3.1. Phase and Microstructure
Figure 1 shows the XRD patterns of the Ni
0.22Cu
0.31Zn
0.47Fe
2O
4 ferrites doped with 0.3 wt% Bi
2O
3 +
xCuO (
x = 0.2, 0.4, 0.6, and 0.8 wt%). The diffraction patterns revealed that all the ferrites exhibited the cubic spinel single-phase structure (JCPDS card No. 51-0386); the XRD peaks corresponded to the (220), (311), (400), (511), and (440) crystal planes of this structure, as shown in
Figure 1. The XRD patterns demonstrated that the low-temperature sintering (900 °C) of the doped NiCuZn samples was successful, and the addition of a small quantity of Bi
2O
3–CuO had no influence on the formation of the NiCuZn polycrystalline spinel structure.
Figure 2 shows the SEM images of the NiCuZn samples with different Bi
2O
3–CuO contents at ×10K magnification. The crystal grains and grain boundaries could be clearly observed in all samples. These SEM results indicate that the addition of 0.3 wt% Bi
2O
3 and various amounts of CuO was beneficial for reducing the sintering temperature of NiCuZn, so that the polycrystalline phase could be successfully synthesized at a sintering temperature of 900 °C. As the CuO content increased, the particle size and pores changed. Specifically, for
x = 0.2 wt% (the Bi
2O
3 amount was constant at 0.3 wt%), the microstructure of the sample was not dense, with a small number of small grains and numerous pores. As x increased to 0.6 wt%, the grain size gradually became uniform, the density of the sample increased, and the number of pores decreased. As x increased further to 0.8 wt%, a structure combining small and large grains appeared; furthermore, the grains were extremely large and not uniform in size. This phenomenon was related to the CuO flux. The increase in CuO content can effectively promote the densification of the sample, but as the CuO content exceeds a certain threshold, a typical bimodal heterogeneous structure appears; this is similar to what happens when over-doping a material. Therefore, when Bi
2O
3–CuO was added, a solution–reprecipitation process occurred. At this point, the activation energy required for grain growth decreased, and the grain size and density increased accordingly. Therefore, incorporating an appropriate amount of Bi
2O
3–CuO into NiCuZn ferrites can reduce the sintering temperature and improve the microstructure of the sample, which in turn affects the magnetic properties of the sample.
Figure 3 shows the schematic of the low-temperature sintering mechanism of the sample with the addition of the Bi
2O
3–CuO flux. When the NiCuZn ferrite was sintered at a sintering temperature greater than 800 °C, the Bi
2O
3–CuO flux started to soften, the crystal grains started to rearrange, and the pores started to be filled. As the sintering temperature continued to increase, the grains gradually started to grow because the capillary force generated by the liquid phase formed by Bi
2O
3–CuO at the grain boundaries promoted grain growth, causing the grains to increase gradually in size. As the sintering temperature was further increased to 900 °C, that is, the final stage of the solid-state sintering process, the grains had sufficient energy to grow fully, and they were homogenized and densified; this was how the fully reacted NiCuZn ferrite was finally obtained via low-temperature sintering. The Bi–O and Cu–O ionic bonds in the sample absorbed energy, broke, and ionized; therefore, the addition of an excessive Bi
2O
3–CuO flux amount led to an excessive number of free Cu
2+ and Bi
3+ ions, which resulted in abnormal grain growth.
Figure 4 shows the grain size distribution of the samples with different Bi
2O
3–CuO flux contents. As shown in
Figure 4, as the Bi
2O
3–CuO content increased, the average grain size gradually increased, and more large-sized grains appeared. For
x = 0.2 wt%, approximately 86.8% of the grains had sizes in the range of 0.5–1.7 μm. For
x = 0.6 wt%, around 89.6% of the grains have sizes in the range of 0.7–2.1 μm. It can be seen from the histograms that there were no extremely small or abnormally large grains. This was mainly due to the fact that at this sintering temperature, the addition of an optimal Bi
2O
3–CuO amount provided a suitable activation energy, enhanced the compactness of the sample, effectively suppressed the growth of abnormal grains, and finally resulted in the formation of a uniform and dense microstructure with a narrow grain-size distribution. For
x = 0.8 wt%, approximately 88.2% of the grains had sizes in the range of 0.7–2.5 μm, and 3.4% of the grains were abnormally large (with sizes in the range of 2.7–2.9 μm); this was related to the excessive number of Cu
2+ and Bi
3+ ions that were generated at such a high x value. The obtained histograms are in agreement with the above analysis.
Figure 5 shows the bulk density of the NiCuZn samples. The bulk density was measured via Archimedes’ method at room temperature using distilled water as the buoyancy liquid. The values of the bulk density were 4.43, 4.62, 4.88, and 4.95 g/cm
3 for
x = 0.2, 0.4, 0.6, and 0.8 wt%, respectively. The bulk density increased monotonically with increasing Bi
2O
3–CuO content and was thus consistent with the trend inferred from the SEM images. Porosity was also a key factor affecting the magnetic and dielectric properties of samples. Porosity and bulk density are closely related and there is an inverse relationship between them. It can be expressed by the following formula: Porosity = 1 − bulk density/theoretical density. The calculated data are shown in
Table 1. Fitting results for the XRD patterns were accomplished using the Jade 6.0 software, and the theoretical density was calculated, and is given in
Table 1. It can be seen that the porosity first decreased and then increased, which also corresponded to the microstructure of the SEM image. The density of a sample is related to its magnetic, dielectric, and gyromagnetic properties. Analysis of these properties is described in the following section.
3.2. Soft Magnetic Properties
Figure 6 shows the variations in the complex permeability spectra (μ′ and μ″) of the samples with different Bi
2O
3–CuO concentrations in the frequency range of 1 MHz–1 GHz. It can be seen from the figure that with the increase in the Bi
2O
3–CuO flux content, the magnetic permeability (μ′ @1 MHz) first increased and then decreased, while μ″ changed to a smaller extent. Interestingly, a lower value of μ″ endows the sample with a better quality factor (Q). The μ′ values at 1 MHz were 224.2, 230.5, 245.4, and 240.5 for the four samples, respectively. The permeability increased significantly and peaked at
x = 0.6 (μ′ = 245.4), mainly due to the increase in the sample density and composition. The magnetic permeability of ferrites is mainly determined by their composition, microstructure, porosity, and density [
12]. The porosity causes the magnetic permeability of the sample to not change linearly with the doping amount, improving the increase in the magnetic permeability. In addition to the changes in porosity and density caused by the experimental process, there are many factors that affect the magnetic permeability of NiCuZn ferrite. According to the literature, the key factors are as follows: (i) the saturation magnetization
Ms of the NiCuZn ferrites; (ii) the magnetocrystalline anisotropy constant K1 and the hysteresis stretching coefficient λ0; and (iii) the microstructure (pore and grain sizes). The relationship between the initial permeability, saturation magnetization, and grain size can be expressed as:
where
μi is the magnetic permeability and
D is the average grain size. The
Ms of the samples is closely related to their composition. The Ni
0.22Cu
0.31Zn
0.47Fe
2O
4 composition used in this work had a better saturation magnetization than other NiCuZn compositions [
17,
18]. Indeed, the
Ms value of NiCuZn ferrites is unlikely to vary significantly, and increasing
Ms results in a higher
K1, as shown by the following equation:
where
Hc is the coercive field. By substituting Equation (3) into Equation (2), it can be seen that the change in magnetic permeability is mainly related to the saturation magnetization and the average grain size. With the increase in the Bi
2O
3–CuO content, due to the liquid-phase sintering mechanism, the grain growth in the NiCuZn ferrites is promoted, the grains increase in size until they are fully grown, and the uniformity and compactness of the ferrites increase. The best low-temperature-sintered NiCuZn ferrite was obtained for
x = 0.6 wt%. For this Bi
2O
3–CuO content, the magnetic permeability was the highest (245.4). For
x = 0.8 wt%, the permeability was reduced due to the occurrence of abnormal grain growth. Therefore, by adding Bi
2O
3–CuO to NiCuZn ferrites, their microstructure can be tailored, and the magnetic properties can be correspondingly tuned.
Figure 7 shows the complex permittivity of the NiCuZn ferrites as a function of frequency between 1 MHz and 1 GHz.
Figure 7a shows the measured dielectric constant
ε′, and
Figure 7b shows the measured dielectric loss tangent (tan
δ =
ε″/
ε′). As shown in the figure, the values of
ε′ (@1 MHz) for
x = 0.2, 0.4, 0.6, and 0.8 wt% were 26.8, 25.9, 24.4, and 23.1, respectively. The dielectric constant of the sample did not change linearly with the doping amount because, in addition to the change in electronic polarization and microstructural changes caused by the doping amount, the porosity also affects the dielectric constant of the sample. This resulted in a difference between the theoretically predicted value of the dielectric constant of the sample and the experimental value, and experiments were necessary. This dependence of
ε′ on the CuO content may have been related to electronic polarization and microstructural changes. The value of
ε′ (@1 MHz) decreased with increasing Bi
2O
3–CuO content, which was due to the fact that the Bi
3+/Cu
2+ ions increased the local charge and reduced the dielectric constant. The Bi
3+/Cu
2+ ions present in the sample had a strong conductivity and a low dielectric constant. The permittivity remained stable over a wide frequency range, which is a typical dielectric behavior of NiCuZn ferrites [
16]. According to previous studies, NiCuZn ferrites are mainly characterized by four polarization mechanisms, namely electronic polarization (
αe, which occurs at 10
15 Hz), ionic polarization (
αa, which occurs at 10
10–10
13 Hz), dipolar polarization (
αo, which occurs at 10
3–10
6 Hz), and interfacial polarization (
αi, which occurs below 10
3 Hz). These different polarization mechanisms contribute differently to the overall polarization of the ferrites at different frequencies. However, as the NiCuZn ferrites were prepared via the traditional solid-state reaction method, their dielectric behavior was affected by many other factors in addition to the polarization, including grain boundary defects, changes in the free charges, and distortion effects. The dielectric loss had a similar behavior to that of
ε′. This may be correlated to the fact that domain wall motion has droop values, and hence the losses were lower. The dielectric loss tangent was small and ranged from 0.5 × 10
−3 to 3 × 10
−3. The presence of Cu
2+ ions in the samples is one of the reasons for the small dielectric loss tangent across the investigated frequency band. tan
δ can be expressed as:
where tan
δ0 is the dielectric loss of a densely structured material,
P is the porosity, and
C is a constant. Therefore, obtaining a suitable NiCuZn ferrite structure with a low number of pores at an appropriate CuO content is important for reducing the dielectric loss. The dielectric loss tangent is a key evaluation parameter when a material is used in an electronic device, as large dielectric losses result in electrical energy consumption and cause the device to heat up. This heating can damage the insulation and even affect the normal operation of the device.
Figure 8a shows the magnetic hysteresis loops (
M–
H) measured up to 2.5 kOe at room temperature. All NiCuZn samples showed a typical soft magnetic behavior and a low coercivity under an external magnetic field. The specific values of the
Ms and
Hc of the ferrites with different Bi
2O
3–CuO contents were calculated and are displayed in
Figure 8b. The results show that
Ms and
Hc gradually increased with increasing
x. For
x = 0.2, 0.4, 0.6, and 0.8 wt%, the
Ms values were 24.32, 25.65, 26.58, and 28.06 emu/g, respectively, and the
Hc values were 29.52, 32.89, 34.24, and 45.86 Oe, respectively. The variation in
Ms with CuO content can be attributed to the modification of the microstructure of the ferrites due to the incorporation of the magnetic ions (Cu
2+). It has been reported that a high density and a uniform grain size are beneficial for obtaining ferrites with a high
Ms value. As discussed above, the increase in the Cu
2+ ion content led to an increase in the ferrite density and grain size, which in turn increased the
Ms value. With the introduction of Cu
2+ ions, the defects of the sample were increased, which affected the pinning and increased the resistance to domain wall displacement, thereby increasing the
Hc.
3.3. Gyromagnetic Properties
Figure 9 shows the FMR linewidth (Δ
H) of the NiCuZn samples with various amounts of added Bi
2O
3–CuO and the corresponding fittings using a Lorentzian function. The experimental data were fitted well using the following Lorentz distribution:
where
A is the area between the curve baseline and the curve and
w is the full width at half maximum; the other fitting parameters are listed in
Table 2. The
R2 values of the parameters derived from the fitting were all greater than 0.987, demonstrating the validity of using a Lorentz distribution to fit the data. The Lorentzian curve fits the data better when the FMR linewidth is smaller.
Figure 10 shows the 4π
Ms and Δ
H of the NiCuZn ferrites as a function of the Bi
2O
3–CuO content. The value of 4π
Ms was determined by the saturation magnetization and density of the sample. The results show that as the Bi
2O
3–CuO content increased, 4π
Ms increased monotonously, while Δ
H first decreased and then increased. For
x = 0.08 wt%, 4π
Ms reached the maximum value of 1744 Gauss. For
x = 0.06 wt%, Δ
H reached the minimum value of 228 Oe. An appropriate amount of Bi
2O
3–CuO promotes grain growth in the NiCuZn ferrites, which increases the
Ms, density, and average grain size, resulting in an increase in 4π
Ms. For
x = 0.2, 0.4, 0.6, and 0.8 wt%, the values of 4π
Ms were 1353, 1488, 1629, and 1744 Gauss, respectively, and the Δ
H values were 370, 292, 228, and 235 Oe @9.3 GHz, respectively. Both 4π
Ms and Δ
H are important gyromagnetic parameters of microwave ferrites, and determine whether they are suitable for use in microwave devices. Main performance (4π
Ms) is related to the loss, bandwidth, and power capacity of microwave devices. According to previous research [
15], the change trend in Δ
H also can be explained by the following equation:
where Δ
Hint is the intrinsic line widths,
Ha is the random anisotropy field, and the last part is attributed to the porosity of the grains. Thus, the reduction in Δ
H was due to an enhancement of 4π
Ms and an increase in porosity. The results imply that the reduction in small grains can enhance the uniformity of ferrite grains and lower Δ
H via appropriate CuO substitution [
19,
20]. The Δ
H is a macroscopic physical quantity that reflects the damping experienced by the magnetization during its precession. It is related to the forward loss and working bandwidth of the device. The Δ
H should be as narrow as possible.