microstructural and electromagnetic properties of mn–zn ferrites with low melting-point...

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International Journal of Modern Physics B Vol. 27, No. 4 (2013) 1350003 (12 pages) c World Scientific Publishing Company DOI: 10.1142/S0217979213500033 MICROSTRUCTURAL AND ELECTROMAGNETIC PROPERTIES OF Mn Zn FERRITES WITH LOW MELTING-POINT NONMAGNETIC Sb 3+ IONS X. L. FU School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China [email protected] Q. K. XING, Z. J. PENG , C. B. WANG and Z. Q. FU School of Engineering and Technology, China University of Geosciences, Beijing 100083, P. R. China [email protected] L. H. QI and H. Z. MIAO State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, P. R. China Received 18 April 2012 Revised 22 October 2012 Accepted 15 November 2012 Published 10 December 2012 The doping effects of low melting-point nonmagnetic Sb 3+ ions on the microstructure and electromagnetic properties of Mn–Zn ferrites were studied. All the samples were prepared by traditional ceramic technique. According to the investigation on the mi- crostructure, it was found that all the samples consisted of ferrite phases with typical spinel cubic structure, and with increasing doping content of Sb 3+ ions, the lattice con- stant of the ferrites decreased but the grain size increased; the elemental analysis taken on the ferrite grain and grain boundary indicated that a portion of Sb 3+ ions entered into the ferrite lattice. Through the measurement of magnetic properties, it was re- vealed that, the saturation magnetization and initial permeability of the samples rose with small doping content of Sb 3+ ions but decreased with additional Sb 3+ doping; the Curie temperature decreased monotonously with Sb 3+ doping; and the coercivity rose with increasing doping content of Sb 3+ ions. The analysis of dielectric properties indi- cated that the dielectric constant of the doped Mn–Zn ferrites increased with increasing doping content of Sb 3+ ions. Keywords : Mn–Zn ferrite; Sb 3+ ions; doping; electromagnetic properties. PACS numbers: 75.50.2y, 81.40.Tv, 81.40.Rs 1350003-1 Int. J. Mod. Phys. B 2013.27. Downloaded from www.worldscientific.com by "UNIV OF MINNESOTA, TWIN CITIES" on 05/05/13. For personal use only.

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Page 1: MICROSTRUCTURAL AND ELECTROMAGNETIC PROPERTIES OF Mn–Zn FERRITES WITH LOW MELTING-POINT NONMAGNETIC Sb               3+               IONS

December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

International Journal of Modern Physics BVol. 27, No. 4 (2013) 1350003 (12 pages)c© World Scientific Publishing Company

DOI: 10.1142/S0217979213500033

MICROSTRUCTURAL AND ELECTROMAGNETIC

PROPERTIES OF Mn Zn FERRITES WITH LOW

MELTING-POINT NONMAGNETIC Sb3+ IONS

X. L. FU

School of Science, Beijing University of Posts and Telecommunications,

Beijing 100876, P. R. China

[email protected]

Q. K. XING, Z. J. PENG∗, C. B. WANG and Z. Q. FU

School of Engineering and Technology, China University of Geosciences,

Beijing 100083, P. R. China∗[email protected]

L. H. QI and H. Z. MIAO

State Key Laboratory of New Ceramics and Fine Processing,

Tsinghua University, Beijing 100084, P. R. China

Received 18 April 2012Revised 22 October 2012

Accepted 15 November 2012Published 10 December 2012

The doping effects of low melting-point nonmagnetic Sb3+ ions on the microstructureand electromagnetic properties of Mn–Zn ferrites were studied. All the samples wereprepared by traditional ceramic technique. According to the investigation on the mi-crostructure, it was found that all the samples consisted of ferrite phases with typicalspinel cubic structure, and with increasing doping content of Sb3+ ions, the lattice con-stant of the ferrites decreased but the grain size increased; the elemental analysis takenon the ferrite grain and grain boundary indicated that a portion of Sb3+ ions enteredinto the ferrite lattice. Through the measurement of magnetic properties, it was re-vealed that, the saturation magnetization and initial permeability of the samples rosewith small doping content of Sb3+ ions but decreased with additional Sb3+ doping; theCurie temperature decreased monotonously with Sb3+ doping; and the coercivity rosewith increasing doping content of Sb3+ ions. The analysis of dielectric properties indi-cated that the dielectric constant of the doped Mn–Zn ferrites increased with increasingdoping content of Sb3+ ions.

Keywords: Mn–Zn ferrite; Sb3+ ions; doping; electromagnetic properties.

PACS numbers: 75.50.2y, 81.40.Tv, 81.40.Rs

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

X. L. Fu et al.

1. Introduction

Manganese–zinc (Mn–Zn) ferrites are fine ceramic ferromagnetic materials possess-

ing excellent magnetic properties, such as high initial permeability, low loss, high

saturation magnetization and relatively high Curie temperature. Thus, they have

been extensively adopted in industrial applications, such as recording heads, choke

coils and communication pulse transformers.1,2

The properties of Mn–Zn ferrites are known to be determined by their mi-

crostructures. The spinel structure of the ferrites consists of two interpenetrating

sublattices, forming two types of sites, tetrahedral (A) and octahedral (B) sites,

where metal ions are located. In the crystal structure of Mn–Zn ferrite, Zn2+ and

Mn2+ ions occupy A sites, Fe2+ ions occupy B sites and Fe3+ ions occupy either A

or B sites randomly.3,4 And the metal ions are feasible to be replaced by other ions,

causing the modification of magnetic and electric properties of Mn–Zn ferrites.

In previous studies, many additives were introduced into Mn–Zn ferrites in order

to improve their properties, such as TiO2, CoO, Cr2O3, NiO, CuO, Bi2O3, WO3

and CaO.5–12 These additives affect properties of Mn–Zn ferrites by different mech-

anisms. Some ions with suitable radius, for example, Ti4+, Co2+, Cr3+ and Ni2+,

can affect the properties of Mn–Zn ferrites because these ions can enter into the

spinel lattice and replace the metallic cations in the regular A or B sites. Additives

like CuO and Bi2O3 can promote the grain growth of Mn–Zn ferrites, because the

melting point of these additives is far below the sintering temperature and create a

thin layer of liquid phase during sintering. In addition, certain additives like CaO

can reduce the eddy-current loss of ferrites, thus decreasing the total power loss,

because this kind of dopants can create a highly electrical insulating film around

the ferrite grains, increasing the electrical resistivity of the materials.

As far as the additives adopted in previous works, most of the metallic cations

introduced to Mn–Zn ferrites were magnetic impurity, such as Co3+, Gd3+, and

so forth, while the report about the effects of nonmagnetic cations on Mn–Zn fer-

rites has been very limited. Sb2O3 is a common metallic oxide with a low melting

point of 656 ◦C which can form certain amount of liquid phase promoting the grain

growth during sintering, but the report about the effect of Sb3+ ions on Mn–Zn

ferrites is unavailable. So in this paper, in order to investigate the influence of non-

magnetic cations on Mn–Zn ferrites, Sb2O3 which contains nonmagnetic Sb3+ ions

was introduced into the ferrites, and the effect of doping level of Sb3+ ions on the

microstructural and electromagnetic properties of Mn–Zn ferrites was studied.

2. Experimental Procedures

2.1. Sample preparation

A series of Mn–Zn ferrite samples with a basic composition of Mn0.5Zn0.5Fe2O4

doped with different amounts of Sb2O3 were prepared by traditional ceramics

process.13 First, Fe2O3, MnO2, and ZnO raw powders of analytical grade were

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

Microstructural and Electromagnetic Properties of Mn–Zn Ferrites

weighed in stoichiometric proportion and mixed for 24 h by ball-milling with de-

ionized water as milling medium and TZP ZrO2 balls as grinding medium. For the

ball-milling, the weight ratio of raw powder to grinding media was 1:2. After drying

the homogenized slurries, the resultant powder chunks were pre-sintered at 800 ◦C

in air for 2 h. The pre-sintered powder was then divided into five groups evenly and

0.5 wt% polyvinyl alcohol (PVA) as binder, 0.5 wt% Davon C as dispersant and

different amounts of Sb2O3 (in which the contents of Sb3+ ions are 0, 0.5, 1.0, 1.5

and 2.0 mol%, respectively) were added. After that, the mixtures were re-milled

for 24 h. After second drying, the powder chunks were grinded and sieved into fine

powders. Then toroid samples of 20 mm in outer diameter, 10 mm inner diameter

and 3 mm thickness, pellets of 6 mm in diameter and 3 mm thickness, and pellets

of 18 mm in diameter and 3 mm thickness were prepared with the resultant fine

powders, respectively. Finally, all the green samples were sintered at 1300 ◦C for 4 h

under controlled N2/O2 atmosphere and cooled under equilibrium conditions, after

which a thin film of silver paste was coated on both surfaces of the bigger pellets

and electrodes were prepared by baking them at 500 ◦C.

2.2. Material characterization

Phase purity and composition were characterized by X-ray diffraction (XRD,

D/max-RB, CuKα radiation, and λ = 1.5418 A) with a continuous scanning mode

at a speed of 6 ◦/min, and the obtained XRD patterns were analyzed by software

MDI Jade. The microstructure and elemental composition were investigated on the

fracture surfaces of the samples by thermal field emission scanning electron micro-

scope (SEM, LEO-1530) equipped with an energy dispersive X-ray spectroscopy

(EDX), and the grain size of the samples was calculated from the micrographs by

software Lince PC with linear intercept method. The saturation magnetization (Ms)

and coercivity (Hc) were obtained from hysteresis loops of the samples measured by

a vibrating sample magnetometer (VSM, LakeShore 7307) with a maximum mag-

netic field of 10 KOe. Curie temperatures (Tc) were calculated from M–T curves

measured also by VSM. Using an impedance analyzer (Agilent E4991A), the fre-

quency dependency (from 1 to 100 MHz) of permeability (µi) and the frequency

dependency (from 1 to 40 MHz) of dielectric constant (ε′) of the samples were

recorded. All these measurements except Tc were carried out at room temperature.

3. Results and Discussion

3.1. Composition and microstructures

Figure 1 shows the XRD patterns of the as-prepared Mn–Zn ferrites with different

doping contents of Sb3+ ions. It can be seen from this figure that all the specimens

contained pure ferrite phase of spinel cubic structure without any other phases

under the proposed doping content of Sb3+ ions.

The lattice constants of the ferrite phases in the as-prepared samples were cal-

culated from the XRD data, which are illustrated in Fig. 2. It can be seen that the

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Fig. 1. XRD patterns of the as-prepared Mn–Zn ferrites with different doping contents of Sb3+

ions.

Fig. 2. Lattice constants of the as-prepared Mn–Zn ferrites with different doping contents ofSb3+ ions.

lattice constant of the samples decreased slightly with increasing doping amount

of Sb3+ ions, indicating that the doping of Sb3+ ions would cause shrinkage of the

ferrite lattice. According to Ref. 14, Sb3+ can be oxidized to Sb5+ at 1100–1200◦C.

After doping, some of the Sb3+ ions would be oxidized to Sb5+ ions at the applied

sintering temperature, and the radius Fe3+ ion (0.67 A) is smaller than that of Sb3+

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

Microstructural and Electromagnetic Properties of Mn–Zn Ferrites

ion (0.76 A) but a little larger than that of Sb5+ ion (0.60 A).15 So the decrease in

lattice constant could be attributed to the substitution of Sb5+ ions with smaller

radius for Fe3+ ions in A or B site. In this work, it was more possible that the

nonmagnetic Sb5+ ions entered into the A sublattice replacing the Fe3+ ions there,

and this supposition quite agreed with the explanation on saturation magnetization

and Curie temperature. In the meantime, when Fe3+ ions are replaced by Sb5+ ions

with large valence, lattice distortion and more cation vacancies would be produced

in order to balance the electric charges, thereby causing the lattice contraction and

thus the decrease of lattice constant.

Figure 3 illustrates the SEM micrographs taken from the fracture surfaces of the

as-prepared samples with different doping contents of Sb3+ ions, and the grain sizes

(a) (b)

(c) (d)

(e)

+A

+B

Fig. 3. Typical SEM images of the as-prepared Mn–Zn ferrites with different doping contents ofSb3+ ions: (a) 0 mol%, (b) 0.5 mol%, (c) 1.0 mol%, (d) 1.5 mol% and (e) 2.0 mol%.

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X. L. Fu et al.

Fig. 4. Grain size of the as-prepared Mn–Zn ferrites with different doping contents of Sb3+ ions.

of the corresponding ferrites were calculated from these graphs, which are shown

in Fig. 4. It can be seen that with increasing doping contents of Sb3+ ions, the

grain size of the samples increases. The melting point of Sb2O3 is 656 ◦C, which is

far below the sintering temperature of the ferrites. So the main cause accounting

for the increase in ferrite grain size might be the liquid-phase sintering which can

promote the rapid grain growth.9

In order to confirm the distribution of Sb3+ ions in the samples, EDX analysis

was carried out on the fracture surfaces of typical Mn–Zn ferrite sample as shown

in Fig. 3(c), on which Spot A was a typical grain, and Spot B was a typical grain

boundary, respectively. The obtained EDX spectra are illustrated in Fig. 5 and their

corresponding analysis results are listed in Table 1. The EDX result from Spot A

reveals that the ferrite grain contains certain amount of Sb3+ ions, supporting

indirectly the entering of Sb3+ ions into the sublattice of ferrites. Compared with

the XRD results presented above, it can be confirmed that after the addition of

Sb3+ ions, the main phase of the samples was Sb-doped Mn–Zn ferrite. However,

from the EDX analysis result of Spot B, it can be seen that there are more Sb3+

ions on the grain boundary. As listed in Table 1, there are about quadruple as

much Sb3+ ions on the grain boundary as that on the ferrite grain, although the

analysis is semi-quantitative, which indicates that there is certain amount of Sb2O3

gathering on the grain boundary. So according to the result of EDX analysis, it can

be concluded that after doping, a small quantity of Sb3+ ions can enter into the

ferrite lattice and the left gathers on the grain boundary as fluxing agent, causing

the increase of grain size as shown in Fig. 4.

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

Microstructural and Electromagnetic Properties of Mn–Zn Ferrites

(a)

(b)

Fig. 5. EDX spectra taken from different areas on the fracture surface of typical Mn–Zn ferritesample with 1.0 mol% Sb3+ ions: (a) on grain (Spot A as shown in Fig. 3(c)); (b) on grainboundary (Spot B as shown in Fig. 3(c)).

Table 1. EDX analysis results from Fig. 5 taken from different areas on the frac-ture surface of typical Mn–Zn ferrite sample with 1.0 mol% Sb3+ ions as shown inFig. 3(c).

Element O Mn Fe Zn Sb

Atom percentage on grain (%) 44.76 7.95 39.72 7.45 0.12

Atom percentage on grain boundary (%) 45.20 7.97 38.84 7.46 0.53

3.2. Magnetic performance

The saturation magnetization Ms of the as-prepared Mn–Zn ferrite samples with

different doping contents of Sb3+ ions are shown in Table 2. It can be seen that Ms

of the samples increased with increasing doping content of Sb3+ ion up to 1.0 mol%,

and then decreased when more Sb3+ ions were doped. According to the molecular

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Table 2. Basic magnetic parameters of the as-prepared Mn–Zn fer-

rites with different doping contents of Sb3+ ions.

Content of Sb3+ (mol%) 0 0.5 1.0 1.5 2.0

Ms (emu/g) 52.40 59.01 59.29 51.33 40.68

Hc (Oe) 1.03 1.08 1.17 1.22 1.12

Tc (◦C) 179 177 163 158 144

magnetization, the net magnetization M is the result of the different magnetic

moments in the sublattice (M = |Mb − Ma|, where Mb is the magnetic moment

at the B sites and Ma is the magnetic moment at the A sites), which depends

upon the cation occupancy.4,16 When Sb3+ ions entered into the lattice of Mn–Zn

ferrite, it was supposed that these nonmagnetic ions replaced Fe3+ ions occupying

A sites, causing the decrease of magnetic moment at the A sites. So Ms of the Sb-

substituted ferrite samples increased with increasing doping content of Sb3+ ions

up to 1.0 mol%, because the |Mb −Ma| increased when introducing Sb3+ ions into

the ferrites. However, Ms decreased with additional Sb3+ doping. This could be

explained as follows. Lattice defect and distortion increased as the introduction of

Sb3+ ions, which caused the decrease of Ms. So although the |Mb −Ma| increased

when introducing Sb3+ ions into the ferrites, the ferrite lattice was damaged when

more Sb3+ ions were introduced, and a decrease of Ms could be expected when

additional Sb3+ ions were doped.

The coercivity of the as-prepared Mn–Zn ferrite samples with different doping

contents of Sb3+ ions are also shown in Table 2. It can be seen that the coercivity of

the samples increased with the doped Sb3+ ion content up to 1.5 mol%, presenting

a maximum value of 1.22 Oe, after which it decreased with further increasing Sb3+

ion content. Coercivity is the amount of reverse magnetic field which must be

applied to a magnetic material to drive the magnetic flux return to zero.17 For

soft ferrites, it is caused by the resistance of domain wall displacement. After the

introduction of Sb3+ ions into the ferrites, impurities like Sb2O3 which did not take

part in the chemical reaction distributed on the grain boundary, breaking and acting

against the displacement of domain walls, so when the doping amount of Sb3+ ions

was less than 1.5 mol%, due to the foreign phase of Sb2O3, the samples doped

with more Sb3+ ions were expected to have larger coercivity. At the same time,

coercivity of ferrites depends inversely on grain sizes. Larger grains tend to consist of

a greater number of domain walls. The magnetization or demagnetization caused by

domain wall movement requires less energy than that required by domain rotation.18

In contrast with the contribution of domain rotation, the contribution of domain

wall movement, which needs less energy when the materials are magnetized or

demagnetized, increases as the number of walls increases with increasing grain sizes.

Therefore, the samples having relatively larger grains are expected to have lower

coercivity. As shown in Fig. 4, the grain size of the as-prepared samples increased

with increasing doping amount of Sb3+ ions. When the doping content of Sb3+

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Microstructural and Electromagnetic Properties of Mn–Zn Ferrites

ions increased from 0 to 1.5 mol%, the contribution of impurities like Sb2O3, which

did not take part in the chemical reaction distributing in the grain boundary area,

played a leading role in domain wall displacement, causing an increasing coercivity,

after which, the contribution of the increasing grain size dominated the domain

wall displacement, leading to a decreasing coercivity. So the coercivity of the as-

prepared samples initially showed a rise with increasing doping content of Sb3+ ions,

but dropped down when the content of Sb3+ ions was more than 1.5 mol%.

In Table 2, it can be also seen that the Curie temperature Tc of the samples de-

creased monotonously with increasing doping amount of Sb3+ ions. Curie temper-

ature depends on the A–B exchange effect (the strongest one in all the three kinds

of exchange effects, A–A, B–B and A–B).19 The decrease in Tc of the as-prepared

Mn–Zn ferrites after the introduction of Sb3+ ions was due to the replacement of

Sb3+ ions at the expense of Fe3+ ions at the A sites, as a result of the weakening

of the A–B exchange interaction strength, in which the interaction between iron

ions played a leading role.20 As mentioned in Ref. 3, A sites contained less iron ions

than B sites. When Sb3+ ions entered into A sites, some Fe3+ ions were replaced

and pushed into B sites, reducing the quantity of iron ions at the A sites. So the

A–B exchange effect was weakened, and the measured Tc decreased.

The initial permeability (µi) dispersion spectra of the as-prepared samples with

different doping contents of Sb3+ ions are presented in Fig. 6. It is shown that µi

increased with increasing doping amount of Sb3+ ions, reaching a maximum for the

sample with Sb3+ ion content being 0.5 mol% and decreased with further doping

of Sb3+ ions. According to Ref. 21, without considering other factors (for example,

impurities, pores, and so on), the value of µi in dense Mn–Zn ferrites depends on

Fig. 6. Initial permeability dispersion spectra of the as-prepared Mn–Zn ferrites with differentdoping contents of Sb3+ ions.

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X. L. Fu et al.

grain size and increases with the increase of grain size in the range below 30 µm. So

samples with larger grain size might present a higher value of µi, and that was why

the rise of µi in the present study when the doping content of Sb3+ ions increased

from 0 to 0.5 mol% could be expected. However, µi is influenced by many factors.

Theoretically, µi is correlated to two different magnetizing mechanisms: the spin

rotational magnetizing inside the domains and the domain wall motion.22,23 When

too much more Sb3+ ions were introduced, the excessive Sb2O3 which did not

take part in the chemical reaction resulted in the creation of grain boundary phase

consisted of crystallographically distorted and possibly nonmagnetic layers. These

grain boundary layers, which increased with increasing doping amount of Sb3+

ions, hindered the domain wall motion and decreased the magnetic permeability,

although they enlarged the grain size of the as-prepared ferrite samples. So µi

increased with increasing doping amount of Sb3+ ions, reaching a maximum for

the samples with doping content of Sb3+ ions being 0.5 mol% and decreased with

further increasing doping amount of Sb3+ ions.

3.3. Dielectric performance

The variations of ε′ with frequency for the as-prepared ferrites with different doping

contents of Sb3+ ions are shown in Fig. 7. It is noticed that ε′ increased with

increasing doping amount of Sb3+ ions, reaching a maximum for the samples with

Sb3+ doping content more than 1.5 mol%. It is known that the dielectric behavior of

ferrites depends on the number of available Fe2+ ions in the B sites of ferrites. The

electronic exchange such as Fe2+ ↔ Fe3+ results in a local displacement of electrons,

Fig. 7. Frequency dependence of dielectric constant of the as-prepared Mn–Zn ferrites with dif-ferent doping contents of Sb3+ ions.

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

Microstructural and Electromagnetic Properties of Mn–Zn Ferrites

which determines the polarization, and thus the dielectric constant of ferrites.24–26

As mentioned before, Sb3+ ions could enter into the ferrite lattice and replace the

Fe3+ ions at the A sites. These replaced Fe3+ ions by Sb3+ ions would be pushed

into B sites, and owing to this replacement, the content of Fe ions at the B sites

increased and the electron exchange interaction Fe3+ ↔ Fe2+ was enhanced, thus

the increase of ε′ could be expected. However, when the Sb3+ doping amount was

more than 1.5 mol%, the amount of Sb3+ ions entering into A sites did not increase

for the saturation of Sb3+ doping in the ferrite, leading to a constant high value

of ε′. So after increasing to a maximum, the dielectric constant of the as-prepared

samples would keep a constant high level when the doping amount of Sb3+ ions

was more than 1.5 mol%.

4. Conclusions

Mn–Zn ferrites with different doping contents of low melting-point nonmagnetic

Sb3+ ions were prepared by two-step synthesis method. The conclusions can be

summarized as follows:

(1) All the samples with a doping content of Sb3+ ions no more than 2.0 mol%

contained pure ferrite phase of a typical spinel cubic structure. With increas-

ing doping amount of Sb3+ ions, more Sb3+ ions entered into A sites, caus-

ing a decrease in lattice constant. The doping of Sb3+ ions could create a

liquid-phase on the grain boundary and promote the grain growth of Mn–Zn

ferrites.

(2) The saturation magnetization and initial permeability initially rose after the

doping of Sb3+ ions, but dropped down with additional Sb3+ doping, indicat-

ing that the introduction of appropriate amount of Sb3+ ions could improve

them of Mn–Zn ferrites. The Curie temperature decreased monotonously with

increasing doping amount of Sb3+ ions. The coercivity showed a rise with in-

creasing doping content of Sb3+ ions at first, but dropped down when Sb3+

content was more than 1.5 mol%.

(3) The introduction of Sb3+ ions into ferrites was against obtaining Mn–Zn ferrites

of low dielectric constant. The dielectric constant of the ferrites presented a rise

with increasing doping content of Sb3+ ions and kept a constant high level when

the doping amount of Sb3+ ions was more than 1.5 mol%.

Acknowledgments

The authors would like to thank the financial support for this work from the Na-

tional Natural Science Foundation of China (Grant Nos. 60806005, 61274015 and

51172030), the Transfer and Industrialization Project of Sci-Tech Achievement (Co-

operation Project between University and Factory) from Beijing Municipal Com-

mission of Education, and State Key Laboratory of New Ceramic and Fine Pro-

cessing, Tsinghua University (Grant No. KF0903).

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December 11, 2012 10:35 WSPC/Guidelines-IJMPB S0217979213500033

X. L. Fu et al.

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