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Hysteresis and initial permeability behavior of vanadium-substituted lithium–zinc–titanium ferrite
ARTICLE IN PRESS
Physica B 352 (2004) 86–90 www.elsevier.com/locate/physb
Hysteresis and initial permeability behavior of vanadium-substituted lithium–zinc–titanium ferrite Mamata Maisnama, Sumitra Phanjoubama, H.N.K. Sarmaa, L. Radhapiyari Devib, O.P. Thakurb, Chandra Prakashb, a Department of Physics, Manipur University, Canchipur, Imphal 795003, India Electroceramics Group, Solid State Physics Laboratory, Lucknow Road, Delhi 110 054, India
b
Received 7 June 2004; received in revised form 23 June 2004; accepted 23 June 2004
Abstract Li–Zn–Ti ferrite samples, with compositional formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4, ‘t’ ranging from 0.0 to 0.25 in steps of 0.05 were prepared by the ceramic route. XRD results confirmed the single-phase spinel structure of the samples. SEM photomicrographs have revealed the grain size of the samples. B–H loops have been traced for all the samples and the various hysteresis parameters like coercivity, remanence and remanence ratio have been studied as a function of composition. Compositional dependence of initial permeability (mi), the frequency dispersion of initial permeability and the corresponding loss, tan dm have been studied. The possible mechanisms involved are discussed. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Gg Keywords: Lithium ferrites; Vanadium; Permeability; Hysteresis; B–H loop
1. Introduction Polycrystalline ferrites are widely used for electronic devices. They form a complex system composed of crystallites, grain boundaries and pores. They constitute a class of good dielectric material with high resistivity. The magnetic Corresponding author. Tel: +011-23921692; fax: +011-
23913609. E-mail address: [email protected] (C. Prakash).
properties of these materials are determined by chemical compositions, microstructure and process mechanism [1,2]. Among them lithium ferrites are the most versatile and are extensively studied by many workers [3]. The properties of interest are their high Curie temperature, squareness of hysteresis loop and high electrical resistivity. Being a good dielectric material with low dielectric and magnetic losses over a wide range of frequencies, excellent temperature performance and low stress sensitivity of remanence, lithium ferrite served as
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.06.059
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
the low cost materials for the microwave devices. Their properties are further very sensitive to the type and amount of substituents, methodology of preparation, sintering temperature and atmosphere [3,4]. A variety of lithium ferrites have emerged by substituting metal ions like Zn2+, Ti4+, Mg2+, Al3+, Co2+, Mn3+, Cr3+, Sb5+ etc. in appropriate amount into the formula unit Li0.5Fe2.5O4 in order to optimize the numerous properties of interests [3]. Simultaneous substitution of Zn2+ and Ti4+ in lithium ferrite has been studied earlier [5]. Addition of V2O5 in some of the ferrite system has been found to be an effective sintering aid and promote certain electrical properties [6,7]. The substitution of V5+ in lithium ferrite has also been studied earlier [8]. The purpose of the present work is to study the overall effect of V5+substitution on the microstructure, hysteresis parameters and initial permeability of Li–Zn–Ti ferrite system.
87
obtained from the torroids with primary and secondary windings of about 80 turns of enameled copper wire using a computer controlled hysteresis loop tracer at an applied frequency of 50 Hz and the applied field is made high enough to ensure magnetic saturation. Inductance, L and the magnetic loss, tan dm were measured from the torroids of each composition in the frequency range 100 Hz to 1 MHz using a Precision Impedance Analyzer [Agilent 4294 A]. Initial permeability was calculated using the formula [9], mi ¼ 2pL= N 2 hm0 lnðR=rÞ ; where, L is the inductance [H], R and r are the outer and inner radius of the torroid[m], N is the number of turns of inductor, h is the height of the torroid[m] and m0 is the magnetic permeability of vacuum:4px107[H/m]. All the measurements were carried out at room temperature.
3. Results and discussions 2. Experimental Polycrystalline samples with the representative formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4 where 0.0 ptp 0.25 in steps of 0.05 were prepared by the conventional ceramic method. AR grade (99.9% purity) chemicals Li2CO3, ZnO, TiO2, V2O5 and Fe2O3 were weighed in stoichiometric proportion and was thoroughly mixed in water medium by ball milling with Zirconia balls for 5 h. The resulting mixtures were dried, crushed and calcined at 600 1C for 3 h. The reacted powders were ball milled again with distilled water as wetting agent for another 5 h and dried. The dried and sieved powders were pressed into pellets and torroids with an applied pressure of 50 kN using a small amount of PVA as binder. These pressed samples were sintered finally at 950 1C for 2 h. X-ray diffraction (XRD) analysis has been done on the samples for the structural determination. Archimedes principle was used to measure the density (dexp) and compared with X-ray density (dx). The porosity of each sample was calculated using the formula p=(dxdexp)/dx. The SEM photomicrographs were recorded on the fractured surface of each composition. The B–H loops were
XRD analysis has confirmed the single phase with spinel structure for all the samples. The lattice constant, ‘a’ as calculated from the XRD data has been observed to be almost constant within the experimental error varying from 8.35 A˚ to 8.36 A˚.This can be explained from the compositional formula that one Fe3+ ion (0.67 A˚) is being replaced by 0.5Li+and 0.5 V5+ with an average ionic radius of 0.665 A˚ (ionic radius of Li+ and V5+ being 0.74 A˚ and 0.59 A˚ respectively) [5]. On this basis, the change in lattice parameter is not expected. The experimental density has been found to decrease with the increase of vanadium substitution, and this variation agrees well with that of X-ray density. The porosity has been found to increase with substitution and is depicted in Fig. 3. Fig. 1 shows the SEM photomicrographs for the samples with t=0.05, 0.1, 0.15 and 0.20. These photomicrographs have been taken under the same magnification ( 1300 magnification) and the same scale for all the samples. It has been observed that the average grain size of the samples increases slightly for t upto 0.1 and then on further substitution, it decreases gradually. As the substitution increases from t=0.1, some finer grains
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
88
Fig. 1. SEM microphotographs for the systems with compositional formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4: (a) t=0.05, (b) t=0.1, (c) t=0.15 and (d) t=0.2.
3000
16
4000 0.00
3000
2500
0 -1000
Porosity (%)
1000 B(G)
14
0.05 0.10 0.15 0.20 0.25
2000 1500
12
1000
Remanence (G)
2000
10
-2000
500
-3000 0
8
-4000
0.00
-20
-10
0
10
20
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t)
H(Oe)
Fig. 2. Hysteresis loops for the Li0.5+tZn0.2Ti0.2VtFe2.12tO4 system.
have been found to be embedded among the bigger grains and these finer grains increase in number with decrease in their sizes. The B–H loops traced on the torroids of each composition have been depicted in Fig. 2. It has been observed from the figure that the loop shrinks in size and also deviates from rectangularity with
Fig. 3. Compositional variation of remanence (Mr) and porosity.
the increase of vanadium concentration. It is known that the shape and size of a B–H loop depends not only on the chemical composition but also on several microstructural properties like porosity, nature of the pores and grain size [10]. Fig. 3 depicts the decrease of remanence (Mr) with concentration and this can be understood from the
ARTICLE IN PRESS
3.5
18
3.0
17
2.5
16
2.0
15
Coercivity (Oe)
89
19
1.5 14 1.0 0.00
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t) Fig. 5. Compositional variation of coercivity and grain size.
300
Initial permeability (µi)
shrinking of the loop with substitution. Porosity has been found to increase with substitution (Fig. 3) and this agrees with the reported observations [2] that remanence varies inversely with porosity. The remanence ratio has been found to decrease with substitution (Fig. 4) as is also indicated by the increased deviation of the loop from rectangularity (Fig. 2). The variation of coercivity with concentration as obtained from the B–H loop data showed a decrease till t=0.1 sample and then increases as depicted in Fig. 5. Similar variation of coercivity has been reported for other ferrite systems [12]. Coercivity being inversely proportional to the grain size [13], the present variation can be understood on the basis of the average grain size variation of the samples [2,12–15]. The initial permeability was measured as a function of frequency for all the samples and the dispersion spectra has been shown in Fig. 6. Initial permeability of polycrystalline ferrites has been found to be dependent on many factors like grain structure, stoichiometry, composition, impurity contents, saturation magnetization, coercivity, magnetostriction, crystal anisotropy and porosity [10,16]. The initial permeability being sensitive to many parameters, it is still difficult to draw a specific conclusion for the variation of initial permeability with concentration. However, initial permeability is found to increase with the increase of grain size [10,11]. This is because bigger grains
Grain Size (µm)
M. Maisnam et al. / Physica B 352 (2004) 86–90
0.00 0.05 0.10 0.15 0.20 0.25
250 200 150
0.1
100
0.05 t=0.0
50 0.15
0 100
1k
0.25
0.2
10k
100k
1M
Frequency(Hz) Fig. 6. Frequency variation of initial permeability.
0.8
Remanence ratio
0.7 0.6 0.5 0.4 0.3 0.2 0.00
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t) Fig. 4. Compositional variation of remanence ratio.
tend to contain more number of domain walls and initial permeability being a result of the reversal of domain wall displacement, the greater the number of domain walls; the higher is the initial permeability. From Fig. 6, it can be noticed that the value increases and then decreases with the increase of vanadium substitution in the low frequency region (below 1 kHz). It can be explained from the effect of average grain size of the samples, which showed similar variation. Also, from Fig. 6 it has been observed that the initial permeability is high at low frequency and above 1 kHz the value becomes lower and remains nearly constant for all the samples. The frequency
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
90
works to suppress the eddy current. Hence, the observed variation with increasing vanadium content [17].
0.100
tanδµ
0.075
Acknowledgements
0.050
0.10 0.05 t=0.0
0.025
0.15
0.000 10k
0.20
Authors from Manipur University are thankful to DRDO, Ministry of Defence for financial assistance.
0.25
100k
1M
Frequency(Hz) Fig. 7. Frequency variation of tan dm for the samples.
dispersion of permeability of polycrystalline ferrites depends on many factors like chemical composition, post sintering density and the microstructure e.g. grain size, porosity and intra or intergranular pores. Initial permeability is reported to be due to the domain wall displacement and remains constant with frequency as long as there is no phase lag between the applied field and the domain wall displacement. The plot of tan dm as a function of frequency is shown in Fig. 7. It has been found that the value is high at lower frequency and decreases maintaining a small value at higher frequencies. At still higher frequencies 1 MHz, tan dm increases rapidly showing a tendency for a resonance loss peak. The resonance frequency gives the operational frequency limit of the sample. At resonance frequency, maximum energy is transferred from the applied field to the lattice resulting in the rise of tan dm [10]. Magnetic loss is reported to decline with decrease in the average grain size and vice versa. The decrease in the grain size increases the alternating current resistance as smaller grain
References [1] J. Smit, H.P.J. Wijn, Ferrites, Wiley, New York, 1965. [2] H. Igarashi, K. Okazaki, J. Am. Ceram. Soc. 60 (1977) 51. [3] P. Kishan, In: V.R.K. Murthy (Ed.), Microwave Materials, Narosa Publishing House, 1993, p. 141. [4] P.D. Baba, et al., IEEE Trans. Magn. 8 (1972) 283. [5] S. Phanjoubam, C. Prakash, Mod. Phys. Lett. B 16 (2002) 1027. [6] L.M. Letyuk, Poroshkovaya Metallurgiya 8 (1975) 59. [7] Jau Ho Jean, Cheng Horng Lee, Jpn. J. Appl. Phys. 40 (2001) 2232. [8] S.V. Salvi, V.P. Khanolkar, Proceedings of the Fifth International Conference on Ferrites, 1989, pp. 459. [9] A.C. Razzitte, S.E. Jacobo, W.G. Fano, J. Appl. Phys. 87 (2000) 6232. [10] A.K. Singh, T.C. Goel, R.G. Mendiratta, O.P. Thakur, C. Prakash, J. Appl. Phys. 92 (2002) 3872. [11] A. Verma, T.C. Goel, R.G. Mendiratta, P. Kishan, J. Magn. Magn. Mater. 208 (2000) 13. [12] J.-H. Nam, W.-G. Hur, J.-H. Oh, J. Appl. Phys. 81 (1997) 4794. [13] M.U. Rana, T. Abbas, J. Magn. Magn. Mater. 246 (2002) 110. [14] P.J. van der Zaag, P.J. van der Valk, M.Th. Rekvelt, Appl. Phys. Lett. 69 (1996) 2927. [15] A.K. Singh, A. Verma, O.P. Thakur, Chandra Prakash, T.C. Goel, R.G. Mendiratta, Mater. Lett. 57 (2003) 1040. [16] K.H. Rao, N.K. Gaur, K. Aggarwal, R.G. Mendiratta, J. Appl. Phys. 53 (1982) 1122. [17] M.K. Ono, T. Hashimoto, F. Nakao, IEEE Trans. Magn. 37 (2001) 2359.
Physica B 352 (2004) 86–90 www.elsevier.com/locate/physb
Hysteresis and initial permeability behavior of vanadium-substituted lithium–zinc–titanium ferrite Mamata Maisnama, Sumitra Phanjoubama, H.N.K. Sarmaa, L. Radhapiyari Devib, O.P. Thakurb, Chandra Prakashb, a Department of Physics, Manipur University, Canchipur, Imphal 795003, India Electroceramics Group, Solid State Physics Laboratory, Lucknow Road, Delhi 110 054, India
b
Received 7 June 2004; received in revised form 23 June 2004; accepted 23 June 2004
Abstract Li–Zn–Ti ferrite samples, with compositional formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4, ‘t’ ranging from 0.0 to 0.25 in steps of 0.05 were prepared by the ceramic route. XRD results confirmed the single-phase spinel structure of the samples. SEM photomicrographs have revealed the grain size of the samples. B–H loops have been traced for all the samples and the various hysteresis parameters like coercivity, remanence and remanence ratio have been studied as a function of composition. Compositional dependence of initial permeability (mi), the frequency dispersion of initial permeability and the corresponding loss, tan dm have been studied. The possible mechanisms involved are discussed. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Gg Keywords: Lithium ferrites; Vanadium; Permeability; Hysteresis; B–H loop
1. Introduction Polycrystalline ferrites are widely used for electronic devices. They form a complex system composed of crystallites, grain boundaries and pores. They constitute a class of good dielectric material with high resistivity. The magnetic Corresponding author. Tel: +011-23921692; fax: +011-
23913609. E-mail address: [email protected] (C. Prakash).
properties of these materials are determined by chemical compositions, microstructure and process mechanism [1,2]. Among them lithium ferrites are the most versatile and are extensively studied by many workers [3]. The properties of interest are their high Curie temperature, squareness of hysteresis loop and high electrical resistivity. Being a good dielectric material with low dielectric and magnetic losses over a wide range of frequencies, excellent temperature performance and low stress sensitivity of remanence, lithium ferrite served as
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.06.059
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
the low cost materials for the microwave devices. Their properties are further very sensitive to the type and amount of substituents, methodology of preparation, sintering temperature and atmosphere [3,4]. A variety of lithium ferrites have emerged by substituting metal ions like Zn2+, Ti4+, Mg2+, Al3+, Co2+, Mn3+, Cr3+, Sb5+ etc. in appropriate amount into the formula unit Li0.5Fe2.5O4 in order to optimize the numerous properties of interests [3]. Simultaneous substitution of Zn2+ and Ti4+ in lithium ferrite has been studied earlier [5]. Addition of V2O5 in some of the ferrite system has been found to be an effective sintering aid and promote certain electrical properties [6,7]. The substitution of V5+ in lithium ferrite has also been studied earlier [8]. The purpose of the present work is to study the overall effect of V5+substitution on the microstructure, hysteresis parameters and initial permeability of Li–Zn–Ti ferrite system.
87
obtained from the torroids with primary and secondary windings of about 80 turns of enameled copper wire using a computer controlled hysteresis loop tracer at an applied frequency of 50 Hz and the applied field is made high enough to ensure magnetic saturation. Inductance, L and the magnetic loss, tan dm were measured from the torroids of each composition in the frequency range 100 Hz to 1 MHz using a Precision Impedance Analyzer [Agilent 4294 A]. Initial permeability was calculated using the formula [9], mi ¼ 2pL= N 2 hm0 lnðR=rÞ ; where, L is the inductance [H], R and r are the outer and inner radius of the torroid[m], N is the number of turns of inductor, h is the height of the torroid[m] and m0 is the magnetic permeability of vacuum:4px107[H/m]. All the measurements were carried out at room temperature.
3. Results and discussions 2. Experimental Polycrystalline samples with the representative formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4 where 0.0 ptp 0.25 in steps of 0.05 were prepared by the conventional ceramic method. AR grade (99.9% purity) chemicals Li2CO3, ZnO, TiO2, V2O5 and Fe2O3 were weighed in stoichiometric proportion and was thoroughly mixed in water medium by ball milling with Zirconia balls for 5 h. The resulting mixtures were dried, crushed and calcined at 600 1C for 3 h. The reacted powders were ball milled again with distilled water as wetting agent for another 5 h and dried. The dried and sieved powders were pressed into pellets and torroids with an applied pressure of 50 kN using a small amount of PVA as binder. These pressed samples were sintered finally at 950 1C for 2 h. X-ray diffraction (XRD) analysis has been done on the samples for the structural determination. Archimedes principle was used to measure the density (dexp) and compared with X-ray density (dx). The porosity of each sample was calculated using the formula p=(dxdexp)/dx. The SEM photomicrographs were recorded on the fractured surface of each composition. The B–H loops were
XRD analysis has confirmed the single phase with spinel structure for all the samples. The lattice constant, ‘a’ as calculated from the XRD data has been observed to be almost constant within the experimental error varying from 8.35 A˚ to 8.36 A˚.This can be explained from the compositional formula that one Fe3+ ion (0.67 A˚) is being replaced by 0.5Li+and 0.5 V5+ with an average ionic radius of 0.665 A˚ (ionic radius of Li+ and V5+ being 0.74 A˚ and 0.59 A˚ respectively) [5]. On this basis, the change in lattice parameter is not expected. The experimental density has been found to decrease with the increase of vanadium substitution, and this variation agrees well with that of X-ray density. The porosity has been found to increase with substitution and is depicted in Fig. 3. Fig. 1 shows the SEM photomicrographs for the samples with t=0.05, 0.1, 0.15 and 0.20. These photomicrographs have been taken under the same magnification ( 1300 magnification) and the same scale for all the samples. It has been observed that the average grain size of the samples increases slightly for t upto 0.1 and then on further substitution, it decreases gradually. As the substitution increases from t=0.1, some finer grains
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
88
Fig. 1. SEM microphotographs for the systems with compositional formula Li0.5+tZn0.2Ti0.2VtFe2.12tO4: (a) t=0.05, (b) t=0.1, (c) t=0.15 and (d) t=0.2.
3000
16
4000 0.00
3000
2500
0 -1000
Porosity (%)
1000 B(G)
14
0.05 0.10 0.15 0.20 0.25
2000 1500
12
1000
Remanence (G)
2000
10
-2000
500
-3000 0
8
-4000
0.00
-20
-10
0
10
20
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t)
H(Oe)
Fig. 2. Hysteresis loops for the Li0.5+tZn0.2Ti0.2VtFe2.12tO4 system.
have been found to be embedded among the bigger grains and these finer grains increase in number with decrease in their sizes. The B–H loops traced on the torroids of each composition have been depicted in Fig. 2. It has been observed from the figure that the loop shrinks in size and also deviates from rectangularity with
Fig. 3. Compositional variation of remanence (Mr) and porosity.
the increase of vanadium concentration. It is known that the shape and size of a B–H loop depends not only on the chemical composition but also on several microstructural properties like porosity, nature of the pores and grain size [10]. Fig. 3 depicts the decrease of remanence (Mr) with concentration and this can be understood from the
ARTICLE IN PRESS
3.5
18
3.0
17
2.5
16
2.0
15
Coercivity (Oe)
89
19
1.5 14 1.0 0.00
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t) Fig. 5. Compositional variation of coercivity and grain size.
300
Initial permeability (µi)
shrinking of the loop with substitution. Porosity has been found to increase with substitution (Fig. 3) and this agrees with the reported observations [2] that remanence varies inversely with porosity. The remanence ratio has been found to decrease with substitution (Fig. 4) as is also indicated by the increased deviation of the loop from rectangularity (Fig. 2). The variation of coercivity with concentration as obtained from the B–H loop data showed a decrease till t=0.1 sample and then increases as depicted in Fig. 5. Similar variation of coercivity has been reported for other ferrite systems [12]. Coercivity being inversely proportional to the grain size [13], the present variation can be understood on the basis of the average grain size variation of the samples [2,12–15]. The initial permeability was measured as a function of frequency for all the samples and the dispersion spectra has been shown in Fig. 6. Initial permeability of polycrystalline ferrites has been found to be dependent on many factors like grain structure, stoichiometry, composition, impurity contents, saturation magnetization, coercivity, magnetostriction, crystal anisotropy and porosity [10,16]. The initial permeability being sensitive to many parameters, it is still difficult to draw a specific conclusion for the variation of initial permeability with concentration. However, initial permeability is found to increase with the increase of grain size [10,11]. This is because bigger grains
Grain Size (µm)
M. Maisnam et al. / Physica B 352 (2004) 86–90
0.00 0.05 0.10 0.15 0.20 0.25
250 200 150
0.1
100
0.05 t=0.0
50 0.15
0 100
1k
0.25
0.2
10k
100k
1M
Frequency(Hz) Fig. 6. Frequency variation of initial permeability.
0.8
Remanence ratio
0.7 0.6 0.5 0.4 0.3 0.2 0.00
0.05
0.10
0.15
0.20
0.25
Vanadium concentration(t) Fig. 4. Compositional variation of remanence ratio.
tend to contain more number of domain walls and initial permeability being a result of the reversal of domain wall displacement, the greater the number of domain walls; the higher is the initial permeability. From Fig. 6, it can be noticed that the value increases and then decreases with the increase of vanadium substitution in the low frequency region (below 1 kHz). It can be explained from the effect of average grain size of the samples, which showed similar variation. Also, from Fig. 6 it has been observed that the initial permeability is high at low frequency and above 1 kHz the value becomes lower and remains nearly constant for all the samples. The frequency
ARTICLE IN PRESS M. Maisnam et al. / Physica B 352 (2004) 86–90
90
works to suppress the eddy current. Hence, the observed variation with increasing vanadium content [17].
0.100
tanδµ
0.075
Acknowledgements
0.050
0.10 0.05 t=0.0
0.025
0.15
0.000 10k
0.20
Authors from Manipur University are thankful to DRDO, Ministry of Defence for financial assistance.
0.25
100k
1M
Frequency(Hz) Fig. 7. Frequency variation of tan dm for the samples.
dispersion of permeability of polycrystalline ferrites depends on many factors like chemical composition, post sintering density and the microstructure e.g. grain size, porosity and intra or intergranular pores. Initial permeability is reported to be due to the domain wall displacement and remains constant with frequency as long as there is no phase lag between the applied field and the domain wall displacement. The plot of tan dm as a function of frequency is shown in Fig. 7. It has been found that the value is high at lower frequency and decreases maintaining a small value at higher frequencies. At still higher frequencies 1 MHz, tan dm increases rapidly showing a tendency for a resonance loss peak. The resonance frequency gives the operational frequency limit of the sample. At resonance frequency, maximum energy is transferred from the applied field to the lattice resulting in the rise of tan dm [10]. Magnetic loss is reported to decline with decrease in the average grain size and vice versa. The decrease in the grain size increases the alternating current resistance as smaller grain
References [1] J. Smit, H.P.J. Wijn, Ferrites, Wiley, New York, 1965. [2] H. Igarashi, K. Okazaki, J. Am. Ceram. Soc. 60 (1977) 51. [3] P. Kishan, In: V.R.K. Murthy (Ed.), Microwave Materials, Narosa Publishing House, 1993, p. 141. [4] P.D. Baba, et al., IEEE Trans. Magn. 8 (1972) 283. [5] S. Phanjoubam, C. Prakash, Mod. Phys. Lett. B 16 (2002) 1027. [6] L.M. Letyuk, Poroshkovaya Metallurgiya 8 (1975) 59. [7] Jau Ho Jean, Cheng Horng Lee, Jpn. J. Appl. Phys. 40 (2001) 2232. [8] S.V. Salvi, V.P. Khanolkar, Proceedings of the Fifth International Conference on Ferrites, 1989, pp. 459. [9] A.C. Razzitte, S.E. Jacobo, W.G. Fano, J. Appl. Phys. 87 (2000) 6232. [10] A.K. Singh, T.C. Goel, R.G. Mendiratta, O.P. Thakur, C. Prakash, J. Appl. Phys. 92 (2002) 3872. [11] A. Verma, T.C. Goel, R.G. Mendiratta, P. Kishan, J. Magn. Magn. Mater. 208 (2000) 13. [12] J.-H. Nam, W.-G. Hur, J.-H. Oh, J. Appl. Phys. 81 (1997) 4794. [13] M.U. Rana, T. Abbas, J. Magn. Magn. Mater. 246 (2002) 110. [14] P.J. van der Zaag, P.J. van der Valk, M.Th. Rekvelt, Appl. Phys. Lett. 69 (1996) 2927. [15] A.K. Singh, A. Verma, O.P. Thakur, Chandra Prakash, T.C. Goel, R.G. Mendiratta, Mater. Lett. 57 (2003) 1040. [16] K.H. Rao, N.K. Gaur, K. Aggarwal, R.G. Mendiratta, J. Appl. Phys. 53 (1982) 1122. [17] M.K. Ono, T. Hashimoto, F. Nakao, IEEE Trans. Magn. 37 (2001) 2359.