Moreover the A-site spin magnetic moment is always opposite to the B-site spins magnetic moment, hence the net magnetic moment is decreased with increasing dopant concentration.. The Fe [r]
(1)Original Article
Structural, electrical and magnetic properties of Mg-Zr co-substituted Ni0.5Zn0.5Fe2O4
K Jalaiaha,b,*, K Chandra Moulic, K Vijaya Babud, R.V Krishnaiahe aChebrolu Engineering College, Chebrolu, Guntur, 522212, India
bDepartment of Physics, Andhra University, Visakhapatnam 530003, India
cDepartment of Engineering, Physics, Andhra University, Visakhapatnam 530003, India dAdvanced Analytical Laboratory, Andhra University, 530003, India
eInstitute of Aeronautical Engineering and Technology, Hyderabad, 500043, India
a r t i c l e i n f o
Article history: Received October 2018 Received in revised form 15 December 2018 Accepted 16 December 2018 Available online 23 December 2018
Keywords: Ferrites XRD TEM SEM Permeability
Saturation magnetization Anisotropy constant
a b s t r a c t
Zr and Mg co-substituted Ni0.5Zn0.5Fe2O4ferrites have been synthesized by the sol-gel auto-combustion
method The X-ray diffraction patterns evidenced the single phase cubic spinel structure The lattice parameter and cell volume are in resemblance trend with the variation of the dopant concentration The similar trend is observed for the crystallite and particle size The porosity and sintered density, however, vary in an opposite way with a variation of the dopant concentration The same variation is found for the drift mobility and DC resistivity The Arrhenius graphs of DC resistivity exhibit the semiconductor nature, for which the activation energy decreased with increasing the dopant concentration Moreover, as the dopant contents increased, the saturation magnetization, net magnetic moment and permeability are reduced, while the coercivity is reinforced Thesefindings can be correlated with the variation of the porosity and grain size
© 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
1 Introduction
In early days iron based magnetic alloys are used in various applications However, their low resistivity made these materials inefficient at high frequencies, which encouraged the eddy current through them This wasted energy is created a serious problem that generated the heat in the circuit Hence, iron based magnetic ma-terials are not favorable in high frequency applications Ferrite materials, in opposite, possess high resistivity and dielectric per-formances and not conduct the electric current readily The advantage of ferrites over magnetic alloys is that they formed a different combination of ferrites with transition metals because the transition metals exhibit magnetic as well as semiconductor properties The porosity is an insignificant factor for ferrites so that the ferrites have been investigated for several years based on this issue In order to get the high resistivity of ferrites researchers
choose different combination here we also choose a new combi-nation with transition metals to get the high resistivity of ferrite material[1,2] Spinal ferrites are a class of magnetic oxides with the general formula of AB2O4 They are categorized as soft and hard ferrites according to their magnetic performance Soft ferrites are easily demagnetized without significant energy need, i.e only a small energy amount is wasted in the form of eddy currents to demagnetize the soft magnetic materials In case of hard ferrites, a significantly higher energy is needed to demagnetize This means that soft magnetic materials possess higher electrical resistivity, thus, they are used in inductors and transformers The magnetic oxides are made from the blend of iron, nickel, zinc, manganese oxides By using these oxides, different combinations of soft ferrites like Manganese-Zinc and Nickel-Zinc have been prepared For inductor cores, the magnetic permeability is the chief parameter
[3,4] In order to improve the core performance at high frequency the grain size, which can be controled by the ferrite preparation technique, plays an important role The solid state ceramic tech-nique is a general ferrite fabricated techtech-nique, in which the con-stituent oxides react at higher temperatures In this case, an unusual grain growth usually occurs due to the non stoichiometry
* Corresponding author Chebrolu Engineering College, Chebrolu, Guntur, 522212, India
E-mail address:kjalu4u@gmail.com(K Jalaiah)
Peer review under responsibility of Vietnam National University, Hanoi
Contents lists available atScienceDirect
Journal of Science: Advanced Materials and Devices j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d
https://doi.org/10.1016/j.jsamd.2018.12.004
(2)and inhomogeneity of ferrite materials[5] To control this unusual grain growth, we adopted the solution method known as the sol-gel autocombustion method in which the constituent oxides react at lower temperatures So, the precursor material becomes stoi-chiometry and homogeneity with controlled grain size In the present study, the correlation between structural, electrical and magnetic properties of Mg-Zr co-substituted Ni0.5Zn0.5Fe2O4 are discussed in connection with the dopant concentration
2 Experimental
The Zr and Mg co-substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4have been prepared by sol-gel auto combustion method, x values vary from the 0.08 to 0.4 in steps of 0.08 with% The starting mate-rials of all metal nitrates with AR grade Nickel nitrate (Ni(NO3)2.6H2O), zinc nitrate (Zn (NO3)2.6H2O), Magnesium ni-trate (Mg(NO3)2.6H2O), Zirconyle nitrate (ZrO (NO3)2), ferric citrate (Fe C6H8O7.H2O) and citric acid (C6H8O7.H2O) are used for synthesis of Ni0.5Zn0.5ZrxMgxFe2-2xO4(x¼ 0.08, 0.16, 0.24, 0.32, 0.4) The stoichiometric weights of metal nitrates dissolved in deionized water and the citric acid added to the solution as per the oxygen ions present in chemical formula, later 50 ml ethylene glycol added to the solution[6] The ammonia solution added drop wise to adjust the PH value of for thefinal solu-tion Then the neutralizing solution heated to 600oCe700C for
8e10 h with continuous stirring After 8e10 h the solution
turned into a viscous on the formation of gel, then the tem-perature of a gel rise to 100C drying,finally a powder form of
samples obtained [7] The obtained powders processed for
simple experimental needs Structural studies
Fig shows the XRD patterns of Mg and Zr co-substituted Ni0.5Zn0.5Fe2O4 Here the XRD patterns provide the evidence for single phase cubic spinel and no extra peaks are observed throughout while the doping concentration is increased The lattice constant is calculated from XRD peaks, using the following equation
aẳ dph2ỵ k2ỵ l2
where d is the space between the lattice planes The lattice constant and cell volumes are shown inFig 2a with a variation of dopant concentration The increase in the lattice constant has resulted in
mismatches between the substitute ions and host ions ionic radius The Fe3ỵ (0.67) ions radius is small when compared with Zr (0.80Å) and Mg (0.72 Å) ionic radii Hence the substitution of Zr and Mg in place of the Fe3ỵions unit cell will bulge promptly and as a result the lattice constant increases with increasing dopant con-centration[8] The X-ray density is estimated from the following equation
Dx¼ 8M Naa3
where M is the molar mass, Na is the Avogadro number and“a” is the lattice constant The X-ray density increases with increasing dopant concentration from x¼ 0.08 to x ¼ 0.32, later it is slightly decreased to x¼ 0.4 However, overall X-ray density increases with increasing dopant concentration The increase in X-ray density may be due to the lattice constant which is dominated by the molar mass as shown in the above equation because the increase in the lattice constant decreases the X-ray density The ratio between the sintered density and X-ray density gives the porosity of prepared samples The porosity of prepared samples is estimated from the following equation
p¼ ds dx
where“ds” and “dx” are sintered and x-ray densities respectively The porosity and sintered density are shown in Fig 2b with a variation of dopant concentration FromFig 2b it is clear that both the parameters exhibit opposite trend with a variation of dopant concentration The sintered density is decreased as a result of lag-ging the sintering rate of material The sintering rate of material is lagging due to the volatilization of zinc at higher temperature Since the melting point of zinc is less than those of other constituent ions, the material becomes non stoichiometry[9] To minimize the non stoichiometry property of the material, the excess of ferric oxide is changed as ferrous oxide, i.e., Fe3ỵions are changed as Fe2ỵions in the sintering process The presence of Fe2ỵions in the material lags the sintering rate of material, hence sintered density is decreased
[10] The decrease in the sintered density results in the develop-ment of pores in the material
4 Surface morphology
The crystallite size is estimated from the following equation
D¼0:94*b l cosq
wherelis the wavelength of Cu radiation andbis the full width half maximum of (3 1) peak The FWMH is decreased with increasing substituting ionic radii so that the decrease in the FWHM increases the crystallite size since crystallite size and FWHM are inversely related in the above equation.Fig 2c shows the crystallite size and particle size with a variation of dopant concentration The TEM pictures are shown inFig The particle size is measured from TEM pictures by using image-j software The particle size increased with increasing dopant concentration as a result of the agglomeration nature of crystallites[11] From
Fig 2c we conclude that both the crystallite size and the particle size are in comparable nano size The SEM micrographs of pre-pared samples are shown inFig The grain size is measured from SEM micrographs by using the image-j software The grain size decreased with increasing dopant concentration The decrease in grain size is due to the development of pores in the material during the sintering of material
Fig X-ray diffraction patterns of Ni0.5Zn0.5ZrxMgxFe2-2xO4samples with x¼ 0.08,
0.16, 0.24, 0.32, and 0.4
(3)5 DC resistivity
The ferrites exhibit the semiconducting nature since ferrites are composed of transition elements and all transition elements show the semiconducting nature.Fig 5shows composition variation of DC resistivity and drift mobility of prepared ferrite samples The DC resistivity of ferrite samples decreased with increasing doping concentration The decrease in DC resistivity because of the increased electronic conduction between the paramagnetic region (Fe2ỵions) to ferromagnetic (Fe3ỵions) region [12] That is the electronic exchange has occurred in ferrites from Fe2ỵ(n-type) to Fe3ỵ(p-type) InFig 5the drift mobility varies opposite to DC re-sistivity with increasing doping concentration, since the decrease in DC resistivity increases the mobility of electrons The Arrhenius plots drawn between DC resistivity and inverse temperature in the range of 300 K and 620 K show that all plots are less curved So these plots reveal the semiconducting nature of prepared samples The Arrhenius plots for the present study are shown inFig The semi conductivity of ferrite samples is described by the following equation
s¼soexp D
E kBT
where so is the constant,DE is the activation energy, KB is the Boltzmann constant and T is the absolute temperature The graph
betweensand 1/T gives more or less a curved line TheDE equals 0.1eV for stoichiometry composition andDE reaches 0.5eV for low conductivity ferrites[13] For the present study the Activation en-ergyDE decreased from 0.17eV to 0.11eV i.e the activation energy, decreased with increasing dopant concentration and it is shown in
Fig The decrease in activation energy is due to increase of jumping frequency of electrons from the paramagnetic region (Fe2ỵ) to the ferromagnetic region (Fe3ỵ)[14]
6 Magnetic properties
The magnetic properties of Mg and Zr substituted Ni0.5Zn0.5
-Fe2O4ferrites are calculated by using the M-H loops shown in
Fig All the M-H loops are with less loss of magnetic energy and the M-H loop data is collected at room temperature The satura-tion magnetizasatura-tion and the corresponding net magnetic moment are estimated from M-H loops Both the saturation magnetization and the corresponding net magnetic moment are in decreasing trend with increasing dopant concentration as shown inFig 9a The decrease in saturation magnetization is due to the decrease of Fe3ỵions in general formula with the substitution of Mg and Zr ions in place of Fe3ỵions The presence of Fe3ỵions in the material needs a much moreflux to orient in the applied eld direction Since Fe3ỵions behave like ferromagnetic ions the Fe3ỵions need
higher ux density to orient in the eld direction [15] The
(4)decreased Fe3ỵions in material need lesserflux density to orient in
the field direction Hence the saturation magnetization is
decreased with increasing dopant concentration Father the net magnetic moment of the material is calculated using the following equation
M¼ MA MB
here MAand MB are the magnetic moments of A-site and B-site respectively From the above equation the resultant magnetic
Fig Transmission electron micrographs of Ni0.5Zn0.5ZrxMgxFe2-2xO4along with selected area Electron diffraction patterned of samples
(5)Fig Schematic SEM photo graphs of Zr and Mg Co substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4
(6)moment of material is the difference between the B-site magnetic moment and A-site magnetic moment The increase in A-site magnetic moment decreases the resultant material magnetic moment The substituted Mg and Zr in place of Fe3ỵions, occupy the A-site and B-sites for their comfortablefit in lattice sites While Zr enters A-site, it replaces the Fe3ỵions from A-site to B-site To give place for Fe3ỵions in B-site the Ni2ỵions are converted as Ni3ỵions by releasing an electron And by taking the electron from Ni ion, Fe3ỵion is changed as Fe2ỵion [16,17] Moreover the A-site spin magnetic moment is always opposite to the B-site spins magnetic moment, hence the net magnetic moment is decreased with increasing dopant concentration The Fe3ỵions from A-site will be arranged anti parallel in B-site upto certain concentration, later Fe3ỵions from A-site will be arranged on B-site with canting posi-tion This gives an angle between the Aesite Fe3ỵions and B-site-Fe3ỵions called Y-K angle[18] The Y-K angle is calculated by using the following equation
nBẳ ỵ xịcosaYK 51 xÞ Fig Variation of activation energy with dopant concentration
Fig Magnetization versus magneticfield (M-H) curves of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4 at room temperature
(7)The variation of Y-K angles with dopant concentration is shown inFig 9b FromFig 9b it is clear that Y-K angles increased with increasing dopant concentration The increase in the Y-K angles suggests the increase of AeB interaction[19] The coercive field is a field where the magnetization becomes zero in reverse order The composition variation of Coercivefield and porosity is shown inFig 9c FromFig 9c it is concluded that the increase in the porosity increases the coercivefield According to J Smith and H.P.J Wijn the increase in the porosity of the material will affect
the reverse magnetization of material [20] On removing the
applied magneticfield magnetic dipoles will not come to initial
orientation since the magnetic dipoles lag by field (i.e the
magnetic dipoles suffer by residualflux) This lagging of field is affected by the porosity of samples[21] Hence an increase in porosity increases the coercivefiled
7 Magnetic permeability
Permeability is the property of a magnetic material which measures its ability to support the formation of magneticfields within itself The extent of the magnetization of a material denotes the response to an applied magneticfield The permeability of the material is estimated from the following equation
m¼ L L0
Fig Variation of net magnetic moment and saturation magnetization (a), Y-K angles (b), coercivefield and porosity (c), and permeability and grain size (d) with dopant concentration
(8)where L is the measured inductance of the torroids and Lo is calculated as follows
Lo¼ 4:606N2log
OD ID
t 109Henry
Fig 9d shows the variation of the initial permeability and grain size with the dopant concentration FromFig 9d it is clear that the permeability decreases with increasing dopant concentration, since the permeability and the grain size are related as shown in the following equation
K¼ cd2
here K is the permeability, c is the dimension less constant and d is the grain size Hence permeability is directly proportional to the square of the grain size The materials composed with grains include the atomic dipoles or spin dipoles[22] The existed atomic dipoles or spin dipoles in grains are oriented randomly By the application of externalfields, the atomic dipoles or spin dipoles in grains align with thefield direction This is related to the induced
magneticflux in the magnetic material, which continues to
in-crease up to a certain frequency In this case, a resonance peak will appear where the frequency of the appliedfield equals the spin dipoles or atomic dipoles It means that the maximum magnetic flux is induced in the material at the resonance frequency Later
atomic dipoles will not follow the applied field According to
literature survey the resonance peak appearance connects to: (i) inhomogeneous material, (ii) crystalline magnetic anisotropy, (iii) the combination of the magnetic anisotropy and the
ferromag-netic exchange fields, (iv) the domain walls and (v) the
elec-tromagnetic body resonance The frequency variation of
permeability in the present study is shown inFig 10 From the
Fig 10 it is clear that all samples exhibit the resonance peak around the 12 MHz to 13 MHz The resonance effects occur in all ferrous and paramagnets In particular, it is not peculiar to ferrites in its simple form Generally, it has been considered that the resonance in ferrites accounts for a large part of the magnetic dispersion of ferrites The permeability arises from the rotation of magnetic dipoles rather than from a domain wall displacement process The domain wall displacement does not account for magnetic dispersion at higher frequency[23] More complex type resonances are considered in ferromagnetic and antiferromag-netic materials, the sample shape anisotropy is taken into account in this case Sometimes there may be two or more resonance frequencies possible in an accessible range of frequency In this case, domain wall effects will be considered The moving wall sets up a magnetic double layer in the wall, and as a result the addi-tional energy acquires its static value Another resonance fre-quency appears due to body-resonance which accounts for the high permeability and high permittivity[24] Both are comparable at body resonance frequency and as a result, the permeability and permittivity of a material may give too small values The perme-ability and anisotropy constant are shown inFig 11with dopant concentration The permeability and anisotropy constant are related as shown in following expression
mi∞ M2sD
K
From the above relation, the initial permeability is directly proportional to the square of saturation magnetization, and inversely proportional to anisotropy constant The permeability strongly depends on the homogeneity of the material That means, permeability depends on the grain size, intra and intergranular porosity of material If they are not explained well, then the
Table:
The structural data of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4
Dopant concentration Lattice parameter(Å) Crystallite size (nm) X-ray density g/cm3
Porosity (%) Sintered density g/cm3
Grain size (mm)
Particle size (nm)
0.08 8.2997 5.3857 5.5237 10.99 4.9166 2.2286 25.1005
0.16 8.2996 5.3112 5.6840 14.34 4.8685 2.1454 27.7178
0.24 8.3072 5.1105 5.7482 16.16 4.8191 2.0556 29.6136
0.32 8.3367 5.5166 5.7665 17.31 4.7682 1.9542 32.3956
0.4 8.3908 5.5663 5.733 19.12 4.6370 1.8775 37.3752
Table:
The DC resistivity data of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4
Dopant concentration DC resistivity(r) U-cm
Drift mobility(h) 1036 Activation energy (DE) eV
0.08 1.92775E6 1.5834 0.1765
0.16 889033 1.7539 0.1673
0.24 430824 2.9249 0.1509
0.32 243293 4.62057 0.1411
0.4 89791 6.1224 0.1172
Table:
The magnetic properties of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4
Dopant concentration Net Magnetic momenthB
Saturation magnetization emu/gm Coercive field (Hc)Oe Anisotropy constant(K)
Y-K angles (⁰) Permeability
0.08 5.8800 65.4921 11.4795 80.1051 35.3507 114
0.16 5.6074 60.5877 12.8929 105.62 42.7818 84
0.24 4.8321 51.4706 30.7264 117.13 48.4878 52
0.32 3.9987 42.3480 43.6102 134.71 54.1299 33
0.4 3.2924 34.7691 44.2298 200.68 58.5468 25
(9)permeability mechanism must be governed by some other
mechanism of magnetic anisotropy and magnetostriction [25]
There are three types of magnetic anisotropy (1) crystal structure, (2) grain shape and (3) applied stress or residual stresses The crystal structure anisotropy is independent of grain size and shape and it can be easily observed by measuring the magnetic curves in different crystal directions The interaction of the spin magnetic moment with the crystal lattice gives easy and hard directions The magnetized body produces the poles or charge distribution at the surfaces As a result, the magnetized body itself acts as another
source of the magnetic field called a demagnetizing field This
demagnetizingfield acts opposite to the magnetizing field, and it
happens by applying a magneticfield in the material hence the
permeability decreases In short, decreasing the shape of magnetizing body effects the permeability In case of round sha-ped magnetized body, the anisotropy constant will be higher and for cube shape, the anisotropy constant will be low The perme-ability will be low for round shaped magnetize body, and for cube shape it will be higher FromFig 4, magnetized bodies other than the cube shape should be grown, so that the anisotropy constant will be high As a result, the permeability decreases with increasing dopant concentration The third one arises due to the spin-orbit coupling that produces strain along the crystallo-graphic axis So, the magnetized body will change directions when magnetized[13]
8 Conclusion
The Zr and Mg co-substituted Ni0.5Zn0.5Fe2O4 ferrites have been prepared by sol-gel auto combustion method The investi-gated samples revealed the semiconducting nature, in which the activation energydecreased with increasing dopant concentra-tion The XRD patterns confirm the single phase cubic spinel and no secondary phase was identified by this analysis The lattice constant, cell volume as well as the porosity of samples increased with increasing the dopant concentration The density of material, as a consequence, decreased by pores developed in the material The crystallite and particle sizes are comparable in the nano scale As the dopant content varies, the DC resistivity and drift mobility varied in the opposite way The saturation magnetization, net magnetic moments and permeability are reduced with increasing
dopant concentration, while the coercive field and anisotropy
constant are enhanced The Y-K angles increase with increasing dopant concentration Electrical and magnetic properties have been discussed in good correlation with the structural behaviour (seeTables 1e3)
References
[1] Muhammad Ajmal, Asghari Maqsood, Structural, electrical and magnetic properties of Cu1xZnxFe2O4ferrites (0x1), J Alloy Comp 460 (2008) 54e59,https://doi.org/10.1016/j.jallcom.2007.06.019
[2] Muhammad Ajmal, Asghari Maqsood, Influence of zinc substitution on structural and Electrical properties of Ni1xZnxFe2O4ferrites, Mater Sci Eng B 139 (2007) 164e170,https://doi.org/10.1016/j.mseb.2007.02.004
[3] M.A Ahmeda, N Okashab, M Gabalc, Transport and Magnetic Properties of Co-Zn-La Ferrite Materials Chemistry and Physics, vol 83, 2004, pp 107e113 http://doi:10.1016/j.matchemphys.2003.09.008
[4] J.M Haspers Ferrites, Their Properties and Applications Modern Matrials, vol 3, 1962, pp 259e341.https://doi.org/10.1016/B978-1-4831-9657-2.50009-7 [5] J.E Knowles, Permeability mechanisms in manganese zinc ferrites, J Phys Colloq 38 (C1) (1977) C1-C27eC1-C30 https://doi.org/10.1051/jphyscol: 1977104
[6] K Jalaiah, K Vijaya Babu, K Rajashekhar Babu, K Chandra Mouli, Structural and dielectric studies of Zr and Co co-substituted Ni0.5Zn0.5Fe2O4using sol-gel auto combustion method, Results Phys (2018) 1417e1424.https://doi.org/ 10.1016/j.rinp.2018.04.024
[7] A Sutka, G Mezinskis, Sol-gel auto-combustion synthesis of spinel-type ferrite nanomaterials, Front Mater Sci (2012) 128e141.https://doi/10 1007/s 11706-012-0167-3
[8] A.D.P Rao, S.B Raju, S.R Vadera, D.R Sharma, Mossbauer studies of Sn4ỵ/ Nb5ỵsubstituted Mn-Zn ferrite, Bull Mater Sci 26 (5) (2003) 505e507.http:// doi:10.1007/bf02707348
[9] K Jalaiah, K Chandra mouli, P.S.V Subba Rao, B Sreedhar, Structural and dielectric properties of Zr and Cu co-substituted Ni0.5Zn0.5Fe2O4, J Magn Magn Mater 432 (2017) 418e424.http://doi:10.1016/j.jmmm.2017.02.013 [10] M ManjurulHaquea, M Huqa, M.A Hakim Densification, Magnetic and
dielectric behaviour of Cu-substituted Mg-Zn ferrites, Mater Chem Phys 112 (2008) 580e586.https://doi.org/10.1016/j.matchemphys.2008.05.097 [11] K Jalaiah, K Vijaya Babu, Structural, magnetic and electrical properties of nickel
doped Mn-Zn spinel ferrite synthesized by sol-gel method, J Magn Magn Mater 423 (2017) 275e280.https://doi.org/10.1016/j.jmmm.2016.09.114 [12] B Parvatheeswara Rao, K.H Rao, Effect of sintering conditions on resistivity
and dielectric properties of Ni-Zn ferrites, J Mater Sci 32 (1997) 6049e6054 https://link.springer.com/article/10.1023/A:1018683615616
[13] A Fairweather, F.F Roberts, A.J.E Welch, Ferrites, Post Office Research Station, vol 142, Dollis Hill, London, 1982, pp 142e169.http://iopscience.iop.org/ article/10.1088/0034-4885/15/1/306/pdf
[14] S.S Bellad, R.B Pujar, B.K Chougule, Structural and magnetic properties of some Li-Cd ferrites, Mater Chem Phys 52 (1998) 166e169.https://doi.org/ 10.1016/S0254-0584(98)80019-9
[15] S.S Bellad, B.K Chougule, Composition and frequency dependent dielectric properties of Li-Mg-Ti ferrites, Mater Chem Phys 66 (2000) 58e63.https:// doi.org/10.1016/S0254-0584(00)00273-X
[16] R.B Pujar, S.S Bellad, S.C Watawe, B.K Chougule, Magnetic properties and microstructure of Zr4ỵsubstituted Mg-Zn ferrites, Mater Chem Phys 57 (1999) 264e267.https://doi.org/10.1016/S0254-0584(98)00227-2 [17] P.N Vasambekar, C.B Kolekar, A.S Vaingankar, Magnetic behaviour of Cd2ỵ
and Cr3ỵsubstituted cobalt ferrites, Mater Chem Phys 60 (1999) 282e285 https://doi.org/10.1016/S0254-0584(99)00062-0
[18] G Alvarez, H Montiel, J.F Barron, M.P Gutierrez, R Zamorano, YafeteKittel-type magnetic ordering in Ni0.35Zn0.65Fe2O4 ferrite detected by magneto-sensitive microwave absorption measurements, J Magn Magn Mater 322 (2010) 348e352.https://doi:10.1016/j.jmmm.2009.09.056
[19] K Jalaiah, K Vijaya Babu, K Chandra mouli, P.S.V Subba Rao, Effect on the structural, DC resistivity and magnetic properties of Zr and Cu co-Sub-stitutedNi0.5Zn0.5Fe2O4using sol-gel auto-combustion method, Phys B Condens Matter 534 (2018) 125e133.https://doi.org/10.1016/j.physb.2018.01.026 [20] J Smit, H.P.J Wijn, Ferrites, John Wiley, New York, 1959, p 144
[21] A.A Sattar, A.M Samy, Effect of Sm substitution on the magnetic and electrical properties of Cu-Zn ferrite, J Mater Sci 37 (2002) 4499e4502.https://link springer.com/article/10.1023/A:1020614300002
[22] A Globus, H Pascard, V Cagan, Distance between magnetic ions and funda-mental properties in ferrites, J Phys Colloq (1977) 163e168.https://doi.org/ 10.1051/jphyscol:1977132
[23] A Verma, T.C Goel, R.G Mendiratta, Frequency variation of initial perme-ability of Ni-Zn ferrites prepared by the citrate precursor method, J Magn Magn Mater 210 (2000) 274e278.https://doi.org/10.1016/S0304-8853(99) 00451-5
[24] Z Yue, J Zhou, L Li, H Zhang, Z Gui, Synthesis of nanocrystalline Ni-Cu-Zn ferrite powders by sol-gel auto-combustion method, J Magn Magn Mater 208 (2000) 55e60.https://doi.org/10.1016/S0304-8853(99)00566-1 [25] S Ramesh, B.C Sekhar, P.S.V.S Rao, B.P Rao, Microstructural and magnetic