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Complex permeability and electromagnetic wave absorption properties of amorphous alloy–epoxy composites
Journal of Non-Crystalline Solids 351 (2005) 75–83 www.elsevier.com/locate/jnoncrysol
Complex permeability and electromagnetic wave absorption properties of amorphous alloy–epoxy composites K.M. Lim a, K.A. Lee b, M.C. Kim b, C.G. Park
a,*
a
b
Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-ku, Pohang 790-784, South Korea Casting Process Research Team, Research Institute for Science and Technology (RIST), San 32 Hyoja-dong, Nam-ku, Pohang 790-785, South Korea Received 18 December 2003
Abstract Electromagnetic wave absorption properties of amorphous alloy–epoxy composites have been investigated with various amorphous alloy particle sizes and fractions in the 45 MHz to 10 GHz frequency range. The fraction of amorphous alloy in amorphous alloy–epoxy composites varied from 30 to 60 vol.% at a fixed amorphous alloy particle size and the size of amorphous alloy particles was varied from several lm to 125 lm at a fixed amorphous alloy particle fraction. Complex permeability (l), permittivity (e) of composites and reflection loss were measured by the reflection/transmission technique. The composites with small sized amorphous alloy particles (<26 lm) and a small amount of particles (<50%) had good reflection loss values less than 20 dB with thin thickness (<1 cm). The decreasing amorphous alloy particle size and fraction in amorphous alloy–epoxy composites resulted in a high minimum reflection loss frequency and small minimum reflection loss thickness. Variations of minimum reflection loss frequency and thickness of composites resulted from variations of materials constants such complex permeability, permittivity and resonance frequency. Changes in materials variables were due to the demagnetization effect and the eddy current effect, which operate differently in composites according to amorphous alloy particle size and fraction. 2004 Elsevier B.V. All rights reserved.
1. Introduction As the use of electronic devices such as cellular phones and personal computers becomes more common, social concerns are being raised about the harmful effects of electromagnetic waves which these devices emit on other devices and the human body [1]. The most effective solution for this problem is to eliminate the emitted and reflected waves from such electronic devices by absorbing the electromagnetic waves. Electromagnetic wave absorbers are materials that effectively attenuate the intensity of electromagnetic waves by absorbing them [2]. *
Corresponding author. Tel.: +82 54 279 2826; fax: +82 54 279 5090. E-mail address: [email protected] (C.G. Park). 0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.09.025
In general, electromagnetic wave absorbers can be divided into two typical application fields – military and civilian applications. Electromagnetic wave absorbers must have excellent reflection loss values over 20 dB (>90% absorption), and good formability to fabricate thin plates in both application fields. Compared with military applications, civilian applications require absorbers to be thin, since most absorbers must fit in a small sized electronic devices [3]. Spinel ferrite–polymer composites are representative narrow-band electromagnetic wave absorbers for use in several hundred megahertz to several gigahertz frequency range [3–6]. The merits of spinel ferrite–polymer composite absorbers are their adequate reflection loss due to large magnetic loss and ease of theoretical design for practical applications [7]. However, the major limitation for expanding the application of ferrite–polymer
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K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
composites is that they should be thick to obtain adequate reflection loss. That is caused by low real parts of complex permeability (lr) and permittivity (er) of ferrite composites, which results from their low conductivity and SneokÕs limit in high frequency ranges [4,7,8]. The development of new thinner electromagnetic wave absorbers using amorphous alloys has been attempted in order to overcome the ferrite–polymer composites problem [9]. Since the permeability of amorphous alloys rapidly decreases with increasing frequency due to eddy current loss [10,11], composites which are fabricated by dispersing amorphous alloy particles in a polymer matrix are generally used in high frequency applications [12,13]. However, the application of amorphous alloy composites as absorbers is restricted by large surface reflection of electromagnetic wave due to their relatively large complex permittivity values compared to complex permeability values [9]. The surface reflection of electromagnetic waves in absorbers bonded to perfect reflectors (metal plate) is represented by the impedance matching condition (zero reflection condition) which strongly depends on absorber thickness and materials constants (complex permeability and complex permittivity) [7]. Also, the materials constants of composite materials can be controlled by structural factors such as magnetic material particle size and fraction in composites [7,14,15], which can makes it possible to design amorphous alloy composites that have low complex permittivity by controlling amorphous alloy particle size and fraction. In order to achieve this, clear understanding about the relationship between materials constants and structural factors must be advanced. However, very few systematically researched reports have been made on materials constants and electromagnetic wave absorption properties related to structural factors. In this study, the effects of structural factors such as amorphous alloy particle size and fraction on electromagnetic wave absorption properties of amorphous alloy–epoxy composites have been investigated in terms of materials constants. The relationship between structural factors and materials constants was also studied by analyzing frequency dispersion of materials constants and conductivity of various amorphous alloy–epoxy composites with different amorphous alloy particle sizes and fractions.
2. Experimental procedures In this study, we used commercially available Fe78.4Si12B9.6 amorphous alloy strip (AT & T, China). Amorphous alloy powders were prepared by crushing amorphous alloy strip after isothermal annealing heattreatment in a vacuum atmosphere. Amorphous alloy powders were mixed with epoxy resin to make amor-
phous alloy–epoxy composite samples. The fabrication conditions of these samples are summarized in Table 1. Complex permeability (l = lr jli) and complex permittivity (e = er jei) were evaluated by measuring the reflection coefficient (S11) and transmission coefficient (S21) in the 45 MHz to 10 GHz frequency range using an HP 8510C network analyzer. During measurement, a cylindrical sample (7 mm in outer diameter and 3.04 mm in inner diameter) was mounted in a coaxial sample holder. In the case of narrow band electromagnetic wave absorbers, frequency range, in which materials can absorb electromagnetic wave, is limited to matching frequency. Since absorbers have their best absorbing properties with matching thickness, the determination of matching thickness must be advanced. The impedance matching condition can be numerically evaluated by solving the following equation [7]. rffiffiffi l 2pfd pffiffiffiffiffiffiffiffi Z IN ¼ tanh j l e ¼ 1; ð1Þ e c where ZIN is a normalized input impedance, l and e represent complex permeability and permittivity, d is the thickness of an absorber, and f is input wave frequency. Eq. (1) describes the zero-reflection condition at the surface of the absorber bonded to a metal plate. In this study, we used the Ôimpedance matching solution mapÕ method proposed by Musal et al. [14] and Kim et al. [16]. The reflection loss – C of a composite was obtained, using measured complex permeability and permittivity by the following well-known equations [10] at the matching thickness calculated by Eq. (1) : Z IN 1 ; Z IN þ 1 rffiffiffi l 2pfd pffiffiffiffiffiffiffiffi ¼ tanh j le : e c
CðdBÞ ¼
ð2Þ
Z IN
ð3Þ
Table 1 Composite sample fabrication condition (panel A) amorphous alloy particle sizes (S1–S6) at fixed particle fraction, (panel B) amorphous alloy particle fraction (F1–F4) at fixed particle size Sample
Fraction (vol.%)
Particle size (lm)
Panel A S1 S2 S3 S4 S5 S6
48 48 48 48 48 48
10 10–26 26–38 38–63 63–90 90–125
Panel B F1 F2 F3 F4
30 40 50 60
10–26 10–26 10–26 10–26
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
In addition, the electrical resisitvities of composites samples were measured by 2-probe method.
3. Results 3.1. Effects of amorphous alloy particle size on complex permeability (l) and permittivity (e) spectra of composites The frequency dependence of complex permeability (l = lr jli) for amorphous alloy–epoxy composites with different amorphous alloy particle size is shown in Fig. 1. The real part of complex permeability values (lr) of all composites decreased with increasing frequency as in Fig. 1(a). In composites containing larger amorphous alloy particles (S4–S6 composites), lr values drastically decreased from near 100 MHz, and the remaining composites (S1–S3 composites) fabricated
7
Real part of permeability [µ r ]
S6 6
S5
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~125µm)
0.1 1 Frequency [GHz]
10
S4 5 4
S3 S2 S1
3 2 1 0
Imaginary part of permeability [µi]
(a)
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
4
3
S6
2
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125 µm)
S3 S4 S2
1
S1 S5
0 (b)
0.1 1 Frequency [GHz]
10
Fig. 1. Variation in (a) the real part of permeability (lr) and (b) imaginary part of permeability (li) of amorphous alloy–epoxy composites depending on amorphous alloy particle size.
77
with smaller amorphous alloy particles (<38 lm) had frequency ranges, in which they maintained their lr values, which began to decrease near 1 GHz. From these results, we found that relaxation frequency, at which lr value begins to decrease, increased with decreasing amorphous alloy particle size. This variation of relaxation frequencies in composites results in increases of lr value with decreasing amorphous alloy particle size in the high frequency range above 1 GHz. In particular, the lr value of S1 composite (<10 lm), which had the lowest lr value below 1 GHz, is larger than that of other composites. In Fig. 1(b) which shows the frequency dispersion of the imaginary part of complex permeability (li), resonance frequency, fli ;max , at which li has a maximum value, gradually increases with decreasing amorphous alloy particle size from 0.27 GHz to 3.98 GHz. Generally, magnetization of magnetic materials is caused by domain wall motion and rotation magnetization in the low frequency range. Rotation magnetization is the main mechanism in the high frequency region [17]. The decrease of particle size in composites can affect l and fli ;max of composites materials in two ways. First, decreased powder size results in demagnetization field effect enhancement and which reduces permeability values in the low frequency range and increases domain wall resonance frequency [17]. Second, small particle may have shorter domain wall length than large particles. Since the average domain diameter in amorphous alloy is about 100 lm [18], the domain wall length can decrease with decreasing power size. The decrease in domain wall length results in reducing the width of domain wall vibration and increasing vibration frequency. When considering only magnetization mechanisms, the decrease of lr value in low frequency and the increase of fli ;max in composite obtaining small particle are due to the increase of demagnetization field effect and the diminution of the magnetization effect induced by domain wall motion. However, since the eddy current can also affect on the l of magnetic metallic materials, eddy current effect must also be considered to ascertain the effect of amorphous alloy particle size on complex permeability of composites. This fact can be confirmed from the variation in e of composites (Fig. 2). Complex permittivity (e = er jei) can be described by the following equation [19]: r e ¼ er jei ¼ er j ; ð4Þ x e0 where r is electric conductivity, e0 represents free space permittivity, and x is frequency. This equation means that e is proportional to electric conductivity. In Fig. 2, e values of composites increased with increasing amorphous alloy particle size. The e values of composites obtaining small amorphous alloy particles (S1–S4) were nearly constant independent of frequency, but
78
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
S6 40 35
S4
30 S3 25
S5
S1 20 15
S2 0.1
(a)
1
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125 µm)
S6
15
10
S4
4.0
Matching frequency [GHz]
20
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
3.5 3.0
250 200
2.0 150 1.5 100
1.0
50
0.0
S5
S3 S1 0.1
300
2.5
0.5
5
0
350 matching frequency matching thickness
0 S1
S2
Matching thickness [mm]
Imaginary part of permittivity [ε i ]
10
values of the real part of complex permittivity (er) and dielectric tangent loss (tan de = ei/er) were used to determinate matching condition. In Fig. 3, the matching frequency of composites increased from 0.12 GHz (S6) to 3.13 GHz (S1) with decreasing amorphous alloy particle size. The dependence of matching frequency variation on amorphous alloy particle size corresponded to that of fli ;max as shown in Fig. 4. Since lr value abruptly decreases and li value has maximum value near fli ;max , magnetic loss is maximized at near fli ;max . Most magnetic materials use this magnetic resonance for wave absorption and the matching frequency of magnetic absorbers appears at near resonance frequency [3,8]. Thus, the increase in matching frequency with decreasing amorphous alloy particle size resulted from the var-
Frequency [GHz] 25
(b)
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125µm)
S2
S3
S4
S5
S6
Sample
1
10
Frequency [GHz]
Fig. 2. Variation in (a) the real part of permeability (er) and (b) imaginary part of permeability (ei) of amorphous alloy–epoxy composites depending on amorphous alloy particle.
those of composites fabricated with large particles (S5– S6) gradually decreased with increasing frequency. The difference in behavior of e with frequency means that composites have different conductivity values according to amorphous alloy particle size. Thus, we could assume that eddy current had a different effect on l of composites according to amorphous alloy particle size. 3.2. Effects of amorphous alloy powder size on electromagnetic wave absorption properties of composites
Fig. 3. Matching frequency and thickness values of amorphous alloy– epoxy composites determined by impedance matching solution map as a function of amorphous alloy particle size in amorphous alloy–epoxy composites.
4.5 Resonance frequency
4.0
matching frequency
3.5
Frequency [GHz]
Real part of permittivity [εr ]
45
3.0 2.5 2.0 1.5 1.0
Fig. 4 shows the impedance matching frequency and thickness as a function of amorphous alloy particle size. The matching frequency and thickness of composites were determined using the Ôimpedance matching solution mapÕ method. As shown in Fig. 2, the e of composites obtaining large amorphous alloy particles (S4–S6) decreased with increasing frequency. Thus, the average
0.5 0.0 S1
S2
S3
S4
S5
S6
Sample Fig. 4. Relationship between matching frequency and resonance frequency as a function of amorphous alloy particle size in amorphous alloy–epoxy composites.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
3.3. Effects of amorphous alloy powder fraction on complex permeability (l) and permittivity (e) spectra of composites The frequency dependence of l for amorphous alloy– epoxy composites with different amorphous alloy particle fractions is shown in Fig. 6. The lr values of composites increased with increasing amorphous alloy particle fraction in the low frequency range below 3 GHz due to the increase of amorphous alloy particle
0
Real part of permeability [µr]
F4 (60%) 8
6
4
F3 (50%) F2 (40%) F1 (30%)
2
0
(a)
0.1
1
10
Frequency [GHz]
5.0
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
4.5 4.0 3.5
F4 (60%)
3.0 2.5
F3 (50%)
2.0 1.5 1.0
F2 (40%) F1 (30%)
0.5 0.0
-10
Reflection loss [dB]
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
10
Real part of permeability [µi]
iation of fli ;max . The matching thickness of composites was inversely proportional to matching frequency. The reason for the variation of fli ;max with different amorphous alloy particle sizes will be discussed later. The minimum reflection losses of composites are shown in Fig. 5, and frequency and thickness of composites for obtaining minimum reflection loss are summarized in Table 2. S1 and S2 composites fabricated with small amorphous alloy particles smaller than 26 lm had reflection loss values smaller than 50 dB with thickness less than 5 mm. However, S3–S6 composites fabricated by large powder (> 26 lm) required thicknesses larger than 1 cm.
79
0.1
(b)
1
10
Frequency [GHz]
S6(90~125 µm)
-20
Fig. 6. Variation in (a) the real part of permeability (lr) and (b) imaginary part of permeability (li) of amorphous alloy–epoxy composites depending on amorphous alloy particle fraction.
S5(63~90 µm) S4(38~63 µm)
-30
-40
S3(26~38 µm)
S2(10~26 µm)
-50 0.1
S1(<10 µm)
1
10
Frequency [GHz] Fig. 5. Minimum reflection loss of amorphous alloy–epoxy composites according to amorphous alloy particle size.
Table 2 Minimum reflection loss frequency, fmin and thickness, dmin of amorphous alloy–polymer composites with different amorphous alloy particle sizes Sample
S1
S2
Minimum reflection loss frequency [GHz] Minimum reflection loss thickness [mm]
3.13
1.79
3
5.4
S3 0.37 17.8
S4 0.22 31
S5 0.14 33
S6 0.09 55
amount. All composites had nearly similar lr values in the high frequency range above 3 GHz. However, F4 composite with larger amorphous alloy particle fraction had the lowest lr value in the high frequency range due to the rapid decrease of lr as the case of S4–S6 composites in part 3.1. Fig. 6(b) shows the frequency dispersion of li according to amorphous alloy particle fraction. The resonance frequency, fli ;max values of composites gradually increased with decreasing amorphous alloy particle fraction from 1.07 GHz to 1.99 GHz. Fig. 7 shows the variation of e according to amorphous alloy particle fraction. e values increased with increasing amorphous alloy particle fraction due to the increase of amorphous alloy particle in composites, which mainly contributes to e. Also, the e values of composites obtaining small amount of amorphous alloy particle (F1–F2) were almost constant in nearly all frequency ranges, but those of composites fabricated with large amounts of amorphous alloy particle (F3– F4) gradually decrease with increasing frequency.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
Imaginary part of permeability [εi]
80
3.4. Effects of amorphous alloy powder fraction on electromagnetic wave absorption properties of composites
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
15
F4 (60%)
10
5
F3 (50%) F2 (40%)
F2 (40%) 0 0.1
(a)
1 Frequency [GHz]
10
50
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
F4 (60%)
40
4.5
F3 (50%)
4.0
30 20 10
matching frequency resonance frequency
5.0
Frequency [GHz]
Real part of permittivity [εr]
60
Fig. 8 shows the impedance matching frequency and thickness determined by the Ôimpedance matching solution mapÕ method. In Fig. 8, the matching frequency of composites increased from 0.97 GHz (F3) to 4.72 GHz (F1) with decreasing amorphous alloy particle fraction. Since F4 composites obtaining the largest amount of amorphous alloy particle had very large e, it is impossible to obtain matching conditions theoretically. The dependence of variation of matching frequency on amorphous alloy particle fraction corresponds to that of fli ;max (Fig. 9). Also, the matching thickness of composites gradually increased with increasing amorphous alloy particle fraction.
F2 (40%) F1 (30%)
3.5 3.0 2.5 2.0 1.5
0 0.1 (b)
1 Frequency [GHz]
10
1.0 0.5
Fig. 7. Variation of (a) the real part of permittivity (er) and (b) imaginary part of permeability (ei) of amorphous alloy–epoxy composites depending on amorphous alloy particle fraction.
F1
F2
F3
F4
Sample Fig. 9. The relationship between matching frequency and resonance frequency as a function of amorphous alloy particle fraction in amorphous alloy–epoxy composites.
7
6
0
matching frequency
-10
4
5
3
2 4 1
Reflection loss [dB]
6
Matching thickness [mm]
Matching frequency [GHz]
matching thickness
5
-20 -30 -40 -50 -60
0 F2
F3
Sample
Fig. 8. Matching frequency and thickness values of amorphous alloy– epoxy composites determined by impedance matching solution map as a function of amorphous alloy particle fraction.
F1(30%) F3(50%) F2(40%)
3 F1
F4(60%)
-70 0.1
1 Frequency [GHz]
10
Fig. 10. Minimum reflection loss of amorphous alloy–epoxy composites according to amorphous alloy particle fraction.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 Table 3 Minimum reflection loss frequency, fmin and thickness, dmin of amorphous alloy–polymer composites with different amorphous alloy particle fractions Sample
F1
F2
F3
Minimum reflection loss frequency [GHz] Minimum reflection loss thickness [mm]
4.70
2.19
0.99
3.1
5.2
5.97
F4 0.29 12
The minimum reflection losses of composites are shown in Fig. 10, and frequency and thickness of composites for obtaining minimum reflection loss are summarized in Table 3. The composites fabricated with small amounts of amorphous alloy particle (<50%) had reflection loss values smaller than 50 dB with thicknesses of about 3–6 mm. However, F4 composite should have a thickness thicker than 12 mm. This means that it is impossible to make thin wave absorbers with amorphous alloy–epoxy composites obtaining amorphous alloy particle fractions above 50%.
4. Discussion Independent of amorphous alloy particle size and fraction, the minimum reflection loss of all amorphous alloy–epoxy composites was 20 dB except S6 composite at matching condition as shown in Figs. 5 and 10. Impedance matching condition means a designed condition, which hinders the reflection of electromagnetic waves at absorber surfaces and promotes the attenuation of electromagnetic waves inside absorbers. Thus, it is natural to obtain high absorption efficiency in amorphous alloy composites at matching condition. As mentioned in the introduction, materials must have thin thickness to be used as absorbers. The thicknesses of S3–S6, and F4 composites were too thick to be used as absorbers. Electromagnetic wave absorption properties of amorphous alloy–epoxy composites, such as matching frequency and thickness strongly depend on materials constants. The reason for the difference of electromagnetic wave absorption properties can be found in the difference of materials constants in composites. First, we will discuss frequency variation in which composites have minimum reflection loss according to amorphous alloy particle size and fraction. As shown in Figs. 4 and 9, matching frequency depended on fli ;max . The frequency dispersion of lr in soft magnetic metal systems is attributed to (1) magnetic resonance including domain wall motion and spin rotation as mentioned in Section 3 and (2) the rapid decrease of real part of permeability due to the eddy current effect induced by high conductivity. Eddy current causes decrease of effective volume, which contributes to the permeability of
81
magnetic metals, owing to decrease in skin depth of electromagnetic waves. Since soft magnetic metals have higher conductivity than other soft magnetic systems, these two magnetization mechanisms compete with each other [12]. Skin depth, d, induced by eddy current loss can be described by the following equation [20]. 7 10 q ; ð5Þ d¼ 4p2 lf where q is electrical resistivity, l represents permeability, and f is frequency. Since the abrupt decrease of lr can happen after a frequency, at which d is smaller than sample thickness, we can calculate this frequency, feddy, by the following modified equation [12]. feddy ¼
107 q ; 4p2 lt
ð6Þ
where t is sample thickness. Table 4 shows the electrical resistivity of amorphous alloy–epoxy composites. In Table 4(panel A), resistivities of S1–S6 composites (different amorphous alloy particle sizes at fixed fraction) were in the 7–50 X cm range and the increase of amorphous alloy powder size resulted in resistivity increase. In addition, F1 and F2 composites, which had amorphous alloy fraction less than 40%, had very high resistivity of about 104– 106 X cm. The resistivity of F4 composite is 1.99 X cm in Table 4(panel B). This reveals that there are large deviations in composite resistivities according to amorphous alloy particle size and fraction. We evaluated feddy of composites using the resistivity in Table 4 from Eq. (6). Calculated results are shown in Fig. 11. The feddy of S1–S3 composites obtaining small amorphous alloy powder (<38 lm) were much larger than fli ;max , and which means that the eddy current effect has little influence on the complex permeability spectra of these composites (S1–S3). Since the feddy of S4–S6 composites which obtained large amorphous alloy particle (> 38 lm) were smaller than fli ;max , we can confirm that the eddy current effect had an important effect on the complex permeability spectra of these composites (S4– S6). Also, in Fig. 11 (b), the feddy of F1–F3 composites which had low resistivity were located in very larger Table 4 The variation of electrical resistivity of composites as a function of (panel A) amorphous alloy powder size and (panel B) amorphous alloy powder fraction Sample
S1
S2
S3
S4
S5
S6
Panel A Resistivity [X cm]
54.2
46.7
18.3
9.29
9.27
7.62
Panel B Resistivity [X cm]
F1
F2
F3
F4
7.43 · 106
2.35 · 104
48.5
1.99
82
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 10 eddy frequency, f eddy resonance frequency, f µi,max Frequency [GHz]
8
6
4
2
0 S1
(a)
S2
S3 S4 Sample
S5
S6
eddy frequency, f eddy resonance frequency, f µi,max
100000
Frequency [GHz]
10000 1000 100 10 1 0.1 0.01 F1
F2
(b)
F3
F4
Sample
Fig. 11. Relationship between feddy and fli ;max of amorphous alloy– epoxy composites: (a) amorphous alloy particle size and (b) amorphous alloy particle fraction.
frequency ranges than fli ;max , and the feddy of F4 composite is smaller than the fli ;max of this composite. From this result, we found that the eddy current effect increased with increasing amorphous alloy particle fraction. Therefore, the variation of fli ;max , which resulted in the variation of matching frequency of composites, results from the eddy current loss effect and magnetization mechanism which operated independently according to composite resistivity. Secondly, the reason for matching thickness variation in composites according to amorphous alloy powder size and fraction can found in the basic principles for designing absorbers. The relationship between matching thickness and materials constants are defined as the following equation, (in the case of jerj > jlrj, 0 6 tan de = ei/er 6 0.8) [14,20]
fmin times dmin value (Eq. (7)). From in Figs. 1, 2, 6 and 7, increasing amorphous alloy particle size causes the increase of lr and er, which results in the decrease of fm times dm value. Also, fm decreases with increasing amorphous alloy particle size and fraction. Although the increases of lr and er have effect of reducing absorber thickness, the variation of fm has larger effect on absorber thickness in the present study. That is because the degree of decreasing in fm is much larger than those of increasing lr and er. Thus, the variation of fm and dm in composites is due to the variation of fli ;max induced by the difference of demagnetization field and eddy current effect according to amorphous alloy particle size and fraction.
5. Conclusions 1. The amorphous alloy composites had good minimum reflection loss less than 20 dB independent of amorphous alloy particle size and fraction. In particular, minimum reflection loss values of composites with small particle size (<26 lm) and fraction (<50%) were less than 50 dB. However, the thickness of composites with large particle size (>38 lm) and fraction (>50%) was too thick to be used as absorbers. 2. The minimum reflection loss frequency increased and the minimum reflection loss thickness decreased with decreasing amorphous alloy particle size and fraction. Variations of the minimum reflection loss frequency resulted from variation of resonance frequency and which determined the minimum reflection loss thickness of composites. 3. Variations of complex permeability, complex permittivity and resonance frequency according to amorphous alloy particle size and fraction were caused by demagnetization effect and eddy current effect, which operate differently in composites according to amorphous alloy and fraction.
Acknowledgments This work was supported by the ÔKorea Institute of Industrial Technology Evaluation and Planning (ITEP)Õ under contact no. D00-A07-1011-03. The authors would like to thank ITEP for the financial support.
References 4f m d m ¼ ðlr er Þ
1=2
2
1
ð1 þ tan li =lr Þ :
ð7Þ
This equation states that dm is affected by lr, er and fm. There is an inverse relationship between lr, er, and
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Complex permeability and electromagnetic wave absorption properties of amorphous alloy–epoxy composites K.M. Lim a, K.A. Lee b, M.C. Kim b, C.G. Park
a,*
a
b
Department of Materials Science and Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-ku, Pohang 790-784, South Korea Casting Process Research Team, Research Institute for Science and Technology (RIST), San 32 Hyoja-dong, Nam-ku, Pohang 790-785, South Korea Received 18 December 2003
Abstract Electromagnetic wave absorption properties of amorphous alloy–epoxy composites have been investigated with various amorphous alloy particle sizes and fractions in the 45 MHz to 10 GHz frequency range. The fraction of amorphous alloy in amorphous alloy–epoxy composites varied from 30 to 60 vol.% at a fixed amorphous alloy particle size and the size of amorphous alloy particles was varied from several lm to 125 lm at a fixed amorphous alloy particle fraction. Complex permeability (l), permittivity (e) of composites and reflection loss were measured by the reflection/transmission technique. The composites with small sized amorphous alloy particles (<26 lm) and a small amount of particles (<50%) had good reflection loss values less than 20 dB with thin thickness (<1 cm). The decreasing amorphous alloy particle size and fraction in amorphous alloy–epoxy composites resulted in a high minimum reflection loss frequency and small minimum reflection loss thickness. Variations of minimum reflection loss frequency and thickness of composites resulted from variations of materials constants such complex permeability, permittivity and resonance frequency. Changes in materials variables were due to the demagnetization effect and the eddy current effect, which operate differently in composites according to amorphous alloy particle size and fraction. 2004 Elsevier B.V. All rights reserved.
1. Introduction As the use of electronic devices such as cellular phones and personal computers becomes more common, social concerns are being raised about the harmful effects of electromagnetic waves which these devices emit on other devices and the human body [1]. The most effective solution for this problem is to eliminate the emitted and reflected waves from such electronic devices by absorbing the electromagnetic waves. Electromagnetic wave absorbers are materials that effectively attenuate the intensity of electromagnetic waves by absorbing them [2]. *
Corresponding author. Tel.: +82 54 279 2826; fax: +82 54 279 5090. E-mail address: [email protected] (C.G. Park). 0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.09.025
In general, electromagnetic wave absorbers can be divided into two typical application fields – military and civilian applications. Electromagnetic wave absorbers must have excellent reflection loss values over 20 dB (>90% absorption), and good formability to fabricate thin plates in both application fields. Compared with military applications, civilian applications require absorbers to be thin, since most absorbers must fit in a small sized electronic devices [3]. Spinel ferrite–polymer composites are representative narrow-band electromagnetic wave absorbers for use in several hundred megahertz to several gigahertz frequency range [3–6]. The merits of spinel ferrite–polymer composite absorbers are their adequate reflection loss due to large magnetic loss and ease of theoretical design for practical applications [7]. However, the major limitation for expanding the application of ferrite–polymer
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K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
composites is that they should be thick to obtain adequate reflection loss. That is caused by low real parts of complex permeability (lr) and permittivity (er) of ferrite composites, which results from their low conductivity and SneokÕs limit in high frequency ranges [4,7,8]. The development of new thinner electromagnetic wave absorbers using amorphous alloys has been attempted in order to overcome the ferrite–polymer composites problem [9]. Since the permeability of amorphous alloys rapidly decreases with increasing frequency due to eddy current loss [10,11], composites which are fabricated by dispersing amorphous alloy particles in a polymer matrix are generally used in high frequency applications [12,13]. However, the application of amorphous alloy composites as absorbers is restricted by large surface reflection of electromagnetic wave due to their relatively large complex permittivity values compared to complex permeability values [9]. The surface reflection of electromagnetic waves in absorbers bonded to perfect reflectors (metal plate) is represented by the impedance matching condition (zero reflection condition) which strongly depends on absorber thickness and materials constants (complex permeability and complex permittivity) [7]. Also, the materials constants of composite materials can be controlled by structural factors such as magnetic material particle size and fraction in composites [7,14,15], which can makes it possible to design amorphous alloy composites that have low complex permittivity by controlling amorphous alloy particle size and fraction. In order to achieve this, clear understanding about the relationship between materials constants and structural factors must be advanced. However, very few systematically researched reports have been made on materials constants and electromagnetic wave absorption properties related to structural factors. In this study, the effects of structural factors such as amorphous alloy particle size and fraction on electromagnetic wave absorption properties of amorphous alloy–epoxy composites have been investigated in terms of materials constants. The relationship between structural factors and materials constants was also studied by analyzing frequency dispersion of materials constants and conductivity of various amorphous alloy–epoxy composites with different amorphous alloy particle sizes and fractions.
2. Experimental procedures In this study, we used commercially available Fe78.4Si12B9.6 amorphous alloy strip (AT & T, China). Amorphous alloy powders were prepared by crushing amorphous alloy strip after isothermal annealing heattreatment in a vacuum atmosphere. Amorphous alloy powders were mixed with epoxy resin to make amor-
phous alloy–epoxy composite samples. The fabrication conditions of these samples are summarized in Table 1. Complex permeability (l = lr jli) and complex permittivity (e = er jei) were evaluated by measuring the reflection coefficient (S11) and transmission coefficient (S21) in the 45 MHz to 10 GHz frequency range using an HP 8510C network analyzer. During measurement, a cylindrical sample (7 mm in outer diameter and 3.04 mm in inner diameter) was mounted in a coaxial sample holder. In the case of narrow band electromagnetic wave absorbers, frequency range, in which materials can absorb electromagnetic wave, is limited to matching frequency. Since absorbers have their best absorbing properties with matching thickness, the determination of matching thickness must be advanced. The impedance matching condition can be numerically evaluated by solving the following equation [7]. rffiffiffi l 2pfd pffiffiffiffiffiffiffiffi Z IN ¼ tanh j l e ¼ 1; ð1Þ e c where ZIN is a normalized input impedance, l and e represent complex permeability and permittivity, d is the thickness of an absorber, and f is input wave frequency. Eq. (1) describes the zero-reflection condition at the surface of the absorber bonded to a metal plate. In this study, we used the Ôimpedance matching solution mapÕ method proposed by Musal et al. [14] and Kim et al. [16]. The reflection loss – C of a composite was obtained, using measured complex permeability and permittivity by the following well-known equations [10] at the matching thickness calculated by Eq. (1) : Z IN 1 ; Z IN þ 1 rffiffiffi l 2pfd pffiffiffiffiffiffiffiffi ¼ tanh j le : e c
CðdBÞ ¼
ð2Þ
Z IN
ð3Þ
Table 1 Composite sample fabrication condition (panel A) amorphous alloy particle sizes (S1–S6) at fixed particle fraction, (panel B) amorphous alloy particle fraction (F1–F4) at fixed particle size Sample
Fraction (vol.%)
Particle size (lm)
Panel A S1 S2 S3 S4 S5 S6
48 48 48 48 48 48
10 10–26 26–38 38–63 63–90 90–125
Panel B F1 F2 F3 F4
30 40 50 60
10–26 10–26 10–26 10–26
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
In addition, the electrical resisitvities of composites samples were measured by 2-probe method.
3. Results 3.1. Effects of amorphous alloy particle size on complex permeability (l) and permittivity (e) spectra of composites The frequency dependence of complex permeability (l = lr jli) for amorphous alloy–epoxy composites with different amorphous alloy particle size is shown in Fig. 1. The real part of complex permeability values (lr) of all composites decreased with increasing frequency as in Fig. 1(a). In composites containing larger amorphous alloy particles (S4–S6 composites), lr values drastically decreased from near 100 MHz, and the remaining composites (S1–S3 composites) fabricated
7
Real part of permeability [µ r ]
S6 6
S5
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~125µm)
0.1 1 Frequency [GHz]
10
S4 5 4
S3 S2 S1
3 2 1 0
Imaginary part of permeability [µi]
(a)
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
4
3
S6
2
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125 µm)
S3 S4 S2
1
S1 S5
0 (b)
0.1 1 Frequency [GHz]
10
Fig. 1. Variation in (a) the real part of permeability (lr) and (b) imaginary part of permeability (li) of amorphous alloy–epoxy composites depending on amorphous alloy particle size.
77
with smaller amorphous alloy particles (<38 lm) had frequency ranges, in which they maintained their lr values, which began to decrease near 1 GHz. From these results, we found that relaxation frequency, at which lr value begins to decrease, increased with decreasing amorphous alloy particle size. This variation of relaxation frequencies in composites results in increases of lr value with decreasing amorphous alloy particle size in the high frequency range above 1 GHz. In particular, the lr value of S1 composite (<10 lm), which had the lowest lr value below 1 GHz, is larger than that of other composites. In Fig. 1(b) which shows the frequency dispersion of the imaginary part of complex permeability (li), resonance frequency, fli ;max , at which li has a maximum value, gradually increases with decreasing amorphous alloy particle size from 0.27 GHz to 3.98 GHz. Generally, magnetization of magnetic materials is caused by domain wall motion and rotation magnetization in the low frequency range. Rotation magnetization is the main mechanism in the high frequency region [17]. The decrease of particle size in composites can affect l and fli ;max of composites materials in two ways. First, decreased powder size results in demagnetization field effect enhancement and which reduces permeability values in the low frequency range and increases domain wall resonance frequency [17]. Second, small particle may have shorter domain wall length than large particles. Since the average domain diameter in amorphous alloy is about 100 lm [18], the domain wall length can decrease with decreasing power size. The decrease in domain wall length results in reducing the width of domain wall vibration and increasing vibration frequency. When considering only magnetization mechanisms, the decrease of lr value in low frequency and the increase of fli ;max in composite obtaining small particle are due to the increase of demagnetization field effect and the diminution of the magnetization effect induced by domain wall motion. However, since the eddy current can also affect on the l of magnetic metallic materials, eddy current effect must also be considered to ascertain the effect of amorphous alloy particle size on complex permeability of composites. This fact can be confirmed from the variation in e of composites (Fig. 2). Complex permittivity (e = er jei) can be described by the following equation [19]: r e ¼ er jei ¼ er j ; ð4Þ x e0 where r is electric conductivity, e0 represents free space permittivity, and x is frequency. This equation means that e is proportional to electric conductivity. In Fig. 2, e values of composites increased with increasing amorphous alloy particle size. The e values of composites obtaining small amorphous alloy particles (S1–S4) were nearly constant independent of frequency, but
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K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
S6 40 35
S4
30 S3 25
S5
S1 20 15
S2 0.1
(a)
1
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125 µm)
S6
15
10
S4
4.0
Matching frequency [GHz]
20
S1 (below 10 µm) S3 (26 ~ 38 µm) S5 (63 ~ 90 µm)
3.5 3.0
250 200
2.0 150 1.5 100
1.0
50
0.0
S5
S3 S1 0.1
300
2.5
0.5
5
0
350 matching frequency matching thickness
0 S1
S2
Matching thickness [mm]
Imaginary part of permittivity [ε i ]
10
values of the real part of complex permittivity (er) and dielectric tangent loss (tan de = ei/er) were used to determinate matching condition. In Fig. 3, the matching frequency of composites increased from 0.12 GHz (S6) to 3.13 GHz (S1) with decreasing amorphous alloy particle size. The dependence of matching frequency variation on amorphous alloy particle size corresponded to that of fli ;max as shown in Fig. 4. Since lr value abruptly decreases and li value has maximum value near fli ;max , magnetic loss is maximized at near fli ;max . Most magnetic materials use this magnetic resonance for wave absorption and the matching frequency of magnetic absorbers appears at near resonance frequency [3,8]. Thus, the increase in matching frequency with decreasing amorphous alloy particle size resulted from the var-
Frequency [GHz] 25
(b)
S2 (10 ~ 26 µm) S4 (38 ~ 63 µm) S6 (90 ~ 125µm)
S2
S3
S4
S5
S6
Sample
1
10
Frequency [GHz]
Fig. 2. Variation in (a) the real part of permeability (er) and (b) imaginary part of permeability (ei) of amorphous alloy–epoxy composites depending on amorphous alloy particle.
those of composites fabricated with large particles (S5– S6) gradually decreased with increasing frequency. The difference in behavior of e with frequency means that composites have different conductivity values according to amorphous alloy particle size. Thus, we could assume that eddy current had a different effect on l of composites according to amorphous alloy particle size. 3.2. Effects of amorphous alloy powder size on electromagnetic wave absorption properties of composites
Fig. 3. Matching frequency and thickness values of amorphous alloy– epoxy composites determined by impedance matching solution map as a function of amorphous alloy particle size in amorphous alloy–epoxy composites.
4.5 Resonance frequency
4.0
matching frequency
3.5
Frequency [GHz]
Real part of permittivity [εr ]
45
3.0 2.5 2.0 1.5 1.0
Fig. 4 shows the impedance matching frequency and thickness as a function of amorphous alloy particle size. The matching frequency and thickness of composites were determined using the Ôimpedance matching solution mapÕ method. As shown in Fig. 2, the e of composites obtaining large amorphous alloy particles (S4–S6) decreased with increasing frequency. Thus, the average
0.5 0.0 S1
S2
S3
S4
S5
S6
Sample Fig. 4. Relationship between matching frequency and resonance frequency as a function of amorphous alloy particle size in amorphous alloy–epoxy composites.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
3.3. Effects of amorphous alloy powder fraction on complex permeability (l) and permittivity (e) spectra of composites The frequency dependence of l for amorphous alloy– epoxy composites with different amorphous alloy particle fractions is shown in Fig. 6. The lr values of composites increased with increasing amorphous alloy particle fraction in the low frequency range below 3 GHz due to the increase of amorphous alloy particle
0
Real part of permeability [µr]
F4 (60%) 8
6
4
F3 (50%) F2 (40%) F1 (30%)
2
0
(a)
0.1
1
10
Frequency [GHz]
5.0
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
4.5 4.0 3.5
F4 (60%)
3.0 2.5
F3 (50%)
2.0 1.5 1.0
F2 (40%) F1 (30%)
0.5 0.0
-10
Reflection loss [dB]
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
10
Real part of permeability [µi]
iation of fli ;max . The matching thickness of composites was inversely proportional to matching frequency. The reason for the variation of fli ;max with different amorphous alloy particle sizes will be discussed later. The minimum reflection losses of composites are shown in Fig. 5, and frequency and thickness of composites for obtaining minimum reflection loss are summarized in Table 2. S1 and S2 composites fabricated with small amorphous alloy particles smaller than 26 lm had reflection loss values smaller than 50 dB with thickness less than 5 mm. However, S3–S6 composites fabricated by large powder (> 26 lm) required thicknesses larger than 1 cm.
79
0.1
(b)
1
10
Frequency [GHz]
S6(90~125 µm)
-20
Fig. 6. Variation in (a) the real part of permeability (lr) and (b) imaginary part of permeability (li) of amorphous alloy–epoxy composites depending on amorphous alloy particle fraction.
S5(63~90 µm) S4(38~63 µm)
-30
-40
S3(26~38 µm)
S2(10~26 µm)
-50 0.1
S1(<10 µm)
1
10
Frequency [GHz] Fig. 5. Minimum reflection loss of amorphous alloy–epoxy composites according to amorphous alloy particle size.
Table 2 Minimum reflection loss frequency, fmin and thickness, dmin of amorphous alloy–polymer composites with different amorphous alloy particle sizes Sample
S1
S2
Minimum reflection loss frequency [GHz] Minimum reflection loss thickness [mm]
3.13
1.79
3
5.4
S3 0.37 17.8
S4 0.22 31
S5 0.14 33
S6 0.09 55
amount. All composites had nearly similar lr values in the high frequency range above 3 GHz. However, F4 composite with larger amorphous alloy particle fraction had the lowest lr value in the high frequency range due to the rapid decrease of lr as the case of S4–S6 composites in part 3.1. Fig. 6(b) shows the frequency dispersion of li according to amorphous alloy particle fraction. The resonance frequency, fli ;max values of composites gradually increased with decreasing amorphous alloy particle fraction from 1.07 GHz to 1.99 GHz. Fig. 7 shows the variation of e according to amorphous alloy particle fraction. e values increased with increasing amorphous alloy particle fraction due to the increase of amorphous alloy particle in composites, which mainly contributes to e. Also, the e values of composites obtaining small amount of amorphous alloy particle (F1–F2) were almost constant in nearly all frequency ranges, but those of composites fabricated with large amounts of amorphous alloy particle (F3– F4) gradually decrease with increasing frequency.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83
Imaginary part of permeability [εi]
80
3.4. Effects of amorphous alloy powder fraction on electromagnetic wave absorption properties of composites
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
15
F4 (60%)
10
5
F3 (50%) F2 (40%)
F2 (40%) 0 0.1
(a)
1 Frequency [GHz]
10
50
F1 (30 %) F2 (40 %) F3 (50 %) F4 (60 %)
F4 (60%)
40
4.5
F3 (50%)
4.0
30 20 10
matching frequency resonance frequency
5.0
Frequency [GHz]
Real part of permittivity [εr]
60
Fig. 8 shows the impedance matching frequency and thickness determined by the Ôimpedance matching solution mapÕ method. In Fig. 8, the matching frequency of composites increased from 0.97 GHz (F3) to 4.72 GHz (F1) with decreasing amorphous alloy particle fraction. Since F4 composites obtaining the largest amount of amorphous alloy particle had very large e, it is impossible to obtain matching conditions theoretically. The dependence of variation of matching frequency on amorphous alloy particle fraction corresponds to that of fli ;max (Fig. 9). Also, the matching thickness of composites gradually increased with increasing amorphous alloy particle fraction.
F2 (40%) F1 (30%)
3.5 3.0 2.5 2.0 1.5
0 0.1 (b)
1 Frequency [GHz]
10
1.0 0.5
Fig. 7. Variation of (a) the real part of permittivity (er) and (b) imaginary part of permeability (ei) of amorphous alloy–epoxy composites depending on amorphous alloy particle fraction.
F1
F2
F3
F4
Sample Fig. 9. The relationship between matching frequency and resonance frequency as a function of amorphous alloy particle fraction in amorphous alloy–epoxy composites.
7
6
0
matching frequency
-10
4
5
3
2 4 1
Reflection loss [dB]
6
Matching thickness [mm]
Matching frequency [GHz]
matching thickness
5
-20 -30 -40 -50 -60
0 F2
F3
Sample
Fig. 8. Matching frequency and thickness values of amorphous alloy– epoxy composites determined by impedance matching solution map as a function of amorphous alloy particle fraction.
F1(30%) F3(50%) F2(40%)
3 F1
F4(60%)
-70 0.1
1 Frequency [GHz]
10
Fig. 10. Minimum reflection loss of amorphous alloy–epoxy composites according to amorphous alloy particle fraction.
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 Table 3 Minimum reflection loss frequency, fmin and thickness, dmin of amorphous alloy–polymer composites with different amorphous alloy particle fractions Sample
F1
F2
F3
Minimum reflection loss frequency [GHz] Minimum reflection loss thickness [mm]
4.70
2.19
0.99
3.1
5.2
5.97
F4 0.29 12
The minimum reflection losses of composites are shown in Fig. 10, and frequency and thickness of composites for obtaining minimum reflection loss are summarized in Table 3. The composites fabricated with small amounts of amorphous alloy particle (<50%) had reflection loss values smaller than 50 dB with thicknesses of about 3–6 mm. However, F4 composite should have a thickness thicker than 12 mm. This means that it is impossible to make thin wave absorbers with amorphous alloy–epoxy composites obtaining amorphous alloy particle fractions above 50%.
4. Discussion Independent of amorphous alloy particle size and fraction, the minimum reflection loss of all amorphous alloy–epoxy composites was 20 dB except S6 composite at matching condition as shown in Figs. 5 and 10. Impedance matching condition means a designed condition, which hinders the reflection of electromagnetic waves at absorber surfaces and promotes the attenuation of electromagnetic waves inside absorbers. Thus, it is natural to obtain high absorption efficiency in amorphous alloy composites at matching condition. As mentioned in the introduction, materials must have thin thickness to be used as absorbers. The thicknesses of S3–S6, and F4 composites were too thick to be used as absorbers. Electromagnetic wave absorption properties of amorphous alloy–epoxy composites, such as matching frequency and thickness strongly depend on materials constants. The reason for the difference of electromagnetic wave absorption properties can be found in the difference of materials constants in composites. First, we will discuss frequency variation in which composites have minimum reflection loss according to amorphous alloy particle size and fraction. As shown in Figs. 4 and 9, matching frequency depended on fli ;max . The frequency dispersion of lr in soft magnetic metal systems is attributed to (1) magnetic resonance including domain wall motion and spin rotation as mentioned in Section 3 and (2) the rapid decrease of real part of permeability due to the eddy current effect induced by high conductivity. Eddy current causes decrease of effective volume, which contributes to the permeability of
81
magnetic metals, owing to decrease in skin depth of electromagnetic waves. Since soft magnetic metals have higher conductivity than other soft magnetic systems, these two magnetization mechanisms compete with each other [12]. Skin depth, d, induced by eddy current loss can be described by the following equation [20]. 7 10 q ; ð5Þ d¼ 4p2 lf where q is electrical resistivity, l represents permeability, and f is frequency. Since the abrupt decrease of lr can happen after a frequency, at which d is smaller than sample thickness, we can calculate this frequency, feddy, by the following modified equation [12]. feddy ¼
107 q ; 4p2 lt
ð6Þ
where t is sample thickness. Table 4 shows the electrical resistivity of amorphous alloy–epoxy composites. In Table 4(panel A), resistivities of S1–S6 composites (different amorphous alloy particle sizes at fixed fraction) were in the 7–50 X cm range and the increase of amorphous alloy powder size resulted in resistivity increase. In addition, F1 and F2 composites, which had amorphous alloy fraction less than 40%, had very high resistivity of about 104– 106 X cm. The resistivity of F4 composite is 1.99 X cm in Table 4(panel B). This reveals that there are large deviations in composite resistivities according to amorphous alloy particle size and fraction. We evaluated feddy of composites using the resistivity in Table 4 from Eq. (6). Calculated results are shown in Fig. 11. The feddy of S1–S3 composites obtaining small amorphous alloy powder (<38 lm) were much larger than fli ;max , and which means that the eddy current effect has little influence on the complex permeability spectra of these composites (S1–S3). Since the feddy of S4–S6 composites which obtained large amorphous alloy particle (> 38 lm) were smaller than fli ;max , we can confirm that the eddy current effect had an important effect on the complex permeability spectra of these composites (S4– S6). Also, in Fig. 11 (b), the feddy of F1–F3 composites which had low resistivity were located in very larger Table 4 The variation of electrical resistivity of composites as a function of (panel A) amorphous alloy powder size and (panel B) amorphous alloy powder fraction Sample
S1
S2
S3
S4
S5
S6
Panel A Resistivity [X cm]
54.2
46.7
18.3
9.29
9.27
7.62
Panel B Resistivity [X cm]
F1
F2
F3
F4
7.43 · 106
2.35 · 104
48.5
1.99
82
K.M. Lim et al. / Journal of Non-Crystalline Solids 351 (2005) 75–83 10 eddy frequency, f eddy resonance frequency, f µi,max Frequency [GHz]
8
6
4
2
0 S1
(a)
S2
S3 S4 Sample
S5
S6
eddy frequency, f eddy resonance frequency, f µi,max
100000
Frequency [GHz]
10000 1000 100 10 1 0.1 0.01 F1
F2
(b)
F3
F4
Sample
Fig. 11. Relationship between feddy and fli ;max of amorphous alloy– epoxy composites: (a) amorphous alloy particle size and (b) amorphous alloy particle fraction.
frequency ranges than fli ;max , and the feddy of F4 composite is smaller than the fli ;max of this composite. From this result, we found that the eddy current effect increased with increasing amorphous alloy particle fraction. Therefore, the variation of fli ;max , which resulted in the variation of matching frequency of composites, results from the eddy current loss effect and magnetization mechanism which operated independently according to composite resistivity. Secondly, the reason for matching thickness variation in composites according to amorphous alloy powder size and fraction can found in the basic principles for designing absorbers. The relationship between matching thickness and materials constants are defined as the following equation, (in the case of jerj > jlrj, 0 6 tan de = ei/er 6 0.8) [14,20]
fmin times dmin value (Eq. (7)). From in Figs. 1, 2, 6 and 7, increasing amorphous alloy particle size causes the increase of lr and er, which results in the decrease of fm times dm value. Also, fm decreases with increasing amorphous alloy particle size and fraction. Although the increases of lr and er have effect of reducing absorber thickness, the variation of fm has larger effect on absorber thickness in the present study. That is because the degree of decreasing in fm is much larger than those of increasing lr and er. Thus, the variation of fm and dm in composites is due to the variation of fli ;max induced by the difference of demagnetization field and eddy current effect according to amorphous alloy particle size and fraction.
5. Conclusions 1. The amorphous alloy composites had good minimum reflection loss less than 20 dB independent of amorphous alloy particle size and fraction. In particular, minimum reflection loss values of composites with small particle size (<26 lm) and fraction (<50%) were less than 50 dB. However, the thickness of composites with large particle size (>38 lm) and fraction (>50%) was too thick to be used as absorbers. 2. The minimum reflection loss frequency increased and the minimum reflection loss thickness decreased with decreasing amorphous alloy particle size and fraction. Variations of the minimum reflection loss frequency resulted from variation of resonance frequency and which determined the minimum reflection loss thickness of composites. 3. Variations of complex permeability, complex permittivity and resonance frequency according to amorphous alloy particle size and fraction were caused by demagnetization effect and eddy current effect, which operate differently in composites according to amorphous alloy and fraction.
Acknowledgments This work was supported by the ÔKorea Institute of Industrial Technology Evaluation and Planning (ITEP)Õ under contact no. D00-A07-1011-03. The authors would like to thank ITEP for the financial support.
References 4f m d m ¼ ðlr er Þ
1=2
2
1
ð1 þ tan li =lr Þ :
ð7Þ
This equation states that dm is affected by lr, er and fm. There is an inverse relationship between lr, er, and
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