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Electrical and magnetic properties of magnesium ferrite ceramics doped with Bi2O3
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Acta Materialia 55 (2007) 6561–6572 www.elsevier.com/locate/actamat
Electrical and magnetic properties of magnesium ferrite ceramics doped with Bi2O3 L.B. Kong *, Z.W. Li, G.Q. Lin, Y.B. Gan
1
Temasek Laboratories, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 13 April 2007; received in revised form 6 August 2007; accepted 6 August 2007 Available online 25 September 2007
Abstract The effects of concentration of Bi2O3 and sintering temperature on DC resistivity, complex relative permittivity and permeability of MgFe1.98O4 ferrite ceramics were studied. The objective of the study was to develop magneto-dielectric materials, with almost equal values of permeability and permittivity, as well as low magnetic and dielectric loss tangent, for the design of antennas with reduced physical dimensions. It was found that the poor densification and slow grain growth rate of MgFe1.98O4 can be greatly improved by the addition of Bi2O3, because liquid phase sintering was facilitated by the formation of a liquid phase layer due to the low melting point of Bi2O3. It was found that 3% Bi2O3 can result in fully sintered MgFe1.98O4 ceramics. The DC resistivities of the MgFe1.98O4 ceramics were increased as a result of the addition of Bi2O3, except for 0.5%. The exceptionally low resistivities of the 0.5% samples were explained by a ‘cleaning’ effect of the small amount of liquid phase at the samples’ grain boundaries. The electrical and magnetic properties of the MgFe1.98O4 ceramics exhibited a strong dependence on the concentration of Bi2O3. The 0.5% samples were found to have the highest dielectric loss tangents, which can be understood similarly to the DC resistivity results. The 2–3% Bi2O3 is required to attain low dielectric loss MgFe1.98O4 ceramics for antenna application. Low concentration of Bi2O3 increased the static permeability of the MgFe1.98O4 ceramics owing to the improved densification and grain growth, while too high a concentration led to decreased permeability owing to the incorporation of the non-magnetic component (Bi2O3) and retarded grain growth. However, the addition of Bi2O3 alone is not able to produce magneto-dielectric materials based on MgFe1.98O4 ceramics, and further work is necessary to modify the permeability using cobalt (Co). Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium ferrite; Densification; Grain growth; DC resistivity; Complex relative permittivity
1. Introduction Conventional antennas for the frequency band of 3– 30 MHz (HF) and 30–300 MHz (VHF) are physically large, and therefore not suitable for portable applications. A pertinent challenge is to reduce the physical dimensions without affecting its electrical performances. The laws of physics indicate that it is potentially possible to use material loading
*
Corresponding author. Tel.: +65 65166910; fax: +65 68726840. E-mail address: [email protected] (L.B. Kong). 1 Present address: EADS Singapore Research and Technology Centre, 41 Science Park Read, Science Park II, Singapore 117610, Singapore.
to scale down the antenna’s physical dimension by a factor of n (refractive index of material), with its electrical dimension unchanged. A class of materials that serves this purpose is thep magneto-dielectric materials with high refractive index ffiffiffiffiffiffiffi (n ¼ l0 e0 , where l 0 is relative permeability and e 0 is relative 0 permittivity) and and e 0 (Z ¼ pffiffiffiffiffiffiffiffiffi ffi almost matching lpffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi [1,2], 0 0 0 0 0 0 l0 l =e0 e ¼ g0 l =e ¼ g0 ; where g0 ¼ l00 =e00 ¼ 1 is impedance of free space and l 0 = e 0 ). The latter condition is particularly important for matching the antenna impedance to free space environment. Moreover, the materials must have sufficiently low magnetic and dielectric loss tangent (6102) to minimize losses in the antennas. Ferrites are potential candidates of magneto-dielectric materials, as they have both magnetic and dielectric
1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.08.011
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properties. To achieve a low magnetic loss tangent, the materials obtained must have a resonant frequency far beyond the desired frequency band of interest for antenna designs. Three types of ferrites can be considered: spinel, garnet and hexaferrite. The resonant frequencies of composites based on spinel and garnet ferrites are from tens to hundreds of megahertz [3–5], while that of hexaferrites can be in the microwave band [6–8]. It is therefore expected to use spinel or garnet ferrite for low frequency applications, and hexaferrites for microwave requirements. In a previous work, the authors exploited composites with epoxy resin as matrix and ferrite powders as fillers, which showed that almost equal values of real permeability and permittivity (to be 6–7) can be obtained [9]. The magnetic loss tangent of the composites is much lower than 102, while it is difficult to reduce the dielectric loss, probably because of the relatively high loss tangent of the polymer matrix [10]. Therefore, it was decided to use ferrite ceramics. Magnesium ferrite (MgFe2O4) has a cubic spinel-type structure, with lattice constant a = 0.83998 nm and space group Fd 3m (ICDD No. 8-1943 and 17-464). It is well known as a soft magnetic n-type semiconductive material, with high resistivity and low magnetic and dielectric losses. Magnesium ferrite and its derivatives have been widely used in microwave technologies [11–13]. Recent studies showed that MgFe1.98O4 can be made to have almost equal values of permeability and permittivity under certain processing conditions [14,15]. The MgFe1.98O4 sample sintered at 1125 °C for 2 h showed l 0 e 0 = 6.7 over 3–30 MHz, together with relatively low magnetic and dielectric loss tangents (<102). Owing to its poor densification characteristic, the MgFe1.98O4 ceramics sintered at 1125 °C is only 70% of its theoretical density. This could be a problem for practical applications where sufficient mechanical properties are required, because porous materials usually have poor mechanical strength. Substitution of Mg with Cu significantly improved the densification and grain growth of MgFe1.98O4, owing to the formation of the low melting point of a eutectic Cu-rich phase. Combined with the modification with Co, a Cu–Co– Mg–Fe system was developed, which exhibited promising magneto-dielectric parameters [14,15]. Similarly, Bi2O3 is an alternative sintering aid for improving the sintering property of magnesium ferrite. However, unlike CuO, Bi2O3 does not reaction with MgFe1.98O4. This paper reports mainly on the effects of Bi2O3 concentration and sintering temperature on the DC resistivity, complex relative permittivity and permeability of MgFe1.98O4 ceramics. Although the effect of Bi2O3 on the sintering behavior of various ferrite materials has been extensively studied, systematic studies on its effect on electrical and magnetic properties are not available, especially for dielectric properties [16–18]. Specifically, it was found that 2–3% Bi2O3 is necessary to attain the low dielectric loss tangent required for antenna designs. This value is higher than those used in the literature, where it is widely accepted that the concentration of dopant should be <1%. It is necessary to note
that Bi2O3 alone is unable to produce desirable magnetodielectric materials based on MgFe1.98O4 ceramics. However, the fact that the real permeability is higher than the real permittivity for samples processed under certain conditions renders the possibility to adjust the permeability using cobalt (Co) in order to achieve matching permittivity and permeability. This work is being carried out in the authors’ laboratory, and the results will be reported elsewhere. 2. Experimental procedure All ferrite samples were synthesized via the conventional solid-state reaction process. Commercially available constituent oxides, Fe2O3 (99% purity, Aldrich, USA), MgO (99+% purity, Aldrich, USA) and Bi2O3 (99+% purity, Aldrich, USA), were used as starting materials. The nominal composition is MgFe1.98O4, with Bi2O3 concentration ranging from 0.5% to 10%. The weighted starting materials were thoroughly mixed using a high-energy ball mill. The milling operation was carried out using a Retsch PM400type planetary ball milling system, with 250 ml tungsten carbide vials. Every vial was filled with 100 tungsten carbide (WC) balls with a diameter of 10 mm as the milling medium. The milling speed was 200 rpm. The ball-to-powder weight ratio was about 40:1. The mixed powders were then compacted and sintered at temperatures ranging from 900 °C to 1150 °C for 2 h in air. Both heating and cooling rates were 5 °C min1. Two types of samples, namely disks (dia. 10 mm and thickness 1.5 mm) and coaxial cylinders (outer dia. 20 mm, inner dia. 10 mm and thickness 2.5 mm), were prepared. Disk samples were used for measurement of permittivity and DC resistivity, while cylinder samples were used for measurement of permeability. The phase compositions of the mixed, milled, calcined and sintered samples were analyzed by X-ray diffractometry (XRD) using a Philips PW 1729 type instrument with Cu Ka radiation. The microstructures and grain morphologies of the sintered samples were examined by field emission scanning electronic microscopy (FESEM) using a JEOL JSM-6340F-type instrument. Grain sizes were used to characterize the grain growth of the sintered samples, which were estimated from the SEM images by the equation G = kL = 1.5 L (where k = 1.5 is a geometry-dependent proportionality constant) [19]. An average grain size with a standard deviation (error) for each sample was obtained by counting a sufficiently large number of grains to ensure accuracy. The densities of the ferrite ceramics were derived from the masses and dimensions of the samples. The DC resistance of the sintered samples was measured using a Megger BMM80 Insulation Multimeter at room temperature, from which DC resistivities were calculated using the dimension of the disk samples. The complex permeability and permittivity of the ceramics were measured using an Agilent E4991A RF impedance/materials analyzer over 1 MHz–1 GHz, with the
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
16453A (permeability) and 16454A (permittivity) test fixture, respectively. Detailed analysis of the measurement techniques can be found in the operational manual from Agilent Technologies [20]. A brief description on the measurement of permittivity and permeability is given below. The application of a time-varying (or AC) electric field to a dielectric material causes some dielectric loss and a delay in the dielectric response to the electric field. Permittivity in an AC electric field is defined as complex relative permittivity e, given by e ¼ e0 je00
ð1Þ
where e 0 and e 0 0 are the real and imaginary permittivity, which represent the amount of energy stored in the dielectric materials from AC electric field and the energy loss to the AC field, respectively. The energy loss is usually characterized by the dielectric loss factor (De), which is expressed as the dielectric loss tangent, the ratio of the imaginary to the real permittivity (tan de ¼ e00 =e0 Þ. The capacitance method was used to measure relative permittivity with a E4991A analyzer. During measurement, disk samples (device under test or DUT) with silver electrode on both sides were placed in-between two circular plates to form a parallel plate capacitor, as shown in Fig. 1a [20,21]. The real and imaginary permittivity were calculated from the capacitance and the dissipation factor, respectively. As the capacitor (C) formed using 16453A has a small capacity because of the large impedance, the equivalent circuit of the capacitor is considered to comprise an equivalent parallel capacitance and an equivalent parallel conductance, as shown in Fig. 1b and c [20,21]. The admittance (Y) of circuit b and the complex admittance (Y*) of circuit c in Fig. 1 can be expressed as Y ¼ j-C ¼ j-jejC 0
ð2Þ
Cp G j C0 Y ¼ G þ j-C p ¼ j-C 0 C0
ð3Þ
where C0 is the capacitance when using air as a dielectric material (without DUT), and x is the angular frequency. Therefore, the complex relative permittivity can be calculated by
a
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Cp G j -C 0 C0 C tC p p ¼ e0 ¼ C 0 e0 A G t e00 ¼ ¼ -C 0 -e0 ARp
ð4Þ
e¼
ð5Þ ð6Þ
where G ¼ R1p (G and Rp are conductance and resistance, respectively), t and A are the thickness and cross-sectional area of the DUT. Errors of the 16453A test fixture include those due to edge capacitance on the edge electrodes (stray capacitance), residual parameters of the test fixture such as electrical length, residual impedance, stray admittance and air gaps caused when sandwiching the DUT between the electrodes. Edge capacitance was calculated internally by the E4991A equipment. Errors due to the residual parameters of the test fixture were effectively minimized by performing OPEN, SHORT and known LOAD calibrations on the DUT contact surface of the test fixture. Silver (paste) electrodes were used to minimize the errors due to air gaps. Similarly, the application of an AC magnetic field to a magnetic material will cause some magnetic loss and delayed induction of magnetic flux. In AC magnetic field, the complex relative permeability l is given by l ¼ l0 jl00 0
ð7Þ 00
where l and l are the real and imaginary permeability, respectively. The real part represents the amount of energy stored in the magnetic material from the AC magnetic field, while the imaginary part is the energy loss to the magnetic field. The loss factor (Dl) is expressed as a loss tangent, which is the ratio of the imaginary to the real permeability (tan dl ¼ l00 =l0 Þ. The E4991A uses the inductance method to measure relative permeability. In this method, a DUT (toroidal core) is wrapped with a wire, and the relative permeability is calculated from the inductance values at the end of the core. The ideal impedance of the test fixture without DUT is given by Zss, and the residual impedance Zres can be calculated from the measured impedance Zsm by Z res ¼ Z sm Z ss
ð8Þ
Errors due to the residual impedance were compensated by the calibration procedure, using the SHORT condition,
c
b A = area t = thickness
C
C
G
Fig. 1. DUT (device under test) of the parallel plate test fixture measurement method (a) and equivalent circuit model of the parallel plate capacitor (b) and (c).
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without the DUT in the test fixture. The impedance after error correction Zcomp is calculated from the measured impedance Zm, with the DUT positioned in the test fixture, as shown in Figs. 2 and 3 [19,20]. The corrected impedance is given by Z comp ¼ Z m Z res
ð9Þ
Assuming that Zss consists only of inductance elements: l c ð10Þ Z ss ¼ j- 0 h ln a 2p The complex relative permeability of the DUT can be determined by l¼
2pðZ m Z sm Þ þ1 j-l0 h ln bc
ð11Þ
where l0 is the relative permeability of air, h, b and c are the thickness, internal and outer diameters of the DUT. 3. Experimental results
XRD measurement, which is probably because of either the insufficient sensibility of the XRD equipment used or the poor crystallinity of second phases, if present. It was found that pure MgFe1.98O4 cannot be fully sintered at <1150 °C. A relative density of 95% can be achieved after sintering at 1150 °C for the samples with 0.5% and 1% Bi2O3, while the relative density of the sample with 2% Bi2O3 is already 96.1% after sintering at 1000 °C for 2 h. A high concentration of Bi2O3 (P3%) resulted in almost full densification, especially at a sintering temperature of P950 °C. The microstructures of pure MgFe1.98O4 samples sintered at temperatures 61100 °C are very porous. The grain growth is very slow with sintering temperature, and all samples experienced only inter-grain fractures. In summary, the addition of Bi2O3 significantly enhanced the densification behavior and grain growth rate, which are attributed to the formation of a liquid phase during the sintering process at high temperatures [16,22]. 3.2. DC resistivity and complex relative permittivity
3.1. Densification and grain growth XRD results (not shown) demonstrated that the addition of Bi2O3 has no significant effect on the phase formation of MgFe1.98O4 under the conditions used in the present study. Bi2O3 phases were also not observed in the
SHORT state
DUT
Zss
Zcomp
Zsm
Zm
Zres
Zres
16454A Fig. 2. Schematic diagram of the 16454A test fixture with and without a DUT.
e
The room temperature DC resistivities of the MgFe1.98O4 ceramics, sintered at different temperature, as a function of the concentration of Bi2O3 are shown in Fig. 4. For doped samples, the DC resistivity increases nearly exponentially as the Bi2O3 concentration increases from 0.5% to 3% and shows no significant change above 3%. Careful inspection reveals that the DC resistivities of the 0.5% samples are slightly lower than those of the pure ones at every sintering temperature. For pure and the lowconcentration-Bi2O3 doped samples, the DC resistivity increases below 1100 °C. A relatively sharp drop in resistivity is observed for the samples after sintering at 1150 °C, especially for those with a low concentration of Bi2O3. For those with a high concentration of Bi2O3, at a given concentration, the general trend is that the DC resistivity increases with increasing temperature initially (from 900 °C to 950 °C) and decreases above 950 °C. Figs. 5–8 show the complex relative permittivity curves of pure MgFe1.98O4 ceramics and the three groups with
DUT
ρr (Ω cm)
h0
h
10
9
10
8
10
7 o
10
6
10
5
900 C o 1000 C o 1100 C
o
950 C o 1050 C o 1150 C
b c
0
2
4
6
8
10
Concentration of Bi2O3 (%) 2a Fig. 3. Cross-sectional diagram of the 16454A test fixture with a DUT.
Fig. 4. DC resistivity of the samples sintered at different temperature as a function of the concentration of Bi2O3. The solid line is a visual guide.
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572 15
o
(b)1050 C 10
ε' ε''
5
Permittivity
10
5
0
0 6
10 15
10
7
8
10
10
9
o
6
10 15
7
10
10
10
5
5
0
0 6
10
7
8
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8
10
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6
10
Frequency (Hz)
7
10
10
8
10
o
Permittivity
ε' ε''
7
10
9
10 o
(c) 1100 C
30
Permittivity
8
10
o
0 6 10
10
7
20
10
10
0
8
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9
o
(d) 1150 C
30
20
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0 6
10
7
10
8
9
10
10
10
6
Frequency (Hz)
10
7
10
8
10
9
Frequency (Hz)
Fig. 6. Complex relative permittivity of the MgFe1.98O4 samples with 0.5% Bi2O3.
o
(a) 1000 C
Permittivity
30
Permittivity
8
9
10
10 o
(c) 1100 C
30
6
7
10
10
10
0
8
9
10
10 o
(d) 1150 C
30 20
7
10
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5
5
0
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9
o
(d) 1150 C
0 6
7
10
8
10
9
10
10
6
10
7
10
8
10
9
Frequency (Hz)
Fig. 8. Complex relative permittivity of the MgFe1.98O4 samples with 2% Bi2O3.
low concentration of Bi2O3 (62%), respectively. These curves can be classified into two types. One is represented by those shown in Fig. 8a–c, where both real and imaginary parts are almost independent of frequency. This class of samples is lossless or of very low loss tangent. All others belong to high-loss samples, which are characterized by frequency-dependent real and imaginary permittivity, especially at low frequency (<100 MHz). The real permittivity and the loss tangent (tgd ¼ e00 =e0 Þ, where e 0 0 and e 0 are real and imaginary permittivity) collected at 1 MHz are illustrated in Figs. 9 and 10, respectively. Fig. 11 shows the real permittivity (at 100 MHz) of all samples as a function of sintering temperature. Pure MgFe1.98O4 samples have a similar dielectric characteristic until 1100 °C, with real permittivity slightly increasing with sintering temperature. A relatively sharp increase in real and imaginary permittivity is observed in the 1150 °C-sintered sample. The addition of 0.5% Bi2O3 obviously worsened the dielectric properties of the MgFe1.98O4 ceramics. Besides the increase in loss tangent,
8
10
Frequency (Hz)
9
10
0% 1%
0.5% 2%
20 15 10
0 6
10
15 10
25
10
20
10
6
o
0 7
o
10 20
30
0 10
10
10
10
6
10
(c) 1100 C
20
10
10
9
(b) 1050 C
30
ε' ε''
20
8
Frequency (Hz)
10
0 6 10
10
10
20
10
5 0
7
15
9
(b) 1050 C
30
10
0
Frequency (Hz)
(a) 1000 C
20
5
o
(b) 1050 C
15
ε' ε''
10 20
Fig. 5. Complex relative permittivity of pure MgFe1.98O4 samples sintered at different temperatures.
30
10
6
o
20
o
(a) 1000 C
15
9
(d) 1150 C
(c) 1100 C
10
10
Permittivity
Permittivity
20
o
(a) 1000 C
Permittivity ε1MHz '
Permittivity
15
6565
6
10
7
10
8
10
9
10
Frequency (Hz)
Fig. 7. Complex relative permittivity of the MgFe1.98O4 samples with 1% Bi2O3.
5
900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 9. Real permittivity (at 1 MHz) of the samples with low concentration of Bi2O (62%).
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MgFe1.98O4 ceramics. A sufficiently low dielectric loss tangent is one of the critical requirements for antenna applications.
1
0% 1%
0.5% 2%
0.1
900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 10. Dielectric loss tangent (at 1 MHz) of the samples with low concentration of Bi2O3 (62%).
Permittivity ε '
100MHz
15 0%
0.5%
1%
2%
12
9 3%
5%
7%
10%
6 900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 11. Real permittivity (at 100 MHz) of the samples as a function of sintering temperature.
both real and imaginary permittivities exhibit a significant increment as a result of the presence of 0.5% Bi2O3. The samples with 1% Bi2O3 possess similar dielectric properties to the pure ones, as the sintering temperature is 61100 °C. The detrimental effect of Bi2O3 on the dielectric loss is still observable for the 1150 °C-sintered sample. At a given concentration, the dielectric loss tangent decreases slightly with increasing sintering temperature, especially in the range 950–1050 °C. The dielectric properties are greatly improved by the addition of 2% Bi2O3. As shown in Fig. 8, both the real and imaginary permittivities stay almost flat over the frequency range studied, as long as the sintering temperature is not >1100 °C. The dielectric property of the 1150 °C-sintered sample is almost the same as that of the pure one sintered at the same temperature. The 3% group has a similar dielectric property to the 2% one, but the former has a lower dielectric loss tangent (results not shown) and is also less sensitive to the 1150 °C sintering. Too high a concentration of Bi2O3 has a negative effect on the dielectric properties. It is therefore concluded that 2–3% Bi2O3 content is appropriate to attain low dielectric loss tangent for
Representative complex relative permeability curves of the ferrite ceramics are shown in Fig. 12. The complex permeability spectra of the ceramics exhibit a common feature. The real permeability l 0 remains almost constant up to a certain frequency, beyond which l 0 begins to decrease. The imaginary permeability l 0 0 remains very low for frequencies below several tens of megahertz, and increases above a certain frequency. A peak in l 0 0 corresponding to the dispersion of l 0 can be identified. The peak shifts to lower frequency as the real permeability increases. To characterize the magnetic properties of ferrite materials, a static permeability l0 is usually used, which can be defined as the real permeability far below the resonance frequency fr, corresponding to the maximum imaginary permeability in the l00 –f curve. Here, the real permeability at 1 MHz is used as the static permeability. Magnetic loss tangent is defined as tan dl = l 0 0 /l 0 . The static permeabilities of the samples with and without Bi2O3, as a function of sintering temperature, are plotted in Fig. 13. The static permeability of the pure sample and the samples with high concentrations of Bi2O3 (P3%) increases monotonically with increasing sintering temperature, while the value of the other samples exhibits a sharp rise at different temperatures, depending on the Bi2O3 content. It is obviously demonstrated that the addition of Bi2O3 greatly improved the magnetic properties of the MgFe1.98O4 ceramics. For example, the static permeability of the 3% samples is nearly three times that of the pure ones, at every sintering temperature. At a given sintering temperature, the static permeability maximizes at a certain concentration of Bi2O3. For instance, the maximum static permeability values of the samples sintered at 1050 °C and 1100 °C are at 2% and 1%, respectively.
20 o
(b)
1100 C (a) 0% (b) 1% (c) 3%
15
Permeability
tgδ1MHz
3.3. Complex relative permeability
(c) μ' μ''
10
(c)
(a)
5
(b) (a)
0
10
6
10
7
10
8
10
9
Frequency (Hz) Fig. 12. Representative complex relative permeability curves.
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
20 0% 1%
0.5% 2%
Permeability μ0
15
10
5 3% 7%
0 900
950
1000
1050
5% 10%
1100
1150
o
Sintering temperature ( C) Fig. 13. Static permeability of the samples as a function of sintering temperature.
4. Discussion 4.1. DC resistivity DC resistivity is one of the most important parameters of ferrite ceramics. Generally, high resistivity is required by most applications. Fully dense polycrystalline ferrite ceramics are considered to consist of highly conductive grains and less-conductive grain boundaries, forming a three-dimensional series–parallel network structure. For pure ferrites, the grain boundary has the same composition as or similar composition to that of the grains. The only difference is that grain boundaries are usually in an amorphous state with various defects and imperfections, compared with grains. Besides, impurities are usually considered to locate at grain boundaries. The presence of impurities is inevitable. Impurities such as Ca and Si are either coming along with the raw materials or introduced during the multi-step sample preparations. In this case, DC resistivities of ferrite ceramics are determined mainly by the fraction of the grain boundaries (grain size). It is necessary to mention that this explanation is only applicable to the samples with full densification. Therefore, the decrease in the DC resistivity for the samples with high concentrations of Bi2O3 (P3%) is due to the increase in grain size (decrease in fraction of grain boundaries) as a result of an increase in sintering temperature (950– 1100 °C). Other factors, including composition stoichiometry, density (porosity), crystal structure perfection and microstructural homogeneity, also have effects on the DC resistivities of ferrite ceramics [23]. Among these, the effect of porosity is particularly important. The presence of porosity increases the DC resistivity of ferrite ceramics because air/ vacuum is a good insulator if the pores are closely trapped and uniformly distributed. Otherwise, porosity is prone to reduce the resistivity of ferrite ceramics, because open pores could provide a possible conduction path for electricity owing to impurities entrapped inside. Pure MgFe1.98O4
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and the samples with low concentration of Bi2O3 (62%) have relatively low densities, especially for those sintered at low temperatures. It is found that these samples have poor mechanical strength and absorbed the solvent of the silver paste used as electrodes; hence, the porosity of these samples is considered to be caused by open pores. For these samples, the increase in the DC resistivity caused by the improved densification is more significant than the decrease due to the increased grain size, so that the DC resistivities increase overall with increasing sintering temperature (61100 °C). Another important factor that is always detrimental to attaining high DC resistivities for ferrite ceramics is the formation of Fe2+ ions. With the presence of Fe2+ ions, electron hopping occurs between Fe2+ and Fe3+. Because the electrons transfer from Fe2+ ion to Fe3+ ion within the octahedral sites, there is no change in the energy state of the crystal as a result of the transition. It has been reported that the presence of 0.3% Fe2+ content in a ferrite ceramic can reduce the DC resistivity by a factor of more than two orders of magnitude [24]. In addition, the presence of Bi2O3 has been reported to be able to promote the formation of Fe2+ ions. At high temperature, Bi3+ ions can be oxidized to Bi5+ ions. The Bi5+ ion has a radius of 0.076 nm for octahedral coordination, which is comparable with the dimension of the octahedral interstition in ferrite (0.071 nm) [16]. The substitution of Fe3+ ions at the B site with Bi5+ ions will produce Fe2+ ions, owing to the requirement of electrical neutralization. However, it appears that the relatively sharp drop in the DC resistivity of all samples after sintering at 1150 °C cannot be ascribed to the formation of Fe2+ ions, because the authors’ previous study on MgFe1.98O4 showed that the effect of Fe2+ usually occurs at a temperature of P1200 °C. It is also hard to attribute this observation to the production of Fe2+ due to the presence of Bi5+. On the one hand, Bi5+ ions are only stable at high temperatures. For example, the temperature used in Ref. [16] was 1340 °C, which is higher than that (1150 °C) in the present study by nearly 200 °C. On the other hand, if Bi5+ ions were indeed present and promoted the formation of Fe2+ ions, the effect should be proportional to the concentration of Bi2O3. The DC resistivities, as well as the dielectric properties (discussed later), of our samples showed that such a proportional relationship is not observed. Therefore, we exclude the role of Fe2+ ions in determining the variation in the DC resistivity and the dielectric properties for the samples sintered at 1150 °C, or at least the effect of Fe2+ ions is not the main factor. It is more likely to be related to the property of the liquid phase, as will be discussed later. With the presence of Bi2O3, the properties of the grain boundaries of the ferrite ceramics were changed. The three-dimensional network grain boundary structure became rich in Bi, which is similar to those observed in ZnO–Bi2O3-based ceramic varistors [22,25]. Experiment has shown that a bismuth-rich phase with an interconnected and continuous network structure is left as the
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ZnO grains are removed preferentially from a fully sintered ZnO–Bi2O3 ceramic via etching with acid [25]. Such a three-dimensional network structure is found to be helpful in facilitating oxygen transport in ZnO–Bi2O3-based ceramic materials. For ferrite ceramics, it could be an additional benefit in terms of improving the samples’ electrical properties, because good oxygen transport helps suppress the formation of Fe2+ ions, which in turn is desirable to ensure a high resistivity in the samples. Koops [26] proposed a simple model to represent the network structure of polycrystalline ferrite material: wellconducting grains (with thickness of d2 and resistivity of qr,2) separated by layers of lower conductivity (with thickness of d1 and resistivity of qr,1). With the assumption of x = d1/d2 1 and qr,1 qr,2, the author derived a formula of measured resistivity [27]: qr ¼
d1 q þ qr;2 ¼ xqr;1 þ qr;2 d 2 r;1
ð12Þ
The grain resistivity (qr,2) can be assumed to be constant, because there is no observable reaction between Bi2O3 and MgFe1.98O4. As a result, the measured DC resistivities are determined by x and qr,1. It has been discussed above that the grain size of the samples has only a slight decrease with increasing concentration of Bi2O3 (from 0.5% to 3%). With increasing concentration of Bi2O3, both x and qr,1 are expected to increase, so that the DC resistivity increased with increasing concentration of Bi2O3 ranging from 0.5% to 3%. Further increase in Bi2O3 led to a saturation of resistivity. This explanation is obviously not applicable to the 0.5% samples. To understand the exceptionally low resistivity for the 0.5% samples as compared with the pure ones, it is necessary to re-examine what was happening throughout the material fabrication process. Fabrication of the Bi2O3doped samples is a multi-step process. First, a liquid phase was formed during heating of the pellets above the melting point of Bi2O3 [16–18]. The liquid layer surrounded and wetted grains by filling the grain boundaries. Secondly, densification and grain growth occurred with the presence of the liquid phase during heating and dwelling at high temperature. Finally, during the cooling process, the Bi2O3-rich liquid phase retracted from the two-grain boundaries to triple- and multiple-grain junctions. The degree of retraction is dependent on the amount of the liquid phase. It has been reported that the Bi2O3-rich liquid phase preferentially dissolved Ca and Si impurities that are usually present at the grain interfaces (two-grain boundaries) [16,28]. One can expect that there must be a critical amount for liquid phase, below which all the liquid phase will be brought to the triple- and/or multiple-grain junctions. In this case, the retraction of the liquid phase will result in ‘cleaner’ two-grain boundaries due to the elimination of the impurities. Such ‘clean’ grain boundaries were observed for Mn–Zn ferrites by Drofenik et al. [16] using transmission electron microscopy (TEM). Samples with ‘cleaner’
grain boundaries are expected to have lower resistivities, because both x and qr,1 in the above formula become smaller. This could be the main reason why the DC resistivities of the 0.5% samples are lower than those of the pure ones. Meanwhile, the sharp drop in the DC resistivity of the samples sintered at 1150 °C, especially for those with low concentration of Bi2O3, can be understood similarly. In summary, the addition of Bi2O3 has two opposite effects on the DC resistivity of the MgFe1.98O4 ferrite ceramics. At a relatively low concentration, the presence of Bi2O3 leads to ‘clean’ grain boundaries and thus a reduced DC resistivity. High concentration helps facilitate the formation of a three-dimensional network grain boundary structure and attain high resistivity. 4.2. Dielectric property High frequency permittivity of ferrite crystals is contributed mainly by the atomic and electronic polarization. The permittivity of polycrystalline ferrite ceramics is additionally affected by microstructure, grain size, density and impurities of the samples. Similar to DC conductivity, porosity (density) also has a double-side effect on permittivity. Close pores (inside grains or at grain boundaries) will reduce permeability because of the unit permittivity of air (pores). Open (interconnected) pores, in the case of absorbing impurities (e.g., water) may increase permittivity, because of the high dielectric constant of water and conductive polarization. The presence of Fe2+ in ferrite materials always contributes to high permittivity because Fe2+ has a larger polarization than Fe3+. Fe3+ ion has a stable d-shell configuration with spherical symmetry of the charge cloud, due to its five d-electrons distributed according to Hund’s rule, whereas Fe2+ ion has an extra electron as compared with Fe3+, which disturbs the symmetry of the charge electron cloud [16]. As a result, the presence of Fe2+ increases the polarization in ferrites, and thus ferrites containing a larger number of Fe2+ ions are likely to exhibit a higher permittivity. However, the high permittivity in this case is undesired because it is always accompanied by an extremely high dielectric loss tangent. Fortunately, it is not the case in the present study, as discussed above. The dielectric loss tangent of polycrystalline ferrite ceramics results from the lag in polarization vs the alternating electric field, which has several contributory factors, such as (i) electron polarization losses, (ii) ion vibration and deformation losses, and (iii) ionic migration losses (including DC conduction loss and ionic jump and dipole relaxation losses). The electron polarization losses are responsible for absorption and color in the visible spectrum. The ion vibration and deformation losses are of importance only in the infrared and not a major concern for frequencies below 10 GHz. Therefore, the main contribution to dielectric losses of ferrite ceramics would be the ion migration losses, where conduction losses are more significant than other losses [23]. Without the presence of
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
Fe2+ ions, the conduction loss is caused mainly by the poor microstructure. Polarization due to conduction loss has a dispersion at 103–104 Hz, but it can extend to a high frequency of less than 100 MHz [23]. Therefore, the frequency-dependent real and imaginary permittivity of the high-loss samples as shown in Figs. 8–11 are caused by the conduction loss due to their porous microstructure. Comparatively, the permittivity contributed by the atomic and electronic polarization is independent of frequency in the frequency range of 1 MHz–1 GHz. With a similar model mentioned above [26], Larsen and Metselaar [29] derived a formula to estimate the static value (es) of the apparent relative permittivity (er) of polycrystalline yttrium iron garnet YIG) ceramics: d1 þ d2 es ¼ ð13Þ ei d1 where ei is the relative permittivity at infinite frequency. Here, one can take the permittivities at 1 MHz and 100 MHz as es and ei, respectively. Obviously, this equation is valid only for the samples with high dielectric loss tangents (low concentration of Bi2O3) and invalid for the lossless ones (high concentration of Bi2O3). Using this equation, the extraordinarily high value of e01 MHz for the 0.5% samples can be readily explained. As discussed above, the ‘cleaning’ effect of the liquid phase layer could lead to a very small ‘effective’ d1 for the 0.5% samples, thus resulting in an unexpectedly high permittivity (Fig. 6). Also, this group of samples has the highest dielectric loss tangent at low frequencies (Fig. 10). The dependence of the permittivity (e0100 MHz ) on sintering temperature (Fig. 11) can be explained by the Maxwell– Wagner effect [23,24], with a permittivity increasing with grain size, because the grain size increases with increasing temperature. The exception for the 0.5% sample sintered at 1150 °C could be related to its high permittivity at low frequency. At a given sintering temperature, the e0100 MHz increases with increasing concentration of Bi2O3, which is probably because the permittivity of Bi2O3 is higher than that of MgFe1.98O4. The difference (De ¼ es ei ¼ e01 MHz e0100 MHz Þ can be used as a measure to represent the contribution of conductive polarization to the permittivity. Because the conduction is due to the porous microstructure, increasing sintering temperature is supposed to improve the microstructure and the e01 MHz (es) is expected to decrease due to the reduction in De. However, Fig. 9 indicates an overall increasing trend in permittivity, which means the decrease in e01 MHz (es) is overcompensated by the increase in e0100 MHz (ei). Again, the relatively sharp change in the permittivity for the samples sintered at 1150 °C is most likely related to the property of the liquid phase, because it is not obviously observed for the pure sample, and the samples become more and more resistive to the high temperature sintering with increasing concentration of Bi2O3. Therefore, it is
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more likely that the sharp decrease in DC resistivity of the doped samples is due to the fact that the ‘cleaning’ effect of the liquid phase was enhanced dramatically at 1150 °C. With increasing concentration of Bi2O3, the amount of liquid phase is increased, and the ‘cleaning’ effect becomes less pronounced because the grain junctions cannot contain all the liquid phase. Additionally, one may notice that the resistivity measurement is less sensitive than the permittivity measurement. This is mainly because, when measuring the DC resistance of the ferrite samples, a ‘steady-state current’ cannot be achieved in a short time owing to the polarization currents arising from trapping states of various types and densities, which is similar to that observed in ZnO– Bi2O3 varistor ceramics [22,25,30]. In contrast, the response of these trapping states to AC field is very prompt. 4.3. Magnetic property Generally, the product of resonance frequency (fr) and static permeability (l0 1) for spinel ferrites can be expressed as a constant by the Snoek-like law: ðl0 1Þfr ¼ C
ð14Þ
For natural resonance, C ¼ 23 cM s (where c is the gyromagnetic ratio and Ms is the saturation magnetization) [31]. For wall resonance, C ¼ C 1 M 2s (where C1 is a constant related to the domain size and the thickness of domain wall) [32]. Therefore, a high static permeability leads to a low resonance frequency, as demonstrated in (Fig. 12). Porosity has been shown to have a strong influence on the permeability of ferrite materials. Owing to the presence of porosity, magnetic poles are created on the surface of ferrite grains (or particles) under an applied magnetic field. A demagnetizing field is thus produced, leading to a decrease in permeability. The magnitude of the demagnetizing field is closely related to the grain size and grain boundary characteristics. According to the magnetic circuit model [33], static permeability l0 is given by: l0 ¼
li ð1 þ Dd Þ 1 þ li Dd
ð15Þ
where li is the intrinsic static permeability of materials without any defects, and D and d are the average grain size and thickness of the grain boundaries. With this model, the variation in l0 as a function of density can be quantitatively understood. In general, with increasing sintering temperature, the increase in grain size (D) and density (qd) leads to a decrease in the d/D ratio, and thus increasing static permeability. As it is difficult to measure d and D directly, the ratio d/D is usually calculated approximately from the measured density (qd) based on the following formula [34]: 1=3 qd;i d ¼ 1 ð16Þ D qd
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where qd,i is the theoretical density of the materials. Since the samples with high concentration of Bi2O3 (P3%) are almost fully sintered in the temperature range 900– 1150 °C, Eq. (16) is thus only able to calculate the ratio (d/D) for pure and the low concentration samples (0.5%, 1% and 2%). Owing to its non-magnetic characteristic, Bi2O3 is not specifically considered in this calculation, but its overall role has been taken into account when estimating the theoretical density of the corresponding samples. It is found that the data of the four samples cannot be fitted well using Eq. (15). The dotted curve, as shown in Fig. 14, was obtained with Eq. (15) using a li of 35 as the intrinsic static permeability (nearly double the maximum static permeability of the samples). The data of the four samples are also included in Fig. 14 for comparison. It is noticed that the static permeabilities of the samples with relatively low densities are all far below the calculated values. Only some points are close to the dotted line. They are the 0.5% sample sintered at 1150 °C, 1% samples sintered at 1050– 1150 °C and 2% samples sintered at 1000–1150 °C. SEM images showed that these samples not only have denser microstructure but also possess larger grains. The magnetization of polycrystalline ferrite ceramics is determined by both spin rotation and domain wall motions. The contribution due to domain wall motion is proportional to grain size. A critical size was observed for ferrite materials, below which domain walls do not exist. The critical size can be in a range 0.1–1 lm, depending on materials. Therefore, it is believed that the relatively low static permeabilities for the samples shown in Fig. 14, as compared with the estimated values, are most likely due to the relatively lessdeveloped domain walls of the samples. Although the 2% sample sintered at 950 °C has observable large grains, its microstructure is still dominated by the fine-grain matrix, thus leading to a static permeability lower than expected. This means that the magnetic circuit model cannot be used to explain fully the present experimental results, mainly because the ratio (d/D) was calculated from the measured density and did not take the effect of critical grain size into account. 20 0% 0.5% 1% 2%
16
μ0
12 8 4 0
0.03
0.06
0.09 δ/D
0.12
0.15
Fig. 14. Static permeability vs d/D for the samples with low concentration of Bi2O3 (62%). The dotted line is calculated using Eq. (15) with li = 30.
For the samples with high concentration of Bi2O3 (P3%), the variation in static permeability with sintering temperature is seemingly only explainable in terms of grain size, because these samples are fully sintered. The increase in the static permeability can be attributed to the increased contribution of domain wall as a result of increase in grain size with sintering temperature. The effects of Bi2O3 on the permeability of various ferrite materials have been reported in the literature. For example, Drofenik et al. [16] studied the effect of Bi2O3 on grain size, microstructure and permeability of Mn0.52Zn0.44Fe2.04O4, one of the high permeability materials. A maximum permeability was obtained in the sample with 0.03% Bi2O3. Further increase in Bi2O3 content led to a gradual decrease in permeability up to a Bi2O3 concentration of 7%. The authors attributed the maximum permeability to the elimination of grain boundary impurity, since samples with ‘clean’ grain boundaries have relatively lower coercivity, thus leading to a decrease in permeability. However, it is necessary to mention that their samples were sintered at a temperature as high as 1340 °C. At such a high sintering temperature, volatilization of Bi2O3 must be taken into account, especially for those samples with a high concentration of Bi2O3, because Bi2O3 usually becomes volatile at P1200 °C [17]. For instance, the relative densities of the samples with 1%, 3% and 7% Bi2O3 were 95%, 90% and 87% [16]. The increase in the amount of the non-magnetic phase and the decrease in density led to a decrease in magnetization and, therefore, to a decrease in the static permeability. A similar result was reported by Kumar et al. [18], who used Bi2O3 (up to 6%) to improve the properties of Ni0.8Zn0.2Fe2O4 ceramics prepared by a soft chemical approach. A maximum permeability (at 5 MHz) of 75 was observed for the 1% sample, as compared with 37 for the pure sample and 48 for the one doped with 6% Bi2O3. The authors attributed the decrease in permeability with increasing concentration of Bi2O3 to the possible incorporation of excess non-magnetic phase at grain boundaries, because the samples had almost the same grain size and density. Obviously, the reduction in permeability is much less than the percentage of the second phase, but no explanation was given in that case. Another example was Ni–Cu–Zn ferrite doped with 61 wt.% Bi2O3 [18]. The samples with highest permeability were found to have Bi2O3 between 0.375% and 0.5%. The authors linked the maximum permeability to the appearance of larger grain size in their samples. These scattered and somehow contradictory results indicate that the effects of Bi2O3 on the magnetic properties of ferrite ceramics are dependent not only on the concentration of Bi2O3, but also on the intrinsic properties and processing conditions of the materials studied. To evaluate the effect of Bi2O3 concentration, the static permeability of the samples sintered at 1150 °C as a function of Bi2O3 concentration is illustrated in Fig. 15. An essentially linear relationship between the static permeability
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
Static permeability
18
Experiment Fitting
17 16 15 14 0
2
4
6
8
10
Concentration of Bi 2O3 (%) Fig. 15. Static permeability vs concentration of Bi2O3 for the samples sintered at 1150 °C.
and Bi2O3 concentration is observed. If using the extrapolated permeability at zero to scale the concentration of the non-magnetic phase, the values obtained are higher than the nominal concentration of Bi2O3, which means that the effect of grain size should also be considered when explaining the magnetic properties of the samples with the concentration of Bi2O3. It is necessary to mention that matching real permeability and permittivity have not been achieved in the MgFe1.98O4 + Bi2O3 system developed in the present study. However, noting that the real permeability is slightly higher than the real permittivity, it is possible to develop magneto-dielectric materials with almost equal permeability and permittivity at low frequency range (3–30 MHz) by adjusting the permeability through the incorporation of cobalt (Co) [35]. This work is been carrying out in the authors’ laboratory and will be reported separately in the future. 5. Conclusions Bi2O3 has been shown to be a good sintering aid for improving the densification behavior and enhancing the grain growth of MgFe1.98O4 ceramics. The beneficial effect of Bi2O3 is attributed to the formation of a liquid phase layer due to the low melting point of Bi2O3. The presence a liquid phase layer facilitated liquid phase sintering instead of the solid reaction sintering of pure MgFe1.98O4. The temperature for full densification decreases with increasing concentration of Bi2O3 at low concentrations. The average grain size has a maximum at a certain concentration, depending on sintering temperature. Too high a concentration of Bi2O3 prevents further grain growth owing to the thickened liquid phase layer. The addition of Bi2O3 has a significant effect on the DC resistivity and dielectric properties of the MgFe1.98O4 ceramics. The samples with 0.5% Bi2O3 have a slightly lower resistivity than pure ones, which can be attributed to the ‘cleaning’ effect of the liquid phase. An increase in
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Bi2O3 concentration leads to an exponential increase in DC resistivity from 0.5% to 3%, due to the formation of a three-dimensional grain boundary network structure with high resistivity. The dependence of the DC resistivity on sintering temperature can be explained in terms of grain growth and microstructural development. The dielectric properties can be understood similarly to the DC resistivities. It is found that 2–3% Bi2O3 is required to attain a low dielectric loss tangent necessary for practical antenna applications. The magnetic properties of the samples with low concentration of Bi2O3 (62%) cannot be simply explained by the magnetic circuit model, because the model does not take into account the effect of critical grain size on the static permeability. At high concentrations, the static permeability decreases with increasing concentrations, which can be ascribed to the increased amount of the non-magnetic phase of Bi2O3, together with the reduced grain size. Further works are needed to achieve magneto-dielectric materials based on the MgFe1.98O4 + Bi2O3 system. Since the real permeability is higher than the real permittivity, it is possible to modify the magnetic properties further by introducing a small amount of cobalt (Co). The incorporation of a small amount of Co can alter the magnetocrystalline anisotropy of most ferrites from negative to positive, owing to the large positive magnetocrystalline anisotropic constant of Co ions. References [1] Mosallaei H, Sarabandi K. IEEE Trans Antennas Propagat 2004;52:1558. [2] Buell K, Mosallaei H, Sarabandi K. IEEE Trans Microwave Theory Tech 2006;54:135. [3] Yusoff AN, Abdullah MH, Ahmand SH, Jusoh SF, Mansor AA, Hamid SAA. J Appl Phys 2002;92:876. [4] Nakamura T. J Appl Phys 2000;88:348. [5] Tsutaoka T. J Appl Phys 2003;93:2789. [6] Pullar RC, Appleton SG, Bhattacharya AK. J Magn Magn Mater 1998;186:326. [7] Singh P, Babbar VK, Razdan A, Srivastava SL, Puri RK. Mater Sci Eng B 1999;67:132. [8] Li ZW, Chen LF, Ong CK. J Appl Phys 2002;92:3902. [9] Kong LB, Li ZW, Chen LF, Lin GQ, Gan YB, Ong CK. In: 3rd international conference on materials for advanced technologies (ICMAT), Singapore, 3–8 July; 2005. [10] Kong LB, Li ZW, Lin GQ, Gan YB. IEEE Trans Mag 2007;43:6. [11] Van Uitert LG. J Appl Phys 1955;26:1289. [12] Van Uitert LG, Schafer JP, Hogan CL. J Appl Phys 1954;25:925. [13] Van Uitert LG. J Appl Phys 1957;28:320. [14] Kong LB, Li ZW, Lin GQ, Gan YB, J Am Ceram Soc, in press. [15] Kong LB, Li ZW, Lin GQ, Gan YB. J Am Ceram Soc 2007;90:2104. [16] Drofenik M, Znidarsic A, Makovec D. J Am Ceram Soc 1998;81:2841. [17] Murbe J, Topfer H. J Electroceram 2006;16:199. [18] Kumar PSA, Sainkar SR, Shrotri JJ, Kulkami SD, Deshpande CE, Date SK. J Appl Phys 1998;83:6864. [19] Mendelson MI. J Am Ceram Soc 1969;52:443. [20] Agilent Technologies. Theory on material measurement, operational manual E. Agilent Part No. E4991-90070, Dec. 2005. [21] Mallick KK, Shepherd P, Green RJ. J Eur Ceram Soc 2007;27:2045. [22] Wong J. J Appl Phys 1980;51:4453.
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[23] Kingery WD, Bowen HK, Uhlmann DR. Introduction to ceramics. 2nd ed. New York: John Wiley; 1976. p. 913–45. [24] Verma A, Dube DC. J Am Ceram Soc 2005;88:519. [25] Clarke DR. J Am Ceram Soc 1999;82:485. [26] Koops CG. Phys Rev 1951;83:12. [27] Miles PA, Westphal WB, Von Hippel A. Rev Mod Phys 1957;29:279. [28] Brooks KG, Rerta Y, Amarakoon VRW. J Am Ceram Soc 1992;75:3065. [29] Larsen PK, Metselaar R. Phys Rev B 1973;8:2016.
[30] Levinson LM, Philipp HR. J Appl Phys 1975;46:1332. [31] Snoek JL. Physica 1948;14:207. [32] Verwell J. In: Smith J, editor. Magnetic properties of materials. New York: McGraw-Hill; 1971. p. 64. [33] Johnson MT, Visser EG. IEEE Trans Mag 1990;26:1987. [34] Nakamura T, Tsutaoka T, Hatakeyama K. J Magn Magn Mater 1994;138:319. [35] Byun TY, Byeon SC, Hong KS, Kim CK. IEEE Trans Mag 1999;35:3445.
Acta Materialia 55 (2007) 6561–6572 www.elsevier.com/locate/actamat
Electrical and magnetic properties of magnesium ferrite ceramics doped with Bi2O3 L.B. Kong *, Z.W. Li, G.Q. Lin, Y.B. Gan
1
Temasek Laboratories, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 13 April 2007; received in revised form 6 August 2007; accepted 6 August 2007 Available online 25 September 2007
Abstract The effects of concentration of Bi2O3 and sintering temperature on DC resistivity, complex relative permittivity and permeability of MgFe1.98O4 ferrite ceramics were studied. The objective of the study was to develop magneto-dielectric materials, with almost equal values of permeability and permittivity, as well as low magnetic and dielectric loss tangent, for the design of antennas with reduced physical dimensions. It was found that the poor densification and slow grain growth rate of MgFe1.98O4 can be greatly improved by the addition of Bi2O3, because liquid phase sintering was facilitated by the formation of a liquid phase layer due to the low melting point of Bi2O3. It was found that 3% Bi2O3 can result in fully sintered MgFe1.98O4 ceramics. The DC resistivities of the MgFe1.98O4 ceramics were increased as a result of the addition of Bi2O3, except for 0.5%. The exceptionally low resistivities of the 0.5% samples were explained by a ‘cleaning’ effect of the small amount of liquid phase at the samples’ grain boundaries. The electrical and magnetic properties of the MgFe1.98O4 ceramics exhibited a strong dependence on the concentration of Bi2O3. The 0.5% samples were found to have the highest dielectric loss tangents, which can be understood similarly to the DC resistivity results. The 2–3% Bi2O3 is required to attain low dielectric loss MgFe1.98O4 ceramics for antenna application. Low concentration of Bi2O3 increased the static permeability of the MgFe1.98O4 ceramics owing to the improved densification and grain growth, while too high a concentration led to decreased permeability owing to the incorporation of the non-magnetic component (Bi2O3) and retarded grain growth. However, the addition of Bi2O3 alone is not able to produce magneto-dielectric materials based on MgFe1.98O4 ceramics, and further work is necessary to modify the permeability using cobalt (Co). Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Magnesium ferrite; Densification; Grain growth; DC resistivity; Complex relative permittivity
1. Introduction Conventional antennas for the frequency band of 3– 30 MHz (HF) and 30–300 MHz (VHF) are physically large, and therefore not suitable for portable applications. A pertinent challenge is to reduce the physical dimensions without affecting its electrical performances. The laws of physics indicate that it is potentially possible to use material loading
*
Corresponding author. Tel.: +65 65166910; fax: +65 68726840. E-mail address: [email protected] (L.B. Kong). 1 Present address: EADS Singapore Research and Technology Centre, 41 Science Park Read, Science Park II, Singapore 117610, Singapore.
to scale down the antenna’s physical dimension by a factor of n (refractive index of material), with its electrical dimension unchanged. A class of materials that serves this purpose is thep magneto-dielectric materials with high refractive index ffiffiffiffiffiffiffi (n ¼ l0 e0 , where l 0 is relative permeability and e 0 is relative 0 permittivity) and and e 0 (Z ¼ pffiffiffiffiffiffiffiffiffi ffi almost matching lpffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi [1,2], 0 0 0 0 0 0 l0 l =e0 e ¼ g0 l =e ¼ g0 ; where g0 ¼ l00 =e00 ¼ 1 is impedance of free space and l 0 = e 0 ). The latter condition is particularly important for matching the antenna impedance to free space environment. Moreover, the materials must have sufficiently low magnetic and dielectric loss tangent (6102) to minimize losses in the antennas. Ferrites are potential candidates of magneto-dielectric materials, as they have both magnetic and dielectric
1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.08.011
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properties. To achieve a low magnetic loss tangent, the materials obtained must have a resonant frequency far beyond the desired frequency band of interest for antenna designs. Three types of ferrites can be considered: spinel, garnet and hexaferrite. The resonant frequencies of composites based on spinel and garnet ferrites are from tens to hundreds of megahertz [3–5], while that of hexaferrites can be in the microwave band [6–8]. It is therefore expected to use spinel or garnet ferrite for low frequency applications, and hexaferrites for microwave requirements. In a previous work, the authors exploited composites with epoxy resin as matrix and ferrite powders as fillers, which showed that almost equal values of real permeability and permittivity (to be 6–7) can be obtained [9]. The magnetic loss tangent of the composites is much lower than 102, while it is difficult to reduce the dielectric loss, probably because of the relatively high loss tangent of the polymer matrix [10]. Therefore, it was decided to use ferrite ceramics. Magnesium ferrite (MgFe2O4) has a cubic spinel-type structure, with lattice constant a = 0.83998 nm and space group Fd 3m (ICDD No. 8-1943 and 17-464). It is well known as a soft magnetic n-type semiconductive material, with high resistivity and low magnetic and dielectric losses. Magnesium ferrite and its derivatives have been widely used in microwave technologies [11–13]. Recent studies showed that MgFe1.98O4 can be made to have almost equal values of permeability and permittivity under certain processing conditions [14,15]. The MgFe1.98O4 sample sintered at 1125 °C for 2 h showed l 0 e 0 = 6.7 over 3–30 MHz, together with relatively low magnetic and dielectric loss tangents (<102). Owing to its poor densification characteristic, the MgFe1.98O4 ceramics sintered at 1125 °C is only 70% of its theoretical density. This could be a problem for practical applications where sufficient mechanical properties are required, because porous materials usually have poor mechanical strength. Substitution of Mg with Cu significantly improved the densification and grain growth of MgFe1.98O4, owing to the formation of the low melting point of a eutectic Cu-rich phase. Combined with the modification with Co, a Cu–Co– Mg–Fe system was developed, which exhibited promising magneto-dielectric parameters [14,15]. Similarly, Bi2O3 is an alternative sintering aid for improving the sintering property of magnesium ferrite. However, unlike CuO, Bi2O3 does not reaction with MgFe1.98O4. This paper reports mainly on the effects of Bi2O3 concentration and sintering temperature on the DC resistivity, complex relative permittivity and permeability of MgFe1.98O4 ceramics. Although the effect of Bi2O3 on the sintering behavior of various ferrite materials has been extensively studied, systematic studies on its effect on electrical and magnetic properties are not available, especially for dielectric properties [16–18]. Specifically, it was found that 2–3% Bi2O3 is necessary to attain the low dielectric loss tangent required for antenna designs. This value is higher than those used in the literature, where it is widely accepted that the concentration of dopant should be <1%. It is necessary to note
that Bi2O3 alone is unable to produce desirable magnetodielectric materials based on MgFe1.98O4 ceramics. However, the fact that the real permeability is higher than the real permittivity for samples processed under certain conditions renders the possibility to adjust the permeability using cobalt (Co) in order to achieve matching permittivity and permeability. This work is being carried out in the authors’ laboratory, and the results will be reported elsewhere. 2. Experimental procedure All ferrite samples were synthesized via the conventional solid-state reaction process. Commercially available constituent oxides, Fe2O3 (99% purity, Aldrich, USA), MgO (99+% purity, Aldrich, USA) and Bi2O3 (99+% purity, Aldrich, USA), were used as starting materials. The nominal composition is MgFe1.98O4, with Bi2O3 concentration ranging from 0.5% to 10%. The weighted starting materials were thoroughly mixed using a high-energy ball mill. The milling operation was carried out using a Retsch PM400type planetary ball milling system, with 250 ml tungsten carbide vials. Every vial was filled with 100 tungsten carbide (WC) balls with a diameter of 10 mm as the milling medium. The milling speed was 200 rpm. The ball-to-powder weight ratio was about 40:1. The mixed powders were then compacted and sintered at temperatures ranging from 900 °C to 1150 °C for 2 h in air. Both heating and cooling rates were 5 °C min1. Two types of samples, namely disks (dia. 10 mm and thickness 1.5 mm) and coaxial cylinders (outer dia. 20 mm, inner dia. 10 mm and thickness 2.5 mm), were prepared. Disk samples were used for measurement of permittivity and DC resistivity, while cylinder samples were used for measurement of permeability. The phase compositions of the mixed, milled, calcined and sintered samples were analyzed by X-ray diffractometry (XRD) using a Philips PW 1729 type instrument with Cu Ka radiation. The microstructures and grain morphologies of the sintered samples were examined by field emission scanning electronic microscopy (FESEM) using a JEOL JSM-6340F-type instrument. Grain sizes were used to characterize the grain growth of the sintered samples, which were estimated from the SEM images by the equation G = kL = 1.5 L (where k = 1.5 is a geometry-dependent proportionality constant) [19]. An average grain size with a standard deviation (error) for each sample was obtained by counting a sufficiently large number of grains to ensure accuracy. The densities of the ferrite ceramics were derived from the masses and dimensions of the samples. The DC resistance of the sintered samples was measured using a Megger BMM80 Insulation Multimeter at room temperature, from which DC resistivities were calculated using the dimension of the disk samples. The complex permeability and permittivity of the ceramics were measured using an Agilent E4991A RF impedance/materials analyzer over 1 MHz–1 GHz, with the
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
16453A (permeability) and 16454A (permittivity) test fixture, respectively. Detailed analysis of the measurement techniques can be found in the operational manual from Agilent Technologies [20]. A brief description on the measurement of permittivity and permeability is given below. The application of a time-varying (or AC) electric field to a dielectric material causes some dielectric loss and a delay in the dielectric response to the electric field. Permittivity in an AC electric field is defined as complex relative permittivity e, given by e ¼ e0 je00
ð1Þ
where e 0 and e 0 0 are the real and imaginary permittivity, which represent the amount of energy stored in the dielectric materials from AC electric field and the energy loss to the AC field, respectively. The energy loss is usually characterized by the dielectric loss factor (De), which is expressed as the dielectric loss tangent, the ratio of the imaginary to the real permittivity (tan de ¼ e00 =e0 Þ. The capacitance method was used to measure relative permittivity with a E4991A analyzer. During measurement, disk samples (device under test or DUT) with silver electrode on both sides were placed in-between two circular plates to form a parallel plate capacitor, as shown in Fig. 1a [20,21]. The real and imaginary permittivity were calculated from the capacitance and the dissipation factor, respectively. As the capacitor (C) formed using 16453A has a small capacity because of the large impedance, the equivalent circuit of the capacitor is considered to comprise an equivalent parallel capacitance and an equivalent parallel conductance, as shown in Fig. 1b and c [20,21]. The admittance (Y) of circuit b and the complex admittance (Y*) of circuit c in Fig. 1 can be expressed as Y ¼ j-C ¼ j-jejC 0
ð2Þ
Cp G j C0 Y ¼ G þ j-C p ¼ j-C 0 C0
ð3Þ
where C0 is the capacitance when using air as a dielectric material (without DUT), and x is the angular frequency. Therefore, the complex relative permittivity can be calculated by
a
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Cp G j -C 0 C0 C tC p p ¼ e0 ¼ C 0 e0 A G t e00 ¼ ¼ -C 0 -e0 ARp
ð4Þ
e¼
ð5Þ ð6Þ
where G ¼ R1p (G and Rp are conductance and resistance, respectively), t and A are the thickness and cross-sectional area of the DUT. Errors of the 16453A test fixture include those due to edge capacitance on the edge electrodes (stray capacitance), residual parameters of the test fixture such as electrical length, residual impedance, stray admittance and air gaps caused when sandwiching the DUT between the electrodes. Edge capacitance was calculated internally by the E4991A equipment. Errors due to the residual parameters of the test fixture were effectively minimized by performing OPEN, SHORT and known LOAD calibrations on the DUT contact surface of the test fixture. Silver (paste) electrodes were used to minimize the errors due to air gaps. Similarly, the application of an AC magnetic field to a magnetic material will cause some magnetic loss and delayed induction of magnetic flux. In AC magnetic field, the complex relative permeability l is given by l ¼ l0 jl00 0
ð7Þ 00
where l and l are the real and imaginary permeability, respectively. The real part represents the amount of energy stored in the magnetic material from the AC magnetic field, while the imaginary part is the energy loss to the magnetic field. The loss factor (Dl) is expressed as a loss tangent, which is the ratio of the imaginary to the real permeability (tan dl ¼ l00 =l0 Þ. The E4991A uses the inductance method to measure relative permeability. In this method, a DUT (toroidal core) is wrapped with a wire, and the relative permeability is calculated from the inductance values at the end of the core. The ideal impedance of the test fixture without DUT is given by Zss, and the residual impedance Zres can be calculated from the measured impedance Zsm by Z res ¼ Z sm Z ss
ð8Þ
Errors due to the residual impedance were compensated by the calibration procedure, using the SHORT condition,
c
b A = area t = thickness
C
C
G
Fig. 1. DUT (device under test) of the parallel plate test fixture measurement method (a) and equivalent circuit model of the parallel plate capacitor (b) and (c).
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without the DUT in the test fixture. The impedance after error correction Zcomp is calculated from the measured impedance Zm, with the DUT positioned in the test fixture, as shown in Figs. 2 and 3 [19,20]. The corrected impedance is given by Z comp ¼ Z m Z res
ð9Þ
Assuming that Zss consists only of inductance elements: l c ð10Þ Z ss ¼ j- 0 h ln a 2p The complex relative permeability of the DUT can be determined by l¼
2pðZ m Z sm Þ þ1 j-l0 h ln bc
ð11Þ
where l0 is the relative permeability of air, h, b and c are the thickness, internal and outer diameters of the DUT. 3. Experimental results
XRD measurement, which is probably because of either the insufficient sensibility of the XRD equipment used or the poor crystallinity of second phases, if present. It was found that pure MgFe1.98O4 cannot be fully sintered at <1150 °C. A relative density of 95% can be achieved after sintering at 1150 °C for the samples with 0.5% and 1% Bi2O3, while the relative density of the sample with 2% Bi2O3 is already 96.1% after sintering at 1000 °C for 2 h. A high concentration of Bi2O3 (P3%) resulted in almost full densification, especially at a sintering temperature of P950 °C. The microstructures of pure MgFe1.98O4 samples sintered at temperatures 61100 °C are very porous. The grain growth is very slow with sintering temperature, and all samples experienced only inter-grain fractures. In summary, the addition of Bi2O3 significantly enhanced the densification behavior and grain growth rate, which are attributed to the formation of a liquid phase during the sintering process at high temperatures [16,22]. 3.2. DC resistivity and complex relative permittivity
3.1. Densification and grain growth XRD results (not shown) demonstrated that the addition of Bi2O3 has no significant effect on the phase formation of MgFe1.98O4 under the conditions used in the present study. Bi2O3 phases were also not observed in the
SHORT state
DUT
Zss
Zcomp
Zsm
Zm
Zres
Zres
16454A Fig. 2. Schematic diagram of the 16454A test fixture with and without a DUT.
e
The room temperature DC resistivities of the MgFe1.98O4 ceramics, sintered at different temperature, as a function of the concentration of Bi2O3 are shown in Fig. 4. For doped samples, the DC resistivity increases nearly exponentially as the Bi2O3 concentration increases from 0.5% to 3% and shows no significant change above 3%. Careful inspection reveals that the DC resistivities of the 0.5% samples are slightly lower than those of the pure ones at every sintering temperature. For pure and the lowconcentration-Bi2O3 doped samples, the DC resistivity increases below 1100 °C. A relatively sharp drop in resistivity is observed for the samples after sintering at 1150 °C, especially for those with a low concentration of Bi2O3. For those with a high concentration of Bi2O3, at a given concentration, the general trend is that the DC resistivity increases with increasing temperature initially (from 900 °C to 950 °C) and decreases above 950 °C. Figs. 5–8 show the complex relative permittivity curves of pure MgFe1.98O4 ceramics and the three groups with
DUT
ρr (Ω cm)
h0
h
10
9
10
8
10
7 o
10
6
10
5
900 C o 1000 C o 1100 C
o
950 C o 1050 C o 1150 C
b c
0
2
4
6
8
10
Concentration of Bi2O3 (%) 2a Fig. 3. Cross-sectional diagram of the 16454A test fixture with a DUT.
Fig. 4. DC resistivity of the samples sintered at different temperature as a function of the concentration of Bi2O3. The solid line is a visual guide.
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572 15
o
(b)1050 C 10
ε' ε''
5
Permittivity
10
5
0
0 6
10 15
10
7
8
10
10
9
o
6
10 15
7
10
10
10
5
5
0
0 6
10
7
8
10
8
10
10
9
6
10
Frequency (Hz)
7
10
10
8
10
o
Permittivity
ε' ε''
7
10
9
10 o
(c) 1100 C
30
Permittivity
8
10
o
0 6 10
10
7
20
10
10
0
8
10
9
o
(d) 1150 C
30
20
10
0 6
10
7
10
8
9
10
10
10
6
Frequency (Hz)
10
7
10
8
10
9
Frequency (Hz)
Fig. 6. Complex relative permittivity of the MgFe1.98O4 samples with 0.5% Bi2O3.
o
(a) 1000 C
Permittivity
30
Permittivity
8
9
10
10 o
(c) 1100 C
30
6
7
10
10
10
0
8
9
10
10 o
(d) 1150 C
30 20
7
10
7
5
5
0
10
8
10
9
o
(d) 1150 C
0 6
7
10
8
10
9
10
10
6
10
7
10
8
10
9
Frequency (Hz)
Fig. 8. Complex relative permittivity of the MgFe1.98O4 samples with 2% Bi2O3.
low concentration of Bi2O3 (62%), respectively. These curves can be classified into two types. One is represented by those shown in Fig. 8a–c, where both real and imaginary parts are almost independent of frequency. This class of samples is lossless or of very low loss tangent. All others belong to high-loss samples, which are characterized by frequency-dependent real and imaginary permittivity, especially at low frequency (<100 MHz). The real permittivity and the loss tangent (tgd ¼ e00 =e0 Þ, where e 0 0 and e 0 are real and imaginary permittivity) collected at 1 MHz are illustrated in Figs. 9 and 10, respectively. Fig. 11 shows the real permittivity (at 100 MHz) of all samples as a function of sintering temperature. Pure MgFe1.98O4 samples have a similar dielectric characteristic until 1100 °C, with real permittivity slightly increasing with sintering temperature. A relatively sharp increase in real and imaginary permittivity is observed in the 1150 °C-sintered sample. The addition of 0.5% Bi2O3 obviously worsened the dielectric properties of the MgFe1.98O4 ceramics. Besides the increase in loss tangent,
8
10
Frequency (Hz)
9
10
0% 1%
0.5% 2%
20 15 10
0 6
10
15 10
25
10
20
10
6
o
0 7
o
10 20
30
0 10
10
10
10
6
10
(c) 1100 C
20
10
10
9
(b) 1050 C
30
ε' ε''
20
8
Frequency (Hz)
10
0 6 10
10
10
20
10
5 0
7
15
9
(b) 1050 C
30
10
0
Frequency (Hz)
(a) 1000 C
20
5
o
(b) 1050 C
15
ε' ε''
10 20
Fig. 5. Complex relative permittivity of pure MgFe1.98O4 samples sintered at different temperatures.
30
10
6
o
20
o
(a) 1000 C
15
9
(d) 1150 C
(c) 1100 C
10
10
Permittivity
Permittivity
20
o
(a) 1000 C
Permittivity ε1MHz '
Permittivity
15
6565
6
10
7
10
8
10
9
10
Frequency (Hz)
Fig. 7. Complex relative permittivity of the MgFe1.98O4 samples with 1% Bi2O3.
5
900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 9. Real permittivity (at 1 MHz) of the samples with low concentration of Bi2O (62%).
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MgFe1.98O4 ceramics. A sufficiently low dielectric loss tangent is one of the critical requirements for antenna applications.
1
0% 1%
0.5% 2%
0.1
900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 10. Dielectric loss tangent (at 1 MHz) of the samples with low concentration of Bi2O3 (62%).
Permittivity ε '
100MHz
15 0%
0.5%
1%
2%
12
9 3%
5%
7%
10%
6 900
950
1000
1050
1100
1150
o
Sintering temperature ( C) Fig. 11. Real permittivity (at 100 MHz) of the samples as a function of sintering temperature.
both real and imaginary permittivities exhibit a significant increment as a result of the presence of 0.5% Bi2O3. The samples with 1% Bi2O3 possess similar dielectric properties to the pure ones, as the sintering temperature is 61100 °C. The detrimental effect of Bi2O3 on the dielectric loss is still observable for the 1150 °C-sintered sample. At a given concentration, the dielectric loss tangent decreases slightly with increasing sintering temperature, especially in the range 950–1050 °C. The dielectric properties are greatly improved by the addition of 2% Bi2O3. As shown in Fig. 8, both the real and imaginary permittivities stay almost flat over the frequency range studied, as long as the sintering temperature is not >1100 °C. The dielectric property of the 1150 °C-sintered sample is almost the same as that of the pure one sintered at the same temperature. The 3% group has a similar dielectric property to the 2% one, but the former has a lower dielectric loss tangent (results not shown) and is also less sensitive to the 1150 °C sintering. Too high a concentration of Bi2O3 has a negative effect on the dielectric properties. It is therefore concluded that 2–3% Bi2O3 content is appropriate to attain low dielectric loss tangent for
Representative complex relative permeability curves of the ferrite ceramics are shown in Fig. 12. The complex permeability spectra of the ceramics exhibit a common feature. The real permeability l 0 remains almost constant up to a certain frequency, beyond which l 0 begins to decrease. The imaginary permeability l 0 0 remains very low for frequencies below several tens of megahertz, and increases above a certain frequency. A peak in l 0 0 corresponding to the dispersion of l 0 can be identified. The peak shifts to lower frequency as the real permeability increases. To characterize the magnetic properties of ferrite materials, a static permeability l0 is usually used, which can be defined as the real permeability far below the resonance frequency fr, corresponding to the maximum imaginary permeability in the l00 –f curve. Here, the real permeability at 1 MHz is used as the static permeability. Magnetic loss tangent is defined as tan dl = l 0 0 /l 0 . The static permeabilities of the samples with and without Bi2O3, as a function of sintering temperature, are plotted in Fig. 13. The static permeability of the pure sample and the samples with high concentrations of Bi2O3 (P3%) increases monotonically with increasing sintering temperature, while the value of the other samples exhibits a sharp rise at different temperatures, depending on the Bi2O3 content. It is obviously demonstrated that the addition of Bi2O3 greatly improved the magnetic properties of the MgFe1.98O4 ceramics. For example, the static permeability of the 3% samples is nearly three times that of the pure ones, at every sintering temperature. At a given sintering temperature, the static permeability maximizes at a certain concentration of Bi2O3. For instance, the maximum static permeability values of the samples sintered at 1050 °C and 1100 °C are at 2% and 1%, respectively.
20 o
(b)
1100 C (a) 0% (b) 1% (c) 3%
15
Permeability
tgδ1MHz
3.3. Complex relative permeability
(c) μ' μ''
10
(c)
(a)
5
(b) (a)
0
10
6
10
7
10
8
10
9
Frequency (Hz) Fig. 12. Representative complex relative permeability curves.
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
20 0% 1%
0.5% 2%
Permeability μ0
15
10
5 3% 7%
0 900
950
1000
1050
5% 10%
1100
1150
o
Sintering temperature ( C) Fig. 13. Static permeability of the samples as a function of sintering temperature.
4. Discussion 4.1. DC resistivity DC resistivity is one of the most important parameters of ferrite ceramics. Generally, high resistivity is required by most applications. Fully dense polycrystalline ferrite ceramics are considered to consist of highly conductive grains and less-conductive grain boundaries, forming a three-dimensional series–parallel network structure. For pure ferrites, the grain boundary has the same composition as or similar composition to that of the grains. The only difference is that grain boundaries are usually in an amorphous state with various defects and imperfections, compared with grains. Besides, impurities are usually considered to locate at grain boundaries. The presence of impurities is inevitable. Impurities such as Ca and Si are either coming along with the raw materials or introduced during the multi-step sample preparations. In this case, DC resistivities of ferrite ceramics are determined mainly by the fraction of the grain boundaries (grain size). It is necessary to mention that this explanation is only applicable to the samples with full densification. Therefore, the decrease in the DC resistivity for the samples with high concentrations of Bi2O3 (P3%) is due to the increase in grain size (decrease in fraction of grain boundaries) as a result of an increase in sintering temperature (950– 1100 °C). Other factors, including composition stoichiometry, density (porosity), crystal structure perfection and microstructural homogeneity, also have effects on the DC resistivities of ferrite ceramics [23]. Among these, the effect of porosity is particularly important. The presence of porosity increases the DC resistivity of ferrite ceramics because air/ vacuum is a good insulator if the pores are closely trapped and uniformly distributed. Otherwise, porosity is prone to reduce the resistivity of ferrite ceramics, because open pores could provide a possible conduction path for electricity owing to impurities entrapped inside. Pure MgFe1.98O4
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and the samples with low concentration of Bi2O3 (62%) have relatively low densities, especially for those sintered at low temperatures. It is found that these samples have poor mechanical strength and absorbed the solvent of the silver paste used as electrodes; hence, the porosity of these samples is considered to be caused by open pores. For these samples, the increase in the DC resistivity caused by the improved densification is more significant than the decrease due to the increased grain size, so that the DC resistivities increase overall with increasing sintering temperature (61100 °C). Another important factor that is always detrimental to attaining high DC resistivities for ferrite ceramics is the formation of Fe2+ ions. With the presence of Fe2+ ions, electron hopping occurs between Fe2+ and Fe3+. Because the electrons transfer from Fe2+ ion to Fe3+ ion within the octahedral sites, there is no change in the energy state of the crystal as a result of the transition. It has been reported that the presence of 0.3% Fe2+ content in a ferrite ceramic can reduce the DC resistivity by a factor of more than two orders of magnitude [24]. In addition, the presence of Bi2O3 has been reported to be able to promote the formation of Fe2+ ions. At high temperature, Bi3+ ions can be oxidized to Bi5+ ions. The Bi5+ ion has a radius of 0.076 nm for octahedral coordination, which is comparable with the dimension of the octahedral interstition in ferrite (0.071 nm) [16]. The substitution of Fe3+ ions at the B site with Bi5+ ions will produce Fe2+ ions, owing to the requirement of electrical neutralization. However, it appears that the relatively sharp drop in the DC resistivity of all samples after sintering at 1150 °C cannot be ascribed to the formation of Fe2+ ions, because the authors’ previous study on MgFe1.98O4 showed that the effect of Fe2+ usually occurs at a temperature of P1200 °C. It is also hard to attribute this observation to the production of Fe2+ due to the presence of Bi5+. On the one hand, Bi5+ ions are only stable at high temperatures. For example, the temperature used in Ref. [16] was 1340 °C, which is higher than that (1150 °C) in the present study by nearly 200 °C. On the other hand, if Bi5+ ions were indeed present and promoted the formation of Fe2+ ions, the effect should be proportional to the concentration of Bi2O3. The DC resistivities, as well as the dielectric properties (discussed later), of our samples showed that such a proportional relationship is not observed. Therefore, we exclude the role of Fe2+ ions in determining the variation in the DC resistivity and the dielectric properties for the samples sintered at 1150 °C, or at least the effect of Fe2+ ions is not the main factor. It is more likely to be related to the property of the liquid phase, as will be discussed later. With the presence of Bi2O3, the properties of the grain boundaries of the ferrite ceramics were changed. The three-dimensional network grain boundary structure became rich in Bi, which is similar to those observed in ZnO–Bi2O3-based ceramic varistors [22,25]. Experiment has shown that a bismuth-rich phase with an interconnected and continuous network structure is left as the
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ZnO grains are removed preferentially from a fully sintered ZnO–Bi2O3 ceramic via etching with acid [25]. Such a three-dimensional network structure is found to be helpful in facilitating oxygen transport in ZnO–Bi2O3-based ceramic materials. For ferrite ceramics, it could be an additional benefit in terms of improving the samples’ electrical properties, because good oxygen transport helps suppress the formation of Fe2+ ions, which in turn is desirable to ensure a high resistivity in the samples. Koops [26] proposed a simple model to represent the network structure of polycrystalline ferrite material: wellconducting grains (with thickness of d2 and resistivity of qr,2) separated by layers of lower conductivity (with thickness of d1 and resistivity of qr,1). With the assumption of x = d1/d2 1 and qr,1 qr,2, the author derived a formula of measured resistivity [27]: qr ¼
d1 q þ qr;2 ¼ xqr;1 þ qr;2 d 2 r;1
ð12Þ
The grain resistivity (qr,2) can be assumed to be constant, because there is no observable reaction between Bi2O3 and MgFe1.98O4. As a result, the measured DC resistivities are determined by x and qr,1. It has been discussed above that the grain size of the samples has only a slight decrease with increasing concentration of Bi2O3 (from 0.5% to 3%). With increasing concentration of Bi2O3, both x and qr,1 are expected to increase, so that the DC resistivity increased with increasing concentration of Bi2O3 ranging from 0.5% to 3%. Further increase in Bi2O3 led to a saturation of resistivity. This explanation is obviously not applicable to the 0.5% samples. To understand the exceptionally low resistivity for the 0.5% samples as compared with the pure ones, it is necessary to re-examine what was happening throughout the material fabrication process. Fabrication of the Bi2O3doped samples is a multi-step process. First, a liquid phase was formed during heating of the pellets above the melting point of Bi2O3 [16–18]. The liquid layer surrounded and wetted grains by filling the grain boundaries. Secondly, densification and grain growth occurred with the presence of the liquid phase during heating and dwelling at high temperature. Finally, during the cooling process, the Bi2O3-rich liquid phase retracted from the two-grain boundaries to triple- and multiple-grain junctions. The degree of retraction is dependent on the amount of the liquid phase. It has been reported that the Bi2O3-rich liquid phase preferentially dissolved Ca and Si impurities that are usually present at the grain interfaces (two-grain boundaries) [16,28]. One can expect that there must be a critical amount for liquid phase, below which all the liquid phase will be brought to the triple- and/or multiple-grain junctions. In this case, the retraction of the liquid phase will result in ‘cleaner’ two-grain boundaries due to the elimination of the impurities. Such ‘clean’ grain boundaries were observed for Mn–Zn ferrites by Drofenik et al. [16] using transmission electron microscopy (TEM). Samples with ‘cleaner’
grain boundaries are expected to have lower resistivities, because both x and qr,1 in the above formula become smaller. This could be the main reason why the DC resistivities of the 0.5% samples are lower than those of the pure ones. Meanwhile, the sharp drop in the DC resistivity of the samples sintered at 1150 °C, especially for those with low concentration of Bi2O3, can be understood similarly. In summary, the addition of Bi2O3 has two opposite effects on the DC resistivity of the MgFe1.98O4 ferrite ceramics. At a relatively low concentration, the presence of Bi2O3 leads to ‘clean’ grain boundaries and thus a reduced DC resistivity. High concentration helps facilitate the formation of a three-dimensional network grain boundary structure and attain high resistivity. 4.2. Dielectric property High frequency permittivity of ferrite crystals is contributed mainly by the atomic and electronic polarization. The permittivity of polycrystalline ferrite ceramics is additionally affected by microstructure, grain size, density and impurities of the samples. Similar to DC conductivity, porosity (density) also has a double-side effect on permittivity. Close pores (inside grains or at grain boundaries) will reduce permeability because of the unit permittivity of air (pores). Open (interconnected) pores, in the case of absorbing impurities (e.g., water) may increase permittivity, because of the high dielectric constant of water and conductive polarization. The presence of Fe2+ in ferrite materials always contributes to high permittivity because Fe2+ has a larger polarization than Fe3+. Fe3+ ion has a stable d-shell configuration with spherical symmetry of the charge cloud, due to its five d-electrons distributed according to Hund’s rule, whereas Fe2+ ion has an extra electron as compared with Fe3+, which disturbs the symmetry of the charge electron cloud [16]. As a result, the presence of Fe2+ increases the polarization in ferrites, and thus ferrites containing a larger number of Fe2+ ions are likely to exhibit a higher permittivity. However, the high permittivity in this case is undesired because it is always accompanied by an extremely high dielectric loss tangent. Fortunately, it is not the case in the present study, as discussed above. The dielectric loss tangent of polycrystalline ferrite ceramics results from the lag in polarization vs the alternating electric field, which has several contributory factors, such as (i) electron polarization losses, (ii) ion vibration and deformation losses, and (iii) ionic migration losses (including DC conduction loss and ionic jump and dipole relaxation losses). The electron polarization losses are responsible for absorption and color in the visible spectrum. The ion vibration and deformation losses are of importance only in the infrared and not a major concern for frequencies below 10 GHz. Therefore, the main contribution to dielectric losses of ferrite ceramics would be the ion migration losses, where conduction losses are more significant than other losses [23]. Without the presence of
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Fe2+ ions, the conduction loss is caused mainly by the poor microstructure. Polarization due to conduction loss has a dispersion at 103–104 Hz, but it can extend to a high frequency of less than 100 MHz [23]. Therefore, the frequency-dependent real and imaginary permittivity of the high-loss samples as shown in Figs. 8–11 are caused by the conduction loss due to their porous microstructure. Comparatively, the permittivity contributed by the atomic and electronic polarization is independent of frequency in the frequency range of 1 MHz–1 GHz. With a similar model mentioned above [26], Larsen and Metselaar [29] derived a formula to estimate the static value (es) of the apparent relative permittivity (er) of polycrystalline yttrium iron garnet YIG) ceramics: d1 þ d2 es ¼ ð13Þ ei d1 where ei is the relative permittivity at infinite frequency. Here, one can take the permittivities at 1 MHz and 100 MHz as es and ei, respectively. Obviously, this equation is valid only for the samples with high dielectric loss tangents (low concentration of Bi2O3) and invalid for the lossless ones (high concentration of Bi2O3). Using this equation, the extraordinarily high value of e01 MHz for the 0.5% samples can be readily explained. As discussed above, the ‘cleaning’ effect of the liquid phase layer could lead to a very small ‘effective’ d1 for the 0.5% samples, thus resulting in an unexpectedly high permittivity (Fig. 6). Also, this group of samples has the highest dielectric loss tangent at low frequencies (Fig. 10). The dependence of the permittivity (e0100 MHz ) on sintering temperature (Fig. 11) can be explained by the Maxwell– Wagner effect [23,24], with a permittivity increasing with grain size, because the grain size increases with increasing temperature. The exception for the 0.5% sample sintered at 1150 °C could be related to its high permittivity at low frequency. At a given sintering temperature, the e0100 MHz increases with increasing concentration of Bi2O3, which is probably because the permittivity of Bi2O3 is higher than that of MgFe1.98O4. The difference (De ¼ es ei ¼ e01 MHz e0100 MHz Þ can be used as a measure to represent the contribution of conductive polarization to the permittivity. Because the conduction is due to the porous microstructure, increasing sintering temperature is supposed to improve the microstructure and the e01 MHz (es) is expected to decrease due to the reduction in De. However, Fig. 9 indicates an overall increasing trend in permittivity, which means the decrease in e01 MHz (es) is overcompensated by the increase in e0100 MHz (ei). Again, the relatively sharp change in the permittivity for the samples sintered at 1150 °C is most likely related to the property of the liquid phase, because it is not obviously observed for the pure sample, and the samples become more and more resistive to the high temperature sintering with increasing concentration of Bi2O3. Therefore, it is
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more likely that the sharp decrease in DC resistivity of the doped samples is due to the fact that the ‘cleaning’ effect of the liquid phase was enhanced dramatically at 1150 °C. With increasing concentration of Bi2O3, the amount of liquid phase is increased, and the ‘cleaning’ effect becomes less pronounced because the grain junctions cannot contain all the liquid phase. Additionally, one may notice that the resistivity measurement is less sensitive than the permittivity measurement. This is mainly because, when measuring the DC resistance of the ferrite samples, a ‘steady-state current’ cannot be achieved in a short time owing to the polarization currents arising from trapping states of various types and densities, which is similar to that observed in ZnO– Bi2O3 varistor ceramics [22,25,30]. In contrast, the response of these trapping states to AC field is very prompt. 4.3. Magnetic property Generally, the product of resonance frequency (fr) and static permeability (l0 1) for spinel ferrites can be expressed as a constant by the Snoek-like law: ðl0 1Þfr ¼ C
ð14Þ
For natural resonance, C ¼ 23 cM s (where c is the gyromagnetic ratio and Ms is the saturation magnetization) [31]. For wall resonance, C ¼ C 1 M 2s (where C1 is a constant related to the domain size and the thickness of domain wall) [32]. Therefore, a high static permeability leads to a low resonance frequency, as demonstrated in (Fig. 12). Porosity has been shown to have a strong influence on the permeability of ferrite materials. Owing to the presence of porosity, magnetic poles are created on the surface of ferrite grains (or particles) under an applied magnetic field. A demagnetizing field is thus produced, leading to a decrease in permeability. The magnitude of the demagnetizing field is closely related to the grain size and grain boundary characteristics. According to the magnetic circuit model [33], static permeability l0 is given by: l0 ¼
li ð1 þ Dd Þ 1 þ li Dd
ð15Þ
where li is the intrinsic static permeability of materials without any defects, and D and d are the average grain size and thickness of the grain boundaries. With this model, the variation in l0 as a function of density can be quantitatively understood. In general, with increasing sintering temperature, the increase in grain size (D) and density (qd) leads to a decrease in the d/D ratio, and thus increasing static permeability. As it is difficult to measure d and D directly, the ratio d/D is usually calculated approximately from the measured density (qd) based on the following formula [34]: 1=3 qd;i d ¼ 1 ð16Þ D qd
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where qd,i is the theoretical density of the materials. Since the samples with high concentration of Bi2O3 (P3%) are almost fully sintered in the temperature range 900– 1150 °C, Eq. (16) is thus only able to calculate the ratio (d/D) for pure and the low concentration samples (0.5%, 1% and 2%). Owing to its non-magnetic characteristic, Bi2O3 is not specifically considered in this calculation, but its overall role has been taken into account when estimating the theoretical density of the corresponding samples. It is found that the data of the four samples cannot be fitted well using Eq. (15). The dotted curve, as shown in Fig. 14, was obtained with Eq. (15) using a li of 35 as the intrinsic static permeability (nearly double the maximum static permeability of the samples). The data of the four samples are also included in Fig. 14 for comparison. It is noticed that the static permeabilities of the samples with relatively low densities are all far below the calculated values. Only some points are close to the dotted line. They are the 0.5% sample sintered at 1150 °C, 1% samples sintered at 1050– 1150 °C and 2% samples sintered at 1000–1150 °C. SEM images showed that these samples not only have denser microstructure but also possess larger grains. The magnetization of polycrystalline ferrite ceramics is determined by both spin rotation and domain wall motions. The contribution due to domain wall motion is proportional to grain size. A critical size was observed for ferrite materials, below which domain walls do not exist. The critical size can be in a range 0.1–1 lm, depending on materials. Therefore, it is believed that the relatively low static permeabilities for the samples shown in Fig. 14, as compared with the estimated values, are most likely due to the relatively lessdeveloped domain walls of the samples. Although the 2% sample sintered at 950 °C has observable large grains, its microstructure is still dominated by the fine-grain matrix, thus leading to a static permeability lower than expected. This means that the magnetic circuit model cannot be used to explain fully the present experimental results, mainly because the ratio (d/D) was calculated from the measured density and did not take the effect of critical grain size into account. 20 0% 0.5% 1% 2%
16
μ0
12 8 4 0
0.03
0.06
0.09 δ/D
0.12
0.15
Fig. 14. Static permeability vs d/D for the samples with low concentration of Bi2O3 (62%). The dotted line is calculated using Eq. (15) with li = 30.
For the samples with high concentration of Bi2O3 (P3%), the variation in static permeability with sintering temperature is seemingly only explainable in terms of grain size, because these samples are fully sintered. The increase in the static permeability can be attributed to the increased contribution of domain wall as a result of increase in grain size with sintering temperature. The effects of Bi2O3 on the permeability of various ferrite materials have been reported in the literature. For example, Drofenik et al. [16] studied the effect of Bi2O3 on grain size, microstructure and permeability of Mn0.52Zn0.44Fe2.04O4, one of the high permeability materials. A maximum permeability was obtained in the sample with 0.03% Bi2O3. Further increase in Bi2O3 content led to a gradual decrease in permeability up to a Bi2O3 concentration of 7%. The authors attributed the maximum permeability to the elimination of grain boundary impurity, since samples with ‘clean’ grain boundaries have relatively lower coercivity, thus leading to a decrease in permeability. However, it is necessary to mention that their samples were sintered at a temperature as high as 1340 °C. At such a high sintering temperature, volatilization of Bi2O3 must be taken into account, especially for those samples with a high concentration of Bi2O3, because Bi2O3 usually becomes volatile at P1200 °C [17]. For instance, the relative densities of the samples with 1%, 3% and 7% Bi2O3 were 95%, 90% and 87% [16]. The increase in the amount of the non-magnetic phase and the decrease in density led to a decrease in magnetization and, therefore, to a decrease in the static permeability. A similar result was reported by Kumar et al. [18], who used Bi2O3 (up to 6%) to improve the properties of Ni0.8Zn0.2Fe2O4 ceramics prepared by a soft chemical approach. A maximum permeability (at 5 MHz) of 75 was observed for the 1% sample, as compared with 37 for the pure sample and 48 for the one doped with 6% Bi2O3. The authors attributed the decrease in permeability with increasing concentration of Bi2O3 to the possible incorporation of excess non-magnetic phase at grain boundaries, because the samples had almost the same grain size and density. Obviously, the reduction in permeability is much less than the percentage of the second phase, but no explanation was given in that case. Another example was Ni–Cu–Zn ferrite doped with 61 wt.% Bi2O3 [18]. The samples with highest permeability were found to have Bi2O3 between 0.375% and 0.5%. The authors linked the maximum permeability to the appearance of larger grain size in their samples. These scattered and somehow contradictory results indicate that the effects of Bi2O3 on the magnetic properties of ferrite ceramics are dependent not only on the concentration of Bi2O3, but also on the intrinsic properties and processing conditions of the materials studied. To evaluate the effect of Bi2O3 concentration, the static permeability of the samples sintered at 1150 °C as a function of Bi2O3 concentration is illustrated in Fig. 15. An essentially linear relationship between the static permeability
L.B. Kong et al. / Acta Materialia 55 (2007) 6561–6572
Static permeability
18
Experiment Fitting
17 16 15 14 0
2
4
6
8
10
Concentration of Bi 2O3 (%) Fig. 15. Static permeability vs concentration of Bi2O3 for the samples sintered at 1150 °C.
and Bi2O3 concentration is observed. If using the extrapolated permeability at zero to scale the concentration of the non-magnetic phase, the values obtained are higher than the nominal concentration of Bi2O3, which means that the effect of grain size should also be considered when explaining the magnetic properties of the samples with the concentration of Bi2O3. It is necessary to mention that matching real permeability and permittivity have not been achieved in the MgFe1.98O4 + Bi2O3 system developed in the present study. However, noting that the real permeability is slightly higher than the real permittivity, it is possible to develop magneto-dielectric materials with almost equal permeability and permittivity at low frequency range (3–30 MHz) by adjusting the permeability through the incorporation of cobalt (Co) [35]. This work is been carrying out in the authors’ laboratory and will be reported separately in the future. 5. Conclusions Bi2O3 has been shown to be a good sintering aid for improving the densification behavior and enhancing the grain growth of MgFe1.98O4 ceramics. The beneficial effect of Bi2O3 is attributed to the formation of a liquid phase layer due to the low melting point of Bi2O3. The presence a liquid phase layer facilitated liquid phase sintering instead of the solid reaction sintering of pure MgFe1.98O4. The temperature for full densification decreases with increasing concentration of Bi2O3 at low concentrations. The average grain size has a maximum at a certain concentration, depending on sintering temperature. Too high a concentration of Bi2O3 prevents further grain growth owing to the thickened liquid phase layer. The addition of Bi2O3 has a significant effect on the DC resistivity and dielectric properties of the MgFe1.98O4 ceramics. The samples with 0.5% Bi2O3 have a slightly lower resistivity than pure ones, which can be attributed to the ‘cleaning’ effect of the liquid phase. An increase in
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Bi2O3 concentration leads to an exponential increase in DC resistivity from 0.5% to 3%, due to the formation of a three-dimensional grain boundary network structure with high resistivity. The dependence of the DC resistivity on sintering temperature can be explained in terms of grain growth and microstructural development. The dielectric properties can be understood similarly to the DC resistivities. It is found that 2–3% Bi2O3 is required to attain a low dielectric loss tangent necessary for practical antenna applications. The magnetic properties of the samples with low concentration of Bi2O3 (62%) cannot be simply explained by the magnetic circuit model, because the model does not take into account the effect of critical grain size on the static permeability. At high concentrations, the static permeability decreases with increasing concentrations, which can be ascribed to the increased amount of the non-magnetic phase of Bi2O3, together with the reduced grain size. Further works are needed to achieve magneto-dielectric materials based on the MgFe1.98O4 + Bi2O3 system. Since the real permeability is higher than the real permittivity, it is possible to modify the magnetic properties further by introducing a small amount of cobalt (Co). The incorporation of a small amount of Co can alter the magnetocrystalline anisotropy of most ferrites from negative to positive, owing to the large positive magnetocrystalline anisotropic constant of Co ions. References [1] Mosallaei H, Sarabandi K. IEEE Trans Antennas Propagat 2004;52:1558. [2] Buell K, Mosallaei H, Sarabandi K. IEEE Trans Microwave Theory Tech 2006;54:135. [3] Yusoff AN, Abdullah MH, Ahmand SH, Jusoh SF, Mansor AA, Hamid SAA. J Appl Phys 2002;92:876. [4] Nakamura T. J Appl Phys 2000;88:348. [5] Tsutaoka T. J Appl Phys 2003;93:2789. [6] Pullar RC, Appleton SG, Bhattacharya AK. J Magn Magn Mater 1998;186:326. [7] Singh P, Babbar VK, Razdan A, Srivastava SL, Puri RK. Mater Sci Eng B 1999;67:132. [8] Li ZW, Chen LF, Ong CK. J Appl Phys 2002;92:3902. [9] Kong LB, Li ZW, Chen LF, Lin GQ, Gan YB, Ong CK. In: 3rd international conference on materials for advanced technologies (ICMAT), Singapore, 3–8 July; 2005. [10] Kong LB, Li ZW, Lin GQ, Gan YB. IEEE Trans Mag 2007;43:6. [11] Van Uitert LG. J Appl Phys 1955;26:1289. [12] Van Uitert LG, Schafer JP, Hogan CL. J Appl Phys 1954;25:925. [13] Van Uitert LG. J Appl Phys 1957;28:320. [14] Kong LB, Li ZW, Lin GQ, Gan YB, J Am Ceram Soc, in press. [15] Kong LB, Li ZW, Lin GQ, Gan YB. J Am Ceram Soc 2007;90:2104. [16] Drofenik M, Znidarsic A, Makovec D. J Am Ceram Soc 1998;81:2841. [17] Murbe J, Topfer H. J Electroceram 2006;16:199. [18] Kumar PSA, Sainkar SR, Shrotri JJ, Kulkami SD, Deshpande CE, Date SK. J Appl Phys 1998;83:6864. [19] Mendelson MI. J Am Ceram Soc 1969;52:443. [20] Agilent Technologies. Theory on material measurement, operational manual E. Agilent Part No. E4991-90070, Dec. 2005. [21] Mallick KK, Shepherd P, Green RJ. J Eur Ceram Soc 2007;27:2045. [22] Wong J. J Appl Phys 1980;51:4453.
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[23] Kingery WD, Bowen HK, Uhlmann DR. Introduction to ceramics. 2nd ed. New York: John Wiley; 1976. p. 913–45. [24] Verma A, Dube DC. J Am Ceram Soc 2005;88:519. [25] Clarke DR. J Am Ceram Soc 1999;82:485. [26] Koops CG. Phys Rev 1951;83:12. [27] Miles PA, Westphal WB, Von Hippel A. Rev Mod Phys 1957;29:279. [28] Brooks KG, Rerta Y, Amarakoon VRW. J Am Ceram Soc 1992;75:3065. [29] Larsen PK, Metselaar R. Phys Rev B 1973;8:2016.
[30] Levinson LM, Philipp HR. J Appl Phys 1975;46:1332. [31] Snoek JL. Physica 1948;14:207. [32] Verwell J. In: Smith J, editor. Magnetic properties of materials. New York: McGraw-Hill; 1971. p. 64. [33] Johnson MT, Visser EG. IEEE Trans Mag 1990;26:1987. [34] Nakamura T, Tsutaoka T, Hatakeyama K. J Magn Magn Mater 1994;138:319. [35] Byun TY, Byeon SC, Hong KS, Kim CK. IEEE Trans Mag 1999;35:3445.