Materials Research Bulletin 48 (2013) 3887–3891
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Synthesis and electromagnetic properties of Al/AlOx-coated Ni nanocapsules Xianguo Liu a,*, Chao Feng a, Siu Wing Or b, Chuangui Jin a, Feng Xiao a, Ailin Xia a, Weihuo Li a, Yuping Sun c, Shengsheng Zhao d a
School of Materials Science and Engineering, Anhui University of Technology, Ma’anshan 243002, PR China Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Center for Engineering Practice and Innovation Education, Anhui University of Technology, Ma’anshan 243002, PR China d School of Mechanical and Electrical Engineering, Shenzhen Polytechnic, Shenzhen 518055, PR China b c
A R T I C L E I N F O
A B S T R A C T
Article history: Received 2 December 2012 Received in revised form 27 May 2013 Accepted 31 May 2013 Available online 12 June 2013
Ni nanocapsules with a core of Ni nanoparticle and a shell of amorphous Al/AlOx have been prepared by the arc discharge method. The natural resonance in the Al/AlOx-coated Ni nanocapsules shifts to 6.4 GHz, due to the surface anisotropy of Ni nanoparticles. An optimal RL value of 40.96 dB was observed at 9.2 GHz on a specimen with a matching thickness of 2.40 mm. Theoretical simulation for the microwave absorption using the transmission line theory agrees reasonably well with the experimental results. The frequency of microwave absorption complies with the quarter-wavelength matching model. ß 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Composites A. Nanostructures C. X-ray diffraction D. Dielectric properties
1. Introduction In recent years, with the development of local electronic devices, microwave communication, and the rising pollution of electromagnetic (EM) interference, materials with strong EMwave absorption, in a wide frequency range, thin thickness, low density, and low cost are more and more desirable [1–5]. Recently, much research has been focused on core/shell nanostructures (dielectric shells and magnetic nanoparticles as cores) as EM-wave absorbing materials [1–9]. The core/shell structure improves the impedance matching between the nanostructures and the incident microwaves due to the coupling of the electromagnetic field with both the magnetic core and the dielectric shell [9–11]. A number of nanocapsules with core–shell structure, like a-Fe/SmO, a-Fe/Y2O3, FeCo/Al2O3, Fe/C, Ni/C, and FeNi/C, have been studied [3,4,7,8,12,13]. Excellent EM-wave absorption of materials is known to result from efficient complementarities between the relative permittivity and permeability. Among the nanocapsules with the core–shell structure, Ni-based EM-wave absorbing nanocapsules, such as Ni/ZnO [2], Ni/SiO2 [14], Ni/polyaniline [15], Ni/C [4] and Ni/carbon nanotubes [16], are of great interest due to their typical ferromagnetic characteristics and potential
* Corresponding author. Tel.: +86 555 2311570; fax: +86 555 2311570. E-mail address:
[email protected] (X. Liu). 0025-5408/$ – see front matter ß 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.materresbull.2013.05.110
applications in microwave absorption. Nanoparticles prepared from pure nickel possess the core–shell structure due to natural oxidation of the nanoparticles surfaces. However, alumina is an effective material to form good barrier for spin-polarized tunnel [17], only a few works are devoted to the preparation of Al2O3 nanocomposites, and most are related to magnetic metals or alloys embedded into insulator matrices without core–shell structures. By coating Ni nanoparticles with alumina, the resistivity can be increased, thus reducing losses. In the previous study, Al2O3coated FeCo nanocapsules were synthesized by arc discharge method, which exhibited good EM-wave absorptive properties [13]. AlOx-coated FeNi nanocapsules were also synthesized by arc discharge method and the influence of the AlOx shell on the complex permeability and complex permittivity of FeNi nanoparticles was investigated in detail [18]. The frequency dependence of the microwave absorption obeys the quarter-wavelength (l/4) matching model. According to the model, the minimum reflection loss (RL) can be gained at given frequencies if the thickness of the absorber (tm) satisfies [19,20]: tm ¼
nl nc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 4 4 f m jer jjmr j
ðn ¼ 1; 3; 5; ::::::Þ
(1)
where c is the velocity of light, fm and tm is the peak frequency and the matching thickness of minimum microwave absorptions. l is the wavelength in the materials, mr is the complex permeability at
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fm and er is the complex permittivity at fm. Refer to Eq. (1), the peak frequency fm is inversely proportional to matching thickness tm. In this work, Al/AlOx-coated Ni nanocapsules were fabricated by a modified arc-discharge technique. The complex permittivity and permeability of nanocapsules-paraffin composites with 40 wt.% nanocapsules were analyzed and the microwave absorbing characteristics of composites were evaluated. The dependence of the minimum RL and corresponding frequency on the thickness of composites was studied. 2. Experimental procedure Al/AlOx-coated Ni nanocapsules were prepared by arc discharging a Ni95Al5 alloy ingot in copper crucible in the mixture atmosphere of H2 and Ar. Details of the synthesis procedure can be found elsewhere [1,2,4,7–9,21]. The Ni95Al5 master alloy served as the anode, while the cathode was a tungsten needle of 3 mm in diameter. The anode target was placed into one pit of a watercooled copper crucible. The distance between the anode and the cathode were about 3 mm. A mixture gas of Ar (20,000 Pa) and H2 (4000 Pa) was introduced into an evacuated chamber (7.0 103 Pa) before the arc-discharge. During the experimental process, the current was maintained at 80 A for 10 h, while the voltage was maintained at 20 V. The as-prepared products on the top wall of furnace were collected after being passivated in air for 8 h. The yield of nanocapsules was about 3 g. In order to get the enough nanocapsules for the measurement of reflection loss, the above experiment was repeated several times under the same experimental conditions. The composition and phase purity of the as-prepared samples were analyzed by X-ray diffraction (XRD, Brucker D8 Advance, Germany) at 40 kV voltage and 50 mA current with Cu Ka radiation (l = 1.5418 A˚). Transmission electron microscopy (TEM) and highresolution TEM (HRTEM) images were obtained on a JEOL TEM2010 (Japan) transmission electron microscope at an acceleration voltage of 200 kV. The surface compositions of the nanocapsules were determined by ESCALAB-250 X-ray photoelectron spectroscopy (XPS, UK), with an Al Ka line X-ray source. The Ni nanocapsules-paraffin composite was prepared by uniformly mixing Ni nanocapsules with paraffin, as described in detail elsewhere [1–4,7–9], by pressing them into cylinder-shaped compacts. Then the compact was cut into toroidal shape with 7.00 mm outer diameter and 3.04 mm inner diameter. The EM parameters were measured for paraffin-Ni nanocapsules composite containing 40 wt.% Ni nanocapsules, using an Agilent N5244A vector network analyzer (VNA, USA). Coaxial method was used to determine the EM parameters of the toroidal samples in a frequency range of 2–18 GHz with a transverse EM mode. The VNA was calibrated for the full two-port measurement of reflection and transmission at each port. The complex permittivity and complex permeability were calculated from S-parameters tested by the VNA, using the simulation program of Reflection/ Transmission Nicolson–Ross model [22]. The microwave-absorbing characteristics were evaluated by measuring the reflection loss using an HP8757E scalar quantity network analyzer (USA) in the 2– 18 GHz band range, and the sample sheets (180 mm 180 mm) were mounted onto an aluminum substrate. All the measurements were performed at room temperature. 3. Results and discussion 3.1. Phase and structure XRD pattern in Fig. 1 shows the phase components of the nanocapsules. All sharp reflection peaks could be indexed to Ni with the body-centered-cubic (bcc) structure. It is noteworthy that
Fig. 1. (a) XRD pattern, (b) TEM and (c) HRTEM images of Al/AlOx-coated Ni nanocapsules, and (d) XPS spectrum and the corresponding fitting curves of the Al 2p3/2 electrons on a etching depth of 2 nm.
no Ni oxides peaks are detectable in the XRD patterns, indicating that the core of the nanocapsules may be free from oxidation, due to the protective shell. In the XRD pattern, there are no detectable peaks for Al and Al oxides, indicating the Al and Al oxides are in small amount in the nanocapsules. The morphology, size distribution and core–shell structure of the nanocapsules were well recognizable from the TEM image reported in Fig. 1(b). Most of the nanocapsules as-prepared are irregular sphere shape with the narrow distribution of diameters, ranging from 10 to 30 nm (Fig. 1(b)). The averaged diameter is about 20.9 nm and the averaged shell thickness is about 2.7 nm, after averaging that of more than 200 nanocapsules, which is consistent with 19.9 nm calculated from the XRD (1 1 1) peak according to the Scherrer equation. In Fig. 1(c), the HRTEM image clearly shows the shell/ core structure with a crystalline core and an amorphous shell. In the core, the d-spacing of 0.204 nm corresponds to the lattice plane {1 1 1} of Ni. In order to obtain more information, the nanocapsules were investigated by XPS. The XPS curve of Al 2p3/2 on the surface of nanocapsules is shown in detail in Fig. 1(d). The shell of the nanocapsules can be determined as Al2O3 from the binding energy (BE) peak of 74.7 eV and 74.2 eV [23,24] and as AlxO from the BE peak of 75.5 eV and as Al from the BE peak of 72.1 eV [25,26], using the Lorentzian–Gaussian product function [17]. According to the area of fitting curves, the amount of Al atom with different BE states are estimated to be the same [17]. Clearly, more BE states for Al atoms appear on the surface of nanocapsules. The above mentioned phenomena can be ascribed to the formation mechanism of the nanocapsules. i.e., different evaporating pressures, melting points for nickel and aluminum atoms, during the arc discharging process [17]. For an evaporating pressure of 1.33 103 Pa (105 Torr), the corresponding evaporating temperatures are 1157 8C for Ni and 887 8C for Al. The melting points of Ni and Al are 1453 and 660 8C, respectively [2,13,17,18]. The formation process of the nanocapsules synthesized by the arc discharge includes the evaporation of Ni, Al and their vapor condensation. In the evaporation process, Al atoms take the priority to evaporate and then bump up each other between Ni and Al atoms. When the temperature is decreased, the Ni firstly
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forms nucleus and the Al atoms are near them. These Al atoms are abounded on the surfaces of the Ni solid-solution nanoparticles. When the products are exposed to air, Al atoms are easily oxidized to amorphous Al/AlOx on the surfaces of the nanocapsules to form the core/shell structure.
[29]. In other words, the Ni nanocapsules own a relatively high effective anisotropic energy value and the resonance frequency may shift to the higher frequency (6.4 GHz), which would be significant for their use as EM-wave absorption materials in the microwave range.
3.2. Electromagnetic properties
3.3. EM-wave absorption properties
Fig. 2 shows the frequency dependence of the complex permittivity (er = e0 je00 ) and permeability (mr = m0 jm00 ) of Ni nanocapsules dispersed in paraffin in the frequency range between 2 and 18 GHz. Both the real part (e0 ) and the imaginary part (e00 ) of the complex permittivity display a similar tendency of decreasing with the frequency increasing from 2 to 18 GHz which is due to increased lagging behind of the dipole-polarization response with respect to the electric-field change at higher frequencies. Maximum/minimum values can be found below/above the resonant frequencies in the e0 curve [27]. Accordingly, two peaks are observed in the e00 curve near the resonant frequencies. The resonant frequencies of er in the current frequency range are 9.8 and 14.8 GHz, which may be attributed to interfacial polarization resonance due to the electronegativity difference between the Ni core and the Al/AlOx shell and to permanent electric dipoles resulting from defects in the Al/AlOx shell. In general, the dual dielectric resonances are favorable to the improvement of microwave absorption properties. The frequency dependence of mr is shown in Fig. 2(b). The real part (m0 ) of the complex permeability decreases from 1.15 to 0.98 and then remains almost constant in the frequency range of 12 to 18 GHz. The imaginary part (m0 ) increases slightly at the frequency range of 2 to 6.4 GHz and then decreases gradually at frequencies over 6.4 GHz. It is noteworthy that the maximum value of the m00 appearing at 6.4 GHz implies that the natural resonance occurred in the present Ni nanocapsules. According to the nature resonance equation: 2p fr = gHA [28], where g is the gyromagnetic ratio and HA ¼ 4jK 1 j=3m0 M s , where Ms is the saturation magnetization, HA is the anisotropic field and m0 is the permeability without electromagnetic field. The anisotropic coefficient (K1) for the fcctype bulk nickel which is about 5 103 J/m3, the natural resonance frequency (fr) should be around several tens of megahertz. The anisotropic energy of small size particles, especially in nanometer scale, may be remarkably increased due to the surface anisotropic field affected by very small size effect
It is well known that the reflection loss (RL) can be used to characterize the absorption properties of EM materials. According to the transmission-line model [1–5], the RL of a metal-backed microwave absorbing layer is calculated using the relative complex permeability and permittivity at a given frequency and layer thickness by means of the following equations: jZtanhðkdÞ 1 RL ¼ 20 log rffiffiffiffiffiffiffiffiffiffiffiffi jZtanhðkdÞ þ 1 (2) mr 2p f pffiffiffiffiffiffiffiffiffiffi and k ¼ mr er with Z ¼ c er Here, the materials constants mr = m0 jm00 and er = e0 je00 are the complex permeability and complex permittivity, respectively, d is the absorption layer thickness, and f is the frequency of incident wave. The dip in RL indicates the occurrence of absorption or minimal reflection of the microwave power [30]. The value of RL can be taken as a criterion of absorption properties, e.g., the RL values of 10 dB and 20 dB corresponds to 70% and 99% attenuation, respectively, which are acknowledge to be of practical significance. Fig. 3(a)–(c) shows the obtained relationship between the RL and the EM-wave frequency for the nanocapsules-paraffin samples with various thickness in the 2–18 GHz range by a simulation procedure. As shown in Fig. 3(a) and (b), an optimal RL of 40.96 dB, corresponding to 99.992% absorption, is observed at 9.2 GHz for 2.4 mm thickness layer. It is worth noting that the absorbent with a thickness of 1.6 mm has a RL value of 34.53 dB at 14.6 GHz, due to the dielectric resonance at 14.8 GHz. The intensity and the frequency at the reflection loss minimum depend on the properties and thickness of the materials [30]. Fig. 3(c) shows that the number dips increases with the sample thickness. There is only one shallow dip for the thickness of 1– 3 mm. Two and four complete dips can be observed for t = 4 and 10 mm, respectively. The occurrence of the dips is found to be due to a successive odd number multiple of the quarter wavelength thickness of the material or t = nl/4 (n = 1, 3, 5, 7, 9,. . .), where n = 1
Fig. 2. (a) Relative permittivity and (b) relative permeability of Al/AlOx-coated Ni nanocapsules-paraffin composite as a function of frequency.
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Fig. 3. (a) Two-dimensional representation of RL derived from the measured and of the Ni nanocapsules-paraffin composite as a function of frequency. (b) RL of the Ni nanocapsules-paraffin composite with the thickness range from 1.3 to 3.0 mm. (c) RL of the composite with the thickness range from 4.0 to 10.0 mm. (d) RL of the composites with the different thickness as the function of frequency for simulation and experiment.
corresponds to the first dip at low frequency [30]. The propagating rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wavelength in a material (lm) is expressed by lm ¼ l0 = eg mg where l0 is the free space wavelength. At that particular thickness, the incident and reflected waves in the material are out of phase 1808, resulting in total cancelation of the reflected waves at the airmaterial interface [30]. For t = 10 mm, it can be shown that the dips occur when the thickness equal to 1.2 (l/4), 3.1 (l/4), 5.1 (l/4) and 7.1 (l/4). Calculations performed on other thicknesses give similar results, but the location of each consecutive dip is shifted toward a higher frequency for a smaller value of t [30]. Fig. 3(d) shows the simulation and experimental results for Ni nanocapsules-paraffin composite with the thickness of 1.6 mm and 2.4 mm, respectively. Compared with the theoretical
predictions, the center frequencies of experimental results have shifted to a lower frequency, i.e., red shift, which is consistent with the previous reports [31,32]. In the view of the complexity of EM absorption, the theoretical results agree reasonably well with the experimental results in both the curve pattern and absolute values. The slight discrepancy between the simulated results and experimental ones can be caused by several factors, such as error in fabrication of specimens and measurement of permittivity and reflection loss [31]. More data information could be obtained from the dependence of minimum reflection loss RLm and corresponding frequency fm on thickness for treated composite, as shown in Fig. 4. It is obvious that the RLm shifts to a lower frequency with increasing thickness, and three minimal of RLm can be found, which is similar with the feature of Fe50Ni50 [33], high content barium ferrite [34]. As shown in Fig. 4, when thickness is in the range of 1.3–10.0 mm, minimum RL is <10 dB at the appropriate frequency of 2–15.6 GHz. And, the frequency of microwave absorption complies with the quarterwavelength (l/4) matching model. 4. Conclusion
Fig. 4. Dependence of minimum reflection loss RLm (dB) and corresponding frequency fm (GHz) on the thickness for the paraffin-nanocapsules composites with 40 wt.% Ni nanocapsules.
The Al/AlOx-coated Ni nanocapsules have been synthesized by the arc discharge method, which have the core–shell structure with Ni nanoparticles as cores and Al/AlOx as shells. The resonant frequencies of er in the current frequency range are 9.8 and 14.8 GHz, which may be attributed to interfacial polarization resonance due to the electronegativity difference between the Ni core and the Al/AlOx shell and to permanent electric dipoles resulting from defects in the Al/AlOx shell. The natural resonance in the Al/AlOx-coated Ni nanocapsules shifts to 6.4 GHz, due to the
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surface anisotropy of Ni nanoparticles. An optimal RL value of 40.96 dB was observed at 9.2 GHz on a specimen with a matching thickness of 2.40 mm. Compared with the theoretical predictions, the center frequencies of experimental results have shifted to a lower frequency. Theoretical simulation for the microwave absorption using the transmission line theory agrees reasonably well with the experimental results. The slight discrepancy between the simulated results and experimental ones can be caused by several factors, such as error in fabrication of specimens and measurement of permittivity and reflection loss. The frequency of microwave absorption complies with the quarter-wavelength matching model. Acknowledgement This study was supported by the National Natural Science Foundation of China (Grant Nos. 51201002, 51071001, 11204003 and 21071003), the Guangdong Natural Science Foundation (No. S2011040004468), the Research Grants Council of the HK SAR Government (PolyU 5236/12E), and The Hong Kong Polytechnic University (G-YK59, 4-ZZ7L, and G-YX3V). References [1] X.G. Liu, D.Y. Geng, H. Meng, P.J. Shang, Z.D. Zhang, Appl. Phys. Lett. 92 (2008) 173117. [2] X.G. Liu, J.J. Jiang, D.Y. Geng, B.Q. Li, Z. Han, W. Liu, Z.D. Zhang, Appl. Phys. Lett. 94 (2009) 053119. [3] J.R. Liu, M. Itoh, K.I. Machida, Appl. Phys. Lett. 83 (2003) 4017–4019. [4] X.F. Zhang, X.L. Dong, H. Huang, Y.Y. Liu, B. Lv, J.P. Lei, C.J. Choi, J. Phys. D: Appl. Phys. 40 (2007) 5383–5387. [5] L. Qiao, F.S. Wen, J.B. Wang, F.S. Li, J. Appl. Phys. 103 (2008) 063903. [6] M.S. Cao, X.L. Shi, X.Y. Fang, H.B. Jin, W. Zhou, Y.J. Chen, Appl. Phys. Lett. 91 (2007) 203110. [7] X.G. Liu, B. Li, D.Y. Geng, W.B. Cui, F. Yang, Z.G. Xie, D.J. Kang, Z.D. Zhang, Carbon 47 (2009) 470–474.
3891
[8] X.G.Liu,Z.Q.Ou,D.Y.Geng,Z.Han,J.J.Jiang,W.Liu,Z.D.Zhang,Carbon48(2010)891–897. [9] H. Wang, H.H. Guo, Y.Y. Dai, D.Y. Geng, Z. Han, D. Li, T. Yang, S. Ma, W. Liu, Z.D. Zhang, Appl. Phys. Lett. 101 (2012) 083116. [10] P. Lukanov, V.K. Anuganti, Y. Krupskaya, A.M. Galibert, B. Soula, C. Tilmaciu, A.H. Velders, R. Klingeler, B. Buchner, E. Flahaut, Adv. Funct. Mater. 21 (2011) 3583–3586. [11] R.C. Che, L.M. Peng, X.F. Duan, Q. Chen, X.L. Liang, Adv. Mater. 16 (2004) 401–404. [12] S. Sugimoto, T. Maeda, D. Book, T. Kagotani, K. Inomata, M. Homma, H. Ota, Y. Houjou, R. Sato, J. Alloys Compd. 330 (2002) 301–306. [13] X.G. Liu, D.Y. Geng, H. Meng, B. Li, Q. Zhang, D.J. Kang, Z.D. Zhang, J. Phys. D: Appl. Phys. 41 (2008) 175001. [14] K. Peng, L.P. Zhou, A.P. Hu, Y.H. Tang, D. Li, Mater. Chem. Phys. 111 (2008) 34–37. [15] X.L. Dong, X.F. Zhang, H. Huang, F. Zuo, Appl. Phys. Lett. 92 (2008) 013127. [16] F.S. Wen, H.B. Yi, L. Qiao, H. Zheng, D. Zhou, F.S. Li, Appl. Phys. Lett. 92 (2008) 042507. [17] D.Y. Geng, Z.D. Zhang, W.S. Zhang, P.Z. Si, X.G. Zhao, W. Liu, K.Y. Hu, Z.X. Jin, X.P. Song, Scripta Mater. 48 (2003) 593–598. [18] X.G. Liu, D.Y. Geng, C.J. Choi, J.C. Kim, Z.D. Zhang, J. Nanopart. Res. 11 (2009) 2097– 2104. [19] T. Inui, K. Konishi, K. Oda, IEEE Trans. Magn. 35 (1999) 3148–3150. [20] B.C. Wang, J.Q. Wei, Y. Yang, T. Wang, F.S. Li, J. Magn. Magn. Mater. 323 (2011) 1101–1103. [21] X.G. Liu, D.Y. Geng, X.L. Wang, S. Ma, H. Wang, D. Li, B.Q. Li, W. Liu, Z.D. Zhang, Chem. Commun. 46 (2010) 6956–6958. [22] Y.W. Yun, S.W. Kim, G.Y. Kim, Y.B. Kim, Y.C. Yun, K.S. Lee, J. Electrochem. 17 (2006) 467–471. [23] G. Ertl, R. Hierl, H. Knozinger, N. Thiele, H.P. Urbach, Appl. Surf. Sci. 5 (1980) 49–52. [24] A.K. Dua, V.C. George, R.P. Agarwala, Thin Solid Films 165 (1988) 163–167. [25] J.A. Taylor, J. Vac. Sci. Technol. 20 (1982) 751–755. [26] T. Kendelewicz, W.G. Petro, J.A. Silberman, I. Lindau, W.E. Spicer, J. Vac. Sci. Technol. B 1 (1983) 623–626. [27] Z.H. Wang, Z. Han, D.Y. Geng, Z.D. Zhang, Chem. Phys. Lett. 489 (2010) 187–190. [28] C. Kittel, Phys. Rev. 73 (1948) 155–161. [29] L.L. Diandra, D.R. Reuben, Chem. Mater. 8 (1996) 1770–1783. [30] A.N. Yusoff, M.H. Abdullah, S.H. Ahmad, S.F. Jusoh, A.A. Mansor, S.A.A. Hamid, J. Appl. Phys. 92 (2002) 876–882. [31] K.Y. Park, S.E. Lee, C.G. Kim, J.H. Han, Comp. Sci. Tech. 66 (2006) 576–584. [32] Z.F. Liu, G. Bai, Y. Huang, F.F. Li, Y.F. Ma, T.Y. Guo, X.B. He, X. Lin, H.J. Gao, Y.S. Chen, J. Phys. Chem. C 111 (2007) 13696–13700. [33] J.Q. Wei, Z.Q. Zhang, B.C. Wang, T. Wang, F.S. Li, J. Appl. Phys. 108 (2010) 123908. [34] Z.W. Li, G.Q. Lin, L.B. Kong, IEEE Trans. Magn. 44 (2008) 2255–2261.