Experimental realization of tunable negative permittivity in percolative Fe₇₈Si₉B₁₃/epoxy composites

Abstract

Negative permittivity is one of the most important properties in the realization of double negative medium or negative index materials. In this paper, tunable negative permittivity in the radio frequency range has been obtained in composites with Fe₇₈Si₉B₁₃ amorphous alloy dispersed in an epoxy matrix. The microstructure and dielectric properties of Fe₇₈Si₉B₁₃/epoxy composites are investigated in detail. The results indicate that when the Fe₇₈Si₉B₁₃ content is beyond the percolation threshold, the plasma oscillation of delocalized electrons in interconnected Fe₇₈Si₉B₁₃ leads to negative permittivity. By controlling the effective concentration of free electrons, the negative permittivity of the Fe₇₈Si₉B₁₃/epoxy composites could be easily adjusted. Additionally, the frequency dispersion behaviors of the conductivity conform to the Jonscher's power law below percolation threshold, demonstrating that the conductive mechanism is hopping conduction. The realization of tunable negative permittivity in Fe₇₈Si₉B₁₃/epoxy composites gives a new and high-efficient way toward double negative materials.

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Introduction

In the past decade, double negative materials (DNMs) with simultaneously negative permittivity ε and permeability μ have gained extensive research attention due to their novel potential applications in electronic, microwave and optical fields.^1–3 The medium which had a negative refractive index was first proposed by Veselago theoretically in 1967.⁴ His finding remained an academic curiosity for a long time until 2001, the double negative property was successfully obtained in an artificial periodic metallic structure with arrays of split-ring resonators and wires by Smith et al.⁵ Soon afterwards, various metamaterials composed of arrays of unit cells with various novel structures were proposed to achieve negative permittivity and permeability.^6,7

It is well recognized that the double negative properties in metamaterials are originated by their special artificial structures, such as nonmagnetic split ring resonators and continuous wires,⁵ lithographically patterned inductive–capacitive resonator double-split-ring resonators,⁸ S-shaped resonators,⁹ rather than directly by the materials' nature. In all the artificial structures mentioned above, resonance was considered to be the main mechanism of the realization of the double negative property.¹⁰ In fact, it is also interesting to investigate the possibility of realizing the double negative property directly from the materials' intrinsic properties, rather than from periodic artificial structures. In our previous works, we successfully realized negative permittivity and permeability by using metal/ceramic composites with the construction of the random metallic networks hosted in ceramics, such as Ag/Al₂O₃, Ni/Al₂O₃.^11–13 And soon after, the random composites for DNMs have attracted much attention and many percolative granular composites have been considered as DNMs by T. Tsutaoka et al.^14,15 As conductor/insulator composites, the appearance of negative permittivity is the result of the plasma oscillation of conduction electrons provided by the metallic component occurred beyond but near percolation threshold. And the plasma frequency is determined by effective concentration of electrons. Insulating polymers like epoxy can also be the matrix as a substitute for ceramic on condition that the effective concentration of electrons is under control. The attractive properties of epoxy such as light-weight, chemical inertness, large-scale and machinability could be utilized for realizing truly practical applications which are not fully realized by ceramic materials.¹⁶

Cryomilling is a mechanical attrition technique in which powders are milled with milling balls and a cryogenic liquid.¹⁷ It is well known that, as a conventional technique to prepare fine powder mixtures, room temperature ball milling is not appropriate for the preparation of fine powders containing ductile metal component. Even over, the high energy release during ball milling may result in the reaction of the powders. Cryogenic temperature will embrittle the metal and restrain the mechanochemical reaction of original powders.¹⁸

In this paper, Fe₇₈Si₉B₁₃/epoxy composites with different Fe₇₈Si₉B₁₃ content have been fabricated by using cryomilling combined with hot press forming. The microstructure and electromagnetic properties of the Fe₇₈Si₉B₁₃/epoxy composites are investigated. Interestingly, negative permittivity appeared in the composites when Fe₇₈Si₉B₁₃ contents reach percolation threshold.

Experimental

In this paper, a commercially available Fe₇₈Si₉B₁₃ powder was chosen to be electric component of the composites. For the homogenously dispersion of Fe₇₈Si₉B₁₃ powder in epoxy, powders were cryomilled 20 r s⁻¹ at liquid nitrogen temperature (−196 °C) for 5 min. Then the powder mixtures with Fe₇₈Si₉B₁₃ volume fraction of 71%, 76%, 78%, and 83% were hot-pressed at 80 °C and 35 MPa to form the final round-shape samples with 22 mm in diameter and around 2 mm thick, and the Fe₇₈Si₉B₁₃/epoxy composites were referred to as FSB71, FSB76, FSB78 and FSB83, respectively.

The cryomilling was carried out by a cryomill (Retsch, Germany). The microstructure of bulks was investigated by X-ray diffraction (XRD) and SU-70 field emission scanning electron microscopy (FESEM). The impedance properties of the bulk Fe₇₈Si₉B₁₃/epoxy composites were determined in the frequency range from 10 MHz to 1 GHz at room temperature, by using Agilent E4991A precision impedance analyzer (Agilent Technologies) equipped with 16453A dielectric test fixture. In order to determine the permittivity vs. frequency or various kinds of dielectric parameters, the dielectric test was under AC voltage 100 mV. During the measurement, the real part (ε^′_r) and imaginary part (ε^′′_r) of permittivity were then determined from the following formula,

where, d is the sample thickness, C is the capacitance, R is the resistance, A is the electrode plate area, f is the frequency and ε₀ is the absolute permittivity of free space (8.85 × 10⁻¹² F m⁻¹).

Results and discussion

Fig. 1 shows the XRD patterns of the Fe₇₈Si₉B₁₃ powder and Fe₇₈Si₉B₁₃/epoxy composite. Two broad diffraction peaks reflecting amorphous structure were detected in the XRD patterns of every composite.¹⁹

Fig. 1 (a) X-ray diffraction patterns of Fe₇₈Si₉B₁₃ powder and (b) is the X-ray diffraction patterns of Fe₇₈Si₉B₁₃/epoxy composite with different Fe₇₈Si₉B₁₃ contents.

The SEM images of Fe₇₈Si₉B₁₃/epoxy composites (FSB71 and FSB83) are shown in Fig. 2. It can be observed that the Fe₇₈Si₉B₁₃ distributed uniformly within the resin matrix cryomilled just 5 min (Fig. 2(a) and (c)). In addition the Fe₇₈Si₉B₁₃ combined with resin closely (Fig. 2(b) and (d)).

Fig. 2 SEM images of Fe₇₈Si₉B₁₃/epoxy composite of different Fe₇₈Si₉B₁₃ contents (a and b) FSB71 (c and d) FSB83.

The dielectric spectra of Fe₇₈Si₉B₁₃/epoxy composite with different Fe₇₈Si₉B₁₃ contents are presented in Fig. 3. For samples FSB71 and FSB76, the real part of permittivity ε^′_r is positive and decreases as the frequency vary from 10 MHz to 1 GHz. Further increasing the Fe₇₈Si₉B₁₃ content result in the appearance of negative ε^′_r throughout the whole test frequency range in FSB78 and FSB83.

Fig. 3 Dielectric spectra of Fe₇₈Si₉B₁₃/epoxy composite (a) the real permittivity (the dielectric dispersion can be fitted by Drude model for FSB78 and FSB83), (b) the imaginary permittivity.

Theoretically, the negative permittivity for composites is realized by the plasma oscillation of the delocalized electrons when the conductive phase beyond percolation threshold. As composites of FSB78 and FSB83 are beyond percolation threshold, which is further supported by the conductivity, exhibiting an abrupt increase (shown in Fig. 4). Therefore, the plasma-like negative permittivity for FSB78 and FSB83 samples appeared, and as shown in Fig. 3(a) with the solid lines, the negative behavior can be fitted well by the Drude model,

where ω_p (ω_p = 2πf_p) is the angular plasma frequency, ω = 2πf is the angular frequency of the applied electromagnetic field, ω_τ is the damping parameter, ω₀ is permittivity of vacuum. n_eff is the effective concentration of conduction electrons, m_eff is the effective weight of electron, and e is electron charge (1.6 × 10⁻¹⁹ C). And the fitted results of the f_p by Drude model are 8.09 GHz (FSB78) and 12.82 GHz (FSB83), while the fitted results of the ω_τ are 0.48 GHz (FSB78) and 0.38 GHz (FSB83).

Fig. 4 Frequency dependence of ac conductivity σ^′_ac for Fe₇₈Si₉B₁₃/epoxy composite The solid lines are σ^′_ac of FSB71 and FSB76 fitted by the Jonscher power law in the form of σ^′_ac(f) ∝ (2πf)ⁿ, characterizing hopping conduction behavior.

While for FSB71 and FSB76, the electrons are localized for the metallic region isolated by epoxy. Thus the dielectric constant is positive. The similar behavior for nanopolyaniline/epoxy composites²⁰ and Fe/Al₂O₃ composites were also observed.²¹ Besides, the Im(ε_r), which indicates the losses of Fe₇₈Si₉B₁₃/epoxy composites, increases with increasing Fe₇₈Si₉B₁₃ content, as shown in Fig. 3(b). The origin of the losses in Fe₇₈Si₉B₁₃/epoxy composites is complicated, including eddy current losses, dielectric losses, and ohmic losses.

The frequency dispersions of the real part of ac conductivity at frequency range from 10 MHz to 1 GHz are shown in Fig. 4. It was determined by the formula of σ^′_ac = d/RA, where d is the sample thickness and R is the resistance, A is the electrode plate area. As shown in Fig. 4, the increasing of the Fe₇₈Si₉B₁₃ content results in the improvement of conductivity. It also can be found that the frequency dispersion behavior of the conductivity within a certain range of frequency, represents the Jonscher power law²² in the form of σ^′_ac(f) ∝ (2πf)ⁿ with a different power-law index of n. The σ^′_ac(f) exhibits a characteristic of plateau in the low-frequency region and a frequency dispersion in the high-frequency region with an onset frequency. The value of the exponent n for FSB71 and FSB76 is 0.39 and 0.20 respectively, shows that the conductive mechanism is hopping conduction.²³ That is electrons implement macroscopic conductivity via hopping between adjacent Fe₇₈Si₉B₁₃ under the effect of high frequency electric field.

For FSB78 and FSB83, the σ^′_ac decreases with increasing frequency due to the skin effect of conduction electrons, which is similar to the free electron conduction.

Conclusions

In conclusion, Fe₇₈Si₉B₁₃/epoxy composites with different Fe₇₈Si₉B₁₃ content were prepared by cryomilling. Broad diffraction peaks reflecting amorphous structure are detected in the XRD patterns. The SEM results show that Fe₇₈Si₉B₁₃ distributed uniformly and closely to the resin matrix. The frequency dispersion behaviors of the conductivity within a certain range of frequency are accord with the Jonscher power law, indicating that the conductive mechanism of the composite is hopping conduction. When the Fe₇₈Si₉B₁₃ content exceeds the percolation threshold, the plasma oscillation of delocalized electrons leads to negative permittivity which was fitted well by Drude model.

Acknowledgements

The authors acknowledge the supports of National Natural Science Foundation of China (51172131).

Notes and references

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