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Dielectric behavior of Mn-substituted Co2Z hexaferrites
Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
Dielectric behavior of Mn-substituted Co2Z hexaferrites Jianer Bao*, Ji Zhou, Zhenxing Yue, Longtu Li, Zhilun Gui State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China Received 3 January 2002
Abstract In order to improve the properties of multi-layer chip inductor device, the dielectric constant and loss tangent as functions of frequency, temperature and composition for a series of samples of Ba3Co2Fe2312xMn12xO41 hexagonal ferrites were studied. For all samples, a single Z-type phase was established and the lattice constants were calculated. Results show that dielectric constant increases as sintering temperature increases, dielectric constant and loss tangent decrease as frequency increases and as temperature decreases. These effects are attributed to the Maxwell–Wagner double-layer polarization. As the Mn-substitution increased, samples showed abnormal dielectric behavior in the form of relaxation peaks which shifted toward higher frequencies, dielectric constant e0 and loss tangent also decrease gradually reaching minimum between x ¼ 0:02 and 0:06: The polarization can be explained by the hopping mechanism in that Mn substitution for Fe ions on the B-sites acts to reduce Fe2+ formation. A second mechanism that small polarons may also contribute to the polarization is indicated in this work. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.50.G; 78.20.C; 77.22.C Keywords: Hexagonal ferrite (hexaferrite); Dielectric constant; Loss tangent; Mn-substitution; Polarization mechanism
1. Introduction Co2Z ferrites with hexagonal structure are potential candidates for use as multi-layer chip inductors (MLCI) to be used in the high frequency range of 300–800 MHz [1,2]. These chip inductors are fabricated by interleaving ferrite layers with internal conductors such as silver, and then cofiring the stack to form a monolithic structure [3]. Since ferrites are not only magnetic materials, but *Corresponding author. Tel.: +86-10-62784579; fax:+8610-62771160. E-mail address: [email protected] (J. Bao).
also dielectric materials, there should be an L–C circuit within the monolithic-structured chip inductors. From the frequency dependence of inductance for the devices we made, L–C resonant peaks were found far below the self-resonant frequency of Co2Z hexaferrite. As the capacitance has direct bearing on the dielectric constant, how to lower the dielectric constant of Co2Z hexaferrite without deteriorating the magnetic properties becomes a challenging problem for the high frequency MLCI. As we know, electrical properties of ferrite are derived from many physical and chemical characteristics, and the effect of frequency,
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 3 6 4 - 5
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J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
temperature and composition on the dielectric behavior offer much valuable information about the localized electric charge carrier which in turn helps to elucidate the mechanisms responsible for charge transport phenomena and dielectric behavior. While the dielectric properties and conduction mechanisms for M-type [BaFe12O19] hexaferrites [4–6] and W-type [BaCo2Fe16O27] hexaferrites [7–11] have been studied in the literature, little work has been published concerning the dielectric properties of Co2Z-type hexaferrites before. Moreover, hexaferrites are of interest not only for their dielectric behavior but also for the electrical polarization inherent in their structure. In this work, a systematic study of dielectric behavior and possible polarization mechanisms of Mn-substituted Co2Z hexaferrites have been carried out and results are presented here.
2. Experimental procedure A series of ceramic samples of Z-type hexagonal ferrites of composition Ba3Co2Fe2312xMn12xO41 (0oxo0:1) were prepared by the solid-state reaction technique using stoichiometric proportions of chemical pure BaCO3, Co3O4, Fe2O3 and MnO2 powders. After thorough mixing and grinding, the powders were calcined at 12701C for 6 h and then left to cool at the rate of 41C min1. Later the calcined powders were pressed into disc-shaped pellets of 1.0 cm diameter and sintered at temperatures between 11001C and 12601C followed by slow cooling to reduce the formation of Fe2+ ions. A reduced iron composition was adopted as well to inhibit the formation of Fe2+ ions [1,2]. Hexagonal structure was identified and lattice parameters were calculated by means of a powder X-ray diffractometer (Rigaku) using CuKa radiation. Bulk densities of all samples were measured by the Archimedes method. Frequency dependence of the dielectric constant and loss tangent of silver-coated pellets were measured by an HP4291B impedance analyzer in the frequency range of 10 MHz–1.8 GHz. Temperature dependence of dielectric constant was measured using an HP4192A LF impedance analyzer from room temperature to 1801C.
3. Results and discussion 3.1. Structural analysis X-ray diffractograms confirmed that all samples exhibited a well-defined hexagonal Z-type phase. Using d-spacing values, lattice parameters a and c as well as values of c=a were calculated by a computer program for samples calcined at 12701C for 6 h, and results are given in Table 1. From the table we can see that the values of a and c for all Mn-substituted samples were smaller than those for unsubstituted Co2Z ferrite. We know that the ionic radius of Fe3+, Fe2+, Mn3+ and Mn2+ are ( respectively, hence the 0.64, 0.76, 0.62 and 0.80 A, smaller a and c values may be due to the smaller size of Mn3+ ions. Further study needs to be conducted. The average densities of samples sintered at 11401C for 6 h together with dielectric constants and resistivities measured at room temperatures are given in Table 2. Observed densities are about 95% of XRD density (5.35 g cm3). Results
Table 1 Lattice parameters of substituted ferrites calcined at 12601C for 6h Sample X X X X X X
¼ 0:00 ¼ 0:01 ¼ 0:02 ¼ 0:04 ¼ 0:06 ¼ 0:08
Composition
( a (A)
( c (A)
c=a
Ba3Co2Fe23O41 Ba3Co2Fe22.88Mn0.12O41 Ba3Co2Fe22.76Mn0.24O41 Ba3Co2Fe22.52Mn0.48O41 Ba3Co2Fe22.28Mn0.72O41 Ba3Co2Fe22.04Mn0.96O41
5.893 5.888 5.886 5.888 5.888 5.884
52.303 52.255 52.265 52.283 52.286 52.259
8.875 8.875 8.880 8.880 8.880 8.882
Table 2 The density, dielectric constant and resistivity for the series of samples sintered at 11401C for 6 h (XRD density: 5.35 g cm3) Sample X X X X X X
¼ 0:00 ¼ 0:01 ¼ 0:02 ¼ 0:03 ¼ 0:06 ¼ 0:09
Density (g cm3)
e0 at 300 MHz
rð106 Þ (O cm)
5.10 5.21 5.10 5.10 5.04 5.06
23.54 21.92 19.06 20.38 21.54 22.3
5.695 10.777 35.075 2.679 2.397 1.552
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
700
500 0
1260˚C /5h
600 500 400
0 1 2 3 6
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06
Dielectric Constant
Dielectric Constant
800
300 1 200 2
3
200
1
100
2 3 6 9
0
(a)
8
10
9
10
90
10
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
8
10
9
Frequency(Hz) 45
1160˚C /6h
70 60 50
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
Dielectric Constant
0
80
Dielectric Constant
7
(b)
Frequency(Hz)
0 1 2 3 6 9
300
0
10
1190˚C /6h
0
400
100 6
40 1
30 20 10
10
(c)
133
7
10
8
10
1140˚C /6h 0
35 30 25 20
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06
1 6 3 2
15
9
Frequency(Hz)
40
(d)
10
7
10
8
10
9
Frequency(Hz)
Fig. 1. Dielectric behavior of samples sintered at various temperatures as a function of frequency (a) 12601C/5 h, (b) 11901C/6 h, (c) 11601C/6 h, and (d) 11401C/6 h.
indicate that introduction of a small amount of Mn ions has no great effect on the density of the sintered ferrites, but shows significant effect on the dielectric constant.
3.2. Frequency dependence Fig. 1 shows the real part of dielectric constants e0 of samples sintered at various temperatures as a function of frequency from 10 MHz up to 1.2 GHz. It can be seen from the figures that for pure Co2Z ferrite samples, the dielectric constant at room temperature is found to decrease continuously as the frequency increases. This is the normal dielectric behavior in ferrites and can be attributed to the fact that the electron exchange between Fe2+ and Fe3+ ions and hole transfer between Co3+ and Co2+ ions cannot follow the alternating electric field beyond a critical frequency [4].
For Mn-substituted samples sintered at 12601C and 11901C, a marked decrease in dielectric constant compared with that of unsubstituted Co2Z ferrite is observed; the dielectric constant reaches minimum when x ¼ 0:09: It can also be seen that frequency dispersion decreases with increasing Mn content within the investigated frequency range. For samples with xX0:02 sintered at 11601C and 11401C, abnormal dielectric behavior is observed. As frequency increases, the dielectric constant first remains stable, and then a relaxation peak is found. The relaxation peak shifts toward higher frequencies with increasing Mn concentration. The dielectric relaxation peak takes place when the jumping frequency of electric charge carriers is approximately equal to that of the externally applied AC electric field [4]. From the figures we can also see that with the increase of sintering temperature, the dielectric constant of all samples increases rapidly at low frequencies.
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
134
Frequency dependence of the loss tangent is shown in Fig. 2. It can be seen that, at first loss tangent decreases as the frequency increases and then increases rapidly at the end of the dispersion zone of the dielectric constant. Following that, a
decrease can be expected as exhibited in pure Co2Z ferrite. Similar dielectric and loss tangent behaviors were observed by earlier workers with M-type BaCo2xZnxFe122xO19 hexaferrites [4] and W-type BaCo2xZnxFe16O27 hexaferrites [7].
0.005
0.0020
0.004
tanδ
0.003
0.002
1190˚C /6h
0 1
0.001
0.000
10
(a)
0.0010
1
3 0.0000
7
10
8
Frequency(Hz)
0
0.0005
2
3
6 9
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
1160˚C /6h 0.0015
tanδ
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
10
9
2
10
(b)
7
10
8
10
9
Frequency(Hz)
Fig. 2. Frequency dependence of loss tangent of samples sintered at various temperatures (a) 11901C/6 h, and (b) 11601C/6 h.
Fig. 3. Temperature dependence of dielectric constant at selected frequencies for samples sintered at 11901C for 6 h: (a) x ¼ 0:0; (b) x ¼ 0:01; (c) x ¼ 0:02; and (d) x ¼ 0:06:
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
The decrease in dielectric constant and loss tangent as frequency increases and the increase of dielectric constant with increasing sintering temperature can be explained by Koop’s theory [12] which takes the dielectric structure as an inhomogeneous medium composed of two Maxwell– Wagner type layers [13,14]. In this model, the dielectric structure is imagined to consist of fairly well-conducting ferrite grains separated by poorly conducting grain boundaries. According to Rezlescu model [5,15], electric conduction is similar to that for the dielectric polarization in ferrites; therefore grains have higher values of dielectric constant, while grain boundaries have lower values of dielectric constant. The grain boundaries are effective at low frequencies and therefore are responsible for the very high dielectric constant. The appearance of the low frequency relaxation peaks is related mainly to the grain boundaries. For the low temperature sintered ferrites, the proportion of low dielectric constant grain boundaries is relatively larger than that of the high temperature sintered ferrites, thus the overall dielectric constant is relatively smaller. If only the contribution of the n-type carrier is considered for the polarization, one would find that polarization remains constant up to a certain frequency, beyond which it decreases [16]. The abnormal dielectric behavior exhibited by Mnsubstituted samples may indicate that small polarons are also responsible for the polarization in the investigated pure Co2Z ferrites while in
135
Mn-substituted ferrites, the contribution of the polarons is partially suppressed. This is possible because in solids with large coupling constant and a narrow conduction band, small polaron formation is probable [8]. In oxides of iron group metals especially in ferrites, the overlap of 3d wave function between neighboring metal ions is relatively small. In such a case, the existence of small polarons and the hopping process are very probable. The different distribution of relaxation peak frequencies may be due to different heterogeneous structures existing among these ferrites. 3.3. Temperature dependence The temperature variation of dielectric constant e0 was studied in the temperature range from room temperature to 1801C at fixed frequencies of 0.5, 1, 2 and 3 MHz, and results are plotted in Figs. 3 and 4. As can be seen from the figures, the dielectric constant increases continuously up to a certain temperature and then a relaxation peak is found. The relaxation peak shifts to lower temperatures as the frequencies increase. This is the normal dielectric behavior for ferrites due to the increase in number of electric charge carriers and their drift mobilities which are thermally activated. Fig. 4 shows that the dielectric relaxation peak shifts to higher temperatures with increasing concentration of Mn for xo0:06 and even disappears for x ¼ 0:06 which may be explained by the existence of
Fig. 4. Temperature dependence of dielectric constant (a) 11901C/6h (at 3 MHz), and (b) 12601C/5h (at 2 MHz).
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J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
couplings between Fe2+ and Fe3+ ions. As Mn substitution acts to reduce the concentration of Fe2+ ions, the number of couplings in the Mn substituted ferrites decreases and the relation between the couplings may also become stronger which lead to decreases in temperature sensitivity and the dielectric constant. The mechanism involved in this abnormal phenomenon needs to be studied further. 3.4. Composition dependence Figs. 1 and 4 show that the dielectric constants decrease markedly for samples with x ¼ 0:01 and then decrease gradually reaching a minimum for samples of x ¼ 0:03 0:06: Fig. 2 shows that the loss tangent has the same variation tendency as the dielectric constants. In the literature, the conductivity and consequently the polarization in ferrites have been ascribed in general to the Verwey hopping mechanism between ions of a given element in more than one valence state [17]—that is, ions distributed over crystallographically equivalent sites while electrons jump from one lattice site to another in a diffusion process analogous to the thermal activation encountered in ionic diffusion and conductivity [5]. It is reported that Mn ions occupy octahedral (B) sites [17] while Co and Fe ions partially occupy tetrahedral (A) sites and B sites. It is also known that the B sites of a hexagonal ferrite play a dominant role in the phenomenon of electrical conductivity, and the conduction in these ferrites may be due to hopping of electrons in Fe3þ þ e3Fe2þ at B sites [8]. The substitution of Mn for Fe on the B sites (octahedral sites) acts to reduce Fe2+ concentration through the following buffering reaction: Mn3þ þ Fe2þ -Fe3þ þ Mn2þ : Also, the hopping energy in Mn3þ 2Mn2þ is larger than that in Fe3þ 2Fe2þ : By increasing the replacement of Mn to Fe ions, the number of ferrous and ferric ions at B sites decreases. It seems likely that the concentration of Fe2+ on B sites becomes very small whereas the concentration of Fe3+ on B site remains high. In
terms of a model of electron hopping, the electron exchange is suppressed. Therefore, the dielectric conductivity and consequently the local displacement of electrons in the direction of an external AC electric field (holes in opposite direction) which determines dielectric polarization in ferrites decrease as Mn-substitution increases. Consequently the dielectric constant e0 and loss tangent decrease as x increases for xo0:06: On increasing the substitution above x ¼ 0:06; the newly added Mn ions which have to occupy A sites will force the remaining Fe ions at A sites to migrate to B sites. Hopping probabilities between Mn3+ and Mn2+ may also become appreciable as the concentration of Mn increases. As a result, the dielectric constant increases.
4. Conclusions (1) The dielectric constant and loss tangent decrease as frequency increases and as sintering temperature decreases, which agrees well with the Maxwell–Wagner double-layer model. (2) Frequency dependence of Mn-substituted ferrites shows abnormal dielectric behavior (e0 remains constant up to a frequency and then a relaxation peak is found) which indicates that a second conduction mechanism—small polarons—may also contribute to the polarization. Further investigation about the mechanism involved needs to be carried out. (3) Dielectric constant increases on increasing the temperature due to the increase in number of electric charge carriers and their drift mobilities which are thermally activated. (4) Dielectric relaxation peaks are found for all samples studied at high temperatures, and as the concentration of Mn increases, the relaxation peak shifts to higher temperatures. (5) Dielectric constant and loss tangent decrease markedly after substitution and reach minimums when x ¼ 0:02 0:06: (6) The conduction and polarization behavior in the studied ferrites is due to the hopping of charge carriers between Fe3+ and Fe2+, and the substitution of Mn for Fe on the B sites
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
acts to reduce the Fe2+ concentration through the buffering reaction Mn3þ þ Fe2þ -Fe3þ þ Mn2þ : Mn-substituted Co2Z hexaferrites with low dielectric constant, low loss tangent and high initial permeability have great potential for high frequency multi-layer chip inductor use.
Acknowledgements This work was supported by the High Technology Research and Development Project of the People’s Republic of China (No. 863-715-Z33-06).
References [1] Jianer Bao, Ji Zhou, H. Zhang, Z. Yue, L. Li, Z. Gui, Ferroelectrics 264 (2001) 157. [2] Hongguo Zhang, Ji Zhou, Z. Yue, P. Wu, L. Li, Z. Gui, Mater. Sci. Eng. B 65 (1999) 184.
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[3] Zhenxing Yue, Ji Zhou, L. Li, Z. Gui, J. Magn. Magn. Mater. 208 (2000) 55. [4] A.M. Abo El Ata, M.A. El Hiti, J. De Phys. III 7 (1997) 883. [5] O.S. Josyulu, J. Sobhanadri, Phys. Stat. Sol. A 59 (1980) 323. [6] K. Iwauchi, Y. Ikeda, Phys. Stat. Sol. A 93 (1986) 309. [7] H. Ismael, M.K. El Nimr, A.M. Abou El Ata, M.A. El Hiti, M.A. Ahmed, A.A. Murakhowskii, J. Magn. Magn. Mater. 150 (1995) 403. [8] Y. Purushotham, P.V. Reddy, Inter. J. Moder. Phys. B 10 (3) (1996) 319. [9] V.D. Reddy, Y. Purushotham, M.B. Reddy, P.V. Reddy, Moder. Phys. Lett. B 10 (29) (1996) 1461. [10] A.M. Abo El Ata, M.K. El Nimr, D. El Kony, A.H. AlHammadi, J. Magn. Magn. Mater. 202 (1999) 397. [11] A.M. Abo El Ata, M.A. Ahmed, J. Magn. Magn. Mater. 208 (2000) 27. [12] C. Koops, Phys. Rev. 83 (1951) 121. [13] J. Maxwell, Electricity and Magnetism, Vol. 1, Oxford University Press, London, 1873 (Section 328). [14] K. Wagner, Ann. Phys. 40 (1913) 817. [15] N. Rezlescu, E. Rezlescu, Solid State Commun. 14 (1974) 69. [16] S.R. Murthy, J. Mater. Sci. Lett. 3 (1984) 1049. [17] K.G. Brooks, Y. Berta, V.R.W. Amarakoon, J. Am. Ceram. Soc. 75 (11) (1992) 3065.
Dielectric behavior of Mn-substituted Co2Z hexaferrites Jianer Bao*, Ji Zhou, Zhenxing Yue, Longtu Li, Zhilun Gui State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China Received 3 January 2002
Abstract In order to improve the properties of multi-layer chip inductor device, the dielectric constant and loss tangent as functions of frequency, temperature and composition for a series of samples of Ba3Co2Fe2312xMn12xO41 hexagonal ferrites were studied. For all samples, a single Z-type phase was established and the lattice constants were calculated. Results show that dielectric constant increases as sintering temperature increases, dielectric constant and loss tangent decrease as frequency increases and as temperature decreases. These effects are attributed to the Maxwell–Wagner double-layer polarization. As the Mn-substitution increased, samples showed abnormal dielectric behavior in the form of relaxation peaks which shifted toward higher frequencies, dielectric constant e0 and loss tangent also decrease gradually reaching minimum between x ¼ 0:02 and 0:06: The polarization can be explained by the hopping mechanism in that Mn substitution for Fe ions on the B-sites acts to reduce Fe2+ formation. A second mechanism that small polarons may also contribute to the polarization is indicated in this work. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.50.G; 78.20.C; 77.22.C Keywords: Hexagonal ferrite (hexaferrite); Dielectric constant; Loss tangent; Mn-substitution; Polarization mechanism
1. Introduction Co2Z ferrites with hexagonal structure are potential candidates for use as multi-layer chip inductors (MLCI) to be used in the high frequency range of 300–800 MHz [1,2]. These chip inductors are fabricated by interleaving ferrite layers with internal conductors such as silver, and then cofiring the stack to form a monolithic structure [3]. Since ferrites are not only magnetic materials, but *Corresponding author. Tel.: +86-10-62784579; fax:+8610-62771160. E-mail address: [email protected] (J. Bao).
also dielectric materials, there should be an L–C circuit within the monolithic-structured chip inductors. From the frequency dependence of inductance for the devices we made, L–C resonant peaks were found far below the self-resonant frequency of Co2Z hexaferrite. As the capacitance has direct bearing on the dielectric constant, how to lower the dielectric constant of Co2Z hexaferrite without deteriorating the magnetic properties becomes a challenging problem for the high frequency MLCI. As we know, electrical properties of ferrite are derived from many physical and chemical characteristics, and the effect of frequency,
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 3 6 4 - 5
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J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
temperature and composition on the dielectric behavior offer much valuable information about the localized electric charge carrier which in turn helps to elucidate the mechanisms responsible for charge transport phenomena and dielectric behavior. While the dielectric properties and conduction mechanisms for M-type [BaFe12O19] hexaferrites [4–6] and W-type [BaCo2Fe16O27] hexaferrites [7–11] have been studied in the literature, little work has been published concerning the dielectric properties of Co2Z-type hexaferrites before. Moreover, hexaferrites are of interest not only for their dielectric behavior but also for the electrical polarization inherent in their structure. In this work, a systematic study of dielectric behavior and possible polarization mechanisms of Mn-substituted Co2Z hexaferrites have been carried out and results are presented here.
2. Experimental procedure A series of ceramic samples of Z-type hexagonal ferrites of composition Ba3Co2Fe2312xMn12xO41 (0oxo0:1) were prepared by the solid-state reaction technique using stoichiometric proportions of chemical pure BaCO3, Co3O4, Fe2O3 and MnO2 powders. After thorough mixing and grinding, the powders were calcined at 12701C for 6 h and then left to cool at the rate of 41C min1. Later the calcined powders were pressed into disc-shaped pellets of 1.0 cm diameter and sintered at temperatures between 11001C and 12601C followed by slow cooling to reduce the formation of Fe2+ ions. A reduced iron composition was adopted as well to inhibit the formation of Fe2+ ions [1,2]. Hexagonal structure was identified and lattice parameters were calculated by means of a powder X-ray diffractometer (Rigaku) using CuKa radiation. Bulk densities of all samples were measured by the Archimedes method. Frequency dependence of the dielectric constant and loss tangent of silver-coated pellets were measured by an HP4291B impedance analyzer in the frequency range of 10 MHz–1.8 GHz. Temperature dependence of dielectric constant was measured using an HP4192A LF impedance analyzer from room temperature to 1801C.
3. Results and discussion 3.1. Structural analysis X-ray diffractograms confirmed that all samples exhibited a well-defined hexagonal Z-type phase. Using d-spacing values, lattice parameters a and c as well as values of c=a were calculated by a computer program for samples calcined at 12701C for 6 h, and results are given in Table 1. From the table we can see that the values of a and c for all Mn-substituted samples were smaller than those for unsubstituted Co2Z ferrite. We know that the ionic radius of Fe3+, Fe2+, Mn3+ and Mn2+ are ( respectively, hence the 0.64, 0.76, 0.62 and 0.80 A, smaller a and c values may be due to the smaller size of Mn3+ ions. Further study needs to be conducted. The average densities of samples sintered at 11401C for 6 h together with dielectric constants and resistivities measured at room temperatures are given in Table 2. Observed densities are about 95% of XRD density (5.35 g cm3). Results
Table 1 Lattice parameters of substituted ferrites calcined at 12601C for 6h Sample X X X X X X
¼ 0:00 ¼ 0:01 ¼ 0:02 ¼ 0:04 ¼ 0:06 ¼ 0:08
Composition
( a (A)
( c (A)
c=a
Ba3Co2Fe23O41 Ba3Co2Fe22.88Mn0.12O41 Ba3Co2Fe22.76Mn0.24O41 Ba3Co2Fe22.52Mn0.48O41 Ba3Co2Fe22.28Mn0.72O41 Ba3Co2Fe22.04Mn0.96O41
5.893 5.888 5.886 5.888 5.888 5.884
52.303 52.255 52.265 52.283 52.286 52.259
8.875 8.875 8.880 8.880 8.880 8.882
Table 2 The density, dielectric constant and resistivity for the series of samples sintered at 11401C for 6 h (XRD density: 5.35 g cm3) Sample X X X X X X
¼ 0:00 ¼ 0:01 ¼ 0:02 ¼ 0:03 ¼ 0:06 ¼ 0:09
Density (g cm3)
e0 at 300 MHz
rð106 Þ (O cm)
5.10 5.21 5.10 5.10 5.04 5.06
23.54 21.92 19.06 20.38 21.54 22.3
5.695 10.777 35.075 2.679 2.397 1.552
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
700
500 0
1260˚C /5h
600 500 400
0 1 2 3 6
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06
Dielectric Constant
Dielectric Constant
800
300 1 200 2
3
200
1
100
2 3 6 9
0
(a)
8
10
9
10
90
10
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
8
10
9
Frequency(Hz) 45
1160˚C /6h
70 60 50
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
Dielectric Constant
0
80
Dielectric Constant
7
(b)
Frequency(Hz)
0 1 2 3 6 9
300
0
10
1190˚C /6h
0
400
100 6
40 1
30 20 10
10
(c)
133
7
10
8
10
1140˚C /6h 0
35 30 25 20
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06
1 6 3 2
15
9
Frequency(Hz)
40
(d)
10
7
10
8
10
9
Frequency(Hz)
Fig. 1. Dielectric behavior of samples sintered at various temperatures as a function of frequency (a) 12601C/5 h, (b) 11901C/6 h, (c) 11601C/6 h, and (d) 11401C/6 h.
indicate that introduction of a small amount of Mn ions has no great effect on the density of the sintered ferrites, but shows significant effect on the dielectric constant.
3.2. Frequency dependence Fig. 1 shows the real part of dielectric constants e0 of samples sintered at various temperatures as a function of frequency from 10 MHz up to 1.2 GHz. It can be seen from the figures that for pure Co2Z ferrite samples, the dielectric constant at room temperature is found to decrease continuously as the frequency increases. This is the normal dielectric behavior in ferrites and can be attributed to the fact that the electron exchange between Fe2+ and Fe3+ ions and hole transfer between Co3+ and Co2+ ions cannot follow the alternating electric field beyond a critical frequency [4].
For Mn-substituted samples sintered at 12601C and 11901C, a marked decrease in dielectric constant compared with that of unsubstituted Co2Z ferrite is observed; the dielectric constant reaches minimum when x ¼ 0:09: It can also be seen that frequency dispersion decreases with increasing Mn content within the investigated frequency range. For samples with xX0:02 sintered at 11601C and 11401C, abnormal dielectric behavior is observed. As frequency increases, the dielectric constant first remains stable, and then a relaxation peak is found. The relaxation peak shifts toward higher frequencies with increasing Mn concentration. The dielectric relaxation peak takes place when the jumping frequency of electric charge carriers is approximately equal to that of the externally applied AC electric field [4]. From the figures we can also see that with the increase of sintering temperature, the dielectric constant of all samples increases rapidly at low frequencies.
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
134
Frequency dependence of the loss tangent is shown in Fig. 2. It can be seen that, at first loss tangent decreases as the frequency increases and then increases rapidly at the end of the dispersion zone of the dielectric constant. Following that, a
decrease can be expected as exhibited in pure Co2Z ferrite. Similar dielectric and loss tangent behaviors were observed by earlier workers with M-type BaCo2xZnxFe122xO19 hexaferrites [4] and W-type BaCo2xZnxFe16O27 hexaferrites [7].
0.005
0.0020
0.004
tanδ
0.003
0.002
1190˚C /6h
0 1
0.001
0.000
10
(a)
0.0010
1
3 0.0000
7
10
8
Frequency(Hz)
0
0.0005
2
3
6 9
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
1160˚C /6h 0.0015
tanδ
x=0.0 x=0.01 x=0.02 x=0.03 x=0.06 x=0.09
10
9
2
10
(b)
7
10
8
10
9
Frequency(Hz)
Fig. 2. Frequency dependence of loss tangent of samples sintered at various temperatures (a) 11901C/6 h, and (b) 11601C/6 h.
Fig. 3. Temperature dependence of dielectric constant at selected frequencies for samples sintered at 11901C for 6 h: (a) x ¼ 0:0; (b) x ¼ 0:01; (c) x ¼ 0:02; and (d) x ¼ 0:06:
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The decrease in dielectric constant and loss tangent as frequency increases and the increase of dielectric constant with increasing sintering temperature can be explained by Koop’s theory [12] which takes the dielectric structure as an inhomogeneous medium composed of two Maxwell– Wagner type layers [13,14]. In this model, the dielectric structure is imagined to consist of fairly well-conducting ferrite grains separated by poorly conducting grain boundaries. According to Rezlescu model [5,15], electric conduction is similar to that for the dielectric polarization in ferrites; therefore grains have higher values of dielectric constant, while grain boundaries have lower values of dielectric constant. The grain boundaries are effective at low frequencies and therefore are responsible for the very high dielectric constant. The appearance of the low frequency relaxation peaks is related mainly to the grain boundaries. For the low temperature sintered ferrites, the proportion of low dielectric constant grain boundaries is relatively larger than that of the high temperature sintered ferrites, thus the overall dielectric constant is relatively smaller. If only the contribution of the n-type carrier is considered for the polarization, one would find that polarization remains constant up to a certain frequency, beyond which it decreases [16]. The abnormal dielectric behavior exhibited by Mnsubstituted samples may indicate that small polarons are also responsible for the polarization in the investigated pure Co2Z ferrites while in
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Mn-substituted ferrites, the contribution of the polarons is partially suppressed. This is possible because in solids with large coupling constant and a narrow conduction band, small polaron formation is probable [8]. In oxides of iron group metals especially in ferrites, the overlap of 3d wave function between neighboring metal ions is relatively small. In such a case, the existence of small polarons and the hopping process are very probable. The different distribution of relaxation peak frequencies may be due to different heterogeneous structures existing among these ferrites. 3.3. Temperature dependence The temperature variation of dielectric constant e0 was studied in the temperature range from room temperature to 1801C at fixed frequencies of 0.5, 1, 2 and 3 MHz, and results are plotted in Figs. 3 and 4. As can be seen from the figures, the dielectric constant increases continuously up to a certain temperature and then a relaxation peak is found. The relaxation peak shifts to lower temperatures as the frequencies increase. This is the normal dielectric behavior for ferrites due to the increase in number of electric charge carriers and their drift mobilities which are thermally activated. Fig. 4 shows that the dielectric relaxation peak shifts to higher temperatures with increasing concentration of Mn for xo0:06 and even disappears for x ¼ 0:06 which may be explained by the existence of
Fig. 4. Temperature dependence of dielectric constant (a) 11901C/6h (at 3 MHz), and (b) 12601C/5h (at 2 MHz).
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couplings between Fe2+ and Fe3+ ions. As Mn substitution acts to reduce the concentration of Fe2+ ions, the number of couplings in the Mn substituted ferrites decreases and the relation between the couplings may also become stronger which lead to decreases in temperature sensitivity and the dielectric constant. The mechanism involved in this abnormal phenomenon needs to be studied further. 3.4. Composition dependence Figs. 1 and 4 show that the dielectric constants decrease markedly for samples with x ¼ 0:01 and then decrease gradually reaching a minimum for samples of x ¼ 0:03 0:06: Fig. 2 shows that the loss tangent has the same variation tendency as the dielectric constants. In the literature, the conductivity and consequently the polarization in ferrites have been ascribed in general to the Verwey hopping mechanism between ions of a given element in more than one valence state [17]—that is, ions distributed over crystallographically equivalent sites while electrons jump from one lattice site to another in a diffusion process analogous to the thermal activation encountered in ionic diffusion and conductivity [5]. It is reported that Mn ions occupy octahedral (B) sites [17] while Co and Fe ions partially occupy tetrahedral (A) sites and B sites. It is also known that the B sites of a hexagonal ferrite play a dominant role in the phenomenon of electrical conductivity, and the conduction in these ferrites may be due to hopping of electrons in Fe3þ þ e3Fe2þ at B sites [8]. The substitution of Mn for Fe on the B sites (octahedral sites) acts to reduce Fe2+ concentration through the following buffering reaction: Mn3þ þ Fe2þ -Fe3þ þ Mn2þ : Also, the hopping energy in Mn3þ 2Mn2þ is larger than that in Fe3þ 2Fe2þ : By increasing the replacement of Mn to Fe ions, the number of ferrous and ferric ions at B sites decreases. It seems likely that the concentration of Fe2+ on B sites becomes very small whereas the concentration of Fe3+ on B site remains high. In
terms of a model of electron hopping, the electron exchange is suppressed. Therefore, the dielectric conductivity and consequently the local displacement of electrons in the direction of an external AC electric field (holes in opposite direction) which determines dielectric polarization in ferrites decrease as Mn-substitution increases. Consequently the dielectric constant e0 and loss tangent decrease as x increases for xo0:06: On increasing the substitution above x ¼ 0:06; the newly added Mn ions which have to occupy A sites will force the remaining Fe ions at A sites to migrate to B sites. Hopping probabilities between Mn3+ and Mn2+ may also become appreciable as the concentration of Mn increases. As a result, the dielectric constant increases.
4. Conclusions (1) The dielectric constant and loss tangent decrease as frequency increases and as sintering temperature decreases, which agrees well with the Maxwell–Wagner double-layer model. (2) Frequency dependence of Mn-substituted ferrites shows abnormal dielectric behavior (e0 remains constant up to a frequency and then a relaxation peak is found) which indicates that a second conduction mechanism—small polarons—may also contribute to the polarization. Further investigation about the mechanism involved needs to be carried out. (3) Dielectric constant increases on increasing the temperature due to the increase in number of electric charge carriers and their drift mobilities which are thermally activated. (4) Dielectric relaxation peaks are found for all samples studied at high temperatures, and as the concentration of Mn increases, the relaxation peak shifts to higher temperatures. (5) Dielectric constant and loss tangent decrease markedly after substitution and reach minimums when x ¼ 0:02 0:06: (6) The conduction and polarization behavior in the studied ferrites is due to the hopping of charge carriers between Fe3+ and Fe2+, and the substitution of Mn for Fe on the B sites
J. Bao et al. / Journal of Magnetism and Magnetic Materials 250 (2002) 131–137
acts to reduce the Fe2+ concentration through the buffering reaction Mn3þ þ Fe2þ -Fe3þ þ Mn2þ : Mn-substituted Co2Z hexaferrites with low dielectric constant, low loss tangent and high initial permeability have great potential for high frequency multi-layer chip inductor use.
Acknowledgements This work was supported by the High Technology Research and Development Project of the People’s Republic of China (No. 863-715-Z33-06).
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