads to a higher P_h. In addition, the sample D has smaller grain size and more grain boundaries, which induces the higher P_h [46].

Figure 5:

The relationship between power loss (P_cv) and flux density (B_m) at 20kHz.

Frequency dependence of P_cv for samples at a condition of B_m=10 mT is illustrated in Figure 6. Less than 1 MHz, the sample D has the higher P_cv, the similar result has been displayed in Figure 5. As increasing frequency, the P_cv of sample D is lower than other samples. We have known that the P_cv can be regarded as the sum of P_e and P_r at higher frequency. Observed from Tables 2 and 3, the sample D has smaller grain size and higher resistivity, which results in the lower P_e. Furthermore, substituting La³⁺ and Co²⁺ ions leads to a decrease in number of Fe²⁺ ions, which is beneficial to decrease P_r. Consequently, with a lower P_cv over 1 MHz, the sample D is suitable to applications in high frequency [47].

Figure 6:

The relationship between power loss (P_cv) and frequency at 10mT.