Phase Formation, Microstructure, and Permeability of Fe-Deficient Ni-Cu-Zn Ferrites (II): Effect of Oxygen Partial Pressure

Abstract

We have investigated the phase formation, microstructure, and permeability of stoichiometric and Fe-deficient Ni-Cu-Zn ferrites of composition Ni_0.30Cu_0.20Zn_0.50+zFe_2−zO_4−(z/2) with 0 ≤ z ≤ 0.06 sintered at 1000 °C in various oxygen partial pressures p_O2, which range from 0.21 atm down to 10⁻⁵ atm. The density of the sintered samples is almost independent of the p_O2, whereas the grain size of the Fe-deficient ferrites decreases in more reducing atmospheres. Stoichiometric ferrites show a regular growth of single-phase ferrite grains if sintered in air. Sintering at p_O2 ≤ 10⁻² atm leads to the formation of a small amount of Cu₂O at grain boundaries and triple points. Fe-deficient compositions (z > 0) form Cu-poor stoichiometric ferrites, which coexist with a minority CuO phase homogeneously distributed between the grains after sintering in air. At p_O2 ≤ 10⁻² atm, the CuO grain boundary phase starts to transform into Cu₂O, which concentrates at some triple points at p_O2 = 10⁻² atm, and it is more homogeneously distributed between the ferrite grains at the lower p_O2. Formation of the Cu oxide second phases is investigated using XRD, SEM, and EDX. The permeability at 1 MHz of the stoichiometric ferrites (z = 0) is between µ′ = 200 and µ′ = 300 within the studied range of the p_O2. The permeability at 1 MHz of the Fe-deficient samples decreases with the p_O2, e.g., from µ′ = 750 at p_O2 = 0.21 atm to µ′ = 320 at p_O2 = 10⁻⁵ atm for z = 0.02, respectively.

1. Introduction

Ni-Cu-Zn ferrites are an important group of soft magnetic materials used in many applications, which include power ferrites, EMI devices, and multilayer inductors. These ferrites exhibit a combination of interesting features, including a low sintering temperature T_s, high resistivity, medium permeability, low loss, and good performance up to MHz frequencies [1,2,3,4]. Since the magnetic permeability is strongly correlated to the ferrite composition and microstructure, it is necessary to investigate in detail the effect of sintering conditions on microstructure and magnetic properties in order to design specific sintering protocols for optimum performance. The sintering of bulk samples of Ni-Cu-Zn ferrites is typically performed between 900 °C and 1100 °C, whereas for applications in multilayer inductors, the ferrites are cofired with silver metallization at as low as T_s = 900 °C. Many studies report on the use of sintering additives, microstructure formation, permeability, and DC bias superposition behavior [5,6,7,8]. The influence of composition on the sintering behavior and magnetic properties of Ni-Cu-Zn ferrites was also reported [9,10]. Typically, iron-deficient compositions are used (<50 mol% Fe₂O₃), which translates into a spinel composition with less than two Fe per formula unit, for example, Me_1.02Fe_1.98O_3.99, compared to stoichiometric ferrites with 50 mol% Fe₂O₃ and formula unit MeFe₂O₄. It was shown that such ferrite compositions are beneficial in enhancing densification [11,12,13,14]. As a consequence of Fe deficiency, secondary phases were found to precipitate at grain boundaries and to possibly affect magnetic properties. Tenorite CuO was found to form at triple points or grain boundaries in Fe-deficient Ni-Cu-Zn ferrites after sintering at 900 °C [14] and at 1100 °C [15]. When transmission electron microscopy (TEM) was used, the formation of metallic copper precipitates at grain boundaries was observed [16], whereas other authors report the formation of ZnO secondary phase [17]. A detailed study on the phase composition and microstructure of stoichiometric Ni-Cu-Zn ferrites explored the precipitation of CuO and ZnO after sintering at 1200 °C [18,19].

In the first part of this contribution [20], we reported a systematic study on phase formation, microstructure, and permeability of Fe-deficient Ni_0.30Cu_0.20Zn_0.50+zFe_2−zO_4−(z/2) ferrites with 0 ≤ z ≤ 0.06 as a function of sintering temperature between 900 °C and 1150 °C in air. In part II, we will describe in detail the influence of oxygen partial pressures, p_O2, varying between air (0.21 atm) and 10⁻⁵ atm at a sintering temperature of T_s = 1000 °C. It is found that the grain size decreases with decreasing p_O2. For z > 0, CuO precipitates at grain boundaries and are transformed into Cu₂O at lower oxygen partial pressure. The amount of Cu oxide secondary phases increases with Fe deficiency z. The permeability of the samples is reduced with decreasing p_O2 and grain size in the range of predominant regular grain growth.

2. Materials and Methods

Ferrite powders of composition Ni_0.30Cu_0.20Zn_0.50+zFe_2−zO_4−(z/2) with z = 0.00, z = 0.02, and z = 0.06 were prepared using the standard ceramic route. α-Fe₂O₃ (Voest Alpine, Austria, HPG80); NiO (Inco, Black Nickel Oxide, Grade F); CuO (Alpha Aesar, Germany and ZnO (Harzsiegel Heubach, Germany, standard grade) were used as starting materials. They were wet mixed for 12 h in a rotating polyethylene container with the addition of zirconia grinding media. After drying, the powder was calcined at 900 °C for 2 h and subsequently milled in a planetary ball mill (Pulverisette 7; Fritsch, Idar-Oberstein, Germany) in POM grinding beakers for 4 h (170 rpm) using zirconia grinding media (diameter 1 mm). The powders were compacted using polyvinyl alcohol as a binder to give pellets for sintering studies or toroids for permeability measurements. The samples were sintered for 4 h at 1000 °C (heating/cooling rate 5 K/min) in a PC-controlled gas atmosphere tube furnace with oxygen partial pressure between 0.21 atm ≤ p_O2 ≤ 10⁻⁵ atm (21% O₂ ≤ p_O2 ≤ 0.001% O₂). The gas mixtures were provided by mixing nitrogen and oxygen gas with mass flow controllers, and the p_O2 was monitored at the sample position in the furnace using a zirconia-based oxygen sensor system (Zirox GmbH, Greifswald, Germany). Gas flow rates were constantly held at 20 L/h. The phase composition was studied using X-ray diffraction XRD with Cu-K_α radiation (Bruker AXS, Karlsruhe, Germany, Advance D8). Rietveld refinements were performed using the software TOPAS version 6 (Bruker AXS). The particle size of the powders was measured in aqueous suspensions using laser diffraction (Malvern Mastersizer 2000). The specific surface S of the powders was determined from nitrogen adsorption isotherms (BET, Nova 2000, Quantachrome Instruments, Boynton Beach, FL, USA); a mean particle size d_BET was estimated using the relation d_BET = 6/ρ·S (with density ρ; assuming spherical particles). The bulk density of sintered samples was determined using Archimedes’ method with heptane as a liquid.

The microstructure of the samples was studied on polished and thermally etched samples with a scanning electron microscope (SEM, Ultra 55, Zeiss Microscopy GmbH, Jena, Germany). Samples were polished using 9 µm, 3 µm, 1 µm, and 0.25 µm suspensions for 10 min each step. Samples for microstructure investigations where high grain boundary contrast is desired were thermally etched by a short anneal at 900 °C in the same p_O2 as the original sintering run. The mean grain size G was determined using the thermally etched samples with the line intercept method in combination with a factor of 1.57, as proposed by Mendelson [21]. Elemental analysis was performed on polished samples, without an etching step, in the electron microscope, using a Bruker energy-dispersive X-ray spectroscopy (EDX) system. The permeability of sintered toroids was measured using an Agilent E4991A impedance/materials analyzer.

3. Results

3.1. Powder Properties

Single-phase ferrite powders were obtained after calcination at 900 °C (XRD results not shown here). After milling, the powders show a mean particle size of d₅₀ = 0.7 µm as measured using laser diffraction, which represents the size of powder aggregates. The specific surface of the ferrite powder is S = 5 m²/g, corresponding to a mean primary particle diameter of d_BET = 220 nm.

3.2. Sintering Behavior and Microstructure

Measurements of the mass of the pellets before sintering (after binder burnout at 600 °C for 5 h in air) and after sintering reveal a systematic mass loss (Figure 1). The stoichiometric ferrite (z = 0) shows a very small mass loss upon sintering in air. A significantly larger mass loss of about 0.3% is found after sintering at lower oxygen partial pressures of p_O2 ≤ 10⁻³ atm. The Fe-deficient samples (z = 0.02 and z = 0.06) exhibit a very similar mass loss in air and an enhanced mass loss at lower p_O2, which increases with z.

3.3. Microstructure

SEM micrographs of samples with different values of Fe-deficiency z sintered at 1000 °C in different p_O2 are presented in Figure 2. Thermally etched samples exhibit better grain boundary contrast and were used to determine the grain size. Another set of polished and not thermally etched samples (Figure 3) shows a more realistic microstructure with porosity and secondary phases (and phase distribution) but a lower grain boundary contrast.

By comparing Figure 2 and Figure 3, it is clearly visible that the secondary phase content (white areas) is much smaller in the micrographs of the polished and etched samples (Figure 2). Thermal etching at a temperature of 100 K below the sintering temperature (at the same p_O2 as during sintering) leads to recrystallization processes. Therefore, SEM micrographs without the thermal etch step (Figure 3) were used for quantitative determinations of phase content and composition (see below).

The variation of the sinter density after firing at 1000 °C for 4 h at different p_O2 is shown in Figure 4a. Stoichiometric Ni-Cu-Zn ferrite (z = 0.00) has a density of 5.231(6) g/cm³ after sintering in air, which is increased to about 5.30 g/cm³ (99%) upon reducing the oxygen partial pressure to ≤10⁻² atm. Ferrites with z = 0.02 exhibit excellent densification behavior with density at around 5.30 g/cm³ (99%) in all atmospheres; however, a small tendency of decreasing the density with lowering p_O2 seems to exist. For larger Fe-deficiency (z = 0.06), a somewhat reduced density is observed, with the density decreasing with a more reducing atmosphere.

The evolution of grain size vs. p_O2 (Figure 4b) confirms regular grain growth behavior for all samples; exaggerated grain growth was not observed. The stoichiometric ferrite (z = 0) has grains with an average size of 1.9(1) µm after sintering in air. Sintering in p_O2 = 10⁻² atm gives grains of 5.6 µm in size with a broader grain size distribution. Samples sintered at lower p_O2 show fine-grained microstructures. The Fe-deficient ferrites (z > 0.00) have grain sizes of around 6…7 µm after sintering in air, which smoothly decrease down to about 2…3 µm for samples sintered in p_O2 = 10⁻⁵ atm.

As revealed by electron microscopy, secondary phases exist in some of the sintered ferrites (Figure 3). Whereas the microstructure of the ferrite with z = 0.00 contains a significant content of a second phase at p_O2 ≤ 10⁻⁴ atm only, Fe-deficient ferrites (z > 0) show second phases in all samples. As already observed after sintering at different temperatures in the air (see part I of this publication [20]), the secondary phase is a Cu-rich oxide phase that accumulates at grain boundaries and triple points.

The corresponding Cu elemental maps measured using EDX reveal the concentration and distribution of Cu-rich phases in the microstructures of the sintered ferrites (Figure 5).

For z = 0, the samples sintered in air and 10⁻² atm exhibit a homogeneous Cu distribution, whereas at p_O2 ≤ 10⁻³ atm, Cu-rich islands start to appear in triple points between the grains, signaling the start of ferrite decomposition (Figure 5). In SEM micrographs (Figure 3), on the other hand, second phase formation was observed at p_O2 ≤ 10⁻⁴ atm. The Fe-deficient samples (z = 0.02 and z = 0.06) sintered in air have small Cu-rich regions, which are evenly distributed across the sample’s microstructure. After sintering at p_O2 = 10⁻² atm, both ferrites show larger Cu-rich regions, which are concentrated at some triple points. After sintering in more reducing atmospheres at p_O2 ≤ 10⁻³ atm, small Cu-rich islands tend to appear in many triple points homogeneously distributed between the grains of the main ferrite phase.

The chemical composition of the (i) matrix ferrite grains and (ii) triple points and grain boundary near regions were studied using energy dispersive X-ray analysis (EDX). The Cu content of the ferrite matrix grains significantly decreases (within the given resolution) for samples sintered at oxygen partial pressures between 10⁻² and 10⁻³ (Figure 6a). Please note that the Cu-concentration in the ferrite grains of samples with z = 0.06 is significantly smaller than for z = 0.00 and z = 0.02.

In contrast, the grain boundary-near regions start to develop different chemistries with completely different compositions, compared to matrix grains. In stoichiometric ferrite (z = 0.00), a second phase is present after sintering at p_O2 ≤ 10⁻³ atm (Figure 5). These second-phase regions are rich in Cu (about 55 at%) and O with some Fe (Figure 6b). The measured concentrations of Fe in the grain boundary and triple point regions might be an artifact of the EDX analysis since part of the measured Fe X-ray intensity might be emitted from surrounding ferrite grains (although the triple point areas are larger than 1–2 µm in diameter). On the other hand, the dissolution of iron in tenorite Fe_xCu_1−xO has been reported [22,23].

The elemental distribution analysis of grain boundary-near regions for the Fe-deficient ferrites shows somewhat different results (Figure 6c,d). Cu-rich grain boundary regions are also observed after sintering in air. Reducing the p_O2 during sintering leads to a significant increase in the Cu-concentration and a reduction in the O content, with maximum Cu contents of about 60 at% Cu at p_O2 = 10⁻³ atm. This might indicate a partial phase transition from tenorite CuO (theor. 50 at% Cu and O) to cuprite Cu₂O (theor. 66 at% Cu and 33 at% O) to take place in the Cu-oxide grain boundary phase. Further reduction of the p_O2 results in slightly reduced Cu contents of second phases at grain boundaries. Note that the grain size of the samples sintered at low p_O2 is reduced to about 2…3 µm; hence, the error of the EDX analysis of the grain boundary areas is large, and the signals might contain information from the surrounding grains.

3.4. Phase Formation

The phase composition of the ferrites was also investigated using X-ray diffraction (XRD). A single-phase ferrite with a spinel-type structure was found at z = 0 after sintering in atmospheres with p_O2 ≥ 10⁻³ atm. After sintering at lower p_O2, the strongest peak of cuprite Cu₂O starts to appear with low intensity at about 2θ = 36.4° (Figure 7a). The XRD pattern of the sample with z = 0.02 and z = 0.06 sintered in air exhibits an additional peak besides those of the spinel at 2θ = 38.7°, which is identified as (110) reflection of tenorite CuO. This peak is hardly detectable in the ferrite with z = 0.02 since, in that case, the CuO concentration seems to be close to the XRD detection limit. If the partial pressure of oxygen in the sintering atmosphere is reduced, this CuO peak starts to disappear, and a gradual transition of the grain boundary phase from tenorite CuO to cuprite Cu₂O is observed (Figure 7b,c), which is more pronounced for the ferrite with z = 0.06. The phase compositions of the samples were determined from Rietveld refinements of XRD powder data.

The ferrite lattice parameters, the concentrations of ferrite, tenorite CuO, and cuprite Cu₂O are shown as a function of p_O2 of the sintering atmosphere in Figure 8a–d.

The lattice parameters a₀ of the cubic spinel ferrites with z = 0.00, 0.02, and 0.06 increase with z. Moreover, a₀ also increases somewhat with lowering the p_O2 (for each value of the Fe-deficiency z), indicating a small change in ferrite composition.

The content of ferrite in the samples with z = 0.00 is >99 wt%; however, a slight decrease in ferrite content is observed with the lowering of the p_O2. Correspondingly, the CuO content is negligibly small or within the detection limit (<0.3 wt%) for all samples. On the other hand, the concentration of Cu₂O (Figure 8d) increases with decreasing p_O2 and reaches almost 0.8 wt% at p_O2 = 10⁻⁵ atm.

For the Fe-deficient ferrite with z = 0.02, the ferrite content is 99 wt% after sintering in air and decreases to 98.6 wt% at p_O2 = 10⁻⁵ atm. The CuO content is small (Figure 8c), and the Cu₂O content is somewhat larger, compared to z = 0.00 and reaches 1.1 wt% at p_O2 = 10⁻⁵ atm (Figure 8d). The situation is somewhat clearer for ferrites with larger Fe-deficiency of z = 0.06: the ferrite content (Figure 8b) decreases from 98.9 wt% after sintering in air to 97.5 wt.% at p_O2 = 10⁻⁵ atm. The CuO concentration (Figure 8c) is 0.8 wt% in air (which is the largest one for the three ferrites sintered in air) and slightly decreases to 0.4 wt% at p_O2 = 10⁻⁵ atm. Simultaneously, the cuprite Cu₂O concentration (Figure 8d) is negligibly small after sintering in air but increases to more than 2 wt% after sintering at p_O2 = 10⁻⁵ atm. In summary, the concentration of Cu-rich second phases increases with Fe-deficiency z and with decreasing p_O2 and reaches the following maximum total concentrations at p_O2 = 10⁻⁵ atm: 1.3 ± 0.1 wt.% for z = 0.00, 1.7 ± 0.5 wt.% for z = 0.02, and 2.9 ± 0.1 wt.% for z = 0.06.

3.5. Magnetic Permeability

The complex permeability spectra of the samples are shown in Figure 9. The real parts of the permeability vs. frequency curves exhibit some typical features. The samples show almost constant values of the real part of the permeability µ′ from 1 MHz until a bump at a certain frequency appears, with µ′ strongly decreasing at a higher frequency. The imaginary part of the permeability µ″ has a maximum at the resonance frequency. In accordance with Snoek’s rule, samples with large absolute values of permeability have low resonance frequencies (Figure 9b,c). The samples of the stoichiometric ferrite (z = 0.00) sintered at p_O2 ≤ 10⁻³ atm exhibit a somewhat unusual behavior with a permeability µ′ decreasing between 1 MHz and about 10 MHz (Figure 9a). Usually, the µ′ vs. f curves have a plateau at low frequency below the resonance frequency [24,25], as also observed for ferrites with z > 0 (Figure 9b,c). Simultaneously, µ″ of samples with z = 0 sintered at p_O2 ≤ 10⁻³ atm (Figure 9a) is unusually large at low frequency, indicating additional loss contributions from a second phase.

The variation of the permeability µ′ at 1 MHz vs. p_O2 of the sintering atmosphere is shown in Figure 10. Stoichiometric ferrites (z = 0.00) have lower permeability, roughly between µ′ = 200 and µ′ = 300 within the studied range of oxygen partial pressure p_O2. Fe-deficient ferrites with z = 0.02 show the largest permeability of µ′ = 700 for samples sintered in air. Both Fe-deficient ferrites (z = 0.02 and 0.06), however, show the same general trends: (i) Maximum permeability is found after sintering in air; (ii) The permeability of the Fe-deficient ferrites decreases at lower p_O2.

4. Discussions

The densification, microstructure, phase composition, and magnetic properties of stoichiometric and Fe-deficient ferrites Ni_0.30Cu_0.20Zn_0.50+zFe_2−zO_4−(z/2) with 0.00 ≤ z ≤ 0.06 strongly depend on the sintering conditions, i.e., the sintering temperature T_s, dwell time, and oxygen partial pressure p_O2. It was shown that Fe-deficient Ni-Cu-Zn ferrites contain CuO as a second phase after sintering at 900 °C in air and that nominally Fe-deficient (sub-stoichiometric) compositions consist of a mixture of a Cu-poor stoichiometric main ferrite phase and CuO as secondary phase [14]:

(1)$\mathrm{C}{\mathrm{u}}_{\mathrm{y}}\mathrm{N}{\mathrm{i}}_{1-\mathrm{x}-\mathrm{y}}\mathrm{Z}{\mathrm{n}}_{\mathrm{x}+\mathrm{z}}\mathrm{F}{\mathrm{e}}_{2-\mathrm{z}}{\mathrm{O}}_{4-\mathrm{z}/2}\to \left({\displaystyle \frac{2-\mathrm{z}}{2}}\right)\mathrm{C}{\mathrm{u}}_{{\displaystyle \frac{2\mathrm{y}-3\mathrm{z}}{2-\mathrm{z}}}}\mathrm{N}{\mathrm{i}}_{{\displaystyle \frac{2-2\mathrm{x}-2\mathrm{y}}{2-\mathrm{z}}}}\mathrm{Z}{\mathrm{n}}_{{\displaystyle \frac{2\mathrm{x}+2\mathrm{z}}{2-\mathrm{z}}}}\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_4+{\displaystyle \frac{3\mathrm{z}}{2}}\mathrm{C}\mathrm{u}\mathrm{O}$

For ferrite compositions reported here (y = 0.20 and x = 0.50), Equation (1) results in the formation of a spinel Cu_0.17Ni_0.30Zn_0.53Fe₂O₄ and 0.03 CuO for a Fe-deficiency of z = 0.02, whereas for z = 0.06 the ferrite Cu_0.11Ni_0.31Zn_0.58Fe₂O₄ coexists with 0.09 CuO. The presence of a tenorite CuO grain boundary phase is likely to cause enhanced sintering activity and increased density of Fe-deficient ferrites at sintering temperatures between 900 °C and 1000 °C. In a previous study, we investigated the effect of T_s on the copper oxide grain boundary phase composition and on the microstructure and permeability of the ferrites [20]. Here, we discuss the effect of p_O2 of the atmosphere upon sintering at 1000 °C on the microstructure and magnetic performance of the ferrites.

As shown by SEM, stoichiometric Ni-Cu-Zn ferrite (z = 0.00) exhibits a homogeneous and fine-grained microstructure with regular grain growth after sintering at T_s = 1000 °C in air (Figure 3) and a single ferrite phase as confirmed by XRD (Figure 7). However, the sample sintered at p_O2 = 10⁻² atm has a larger density of 5.30(1) g/cm³ similar to the other samples with z = 0.00 sintered at low p_O2. In addition, the samples sintered at 10⁻² atm exhibit larger grains with an average size of G = 5.6(1.7) µm. Samples sintered under these conditions exhibit high density and larger grains, which seems to be right at the cross-over to exaggerated grain growth (as indicated by the large standard deviation). It has been demonstrated that grain growth in Ni/Zn ferrites sets in when the density is larger than a threshold value of about 98% [26], which seems to be the case here as well. Further reduction of the p_O2 seems to hinder grain growth by suppressing densification. Sintering at p_O2 ≤ 10⁻³ atm leads to the formation of a small amount of a cuprite Cu₂O secondary phase, as demonstrated by XRD (Figure 7 and Figure 8). As shown by SEM (Figure 3 and Figure 5), copper oxide is concentrated at some triple points, and EDX analysis (Figure 6) confirms that this phase is rich in Cu with >50 at% Cu.

Fe-deficient ferrites with z = 0.02 and z = 0.06 show homogeneous microstructures with regular grain growth (Figure 2). The average grain size decreases with decreasing p_O2. Simultaneously, EDX Cu distribution maps show the formation of Cu-rich regions at triple points between the ferrite grains. A quantitative EDX analysis revealed the Cu-oxide at the triple points to be tenorite CuO after sintering in air with about 24–27 at% Cu, 10–17 at% Fe, and about 50 at% oxygen (Figure 6c,d). After sintering at lower p_O2, the Cu content of the grain boundary near regions increases to reach about 67 at% at 10⁻³ atm, indicating a gradual transition into Cu₂O. The coexistence of Cu oxides and ferrite grains was confirmed using XRD (Figure 7). Moreover, a phase transition of the secondary phase from tenorite CuO to cuprite Cu₂O after sintering in more reducing atmospheres was confirmed. The slight increase in the cubic ferrite spinel lattice parameter a₀ vs. z and with reduced p_O2 (Figure 8a) points to a small change in the ferrite composition with z. This is consistent with the observation of decreasing Cu contents in the ferrite matrix grains with decreasing p_O2 (Figure 6a). As a result, the total amount of the secondary Cu-oxide phases increases with the decreasing p_O2 of the sintering atmosphere. In this context, it is worth pointing out that the observed mass loss of sintered samples (Figure 1) seems to correlate with the onset and intensity of segregation processes and secondary phase formation. For z = 0.00, the increase in mass loss between 10⁻² and 10⁻³ atm coincides with the beginning of the segregation of Cu-oxide grain boundary phases at this range of oxygen partial pressures p_O2. A decrease in CuO content and an increase in the Cu₂O phase content in the grain boundary near regions after sintering in more reducing atmospheres is confirmed from Rietveld refinements (Figure 8c,d). Obviously, the Cu oxide phase present at triple points and grain boundaries undergoes a phase transformation:

(2)$2\mathrm{C}\mathrm{u}\mathrm{O}\left(\mathrm{s}\right)\to {\mathrm{C}\mathrm{u}}_2\mathrm{O}\left(\mathrm{s}\right)+{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\mathrm{O}}_2\left(\mathrm{g}\right)$

at starting at about p_O2 ≤ 10⁻² atm and T_s = 1000 °C. This is in agreement with the phase diagram of the system CuO–Cu₂O [27].

The permeability of the ferrites with 0.00 ≤ z ≤ 0.06 is affected by the sintering atmosphere (Figure 10). The permeability (at 1 MHz) of Fe-deficient (z > 0.00) ferrites is larger than that of stoichiometric ferrite, which is due to enhanced grain growth in the presence of Cu oxide second phases. Decreasing the p_O2 of the sintering atmosphere results in reduced permeability, which is a consequence of smaller average grain sizes at more reducing conditions. Smaller grains tend to hinder the migration of domain walls, leading to a decrease in permeability. In addition, as discussed above, the formation of non-magnetic Cu-oxides as secondary phases at grain boundary or triple point areas by segregation from the ferrite matrix phase contributes to the reduction of permeability. Corresponding changes in the ferrite matrix compositions and possible variations in the cation distribution might also add to variations in magnetization and permeability. For z > 0.02, the larger amount of segregated, non-magnetic Cu oxide phases at triple points and grain boundaries tends to reduce the permeability.

As demonstrated in this study, the segregation of Cu oxide grain boundary phases, the corresponding variations in the matrix ferrite grain composition, and the microstructure are considered as major factors controlling the permeability of Fe-deficient Ni-Cu-Zn ferrites. These factors might be controlled by selecting proper sintering protocols with sintering temperature T_s and oxygen partial pressure p_O2 as main parameters.

5. Conclusions

The phase formation, microstructure, and magnetic permeability of Fe-deficient Ni-Cu-Zn ferrites Ni_0.30Cu_0.20Zn_0.50+zFe_2−zO_4−(z/2) (0 ≤ z ≤ 0.06) were investigated as functions of oxygen partial pressures p_O2 at a sintering temperature of 1000 °C:

• (1). Reduction of the oxygen partial pressure of the sintering atmosphere p_O2 leads to increasing segregation of Cu oxide grain boundary phases from the ferrite matrix phase, which begins at p_O2 between 10⁻² atm and 10⁻³ atm for the stoichiometric ferrite and at p_O2 between 0.21 atm and 10⁻² atm for iron-deficient compositions; the secondary CuO tenorite phase formed in air is transformed into Cu₂O cuprite at lower p_O2.

• (2). Mass loss during sintering correlates with segregation and grain boundary phase formation processes.

• (3). Segregation of Cu oxide grain boundary phases after sintering with lower p_O2 affects the densification, grain growth, and permeability of the ferrites.

• (4). Maximum permeability µ′ at 1 MHz is found for z = 0.02 sintered in air.

• (5). For Fe-deficient ferrites (z > 0), the permeability µ′ at 1 MHz decreases with decreasing p_O2.

• (6). Optimum sintering protocols (here, oxygen partial pressure at T_s = 1000 °C) need to be found for each composition z, where an interplay between an optimum ferrite matrix composition and Cu oxide grain boundary phase amount and composition leads to enhanced densification, normal grain growth, and enhanced magnetic permeability.

Author Contributions

Conceptualization, C.P. and J.T.; methodology, C.P.; investigation, C.P.; writing—original draft preparation, C.P.; writing—review and editing, J.T.; supervision, J.T.; project administration, J.T.; funding acquisition, J.T. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are available upon request from the authors.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures

Figure 1. Relative mass loss vs. pO2 after sintering at 1000 °C for ferrites with 0 ≤ z ≤ 0.06.

Figure 2. SEM micrographs (SE mode) of ferrites with z = 0.00, 0.02, and 0.06 sintered at 1000 °C in gas atmospheres with various pO2 (samples polished and thermally etched).

Figure 3. SEM micrographs (SE mode) of ferrites with z = 0.00, 0.02, and 0.06 sintered at 1000 °C in gas atmospheres with various pO2 (samples as fired and polished).

Figure 4. Sinter density (a) and grain size G (b) vs. pO2 after sintering at 1000 °C for ferrites with 0 ≤ z ≤ 0.06.

Figure 5. EDX maps of Cu-distribution in ferrites with z = 0.00, 0.02, and 0.06 sintered at 1000 °C in gas atmospheres with various pO2 (samples as fired and polished).

Figure 6. Chemical composition determined using EDX point scans vs. pO2 during sintering at 1000 °C of (a) Cu content in ferrite matrix grains (z = 0.00, z = 0.02, and z = 0.06) and element concentrations in triple points and grain boundary regions for the following: (b) z = 0.00; (c) z = 0.02; (d) z = 0.06.

Figure 7. XRD patterns of ferrites with z = 0.00 (a), 0.02 (b), and 0.06 (c) sintered at 1000 °C in gas atmospheres with various pO2.

Figure 8. Lattice parameters a0 (a), ferrite content (b), tenorite CuO content (c), and cuprit Cu2O content (d) from Rietveld refinements of ferrites with z = 0.00 (a), 0.02 (b), and 0.06 (c) sintered at 1000 °C in gas atmospheres with various pO2.

Figure 8. Lattice parameters a0 (a), ferrite content (b), tenorite CuO content (c), and cuprit Cu2O content (d) from Rietveld refinements of ferrites with z = 0.00 (a), 0.02 (b), and 0.06 (c) sintered at 1000 °C in gas atmospheres with various pO2.

Figure 9. Permeability spectra of ferrites with z = 0.00 (a), 0.02 (b), and 0.06 (c), sintered at 1000 °C in gas atmospheres with various pO2.

Figure 10. Permeability @ 1 MHz vs. pO2 of the sintering atmosphere of ferrites with 0.00 ≤ z ≤ 0.06.

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