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The effect of sintering temperature on the electromagnetic properties of nanocrystalline MgCuZn ferrite prepared by sol–gel auto combustion method
Materials Letters 122 (2014) 129–132
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
The effect of sintering temperature on the electromagnetic properties of nanocrystalline MgCuZn ferrite prepared by sol–gel auto combustion method Hamed Bahiraei a,n, Morteza Zargar Shoushtari a, Khalil Gheisari b, C.K. Ong c a
Department of Physics, Faculty of Science, Shahid Chamran University, Ahvaz, Iran Department of Materials Science and Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran c Center for Superconducting and Magnetic Materials, Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 November 2013 Accepted 8 February 2014 Available online 17 February 2014
In this work, the nanocrystalline MgCuZn ferrite powder was prepared through the nitrate–citrate autocombustion route. The as-burnt powder after calcination at 600 1C, sintered at different temperatures below silver melting point in the range of 850–950 1C for 4 h. The structural and magnetic properties were investigated as a function of sintering temperatures. The X-ray diffraction patterns exhibited the formation of a single phase cubic spinel structure. The microstructural evaluations showed homogeneous grains and also revealed that the variation of sintering temperature significantly affected the densification and grain growth of the samples. The density, grain size, initial permeability (mi) and saturation magnetization (Ms) of all the samples increased with sintering temperature. The relative quality factor (RQF) also showed highest value for the sample sintered at 950 1C. & 2014 Elsevier B.V. All rights reserved.
Keywords: Magnetic materials Sintering Electroceramics Nanocrystalline materials Initial permeability Electromagnetic properties
1. Introduction The polycrystalline spinel ferrites are important ceramic materials due to their high electrical resistivity, high Curie temperature and thermal stability. These materials are widely used in the fabrication of multi-layer chip inductors (MLCIs) to miniaturize electronic products such as notebooks, cell phones and video cameras. MLCIs are fabricated by arranging alternate layer of ferrite and silver electrodes and then co-fired below silver melting point (961 1C) to prevent the interfacial diffusion of silver [1]. NiCuZn ferrites are used widely for the fabrication of chip inductors. However, the magnetic properties of MgCuZn and NiCuZn ferrites are same but the magnetostriction constant of MgCuZn is lower. Therefore, MgCuZn ferrite will be a potential candidate material for MLCIs with high performance and low cost. Generally, the magnetic properties of ferrites are strongly dependent on the chemical composition and method of preparation [2]. The sol–gel auto combustion method is a promising technique for the preparation of nanosized ferrite powders with high surface energy that exhibit high-sintering activity to dense at less than 950 1C with an optimized microstructure [3]. The aim of this work n
Corresponding author. Tel./fax: þ 98 6113331040. E-mail addresses: [email protected], [email protected] (H. Bahiraei). http://dx.doi.org/10.1016/j.matlet.2014.02.027 0167-577X & 2014 Elsevier B.V. All rights reserved.
is to study the structure, microstructure and electromagnetic properties of nanocrystalline MgCuZn ferrites as a function of sintering temperatures (Ts).
2. Experimental method The Mg0.3Cu0.2Zn0.52Fe1.98O3.99 powder was prepared through the nitrate–citrate auto combustion technique using the analytical grade Ni(NO3)2 6H2O, Zn(NO3)2 6H2O, Cu(NO3)2 3H2O, Fe (NO3)3 9H2O and citric acid. First, the solution of metal nitrates were dissolved in water. Then, an aqueous citric acid solution was added to the mixture in 1:1 M ratio of nitrates to citric acid. After adjusting the pH value with ammonia to 7, the resultant solution was heated at 80 1C under constant stirring to transform into a xerogel. During the heating process, the dried gel burnt out in a self-propagating combustion manner to form a fluffy powder. The as-burnt precursor powder was calcined at 600 1C in air for 2 h, granulated using 2 wt% PVA as a binder and uniaxially to form toroid. Finally, the pressed samples were sintered separately at 850, 875, 900, 925 and 950 1C for 4 h. The structural, microstructural and electromagnetic properties of nanocrystalline MgCuZn ferrites were investigated by X-ray diffraction, scanning electron microscopy, vibrating sample magnetometer
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and RF-Impedance analyzer (Agilent 4991A) with test fixture (Agilent 16453A).
3. Results and discussion Phase analysis: Fig. 1 shows the XRD patterns of the as-burnt, calcined and sintered ferrites. The calcined powder presents the main peaks corresponding to typical Mg–Cu–Zn ferrite spinel
Fig. 1. X-ray diffraction patterns of the MgCuZn ferrite for as-burnt, calcined and sintered samples at different temperatures.
Table 1 Bulk density (ρb), grain size (D), initial permeability (mi) and resonance frequency (fr) of MgCuZn ferrite sintered at different temperatures. Ts (1C)
ρb [g/cm3]
D(lm)
li (1 MHz)
fr (MHz)
850 875 900 925 950
4.51 4.55 4.60 4.77 4.82
0.30 0.41 0.62 0.99 1.21
57.68 67.34 133.41 195.78 229.6
24.23 20.79 11.07 6.87 4.68
phase with good crystallization. Clearly, no any other impurity phases are detected in the pattern. The XRD patterns of the samples sintered at different temperatures show intense sharp peaks that can be indexed as a single phase cubic spinel structure using the standard JCPDS Card no. 08-0234. The figure also shows that the broadening of the diffraction peak decreases from as-burnt to sintered ferrites, which indicates an increase in the nanocrystalline size of samples. The lattice parameter ‘a’ was calculated using the relation 1/d2 ¼ (h2 þk2 þl2)/a2 where (hkl) are the Miller indices and d is the interplanar distance. The values of ‘a’ show no significant variation by Ts, that is in good agreement with [4]. The values of the lattice parameter and the X-ray density are 8.401 Å and 5.118 g/cm3, respectively. Microstructure: Density plays a key role in controlling the properties of polycrystalline ferrites. The variation of bulk density (ρb) is shown in Table 1. It can be seen that the density increases with the sintering temperature. During the sintering process, a force that is generated by the thermal energy drives the grain boundaries to grow over pores and as a result reduces the pores volume and their grain boundaries. The strength of the driving force depends upon the diffusivity of individual grains, sintering temperature and porosity [5]. Obviously, the reduction of pore volume makes the material dense. Fig. 2 shows the typical TEM and SEM photographs of the calcined nanopowder and sintered MgCuZn ferrites, respectively. The calcined powder indicates the spherical particles with an average particle size of 96 nm (Fig. 2(a)). As shown in Fig. 2(b–d), the microstructures reveal that the grain size is influenced by the sintering temperature. With the increase of sintering temperature from 850 to 950 1C (Fig. 2(b–d)), the grain size increases, from 0.3 to 1.2 μm. One can see that the grain size increases, while the porosity decreases with sintering temperature [6]. The micrographs of the samples that were sintered below 900 1C show the existence of many pores distributed at the grain boundaries. Such porous structure can explain why the bulk density is lower than the X-ray density. The results of the bulk density are listed in Table 1. The sample that is sintered at 950 1C shows a dense microstructure and larger grain size. Magnetic properties: It is well-known that permeability and saturation magnetization are influenced by not only the intrinsic factors such as preferential site occupancy, but also the extrinsic factors like density and microstructure (grain size and porosity) [7].
Fig. 2. The micrographs of calcined powder (a) and sintered samples at 850 (b), 900 (c) and 950 1C (d).
H. Bahiraei et al. / Materials Letters 122 (2014) 129–132
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Fig. 3. Frequency dependency of permeability (a), relative quality factor (b) and hysteresis curves (c) of the sintered samples.
Fig. 3(a) shows the real part of initial permeability (mi0 ) of sintered samples at different temperatures as a function of frequency. It can be seen that for each sample the value of mi0 remains constant in the frequency range up to a critical frequency, which is called the resonance frequency (fr). From this figure and Table 1, one can see that mi0 increases with sintering temperature but fr moves towards the lower frequency. This observation is in agreement with the snoek's law which says the initial permeability and resonance frequency are related inversely (mi0 fr ¼Constant) [8]. It is established that the initial permeability is a result of the easy reversal of domain wall displacement in the direction of the applied magnetic field [7]. Comparison of the results of the initial permeability, density and microstructures in Table 1. demonstrates that the initial permeability is correlated with bulk density and grain size of the samples. In the other hand, the relation between initial permeability and grain size due to domain wall motion is given by means of following relation: mi α (M2s D)/K where Ms is the saturation magnetization, D is the average grain size and K is the magnetocrystalline anisotropy constant [5]. Since the large grains tend to minimize their magnetic energy by increasing the number of domain walls; thus, the greater the number of domain walls the higher the initial permeability. Also the fewer amounts of pores and grain boundaries that could be obtained at higher sintering temperature, lead to easy movement of domain walls and as a result high initial permeability. Consequently, ferrites with higher density and larger average grain size possess a higher initial permeability [9]. Fig. 3(b) shows the relative quality factor (RQF) (i.e., RQF¼ mi0 /tan δ, where tan δ is the loss factor) of different samples. For practical application the tan δ is often used as a measure of performance. Low tan δ and high μi0 is required for high frequency magnetic applications. It is observed that the RQF of all samples increases initially, reaching a maximum value and then decreases with frequency due to the resonance-relaxation losses. The sample sintered at 950 1C has the highest value of RQF.
Fig. 3(c) shows the magnetic hysteresis curves of the sintered samples. It is observed that Ms increases with sintering temperature up to 950 1C. The maximum value of saturation magnetization Ms is found to be 40.43 emu/g for sample sintered at 950 1C. This may be due to better the bulk density and decrease in the number of pores in the samples. It should be mentioned that pores act as pinning centers for the electron spins, thereby, lowering the magnetization [10].
4. Conclusion Nanocrystalline MgCuZn ferrite powder prepared through the nitrate–citrate sol–gel auto combustion method, exhibited high sintering activity. The calcined powder indicates the spherical particles with an average particle size of 96 nm. The results of sintered samples at different temperatures showed that the magnetic properties are sensitive to the bulk density and microstructure. It was observed that an increase in the bulk density and grain size due to the sintering temperature, leads to the higher initial permeability and saturation magnetization of the MgCuZn ferrite samples. The maximum values of initial permeability and saturation magnetization is found to be 299.6 at 1 MHz and 40.43 emu/g respectively for the sample sintered at 950 1C.
References [1] Penchal Reddy M, Madhuri W, Balakrishnaiah G, Ramamanohar Reddy N, Siva Kumar KV, Murthy VRK, et al. Microwave sintering of iron deficient Ni– Cu–Zn ferrites for multilayer chip inductors. Curr Appl Phys 2011;11:191–8. [2] Mathur P, Thakur A, Lee JH, Singh M. Sustained electromagnetic properties of Ni–Zn–Co nanoferrites for the high-frequency applications. Mater Lett 2010;64:2738–41. [3] Yan S, Ling W, Zhou E. Rapid synthesis of Mn0.65Zn0.35Fe2O4/SiO2 homogeneous nanocomposites by modified sol gel auto-combustion method. J Cryst Growth 2004;273:226–33.
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H. Bahiraei et al. / Materials Letters 122 (2014) 129–132
[4] Zehani K, Mazaleyrat F, Loyau V, Laboure E. Effect of temperature and time on properties of spark plasma sintered. J Appl Phys 2011;109:07A504. [5] Akther Hossain AKM, Biswas TS, Yanagida T, Tanaka H, Tabata H, Kawai T. Investigation of structural and magnetic properties of polycrystalline Ni0.50Zn0.50 xMgxFe2O4 spinel ferrites. Mater Chem Phys 2010;120:461–7. [6] German RM. Powder Metallurgy Science. 2nd ed. Princeton, NJ: Metal Powder Industries Federation; 1994. [7] Yang Q, Zhang H, Liu Y, Wen Q, Jia L. Microstructure and magnetic properties of microwave sintered NiCuZn ferrite for application in LTCC devices. Mater Lett 2012;79:103–5.
[8] Chand J, Kumar G, Kumar P, Sharma SK, Knobel M, Singh M. Effect of Gd3 þ doping on magnetic, electric and dielectric properties of MgGdxFe2 xO4 ferrites processed by solid state reaction technique. J Alloys Compd 2011;509:9638–44. [9] Globus A, Duplex P. Separation of susceptibility mechanisms for ferrites of low anisotropy. IEEE Trans Magn 1966;MAG-2:441–5. [10] Gabal MA. Effect of Mg substitution on the magnetic properties of NiCuZn ferrite nanoparticles prepared through a novel method using egg white. J Magn Magn Mater 2009;321:3144–8.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
The effect of sintering temperature on the electromagnetic properties of nanocrystalline MgCuZn ferrite prepared by sol–gel auto combustion method Hamed Bahiraei a,n, Morteza Zargar Shoushtari a, Khalil Gheisari b, C.K. Ong c a
Department of Physics, Faculty of Science, Shahid Chamran University, Ahvaz, Iran Department of Materials Science and Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran c Center for Superconducting and Magnetic Materials, Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 November 2013 Accepted 8 February 2014 Available online 17 February 2014
In this work, the nanocrystalline MgCuZn ferrite powder was prepared through the nitrate–citrate autocombustion route. The as-burnt powder after calcination at 600 1C, sintered at different temperatures below silver melting point in the range of 850–950 1C for 4 h. The structural and magnetic properties were investigated as a function of sintering temperatures. The X-ray diffraction patterns exhibited the formation of a single phase cubic spinel structure. The microstructural evaluations showed homogeneous grains and also revealed that the variation of sintering temperature significantly affected the densification and grain growth of the samples. The density, grain size, initial permeability (mi) and saturation magnetization (Ms) of all the samples increased with sintering temperature. The relative quality factor (RQF) also showed highest value for the sample sintered at 950 1C. & 2014 Elsevier B.V. All rights reserved.
Keywords: Magnetic materials Sintering Electroceramics Nanocrystalline materials Initial permeability Electromagnetic properties
1. Introduction The polycrystalline spinel ferrites are important ceramic materials due to their high electrical resistivity, high Curie temperature and thermal stability. These materials are widely used in the fabrication of multi-layer chip inductors (MLCIs) to miniaturize electronic products such as notebooks, cell phones and video cameras. MLCIs are fabricated by arranging alternate layer of ferrite and silver electrodes and then co-fired below silver melting point (961 1C) to prevent the interfacial diffusion of silver [1]. NiCuZn ferrites are used widely for the fabrication of chip inductors. However, the magnetic properties of MgCuZn and NiCuZn ferrites are same but the magnetostriction constant of MgCuZn is lower. Therefore, MgCuZn ferrite will be a potential candidate material for MLCIs with high performance and low cost. Generally, the magnetic properties of ferrites are strongly dependent on the chemical composition and method of preparation [2]. The sol–gel auto combustion method is a promising technique for the preparation of nanosized ferrite powders with high surface energy that exhibit high-sintering activity to dense at less than 950 1C with an optimized microstructure [3]. The aim of this work n
Corresponding author. Tel./fax: þ 98 6113331040. E-mail addresses: [email protected], [email protected] (H. Bahiraei). http://dx.doi.org/10.1016/j.matlet.2014.02.027 0167-577X & 2014 Elsevier B.V. All rights reserved.
is to study the structure, microstructure and electromagnetic properties of nanocrystalline MgCuZn ferrites as a function of sintering temperatures (Ts).
2. Experimental method The Mg0.3Cu0.2Zn0.52Fe1.98O3.99 powder was prepared through the nitrate–citrate auto combustion technique using the analytical grade Ni(NO3)2 6H2O, Zn(NO3)2 6H2O, Cu(NO3)2 3H2O, Fe (NO3)3 9H2O and citric acid. First, the solution of metal nitrates were dissolved in water. Then, an aqueous citric acid solution was added to the mixture in 1:1 M ratio of nitrates to citric acid. After adjusting the pH value with ammonia to 7, the resultant solution was heated at 80 1C under constant stirring to transform into a xerogel. During the heating process, the dried gel burnt out in a self-propagating combustion manner to form a fluffy powder. The as-burnt precursor powder was calcined at 600 1C in air for 2 h, granulated using 2 wt% PVA as a binder and uniaxially to form toroid. Finally, the pressed samples were sintered separately at 850, 875, 900, 925 and 950 1C for 4 h. The structural, microstructural and electromagnetic properties of nanocrystalline MgCuZn ferrites were investigated by X-ray diffraction, scanning electron microscopy, vibrating sample magnetometer
130
H. Bahiraei et al. / Materials Letters 122 (2014) 129–132
and RF-Impedance analyzer (Agilent 4991A) with test fixture (Agilent 16453A).
3. Results and discussion Phase analysis: Fig. 1 shows the XRD patterns of the as-burnt, calcined and sintered ferrites. The calcined powder presents the main peaks corresponding to typical Mg–Cu–Zn ferrite spinel
Fig. 1. X-ray diffraction patterns of the MgCuZn ferrite for as-burnt, calcined and sintered samples at different temperatures.
Table 1 Bulk density (ρb), grain size (D), initial permeability (mi) and resonance frequency (fr) of MgCuZn ferrite sintered at different temperatures. Ts (1C)
ρb [g/cm3]
D(lm)
li (1 MHz)
fr (MHz)
850 875 900 925 950
4.51 4.55 4.60 4.77 4.82
0.30 0.41 0.62 0.99 1.21
57.68 67.34 133.41 195.78 229.6
24.23 20.79 11.07 6.87 4.68
phase with good crystallization. Clearly, no any other impurity phases are detected in the pattern. The XRD patterns of the samples sintered at different temperatures show intense sharp peaks that can be indexed as a single phase cubic spinel structure using the standard JCPDS Card no. 08-0234. The figure also shows that the broadening of the diffraction peak decreases from as-burnt to sintered ferrites, which indicates an increase in the nanocrystalline size of samples. The lattice parameter ‘a’ was calculated using the relation 1/d2 ¼ (h2 þk2 þl2)/a2 where (hkl) are the Miller indices and d is the interplanar distance. The values of ‘a’ show no significant variation by Ts, that is in good agreement with [4]. The values of the lattice parameter and the X-ray density are 8.401 Å and 5.118 g/cm3, respectively. Microstructure: Density plays a key role in controlling the properties of polycrystalline ferrites. The variation of bulk density (ρb) is shown in Table 1. It can be seen that the density increases with the sintering temperature. During the sintering process, a force that is generated by the thermal energy drives the grain boundaries to grow over pores and as a result reduces the pores volume and their grain boundaries. The strength of the driving force depends upon the diffusivity of individual grains, sintering temperature and porosity [5]. Obviously, the reduction of pore volume makes the material dense. Fig. 2 shows the typical TEM and SEM photographs of the calcined nanopowder and sintered MgCuZn ferrites, respectively. The calcined powder indicates the spherical particles with an average particle size of 96 nm (Fig. 2(a)). As shown in Fig. 2(b–d), the microstructures reveal that the grain size is influenced by the sintering temperature. With the increase of sintering temperature from 850 to 950 1C (Fig. 2(b–d)), the grain size increases, from 0.3 to 1.2 μm. One can see that the grain size increases, while the porosity decreases with sintering temperature [6]. The micrographs of the samples that were sintered below 900 1C show the existence of many pores distributed at the grain boundaries. Such porous structure can explain why the bulk density is lower than the X-ray density. The results of the bulk density are listed in Table 1. The sample that is sintered at 950 1C shows a dense microstructure and larger grain size. Magnetic properties: It is well-known that permeability and saturation magnetization are influenced by not only the intrinsic factors such as preferential site occupancy, but also the extrinsic factors like density and microstructure (grain size and porosity) [7].
Fig. 2. The micrographs of calcined powder (a) and sintered samples at 850 (b), 900 (c) and 950 1C (d).
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Fig. 3. Frequency dependency of permeability (a), relative quality factor (b) and hysteresis curves (c) of the sintered samples.
Fig. 3(a) shows the real part of initial permeability (mi0 ) of sintered samples at different temperatures as a function of frequency. It can be seen that for each sample the value of mi0 remains constant in the frequency range up to a critical frequency, which is called the resonance frequency (fr). From this figure and Table 1, one can see that mi0 increases with sintering temperature but fr moves towards the lower frequency. This observation is in agreement with the snoek's law which says the initial permeability and resonance frequency are related inversely (mi0 fr ¼Constant) [8]. It is established that the initial permeability is a result of the easy reversal of domain wall displacement in the direction of the applied magnetic field [7]. Comparison of the results of the initial permeability, density and microstructures in Table 1. demonstrates that the initial permeability is correlated with bulk density and grain size of the samples. In the other hand, the relation between initial permeability and grain size due to domain wall motion is given by means of following relation: mi α (M2s D)/K where Ms is the saturation magnetization, D is the average grain size and K is the magnetocrystalline anisotropy constant [5]. Since the large grains tend to minimize their magnetic energy by increasing the number of domain walls; thus, the greater the number of domain walls the higher the initial permeability. Also the fewer amounts of pores and grain boundaries that could be obtained at higher sintering temperature, lead to easy movement of domain walls and as a result high initial permeability. Consequently, ferrites with higher density and larger average grain size possess a higher initial permeability [9]. Fig. 3(b) shows the relative quality factor (RQF) (i.e., RQF¼ mi0 /tan δ, where tan δ is the loss factor) of different samples. For practical application the tan δ is often used as a measure of performance. Low tan δ and high μi0 is required for high frequency magnetic applications. It is observed that the RQF of all samples increases initially, reaching a maximum value and then decreases with frequency due to the resonance-relaxation losses. The sample sintered at 950 1C has the highest value of RQF.
Fig. 3(c) shows the magnetic hysteresis curves of the sintered samples. It is observed that Ms increases with sintering temperature up to 950 1C. The maximum value of saturation magnetization Ms is found to be 40.43 emu/g for sample sintered at 950 1C. This may be due to better the bulk density and decrease in the number of pores in the samples. It should be mentioned that pores act as pinning centers for the electron spins, thereby, lowering the magnetization [10].
4. Conclusion Nanocrystalline MgCuZn ferrite powder prepared through the nitrate–citrate sol–gel auto combustion method, exhibited high sintering activity. The calcined powder indicates the spherical particles with an average particle size of 96 nm. The results of sintered samples at different temperatures showed that the magnetic properties are sensitive to the bulk density and microstructure. It was observed that an increase in the bulk density and grain size due to the sintering temperature, leads to the higher initial permeability and saturation magnetization of the MgCuZn ferrite samples. The maximum values of initial permeability and saturation magnetization is found to be 299.6 at 1 MHz and 40.43 emu/g respectively for the sample sintered at 950 1C.
References [1] Penchal Reddy M, Madhuri W, Balakrishnaiah G, Ramamanohar Reddy N, Siva Kumar KV, Murthy VRK, et al. Microwave sintering of iron deficient Ni– Cu–Zn ferrites for multilayer chip inductors. Curr Appl Phys 2011;11:191–8. [2] Mathur P, Thakur A, Lee JH, Singh M. Sustained electromagnetic properties of Ni–Zn–Co nanoferrites for the high-frequency applications. Mater Lett 2010;64:2738–41. [3] Yan S, Ling W, Zhou E. Rapid synthesis of Mn0.65Zn0.35Fe2O4/SiO2 homogeneous nanocomposites by modified sol gel auto-combustion method. J Cryst Growth 2004;273:226–33.
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H. Bahiraei et al. / Materials Letters 122 (2014) 129–132
[4] Zehani K, Mazaleyrat F, Loyau V, Laboure E. Effect of temperature and time on properties of spark plasma sintered. J Appl Phys 2011;109:07A504. [5] Akther Hossain AKM, Biswas TS, Yanagida T, Tanaka H, Tabata H, Kawai T. Investigation of structural and magnetic properties of polycrystalline Ni0.50Zn0.50 xMgxFe2O4 spinel ferrites. Mater Chem Phys 2010;120:461–7. [6] German RM. Powder Metallurgy Science. 2nd ed. Princeton, NJ: Metal Powder Industries Federation; 1994. [7] Yang Q, Zhang H, Liu Y, Wen Q, Jia L. Microstructure and magnetic properties of microwave sintered NiCuZn ferrite for application in LTCC devices. Mater Lett 2012;79:103–5.
[8] Chand J, Kumar G, Kumar P, Sharma SK, Knobel M, Singh M. Effect of Gd3 þ doping on magnetic, electric and dielectric properties of MgGdxFe2 xO4 ferrites processed by solid state reaction technique. J Alloys Compd 2011;509:9638–44. [9] Globus A, Duplex P. Separation of susceptibility mechanisms for ferrites of low anisotropy. IEEE Trans Magn 1966;MAG-2:441–5. [10] Gabal MA. Effect of Mg substitution on the magnetic properties of NiCuZn ferrite nanoparticles prepared through a novel method using egg white. J Magn Magn Mater 2009;321:3144–8.