CHAPTER -4. STRUCTURAL, ELECTRICAL AND MAGNETIC PROPERTIES OF Ni-Cu-Zn FERRITE PROCESSED WITH POLYETHYLENE GLYCOL AS CHELATING AGENT

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64 CHAPTER -4 STRUCTURAL, ELECTRICAL AND MAGNETIC PROPERTIES OF Ni-Cu-Zn FERRITE PROCESSED WITH POLYETHYLENE GLYCOL AS CHELATING AGENT 4.1 (a) Introduction A potential ferrite candidate for multi layer chip inductor (MLCI) applications, in general, should possess high initial permeability, high electrical resistivity, low loss, moderate saturation magnetization and good frequency stability of initial permeability. Ni- Zn nanoferrite processed with poly ethylene glycol (PEG) was observed to possess specific saturation magnetization of 75 emu/gm, crystallite size 7.21 nm and particle size 168 nm and Curie temperature 435 C (chapter 3). With a view of improving the initial permeability copper substitution in place of nickel in Ni-Zn ferrite has been studied using PEG as chelating agent. For this purpose, a number of measurements have been carried out using various techniques like X-ray diffraction, scanning electron microscopy, transmission electron microscopy, FTIR, vibration sample magnetometry, and impedance analyzer on the copper substituted nickel zinc ferrite. sintered at 1 C. The observed variations in several parameters viz. lattice constant, crystallite size, volume density, grain size, particle size, Q-factor have been discussed in detail. The chapter comprises of two sections A and B. Section-A deals with structural aspects (crystalline, micro and molecular structures) whereas section-b describes the magnetic properties and dc resistivity. 4.1(b) METHOD OF PREPARATION The samples with composition Ni.65-x Zn.35 Cu x Fe 2 O 4, where x varies from. to.3 in steps of.6 were processed by sol gel method as described in chapter 3. Because of its high molecular weight and high gelling action, the chelating agent PEG, not only it adheres to the ferrite nanoparticles formed at low temperatures but also restricts the growth of ferrite nanoparticles.

65 4.2 RESULTS AND DISCUSSION Structural Properties 4.2 A. X-Ray diffraction (a) Lattice constant X-ray diffraction patterns of all the ferrite samples exhibiting single phase spinel structure have been shown in figures 4.1 and 4.2. The plane indices (hkl) for each peak have been assigned on comparing the measured and standard d-values of the ferrite structure. Lattice constant a and Nelson-Riley function 2 2 1 cos θ cos θ F ( θ ) = + 2 sinθ θ [1, 2] have been estimated for each peak using diffraction angle ө and equation 2 2 2 a = d h + k + l [1]. Nelson-Riley function is known to provide the error involved in the calculation of lattice constant. Precise value of lattice constant can be obtained from the extrapolation of the estimated lattice constant versus Nelson- Riley function (error) graph. The real value of lattice constant corresponds to zero error. 25 Intensity 2 15 1 5 (1 1 1) (2 2 ) (2 2 2) (3 1 1) X =. Ni.65 Zn.35 Fe 2 O 4 (4 ) (4 2 2) (5 1 1) (4 4 ) (6 2 ) (5 3 3) 1 2 3 4 5 6 7 8 9 Figure.4.1 X-ray diffraction pattern of Ni.65 Zn.35 Fe 2 O 4 2θ

66 16 (1 1 1) (2 2 ) (3 1 1) (2 2 2) (4 ) (4 2 2) (5 1 1) (4 4 ) x=.3 12 x=.24 Intensity 8 x=.18 4 x=.12 x=.6 2 4 6 8 2θ Figure.4.2. X-ray diffraction patterns of Ni.65-x Zn.35 Cu x Fe 2 O 4 8.6 8.5 Lattice Parameter(A ) 8.4 8.3 8.2 8.1 8. Figure.4.3. Variation of lattice constant with concentration Figure.4.3. gives the variation of lattice constant with increasing copper concentration. The lattice constant has been observed to increase slightly with the increase in copper content and the observed minute variation can be explained on the basis of the ionic radius of the substituent ion.

67 In general, if the radius of the substituent ion is larger than the displaced ion, the lattice expands and the lattice constant increases. Conversely, if the radius of the substituent ion is smaller than the displaced ion the lattice shrinks and the lattice constant decreases. As the ionic radius of the substituted copper ion (.72 Å) is slightly more than that of the displaced nickel ion (.69 Å), minute increase in lattice constant has been evident with increasing copper concentration. Similar behavior has also been reported in Ni-Cu-Zn ferrites by other researchers [3]. (b) Crystallite size The crystallite size has been determined from Williamson-Hall plots as described in the earlier chapter 3. Table 4.1 gives the average crystallite size with copper concentration. The pictorial variation in crystallite size is not given because the values fluctuate and observed to be a bit out of systematic order. Similar observations have also been reported by other researchers [3]. Table 4.1 Crystallite size of copper substituted nickel zinc ferrites Concentration (x) Crystallite size (nm). 7.21.6 4.96.12 46.96.18 33.56.24 46.95.3 88.13 Density and porosity X-ray density of Ni.65-x Cu x Zn.35 Fe 2 O 4 samples has been determined using the corresponding lattice parameters obtained from X-ray diffraction measurements and molecular weights of the compositions whereas experimental density has been estimated using Archimedes s principle as described in chapter 2. The variations of X-ray and experimental density with copper content of Ni.65-x Cu x Zn.35 Fe 2 O 4 have been shown in figures 4.4 and 4.5.

68 5.6 Density (g/cc) 5.4 5.2 Figure.4.4. Variation of X-ray density with concentration The X-ray density decreases continuously with the increase of copper content and the variation has been very small The continuous decrease in density has been attributed to the increase in lattice constant with copper concentrations. Both the density and lattice constant variations are found to be very poor. 6. 5.5 Density (gm/cc) 5. 4.5 4. Figure.4.5. Variation of experimental density with concentration

69 The experimental density has been observed to decrease initially up to x =.12 followed by an increase with increasing copper content for higher concentrations above x =.12. However the observed variation (.33 gm/cc) in experimental density with copper has also been meager. For smaller initial concentrations of copper, the observed slight decrease in density might be due to the changes occurred in microstructure (grain size section). In general, an increase in density is expected [4, 5] as copper serves as a sintering agent. The variation in experimental density has been noticed to be parallel to that of grain size. The calculated porosity as a function of copper concentration has also been presented in figure 4.6. The porosity variations are in accordance with that of experimental density. 4 3 2 Porosity 1-1 -2-3 Figure.4.6 Variation of porosity as a function of concentration The compacted pellets or toroids of copper substituted ferrite samples exhibited a thin layer of spongy material bluish in color on their surface after a few days of their preparation. The change has been attributed to formation of copper oxide on the surface due to the reaction between copper on the surface of the pellet or toroid and the moisture present in the atmosphere. Earlier, Rezlescu has also reported such kind of observations in copper substituted nickel-zinc ferrites [6]. Hence, the measurements have been made always on freshly prepared samples. B. Transmission electron microscopy (a) Particle size Transmission electron micrographs of basic nickel zinc and copper substituted nickel zinc ferrites are shown in figures 4.7 (a-f). The average particle size estimated from volume averages of number of micrographs lies in the range of 14 to 55 nm. A clear variation of the particle

7 size, unlike that of the crystallite size, with increasing copper concentration is shown in figure 4.8. The particle size increases from 14 nm to 54 nm with rapid initial increase up to x=.12 followed by a slow increase for higher concentrations. For initial concentrations the observed particles are clear and small where as for higher concentrations the particles are large and agglomerate. (a) x=. (b) x=.6 (c) x=.12 (d) x=.18 (e) x=.24 (f) x=.3 Figure 4.7 Transmission electron micrographs of copper substituted Ni-Zn ferrite

71 875 75 625 Particle size (nm) 5 375 25 125..6.12.18.24.3 Figure.4.8 Variation of particle size with concentration C. Scanning electron microscopy (a) Grain size The surface morphology of Ni.65-x Cu x Zn.35 Fe 2 O 4 has been investigated by recording scanning electron micrographs which are given in figures 4.9 (a - f). (a) x =.. (b) x =.6 (c) x =..12 (d) x =.18

72 (e) x =.24 (f) x =.3 Figure 4.9. Scanning electron micrographs of copper substituted Ni-Zn ferrite 4.5 Grain size (µm) 3. 1.5...6.12.18.24..3 Figure.4.1. Variation of grain size with concentration The average grain size of all the ferrite compositions has been estimated using linear intercept method from the micrographs. The average grain size has been observed to increase in two stages throughout the copper concentration studied. The grain size showed a steady slight increase up to x =.12, followed by a rise for x =.18 and again a slight decrease for higher concentrations of copper as given in fig 4.1. Agglomerated and compacted fine granular microstructure has been observed besides the occurrence of lump like structure up to copper concentration x =.12. An improved growth of grain structure has been noticed in the samples for which the copper concentration is above x =.12. The complex microstructure probably is responsible for the observed decrease in density of the sample at lower concentrations of copper as mentioned in density portion. As copper serves as sintering agent and promotes the grain growth, distinct grain formation with significant increase in size is evident at higher concentrations above x =.12.

73 D. FT IR Spectroscopy Although lattice constant variation with copper concentration establishes the entry of copper into the lattice, the occupancy of copper among tetrahedral and octahedral sites can be well understood with the help of FTIR and VSM studies. Figure 4.11 represents FTIR spectra recorded in the range 3 cm -1 to 4 cm -1 on MAGNA 55 Nicolet Instruments Corporation for the all the copper substituted nickel zinc ferrite samples. Each spectrum has been observed to contain two significant absorption bands which appear between 5-59 cm -1 and 4-49 cm -1 are the characteristic bands corresponding to tetrahedral and octahedral sites of a ferrite composition. Figure.4.11 FTIR absorption spectra of Ni.65-xCu x Zn.35 Fe 2 O 4 The observed first band at higher wavenumber of 59 cm -1 (υ 1 ) and the second band at lower wavenumber of 42 cm -1 (υ 2 ) have been attributed to the stretching vibrations of bonds between cation and oxygen ions at tetrahedral and octahedral sites respectively. The difference in the positions of absorption bands (υ 1, υ 2 ), has been attributed to the difference in bond lengths (cation and oxygen ions) within tetrahedral and octahedral sites [7].

74 6 42 Wave number cm -1 59 58 A site Wave number (cm -1 ) 41 B Site 4 Figure.4.12 Variation of wave numbers at A and B sites with concentration 1. OCTAHEDRAL.8 Band intensity.6.4 TETRAHEDRAL.2 Figure.4.13. Intensity variations of tetrahedral and octahedral bands of Ni.65-x Cu x Zn.35 Fe 2 O 4 samples Figure 4.12 shows the variation in wave numbers of (υ 1 and υ 2 ) with copper concentration of the samples. From the spectra, it has been observed that both υ 1 and υ 2 shift towards the lower frequencies with increasing copper concentration. Figure.4.13 shows the intensity variation of tetrahedral and octahedral bands with copper concentration. The gradual increase in intensity of octahedral band with increase in copper concentration indicates that copper enters into octahedral sites and replacing nickel ions. Insignificant minor variation in intensity of tetrahedral band does not throw any information on copper occupancy at tetrahedral sites. It is known that in most of the ferrite systems, nickel and zinc ions show a strong

75 preference to occupy octahedral and tetrahedral sites respectively while Cu 2+ ions can exist at both the sites, though they have strong preference towards octahedral sites [8]. However, in the present study basing on FTIR investigation, copper ions have been reported to occupy octahedral sites only replacing Ni 2+ ions having comparatively smaller ionic radius and lower atomic weight. The site occupancy of copper cannot be decided by FTIR spectral analysis alone. The saturation magnetization measurements which play vital role in providing the cation distribution among the tetrahedral and octahedral sites are presented in the next section. Electrical properties (a) DC resistivity The variation in dc resistivity with increasing copper concentration in Ni-Zn ferrite has been shown in figure.4.14. The resistivity showed an initial gradual increase with copper concentration up to x =.18 and then a gradual decrease for higher concentrations. 2 15 ρ x 1 6 Ω cm 1 5 Figure 4.14 Variation of resistivity with increasing concentration

76 Grain size µ 2.5 2. 1.5 1..5. peg concentration 2 18 16 14 12 1 8 6 4 2 grain size resistivity Resitivity (ρ) Ω1 6 cm Figure 4.15 Grain size and resistivity versus concentration The dc resistivity is an important property to be considered for MLCI applications. The observed resistivity of basic nickel zinc ferrite of present investigation has been found to be more than that reported in bulk samples of the same composition by other researchers [18]. Less values of grain sizes are recorded in the present investigation when compared with that of the bulk Ni- Zn ferrites [19]. Smaller grains provide more number of grain boundaries thereby resulting in higher values of dc resistivity. The observed resistivity variation can be understood on the basis of occurrence of changes in microstructure. The increased grain size with reduced imperfections, in general decreases the resistivity of the sample. The observed smaller, agglomerated, and compacted granular microstructure might be responsible for the observed increased resistivity at lower concentrations of copper substitution in nickel zinc ferrites. At lower concentrations of copper substitution, more than grain size, the variation in porosity is the main parameter in affecting increase in resistivity. Distinct grain formation with significant increase in grain size has been evident at higher concentration which caused the decrease in resistivity with increasing copper content shown in figure 4.15.

77 Magnetic properties (a) Specific saturation Magnetization Figure 4.16 shows room temperature magnetic hysteresis loops of copper substituted nickel zinc ferrites possessing soft ferromagnetic behavior with low coercive force. The saturation magnetization (M s ), magnetic moment, and coercive force (H c ) parameters derived from the magnetic loops for all the samples are given in table 4.2. The variations in the parameters as a function of copper concentration have been discussed in the following paragraphs. Specific Saturation Magnetization (emu/gm) 75 5 25-25 -5-75 x=. x=.6 x=.12 x=.18 x=.24 x=.3-225 -15-75 75 15 225 Applied Field Figure.4.16. Hysteresis loops of Ni.65-x Cu x Zn.35 Fe 2 O 4 Table 4.2 Magnetic properties of copper substituted nickel zinc ferrites Copper concentration (x) Specific saturation magnetization (emu/gm) Magnetic moment (Bohr magnetons) Coercivity (Oe). 71.47 3.27 33..6 7.9 3.1 28.36.12 72. 3.6 22..18 69.81 2.97 1.5.24 69.19 2.95 9.38.3 69.32 2.956 1.2

78 Figure 4.17 shows the variation in saturation magnetization and coercivity with copper concentration. Both specific saturation magnetization and coercivity have been observed to decrease with increasing concentration of copper impurity. The variations can be explained on the basis of superexchange interactions existing among the tetrahedral and octahedral sites of the ferrite lattice. Specific saturation Magnetization (emu/gm) 74 72 7 68 66 28 26 24 22 2 18 16 14 12 1 Coercivity (Oe) Copper content (x) Figure.4.17. specific saturation magnetization and coercive force with concentration According to Neel [9], there exist three kinds of exchange interactions, namely, the interaction between the various magnetic ions located at A-site (AA interaction), the interaction between the various magnetic ions located at B-site (BB interaction) and the interaction of magnetic ions at A-site with those at B-site (AB interaction); of these, AB interaction predominates in strength over AA and BB interactions. These interactions align all the magnetic spins at A-site in one direction comprising A-sublattice and those at B-site in the opposite direction comprising B-sublattice. The net magnetic moment of the lattice is, therefore, the difference between the magnetic moments of B and A sublattices i.e. M B -M A. In general, a decrease in saturation magnetization can be expected in nickel zinc ferrite when copper ions replace nickel ions due to their lower magnetic moment (1 µ B ) as compared to

79 Ni 2+ ions (2 µ B ). However, the site occupancy of copper ions provides the exact information about the decrease of specific saturation magnetization in the sample. On the basis of suggested preferences for site occupancy of various cations, a decrease in saturation magnetization is anticipated in nickel zinc ferrite system on copper substitution provided copper ions replace nickel ions at octahedral sites. This process reduces the magnetic moment of octahedral sub lattice and leads to the decrease in net magnetic moment, M B -M A. The anticipated quantitative decrease of.3 µ B in net magnetic moment coincides with the observed variation. In another possible process, copper ions may occupy both tetrahedral and octahedral sites without affecting A-B exchange interaction. The amount of copper is not too high to affect the A-B exchange interaction. This process reduces the magnetic moments of both the sublattices resulting in decrease of net magnetic moment of the system. The decrease in magnetic moment in this situation is lower than that discussed in the above process. The third process where all the copper ions occupy tetrahedral sites has been ruled out for the simple reason that ferrite material may turn into diamagnetic as the tetrahedral sub lattice gets diluted with copper and lifts A-B exchange interaction. On the basis of the above discussion and existing information about the preferences of various cations in ferrite, cation distribution in copper substituted nickel-zinc ferrite has been proposed in equations (1-6). Zinc and nickel ions prefer to occupy tetrahedral and octahedral sites respectively while iron ions occupy both the sites. Copper substitution replaces nickel ions at octahedral site as suggested by FTIR and VSM measurements..... ---------------------- (1)..... --------------- (2)..... --------------- (3)..... --------------- (4)..... --------------- (5)..... --------------- (6)

8 From the cation distribution, given above in equations (1-6), lattice constants for copper substituted nickel zinc ferrites have been estimated and are found to be in good agreement with the experimentally determined lattice constants reported in table 4.3. Table 4.3 Comparison between calculated and experimental lattice constants a calculated Ǻ a experimental Ǻ. 8.382 8.377.6 8.384 8.383.12 8.387 8.391.18 8.389 8.46.24 8.392 8.415.3 8.394 8.425 (b) Curie temperature Figure 4.18 shows the variation of Curie temperature as a function of copper concentration. A linear decrease in Curie temperature has been observed with increasing concentration of copper. 38 36 Curie temperature C 34 32 3 28 Figure 4.18 Variation of Curie temperature with concentration As copper is diamagnetic, it s incorporation in place of nickel at octahedral site in nickel zinc ferrite decreases the magnetization of B sublattice and consequently lower Curie temperature is expected in case of copper substituted nickel zinc ferrite and the same has been observed. Similar variation has been noticed with copper substitution in nickel zinc ferrites of composition Ni.8-x Cu x Zn.2 Fe 2 O 4 [4].

81 (c) Initial permeability Higher initial permeability and lower loss are desirable parameters to decide the performance of soft magnetic ferrite cores, especially for MLCI applications. Materials with high permeability are required for reducing the number of layers in MLCI and realizing the better miniaturization [1]. In general, initial permeability is dependent on many parameters such as chemical composition, stoichiometry, impurity concentration, saturation magnetization, magnetostriction, crystal anisotropy, sintering density and the microstructure i.e., grain size and porosity [11]. Higher permeabilities are favored by large grain size, high saturation magnetization, low porosity, low crystal anisotropy, low magnetostriction and high purity of the material. Figure 4.19 shows the variation of initial permeability with increasing copper content. Samples with higher copper concentration (x=.18 to.3) exhibited higher values of initial permeability as compared to the samples of lower concentration of copper. The observed variation in initial permeability has been insignificant at lower concentration. Figure 4.2 and 4.21 give the variations in initial permeability, experimental density and grain size as a function of concentration. The graphs have been placed here because they exhibit some common feature which will be discussed below. 2 Initial permeability (µ i ) 15 1 5 Figure 4.19 Variation of initial permeability with concentration The observed variation in initial permeability can be understood on the basis of changes in density and grain size as evident from scanning electron micrographs. Variations in initial permeability are very close to the changes in the volume density as well as grain size. At higher

82 concentration beyond x =.12, the initial permeability follows closely the changes in grain size. It is an established fact that the increase in grain size reduces the number of grain boundaries in a sample and causes an increase in the initial permeability. Initial permeability 5 45 4 35 3 25 2 15 1 5 6. 5.5 5. 4.5 4. Density g/cc Figure 4.2 Initial permeability and density versus concentration Grain size (micro mt) 3. 2.5 2. 1.5 1..5 PEG Samples 25 2 15 1 5 Initial permeability (µ i ). Figure 4.21. Grain size and initial permeability versus concentration

83 Interestingly, the density, the grain size and the initial permeability were found to exhibit similar variation trends with copper concentration. The copper substituted samples can be categorized into two sets namely, lower concentration (first 3 samples) and higher concentration (last 3 samples). The second set has been found to be responsible in producing higher values of density, grain size and initial permeability which may be attributed to due to a common phenomenon involved in the samples. It s well known that increased grain size would always favor higher values of density and permeability [12]. (d) Frequency dependence of initial permeability Figure 4.22 shows the frequency dependence of initial permeability up to 13 MHz for copper substituted nickel zinc ferrite samples. The samples of higher concentration showed a distinct variation in permeability whereas the variations belonging to lower concentrations are overlapped. Permeability 35 3 25 2 15 1 x=. x=.6 x=.12 x=.18 x=.24 x=.3 5 1 1 1E7 Frequency (Hz) Figure 4.22. Frequency dispersion of permeability as a function of copper concentration The frequency dispersion of permeability defines the frequency range in which the ferrites can be operated. Initial permeability remains more or less constant, does not change much with frequency up to a certain value called critical frequency, then falls rapidly by a relaxation process at frequencies around a few megacycles per second. In our study, the initial permeability has been observed to be constant throughout the frequency range studied in all the samples except for x=.18. The critical frequency in case of this sample has been observed to be around 8 MHz. As the values of grain size and initial permeability are relatively less in all other

84 samples of the series, the critical frequency has been expected to lie at higher frequencies, which have not been viewed within the scope of the measurement. The critical frequency is known to depend on saturation magnetization, grain size, initial permeability and dc resistivity [13-17]. The critical frequency is directly proportional to square of the saturation magnetization as well as resistivity and inversely proportional to both the initial permeability and the grain size. In our study, the magnetization showed a decrease, while the grain size and the initial permeability have exhibited an increase with increasing copper substitution in nickel zinc ferrite. As the observed variation in resistivity is not very high, the shift in critical frequency to higher side is not possible. It is suggested that a good method of preparation which changes the order of resistivity greatly could shift the critical frequency to desirable frequency range. Hence nickel zinc ferrites have been processed with polyvinyl alcohol as chelating agent. (e) Loss Tangents and Q factors Low magnetic losses are preferred for the ferrite material useful for MLCI applications. The losses can be reduced by modifying the microstructure such that the material should possess fine grains, high density and high initial permeability [2]. Fine grained microstructure is favorable for increasing the Q factor [2]. The Q factor is used as a measure of performance of the material for practical application. The Q factor is defined as Q = 1/Tanδ, where, Tanδ gives the loss factor. Magnetic loss factors are determined from frequency dispersion of permeability data of samples using an Impedance analyzer. Variation of magnetic loss tangents of the basic and copper substituted nickel zinc ferrite samples with frequency is shown in fig 4.23 (a-b). The quality factor variation with frequency for copper substituted nickel zinc ferrite samples is shown in figure 4.24 (a-b).

85 3 25 2 Tanδ µ 15 1 5 1 1 1E7 Frequency Figure 4.23 (a) Variation of loss tangent with frequency of basic nickel zinc ferrite 15 1 B C D E F 5 Tan δ µ -5-1 1 1 1E7 Frequency (Hz) Figure 4.23 (b) Variation of loss tangent with frequency of copper substituted nickel zinc ferrites

86 basic peg Q factor 8 7 6 5 4 3 2 1-1 1 1 1E7 Frequency Figure 4.24(a) Variation of Q factors with frequency of copper substituted Ni-Zn ferrites 8 Q Factor 7 6 5 4 3 2 X=.6 X=.12 X=.18 X=.24 X=.3 1-1 1 1 1E7 Frequency Figure 4.24(b) Variation of Q factors with frequency of copper substituted nickel zinc ferrites

87 Q factor 2 18 16 14 12 1 8 6 Figure 4.25 Variation of Q factor with copper concentration The grains in all the samples are observed clearly. The observed magnetic loss in case of copper substituted nickel zinc ferrite is of smaller value but slightly higher than that of basic nickel zinc ferrite. Also in basic composition, the magnetic loss has been suppressed whereas Q factor increased with the inclusion of copper up to x=.24. The variation in Q factor at 11 KHz is shown in figure 4.25. At x=.3 (15 mol %), the increase in magnetic loss and the decrease in quality factor are due to the pores present in formed larger grains. However, the observed losses in these samples are less due to their smaller grain sizes. Conclusions In the present studies of copper substituted nickel zinc ferrite samples processed using PEG as chelating agent initial permeability has been observed to be highest for x=.18. But the grain sizes and particle sizes are observed to be large for these samples resulting in the lowering of resistivity. Hence it is necessary for the ferrite material to be a superior candidate that the grain sizes are to be small. In an attempt to have superior properties the same compositions have been processed using PVA as chelating agent and characterized. The VSM analysis and FTIR spectral analysis have been indicating the B site occupancy of copper ions in the case of ferrite samples processed by method 1 and which was confirmed by

88 the comparison of theoretical lattice constant calculated using the proposed distribution and experimental lattice constants. The copper substituted nickel zinc ferrite samples processed by method 2 resulted in smaller grains and particles enhancing the dc resistivity. The initial permeability values of these ferrite samples also enhanced further due to better microstructure, therefore to have a deep survey of the microstructure FESEM measurements have also been taken. Further it has been necessary to carry out the Mossbauer spectral analysis in the case of ferrite samples processed by method 2 to investigate the site occupancy of copper ions.

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