Structural and Magnetic Properties of Cr-Substituted NiCuZn Ferrite

Phase characterization

XRD patterns of various Ni_0.2Cu_0.2Zn_0.6Fe_2–xCr_xO₄ (x = 0.0, 0.25, 0.5, 0.75 and 1.0) ferrites sintered at 1,150°C are shown in Figure 1. It is obvious that these samples were identified to be single spinel ferrite structure. No extra peak corresponding to any other phases can be detected. That is, Cr³⁺ substitutions do not affect the final crystal phase. And the diffraction peak shifts toward the higher angle a little with Cr substitution. According to the site preference energies of ions, Cr³⁺ ions have strong preference for B sites leading to the replacement of Fe³⁺ ions at octahedral sites. The radii of the Cr³⁺ ion (0.062 nm) is littler than that of the Fe³⁺ ion (0.067 nm). Thus, the shift in diffraction peak toward higher angle is caused by the substitution of Cr³⁺ ions for Fe³⁺ ions.

Figure 1:

The XRD patterns for various Ni_0.2Cu_0.2Zn_0.6Fe_2–xCr_xO₄ ferrites.

The lattice parameters and average crystallite sizes of the samples

The lattice parameters (a) and average crystallite sizes (D) of the Ni_0.2Cu_0.2Zn_0.6Fe_2–xCr_xO₄ ferrites as a function of Cr substitution content (x) are shown in Figure 2. The lattice parameters of the samples are calculated by using the relation: a2=(λ2/4sin2θ)⋅(h2+k2+l2), indicating a slightly decreased trend with Cr substitution. Average crystallite sizes of the samples are calculated using the Scherrer formula: D=0.9λ/β⋅cosθ, indicating a decrease with Cr substitution. The ionic radii of Cr³⁺ is very near the ionic radius of Fe³⁺, which indicates that Cr³⁺ ions can easily diffuse into the lattice to substitute Fe³⁺ ions at B site. However, the Cr³⁺ ion of radii is smaller than the Fe³⁺ ions, the Cr³⁺ ions thus enter into the lattice, and swell the lattice, then diminish the lattice parameter which results in distortion of lattice.

Figure 2:

Variation of lattice parameter and average crystallite sizes for the ceramic samples with various Cr content.

Density of the samples

Density plays an important role in the properties of polycrystalline ferrite. The effect of Cr substitution on the ρ is shown in Figure 3. Densities of all samples range from 4.95 to 4.80 g/cm³. The change of density of the total trend is decreasing, but a slight increase from x = 0.25 to 0.5. The increase in ρ can be attributed to the difference in atomic weight of initial and substituted cations (the atomic weight of Cr³⁺ (51.99 amu) < Fe³⁺ (55.85 amu)). The decrease in density may be due to intergranular/intragranular. According to Lange and Kellet [17], densification and grain growth are closely related. ρ decreases with the increase in Cr content, because the molecular weight of the each sample decreases significantly with the addition of Cr content.

Figure 3:

Density for the ceramic samples with various Cr content.

Magnetic properties

Figure 4 gives the permeability variation curves of samples with different Cr content. The initial permeability continually decreases with the increasing of Cr content at 1,150°C. The initial permeability can be expressed as μi∝Ms2/(αK+bλσ)[18], where μ_i is the initial permeability, M_s is the saturation magnetization, K is the crystal magnetic anisotropy, λ is the magnetostriction constant, σ is the inner stress, and α and b are constants. As the molecular magnetization can be described as M=Mb−Ma. On account of site occupancy tendency of ions, Cr³⁺ ions have strong site preference for B sites, and M_b decreases with the B sites replacements. Therefore, the net magnetic moment of M decreased at the same time. Moreover, the saturation magnetization (M_s) is defined as the vector of the magnetic moment within a unit cell and can be expressed as [19]:Ms=8M/a3, where a is the lattice constant. There is a little change from 8.386 to 8.345 Å, thus M is the leading cause of M_s changing. Therefore, M_s reduces gradually with the increasing Cr content due to decreased M. According to the aforementioned relationship of M, M_s and initial permeability μ_i, in our case, the decrease in the initial permeability is mainly attributed to the decrease of the net magnetic moment of M.

Figure 4:

Variation of initial permeability for the samples with various Cr content.

Figure 5 illustrates the behavior of hysteresis loops of all the sintered Ni_0.2Cu_0.2Zn_0.6Fe_2–xCr_xO₄ ferrites. All the ferrite samples show the characteristics of a soft magnetic material with a small coercive force. The value of saturation flux density B_s measurement varied from 149.6 mT (x = 0) to 59.2 mT (x = 1). As can be seen, the substituted ferrites present lower B_r values than the non-substituted ferrite. This figure also indicates that B_s and B_r decrease with the increasing of Cr content. The term of saturation induction (B_s) is expressed as the following equation [19]:

where μ₀ is the vacuum permeability, H is the external magnetic field. B_s shows the same regulation of changes with M_s.

Figure 5:

Magnetic hysteresis loops of Ni_0.2Cu_0.2Zn_0.6Fe_2–xCr_xO₄ ferrites.

Figure 6 shows the frequency dependence of quality factor (Q) for all series samples with different Cr content. The quality factor is often used as a measure of practical application performance. It is clear that Q factor increases with an increase in frequency showing a peak and then decreases with further increase in frequency. It can be seen that the sample has the highest Q value for Ni_0.2Cu_0.2Zn_0.6FeCrO₄. As we mentioned above, the Cr³⁺ ions are in favor of B sites occupancy. Due to the decreasing Fe ions content at B sites caused by occupations, electronics transition among the different valence ions decreases. Furthermore, the Q factor increases with the increasing resistivity of intergranular region resulting from the appearance of Cr oxides.

Figure 6:

Quality factor versus frequency for the ferrite samples with various Cr content.