Effect of Cu Incorporation on Structure, Densification and Magnetic Properties of Polycrystalline LixNi0.2Zn0.8-2xFe2+xO4 Ceramics

The polycrystalline LixNi0.2Zn0.8−2xFex+2O4 and LixNi0.1Cu0.1Zn0.8−2xFex+2O4 (x = 0.0, 0.1, 0.2, and 0.3) ferrites were synthesized by the standard solid-state reaction method. The compound was sintered at 1150 ̊C for 5 hours. The effect of Cu substitution and its impact on the crystal structure, microstructure, complex initial permeability and magnetization of the Ni-Zn ferrites were studied. The effect of Li incorporation on the properties mentioned above was also investigated. X-ray diffraction patterns of the samples indicated a single cubic spinel structure for both the compound. No effect of Cu addition on crystal structure was observed. The density of the ferrites was found to be enhanced because of adding Li whereas the porosity of the samples decreased with the content of Li ions. The average value of grain size increased with the addition of Li content. The samples having Cu ions formed bigger size grains. Frequency-dependent complex initial permeability, loss tangent, and relative quality factor were studied at room temperature using an Impedance analyzer in the range of 100 Hz 120 MHz regions. In the low-frequency region, the prepared samples exhibited a high value of permeability and after a certain frequency, the permeability falls. The value of permeability enhanced with the increase in Li whereas loss tangent was found to be reduced. The relative quality factor graphs described that the compound has excellent frequency stability up to a certain frequency which is suitable to be used in inductors, resistors, capacitors, etc. Initial permeability for LixNi0.1Cu0.1Zn0.8−2xFex+2O4 ferrites was found high than LixNi0.2Zn0.8−2xFex+2O4 which might be attributed to having bigger size grains of Cu containing samples because of easy movement of domain wall in bigger size grains. The values of saturation magnetization (Ms) were calculated for both compounds from M-H hysteresis loops and it enhanced with the increase in Li content which might be related to the How to cite this paper: Liya, H.A., Akter, R., Ahad, A., Khan, M.N.I. and Miah, M.J. (2021) Effect of Cu Incorporation on Structure, Densification and Magnetic Properties of Polycrystalline LixNi0.2Zn0.8−2xFe2+xO4 Ceramics. Journal of Applied Mathematics and Physics, 9, 3211-3229. https://doi.org/10.4236/jamp.2021.912210 Received: October 27, 2021 Accepted: December 28, 2021 Published: December 31, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access


Introduction
The demand for magnetic ceramics in the modern technological world is in-  [3]. In research, it gained a lot of interest because of its low price and easy magnetizing and demagnetizing properties. X-ray crystallography described that the spinel ferrites have a face-centered cubic structure where oxygen ions are packed closely together with the much smaller divalent and trivalent metal ions in the interstitial sites. There are two types of interstitial sites.
If the interstitial sites are denoted by A-and B-respectively, then there are 64Aand 32B-sites in the unit cell of the structure. Considering the substitution atoms in A-site and B-site the spinel ferrites can exhibit ferrimagnetic, antiferromagnetic, and paramagnetic behavior [4].
The cubic structured soft ferrite Ni-Zn possesses good magnetic and electric properties and there is much research is going on to improve their properties.
The Ni-Zn ferrites have potential applications in antenna rods, loading coils and core materials for power transformations in electronics and telecommunications.
Nowadays, a large number of researchers are working on Ni-Cu-Zn ferrites because Ni-Zn ferrites create cation vacancies, unsaturated oxygen ions and excessive electrons due to the loss of Zn during the calcination and sintering process [5]. These unwanted problems are reduced by the substitution of nonmagnetic metal ions (such as Cu) in Ni-Zn ferrites. The substitution of magnetic ion Ni by the Cu modifies the cation distribution process in the system and plays an important role to enhance various properties of Ni-Cu-Zn ferrites [6]- [11]. The Journal of Applied Mathematics and Physics Ni-Cu-Zn ferrites have various excellent properties such as high resistivity, low cost and low sintering temperature. They are used for multilayer chip inductors and electromagnetic interference (EMI) filters. Li substitution in place of Zn in Ni-Zn ferrites is also emerging research because of their high demand in industrial and technological applications. Research on Li substitution in Ni-Cu-Zn ferrites requires more study because a small number of foreign ions in the ferrite can dramatically change its properties. Li and Li substituted ferrites are performed as an excellent material in high-density recording media and absorbers and microwave devices because of their low cost, high saturation magnetization, high Curie temperature, etc. [12]- [17]. They exhibit comparatively better performances over other spinel ferrites. Detailed studies of the effect of Cu 2+ incorporation on structure, density, microstructure, complex initial permeability, and magnetization of Li doped Ni-Zn ferrites have been reported here.

Synthesis
The polycrystalline Li x Ni 0. 2  were blended again for 2 h. One drop of polyvinyl alcohol was added with the mixed powders as a binder for sample preparation. Then toroid-and disc-shaped samples were prepared using a hydraulic press. Finally, the prepared samples were sintered at 1150˚C for 5 h.

Characterization
X-ray diffractometer (Philips PANalytical X'PERT-PRO) with CuK α radiation (λ = 1.541 Å) was used to study the crystal structure of the sintered samples. The lattice parameter ( a ) was calculated using the following relation: where h, k, and l are the Miller indices and d is the interplanar distance. The exact value of a was calculated using the Nelson-Riley function: where θ is the Bragg angle. A straight-line fit was achieved and the exact value of a was obtained from the extrapolation of these lines to F(θ) = 0.
Theoretical density ( th ρ ) was calculated using the following formula:  (4) where m is the mass, r is the radius and t is the thickness of the sample. The porosity (P) of the samples was determined using the following relation: To study the microstructural analysis Scanning Electron Microscopy (SEM) was used. The average grain diameter ( D ) was determined using the Image J software. Wayne Kerr Impedance Analyzer (model: Wayne Kerr 6500B) was used to analyze the i µ′ . The following equation was used to calculate the i µ′ .
diameter of the sample. The relative quality factor (RQF) was calculated using the following equation: where tanδ is the magnetic loss.
A Vibrating Sample Magnetometer (VSM) was used to measure the M-H hysteresis loop and magnetization, coercivity, etc. of the materials were determined from the hysteresis loop.   Table 1.

Crystal Structure
There is a decreasing trend of lattice constant with the variation of Li content is noticed for the prepared samples.      porosity and exhibit good electric and magnetic properties. It is seen in Figure   3(a); the X-ray density decreases with the addition of Li content whereas bulk density is found to be increased. X-ray density is calculated using molecular weight, lattice parameter, etc. Molecular weight of Li (6.941 gm/mol) is lower than that of Zn (65.4 gm/mol) and thus the X-ray density is reducing gradually with the addition of a low molecular weight element by substituting heavy element.

Density Measurement
The variation of porosity with Li content is described in Figure 3(b). It is seen that porosity is reducing with Li content. Voids, pores, etc. remove because of adding Li and thus the compound becomes denser. The sintering environment may also be an important factor to be denser than the prepared samples. Measured values of X-ray density, bulk density, porosity, etc. are presented in Table 1.
It is also noticeable from the graph (Figure 3(a)), the X-ray density is higher than that of bulk density which means when the samples are sintered, they might contain cracks and pores on the microscopic scale and vacancies in the lattice on the atomic scale [21]. The bulk density may have these defects but the X-ray density is precisely measured from the lattice constant, the volume of the unit cell is free from these defects.
Variation of X-ray density and bulk density for Li     Table 1.

Microstructural Study
The average values of grain size are found to be increased with the addition of Li content. The gradual improvement of grain size is attributed might be due to the enhancement of magnetic dipole interaction between the ions because of replacing Zn 2+ and Fe 3+ ions with Li + .
It is seen in Figure 5(b) and in Table 1

Complex Initial Permeability
Information about the factors that control the magnetic properties of materials and also the adjustability of magnetic materials in high-frequency use can be obtained from complex initial permeability. The complex initial permeability is   The influence of spin rotation on initial permeability was found very small than domain wall motion because the motion of the domain wall can continue still in a weak magnetic field [25]. The displacement of the domain wall is varied because of changing sintering temperature and grain size. The motion of the domain wall reduces with the decrease of grain size because the smaller grain contains a lesser number of domain walls and the easy reversal of the domain walls gives initial permeability in the direction of the applied magnetic field. On the other hand, previously published article of Ross [26] and Perduijin et al. [27] reported, when the grain size increases in the ferrite, the permeability increases,

Loss Factor (tanδ)
The frequency dependence of magnetic loss factor (tanδ) at room temperature of the change in an external magnetic field but at high frequency, the domain wall becomes unable to follow the variation of the external magnetic field and this might be attributed to exhibiting constant value. It is seen in Figure 6, the Li content samples have a lower value of tanδ than unsubstituted ones which indicates that the addition of Li affects the reduction of loss tangent. Figure 6 be used in microwave devices [29]. RQF has the maximum value at that frequency level where the magnetic loss tangent has the minimum value. The value of RQF first increases slowly with frequency and then rises quite abruptly making a peak at a certain frequency named resonance frequency. All the samples have a broad peak except the unsubstituted sample. The parent sample may have a peak at a high frequency beyond our measurement range. ferrites although the magnetic material Ni was replaced by nonmagnetic Cu. The overall permeability was found to be enhanced and followed Snoek's law [30].

Relative Quality Factor (RQF)
The addition of Cu in Li x Ni 0.2 Zn 0.8−2x Fe 2+x O 4 ferrites influences density measurement, porosity, and grain size. Moreover, the addition of Cu helps to complete the sintering process properly. The properties of Cu mentioned above contribute to improving the permeability, loss tangent, and relative quality factor. The mechanism has also been explained in terms of spin-disorder, spin canting, and spin-glass-like state in the surface layers of the nanoparticles due to the local chemical disorder, broken exchange interaction and a dissimilar local symmetry for those atoms near the surface. As the divalent Cu 2+ and Zn 2+ cations have a tendency to occupy both sites (octahedral and tetrahedral sites), so they can form the mixed spinel structure. Mixed spinel configurations are characterized by the degree of inversion, which depends strongly on the preparation procedures [34]. The increase in saturation magnetization with increasing Li and

M-H Hysteresis Loop
Here, the bracket () and [] specify the tetrahedral A-site and octahedral B-site, respectively. The cation distribution is attained from a few particulars [37]. They are as follows: 1) Diamagnetic Zn 2+ ion prefers to occupy both the tetrahedral A-site and octahedral B-sites [38] [39]; 2) Ni 2+ prefers to go to the octahedral B-site [40]; 3) it is evident that the Li + ion has tetrahedral site preference in spinel structure and Cu 2+ has octahedral site preference [41].
According to the above cation distribution of the prepared samples and using  [44]. In that case, the total magnetization can be rewritten as (Table 2) Figure 8, it is also noticeable that saturation magnetization is gradually increased with Li and Fe content. The cation distribution reflects this increment because ferromagnetic Ni 2+ (2 μ B ) and paramagnetic Cu 2+ (1 μ B ) ions occupied in the B sites and the diamagnetic Zn and paramagnetic Li occupied in the A-sites; therefore, net magnetic moments have been increased gradually. Expected increased magnetization can be written as, ( )  can be explained based on the magnetocrystalline anisotropy, particle morphology, dimension of the crystals, residual stress, and crystal imperfections [46].

Conclusion
Various