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Calculation of electromagnetic parameter based on interpolation algorithm
Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Calculation of electromagnetic parameter based on interpolation algorithm Wenqiang Zhang a,b,n, Liming Yuan b, Deyuan Zhang b a b
College of Engineering, China Agricultural University, Beijing 100083, PR China Bionic and Micro/Nano/Bio Manufacturing Technology Research Center, Beihang University, Beijing 100191, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 April 2015 Received in revised form 8 May 2015 Accepted 9 May 2015 Available online 15 May 2015
Wave-absorbing material is an important functional material of electromagnetic protection. The waveabsorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Hermite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. & 2015 Elsevier B.V. All rights reserved.
Keywords: Wave-absorbing material Electromagnetic parameter Interpolation algorithm Theoretical calculation Experimental verification
1. Introduction With the rapid development of the electronics industry, radio communication, etc., electromagnetic radiation not only causes serious harm to the commonly used electronic systems such as communication and computer, but also poses a threat to human health [1–9]. As an important functional material of electromagnetic protection, the wave-absorbing material is essential to achieve the incidence, loss and absorption of electromagnetic waves, which can effectively prevent the secondary scattering of electromagnetic waves and has become a research hotspot [4–8]. In the practical applications of wave-absorbing materials, due to their different working frequencies, loss values, environmental characteristics (temperature and humidity, space and mechanical strength) etc. [1,7–9], the optimal monomer or combination needs to be selected from electromagnetic wave absorbing particles that are reported to have different forms and properties and additional structural optimization is required [10–15]. In order to design the desired material quickly and accurately and reduce blindness in investment and experiment, it is necessary to study the calculation and design methods of wave-absorbing materials. Studies have shown that for monolayer wave-absorbing materials, accurate obtaining of the equivalent electromagnetic parameter of the mixed media (complex permittivity (ε ) and complex permeability
(μ )) is of great importance to predict the electromagnetic properties [15].
2. Experimental section 2.1. Build Lagrange interpolation method model and define parameters Lagrange interpolation method is to achieve the interpolation of univariate function. Given that there are n þ1 mutually exclusive real numbers, x0, x1, x2,…, xn, whose corresponding function values are y0, y1, y2,…, yn, the odd function of interpolation is taken as follows: n
lk (x) =
∏ j=0
x − xj xk − x j
(k = 0, 1, …, n)
j≠k
(1)
Obviously, lk(x) has the following properties:
⎧1, (i = k ) lk (xi ) = ⎨ ⎩ 0, (i ≠ k )
(2)
Then the interpolation function can be written as follows: n
n
Corresponding author at: College of Engineering, China Agricultural University, Beijing 100083, PR China. Fax: þ 86 10 62737726. E-mail addresses: [email protected], [email protected] (W. Zhang). http://dx.doi.org/10.1016/j.jmmm.2015.05.028 0304-8853/& 2015 Elsevier B.V. All rights reserved.
p (x) =
∑ lk (x) yk k=0
(3)
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
25
Fig. 1. Electromagnetic parameters of mixtures with different volume fractions of CIP. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
When the above formula is used for the interpolation calculation of electromagnetic parameter, yk is the complex electromagnetic parameter, and lk(x) is a polynomial of the volume fraction of the absorbent. 2.2. Build Hermite interpolation method model and define parameters Given that the function values of n þ1 mutually exclusive points x0, x1, x2,…, xn are y0, y1, y2,…, yn, and the derivative values of m þ1 points in the n þ 1 ones are yi0, yi1 … yim, then the polynomial m+ n+ 1
H (x) =
∑
ak xk
k=0
(6)
where ε is the permittivity, μ is the permeability, i is the additive, h is the substrate, and p is the volume fraction of the additive. Based on the above formula, the derivative of the electromagnetic parameter for the volume fraction can be obtained as follows:
⎧ 2/3 1/3 (ε eff − ε 01/3 ) 3ε eff ⎪ dεeff = ⎪ dp p ⎨ 2/3 1/3 ⎪ dμeff (μ eff − μ 01/3 ) 3μ eff ⎪ = p ⎩ dp
(7)
(4) 2.3. Experimental
satisfies
⎧ H (xi ) = yi ⎪ ⎨ ‵ ⎪ ⎩ H ′ (xik ) = yi k
⎧ ε 1/3 = pε 1/3 + (1 − p) ε 1/3 ⎪ eff i h ⎨ 1/3 1/3 1/3 ⎪ ⎩ μ eff = pμi + (1 − p) μ h
(i = 0, 1, …, n) (k = 0, 1, …, m)
(5)
The pivotal of Hermite method used for the interpolation of the electromagnetic parameter is to solve the derivative of the electromagnetic parameter for individual volume fraction. LLL hybrid theory describes the relationship between the electromagnetic parameter of the mixture and that of each constituent, as follows:
A vector network analyzer was used to measure the EM-wave parameters of the samples in the frequency range of 2–18 GHz. The cylindrical toroidal measurement samples were composed of the isotropic spherical carbonyl iron powder (CIP), anisotropic flaky carbonyl iron powder (FCIP) and bio-flaky particles [14]. To the mixtures containing CIP, the volume fractions of the samples for interpolation calculation were 22%, 31%, 40% and 49%. To the mixtures containing FCIP, the volume fractions of the samples for
26
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Fig. 2. Electromagnetic parameters of mixtures with different volume fractions of FCIP. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
interpolation calculation were 11%, 21%, 30% and 38%. To the mixtures containing bio-flaky particles, the volume fractions of the samples for interpolation calculation were 0.6%, 3.1%, 8.7% and 13.8%. In addition, CIP, FCIP and bio-flaky particles were used respectively to prepare coaxial samples with respective volume fractions of 46%, 34% and 6.7%. The sample had an inner diameter of 3 mm, an outer diameter of 7 mm and a thickness of 2 mm. EMwave absorption properties were evaluated by reflection loss (RL), which was derived from the following formulae: where Zin is the input impedance of absorber, Z0 is the impedance of air and c the velocity of light.
RL = 20 log
Zin = Z 0
μr εr
(Zin − Z 0 ) (Zin + Z 0 )
(8)
⎧ 2πfd ⎫ tanh ⎨j μr εr ⎬ ⎩ c ⎭
(9)
3. Results and discussion Figs. 1–3 show the electromagnetic parameters of different samples with different volume fractions. The Lagrange and Hermite interpolation methods introduced above were used for the
interpolation of the electromagnetic parameters of the samples containing spherical carbonyl iron powder and that containing flaky carbonyl iron powder. The electromagnetic parameters of samples with different volume fractions (46% CIP, 34% FCIP and bio-flaky particles) were calculated (Fig. 4). As can be seen from Fig. 4, the interpolation of the electromagnetic parameter of the mixture with known content of iron powder was conducted first and then the electromagnetic parameter of the mixture with other content of iron powder was calculated. The electromagnetic parameter obtained as the procedures above was of insignificant difference from that actually measured in the experiment. In contrast, both the interpolation methods above were less accurate in calculation of permittivity than the calculation of permeability. Meanwhile, the calculation result of Hermite interpolation is closer to the experimental data than Lagrange interpolation. The prediction of the electromagnetic parameter of the mixture is mainly to prepare for the design of wave-absorbing materials, and the wave-absorbing properties are reflected in the reflection of the patch. For monolayer wave-absorbing structure, the reflection can be calculated with the corresponding formula. The impact of the interpolation calculation of electromagnetic parameter on the reflection of the patch is herein studied. Fig. 5 shows the reflection calculation curve of the patch with thickness of 1 mm and CIP volume fraction of 46%. As can be seen from
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
27
Fig. 3. Electromagnetic parameters of mixtures with different volume fractions of bio-flaky particles. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
Fig. 5, there were certain differences between the electromagnetic parameter calculated with the interpolation method and that experimentally measured, especially in the permittivity. However, the calculated reflection was of little difference at low frequency and of significant difference at high frequency, and the reflection calculated with Hermite interpolation was closer to that calculated with the experimentally measured electromagnetic parameter than Lagrange interpolation. To further explain the effect of the electromagnetic parameter on the reflection, the derivative of the reflection of each frequency point in Fig. 5 for the real part and the imaginary part of the permittivity and permeability was calculated, as shown in Fig. 6. As can be seen from Fig. 6, at low frequency, the change in reflection was mainly from the imaginary part of permeability, and the real and imaginary parts of permittivity and the real part of permeability had insignificant impact on reflection; with increasing frequency, the impact of the real part of permeability on reflection increased gradually, and the impact of the real and imaginary parts of permittivity on the reflection also increased. The imaginary part of permeability still had a certainly significant impact on reflectivity.
4. Conclusions In order to obtain the desired electromagnetic parameter in the design process of wave-absorbing materials, this paper performed Lagrange interpolation and Hermite interpolation on the electromagnetic parameters of the limited number of samples. The results showed that: regardless of isotropic or anisotropic particles added, the interpolation method can predict the electromagnetic parameter of various contents in an accurate manner; Hermite interpolation is more accurate than Lagrange interpolation, and the reflection calculated with the electromagnetic parameter obtained from the interpolation is consistent on the whole with that calculated with the electromagnetic parameter obtained from the experiment. The interpolation algorithm of electromagnetic parameter in this paper is particularly suitable for the optimization design of wave-absorbing materials, which lays a foundation for subsequent application and development of wave-absorbing materials.
28
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Fig. 4. Contrast of calculated and experimental values of electromagnetic parameters. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability (● CIP with volume fraction of 46%; ■ FCIP with volume fraction of 34%; ▲ bio-flaky particles with volume fraction of 6.7%).
Fig. 5. Reflection loss curve (thickness: 1 mm, volume fraction of spherical carbonyl iron powder: 46 vol%).
Fig. 6. Derivation of electromagnetic parameter with reflection loss (thickness: 1 mm, volume fraction of CIP: 46 vol%).
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant no. 51305446) and the National “863” Project of China (Grant no. 2009AA043804). The authors would like to thank Gangxu Yong from Beihang University for EM-parameter test of the samples.
References [1] S.H. Liu, J.M. Liu, X.L. Dong, Electromagnetic Shielding and Absorbing Materials, Chemical Industry Press, Beijing, 2014. [2] Stephen M. Sagar, Frank R. Sharp, Raymond A. Swanson, Brain Res. 417 (1987) 172. [3] L. Lloyd Morgan, Pathophysiology 16 (2009) 137.
29
[4] R. Gary Enbanks, Microwave Absorbing Means, US Patent: 4791419, 1988-1213. [5] Q.X. Jiang, Z.Y. Zhou, Z.H. Jing, Saf. EMC 3 (2011) 9. [6] H. Guan, S. Liu, Y. Duan, J. Cheng, Cem. Concr. Compos. 28 (2006) 468. [7] 〈http://www.sony.net/Products/SC-HP/cx_news/vol25/pdf/emcstw.pdf〉, 2008. [8] 〈http://www.nec-tokin.com/english/product/pdf_dl/flex.pdf15835138191〉, 2009. [9] Wenqiang Zhang, Study on thermal decomposition bio-limited forming of high-performance electromagnetic wave-absorbing particles (A dissertation submitted for the Degree of Doctor of Philosophy), Beihang University, 2012. [10] Jianliang Xie, Chuanlin Lu, Longjiang Deng, Acta Mater. Compos. Sin. 24 (2007) 18. [11] F. Kretz, Z. Gacsi, J. Kovacs, Surf. Coat. Technol. 180 (2004) 575. [12] T. Liu, P.H. Zhou, J.L. Xie, J. Magn. Magn. Mater. 324 (2011) 519. [13] Liang Qiao, Fusheng Wen, Jianqiang Wei, J. Appl. Phys. 103 (2008) 1. [14] W.Q. Zhang, D.Y. Zhang, J. Cai, J. Magn. Magn. Mater. 332 (2013) 15. [15] C. Wang, J.L. Gu, F.Y. Kang, Mater. Rev. 23 (2009) 5.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Calculation of electromagnetic parameter based on interpolation algorithm Wenqiang Zhang a,b,n, Liming Yuan b, Deyuan Zhang b a b
College of Engineering, China Agricultural University, Beijing 100083, PR China Bionic and Micro/Nano/Bio Manufacturing Technology Research Center, Beihang University, Beijing 100191, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 9 April 2015 Received in revised form 8 May 2015 Accepted 9 May 2015 Available online 15 May 2015
Wave-absorbing material is an important functional material of electromagnetic protection. The waveabsorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Hermite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. & 2015 Elsevier B.V. All rights reserved.
Keywords: Wave-absorbing material Electromagnetic parameter Interpolation algorithm Theoretical calculation Experimental verification
1. Introduction With the rapid development of the electronics industry, radio communication, etc., electromagnetic radiation not only causes serious harm to the commonly used electronic systems such as communication and computer, but also poses a threat to human health [1–9]. As an important functional material of electromagnetic protection, the wave-absorbing material is essential to achieve the incidence, loss and absorption of electromagnetic waves, which can effectively prevent the secondary scattering of electromagnetic waves and has become a research hotspot [4–8]. In the practical applications of wave-absorbing materials, due to their different working frequencies, loss values, environmental characteristics (temperature and humidity, space and mechanical strength) etc. [1,7–9], the optimal monomer or combination needs to be selected from electromagnetic wave absorbing particles that are reported to have different forms and properties and additional structural optimization is required [10–15]. In order to design the desired material quickly and accurately and reduce blindness in investment and experiment, it is necessary to study the calculation and design methods of wave-absorbing materials. Studies have shown that for monolayer wave-absorbing materials, accurate obtaining of the equivalent electromagnetic parameter of the mixed media (complex permittivity (ε ) and complex permeability
(μ )) is of great importance to predict the electromagnetic properties [15].
2. Experimental section 2.1. Build Lagrange interpolation method model and define parameters Lagrange interpolation method is to achieve the interpolation of univariate function. Given that there are n þ1 mutually exclusive real numbers, x0, x1, x2,…, xn, whose corresponding function values are y0, y1, y2,…, yn, the odd function of interpolation is taken as follows: n
lk (x) =
∏ j=0
x − xj xk − x j
(k = 0, 1, …, n)
j≠k
(1)
Obviously, lk(x) has the following properties:
⎧1, (i = k ) lk (xi ) = ⎨ ⎩ 0, (i ≠ k )
(2)
Then the interpolation function can be written as follows: n
n
Corresponding author at: College of Engineering, China Agricultural University, Beijing 100083, PR China. Fax: þ 86 10 62737726. E-mail addresses: [email protected], [email protected] (W. Zhang). http://dx.doi.org/10.1016/j.jmmm.2015.05.028 0304-8853/& 2015 Elsevier B.V. All rights reserved.
p (x) =
∑ lk (x) yk k=0
(3)
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
25
Fig. 1. Electromagnetic parameters of mixtures with different volume fractions of CIP. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
When the above formula is used for the interpolation calculation of electromagnetic parameter, yk is the complex electromagnetic parameter, and lk(x) is a polynomial of the volume fraction of the absorbent. 2.2. Build Hermite interpolation method model and define parameters Given that the function values of n þ1 mutually exclusive points x0, x1, x2,…, xn are y0, y1, y2,…, yn, and the derivative values of m þ1 points in the n þ 1 ones are yi0, yi1 … yim, then the polynomial m+ n+ 1
H (x) =
∑
ak xk
k=0
(6)
where ε is the permittivity, μ is the permeability, i is the additive, h is the substrate, and p is the volume fraction of the additive. Based on the above formula, the derivative of the electromagnetic parameter for the volume fraction can be obtained as follows:
⎧ 2/3 1/3 (ε eff − ε 01/3 ) 3ε eff ⎪ dεeff = ⎪ dp p ⎨ 2/3 1/3 ⎪ dμeff (μ eff − μ 01/3 ) 3μ eff ⎪ = p ⎩ dp
(7)
(4) 2.3. Experimental
satisfies
⎧ H (xi ) = yi ⎪ ⎨ ‵ ⎪ ⎩ H ′ (xik ) = yi k
⎧ ε 1/3 = pε 1/3 + (1 − p) ε 1/3 ⎪ eff i h ⎨ 1/3 1/3 1/3 ⎪ ⎩ μ eff = pμi + (1 − p) μ h
(i = 0, 1, …, n) (k = 0, 1, …, m)
(5)
The pivotal of Hermite method used for the interpolation of the electromagnetic parameter is to solve the derivative of the electromagnetic parameter for individual volume fraction. LLL hybrid theory describes the relationship between the electromagnetic parameter of the mixture and that of each constituent, as follows:
A vector network analyzer was used to measure the EM-wave parameters of the samples in the frequency range of 2–18 GHz. The cylindrical toroidal measurement samples were composed of the isotropic spherical carbonyl iron powder (CIP), anisotropic flaky carbonyl iron powder (FCIP) and bio-flaky particles [14]. To the mixtures containing CIP, the volume fractions of the samples for interpolation calculation were 22%, 31%, 40% and 49%. To the mixtures containing FCIP, the volume fractions of the samples for
26
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Fig. 2. Electromagnetic parameters of mixtures with different volume fractions of FCIP. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
interpolation calculation were 11%, 21%, 30% and 38%. To the mixtures containing bio-flaky particles, the volume fractions of the samples for interpolation calculation were 0.6%, 3.1%, 8.7% and 13.8%. In addition, CIP, FCIP and bio-flaky particles were used respectively to prepare coaxial samples with respective volume fractions of 46%, 34% and 6.7%. The sample had an inner diameter of 3 mm, an outer diameter of 7 mm and a thickness of 2 mm. EMwave absorption properties were evaluated by reflection loss (RL), which was derived from the following formulae: where Zin is the input impedance of absorber, Z0 is the impedance of air and c the velocity of light.
RL = 20 log
Zin = Z 0
μr εr
(Zin − Z 0 ) (Zin + Z 0 )
(8)
⎧ 2πfd ⎫ tanh ⎨j μr εr ⎬ ⎩ c ⎭
(9)
3. Results and discussion Figs. 1–3 show the electromagnetic parameters of different samples with different volume fractions. The Lagrange and Hermite interpolation methods introduced above were used for the
interpolation of the electromagnetic parameters of the samples containing spherical carbonyl iron powder and that containing flaky carbonyl iron powder. The electromagnetic parameters of samples with different volume fractions (46% CIP, 34% FCIP and bio-flaky particles) were calculated (Fig. 4). As can be seen from Fig. 4, the interpolation of the electromagnetic parameter of the mixture with known content of iron powder was conducted first and then the electromagnetic parameter of the mixture with other content of iron powder was calculated. The electromagnetic parameter obtained as the procedures above was of insignificant difference from that actually measured in the experiment. In contrast, both the interpolation methods above were less accurate in calculation of permittivity than the calculation of permeability. Meanwhile, the calculation result of Hermite interpolation is closer to the experimental data than Lagrange interpolation. The prediction of the electromagnetic parameter of the mixture is mainly to prepare for the design of wave-absorbing materials, and the wave-absorbing properties are reflected in the reflection of the patch. For monolayer wave-absorbing structure, the reflection can be calculated with the corresponding formula. The impact of the interpolation calculation of electromagnetic parameter on the reflection of the patch is herein studied. Fig. 5 shows the reflection calculation curve of the patch with thickness of 1 mm and CIP volume fraction of 46%. As can be seen from
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
27
Fig. 3. Electromagnetic parameters of mixtures with different volume fractions of bio-flaky particles. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability.
Fig. 5, there were certain differences between the electromagnetic parameter calculated with the interpolation method and that experimentally measured, especially in the permittivity. However, the calculated reflection was of little difference at low frequency and of significant difference at high frequency, and the reflection calculated with Hermite interpolation was closer to that calculated with the experimentally measured electromagnetic parameter than Lagrange interpolation. To further explain the effect of the electromagnetic parameter on the reflection, the derivative of the reflection of each frequency point in Fig. 5 for the real part and the imaginary part of the permittivity and permeability was calculated, as shown in Fig. 6. As can be seen from Fig. 6, at low frequency, the change in reflection was mainly from the imaginary part of permeability, and the real and imaginary parts of permittivity and the real part of permeability had insignificant impact on reflection; with increasing frequency, the impact of the real part of permeability on reflection increased gradually, and the impact of the real and imaginary parts of permittivity on the reflection also increased. The imaginary part of permeability still had a certainly significant impact on reflectivity.
4. Conclusions In order to obtain the desired electromagnetic parameter in the design process of wave-absorbing materials, this paper performed Lagrange interpolation and Hermite interpolation on the electromagnetic parameters of the limited number of samples. The results showed that: regardless of isotropic or anisotropic particles added, the interpolation method can predict the electromagnetic parameter of various contents in an accurate manner; Hermite interpolation is more accurate than Lagrange interpolation, and the reflection calculated with the electromagnetic parameter obtained from the interpolation is consistent on the whole with that calculated with the electromagnetic parameter obtained from the experiment. The interpolation algorithm of electromagnetic parameter in this paper is particularly suitable for the optimization design of wave-absorbing materials, which lays a foundation for subsequent application and development of wave-absorbing materials.
28
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Fig. 4. Contrast of calculated and experimental values of electromagnetic parameters. (a) Real part of permittivity, (b) imaginary part of permittivity, (c) real part of permeability, and (d) imaginary part of permeability (● CIP with volume fraction of 46%; ■ FCIP with volume fraction of 34%; ▲ bio-flaky particles with volume fraction of 6.7%).
Fig. 5. Reflection loss curve (thickness: 1 mm, volume fraction of spherical carbonyl iron powder: 46 vol%).
Fig. 6. Derivation of electromagnetic parameter with reflection loss (thickness: 1 mm, volume fraction of CIP: 46 vol%).
W. Zhang et al. / Journal of Magnetism and Magnetic Materials 393 (2015) 24–29
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant no. 51305446) and the National “863” Project of China (Grant no. 2009AA043804). The authors would like to thank Gangxu Yong from Beihang University for EM-parameter test of the samples.
References [1] S.H. Liu, J.M. Liu, X.L. Dong, Electromagnetic Shielding and Absorbing Materials, Chemical Industry Press, Beijing, 2014. [2] Stephen M. Sagar, Frank R. Sharp, Raymond A. Swanson, Brain Res. 417 (1987) 172. [3] L. Lloyd Morgan, Pathophysiology 16 (2009) 137.
29
[4] R. Gary Enbanks, Microwave Absorbing Means, US Patent: 4791419, 1988-1213. [5] Q.X. Jiang, Z.Y. Zhou, Z.H. Jing, Saf. EMC 3 (2011) 9. [6] H. Guan, S. Liu, Y. Duan, J. Cheng, Cem. Concr. Compos. 28 (2006) 468. [7] 〈http://www.sony.net/Products/SC-HP/cx_news/vol25/pdf/emcstw.pdf〉, 2008. [8] 〈http://www.nec-tokin.com/english/product/pdf_dl/flex.pdf15835138191〉, 2009. [9] Wenqiang Zhang, Study on thermal decomposition bio-limited forming of high-performance electromagnetic wave-absorbing particles (A dissertation submitted for the Degree of Doctor of Philosophy), Beihang University, 2012. [10] Jianliang Xie, Chuanlin Lu, Longjiang Deng, Acta Mater. Compos. Sin. 24 (2007) 18. [11] F. Kretz, Z. Gacsi, J. Kovacs, Surf. Coat. Technol. 180 (2004) 575. [12] T. Liu, P.H. Zhou, J.L. Xie, J. Magn. Magn. Mater. 324 (2011) 519. [13] Liang Qiao, Fusheng Wen, Jianqiang Wei, J. Appl. Phys. 103 (2008) 1. [14] W.Q. Zhang, D.Y. Zhang, J. Cai, J. Magn. Magn. Mater. 332 (2013) 15. [15] C. Wang, J.L. Gu, F.Y. Kang, Mater. Rev. 23 (2009) 5.