Percolative cobalt/silicon nitride composites with tunable negative electromagnetic parameters

Abstract

In this paper, the relationship between the microstructures and electromagnetic properties of cobalt/silicon nitride (Co/Si₃N₄) composites synthesized by an impregnation–calcination process are discussed. The enhanced interconnectivity of cobalt particles led to the appearance of percolation phenomenon and the change of conductive mechanism from hopping conduction to metal-like conduction. The composites above percolation threshold exhibited the negative permittivity and negative permeability behavior, which were mainly ascribed to the plasma oscillation of free electrons and the diamagnetic responses of conductive cobalt network, respectively. The frequency region and magnitude of such negative electromagnetic parameters closely associated with the cobalt content. When the cobalt content reached 35 wt%, simultaneous negative permittivity and negative permeability were realized in the frequency range from 550 MHz to 1 GHz. The experimental exploration of Co/Si₃N₄ composites by tailoring compositions and microstructures has great significance on the development of tunable negative electromagnetic parameter materials.

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1. Introduction

Negative electromagnetic parameter materials (NEPMs) with negative permittivity or/and permeability have received great attention due to their unprecedented electromagnetic properties and exciting applications, such as negative refraction, superlens, optical cloaking, antennas and microwave absorbing and shielding.^1–6 Until now, the study of NEPMs focused on two kinds of materials: the “artificial” metamaterials (AMs) and “natural” materials (NMs). For AMs, the negative electromagnetic parameters mainly originate from electrical or magnetic resonant response in the periodic metallic structures, and closely associated with shape, size and spacing of periodic structures, rather than being inherent in the material.^7–11 In addition, anisotropic electromagnetic properties and complex preparation of periodic structures are still obstacles to hamper many of their practical applications.^9,12,13 Therefore, due to the above reasons, the considerable efforts were directed towards the study of the realization and controlling of negative parameters in NMs by adjusting their compositions and microstructures.^14–19

Fortunately, the negative electromagnetic parameters were achieved in NMs consisting of conductive, magnetic or dielectric component at recent years.^20–27 The theoretical analysis indicates that the negative permittivity is attributed to the dielectric resonance or plasma oscillation of free electrons in conductive component and the negative permeability is achieved by magnetic resonances and diamagnetic behavior.^20,28 However, the further investigations focusing on attaining tunable negative electromagnetic parameters for NMs still should be carried out in order to satisfy diverse application requirements. For instance, tunable frequency band of negative parameter is desired in a broad pass-band filter to make ensuring its multi-frequency operations.^29,30

In this work, the cobalt particles were incorporated into the porous Si₃N₄ matrix by wet chemical method at low temperature (500 °C). The Si₃N₄ ceramic is herein selected as the structure matrix due to its low density, high mechanical strength, good thermal shock resistance, excellent thermal–chemical corrosion resistance and low permittivity.³¹ The Si₃N₄ matrix not only act as a matrix to support the Co particles, but also will avoid the Co particles be oxidized into Co oxides. The impregnation–calcination process is potentially superior as it can effectively avoid the unexpected deleterious reactions between Co and Si₃N₄,^32,33 and easily tailor the Co/Si₃N₄ composites' composition and microstructure to control their electromagnetic properties. Interestingly, the composites demonstrated tunable negative electromagnetic parameters in the frequency range from 10 MHz to 1 GHz. For the composites with cobalt content of 35 wt%, simultaneous negative permittivity and negative permeability were realized in the frequency range from 550 MHz to 1 GHz.

2. Experimental

2.1. Materials

High-purity Si₃N₄ powders (α-Si₃N₄ > 93 wt%, shown in Fig. 1) with average diameter of 0.5 μm were purchased from Beiing Tsinghua Unisplendor Founder High-Tech Ceramics Co. Ltd., China. Yttrium oxide (Y₂O₃, purity > 99.9 wt%) powders were supplied by Changzhou Zhuoqun nanotechnology and new materials Co., Ltd. China. Cobalt nitrate (Co(NO₃)₂, AR) powders were supplied by Sinopharm Chemical Reagent Co., Ltd., Beijing, China.

Fig. 1 The SEM image of starting Si₃N₄ power.

2.2. Sample preparation

The porous Si₃N₄ ceramics with the apparent porosity of ∼40% were fabricated by pressureless sintering under flowing nitrogen-gas. The mixtures of Si₃N₄ and 9 wt% Y₂O₃ powder were ball-milled in ethanol for 24 h using high-purity Si₃N₄ grinding media. After drying, the resulting mixtures were sifted and cold isostatic pressed at 40 MPa. Then, the green bodies were sintered at 1690 °C for 2 h in nitrogen atmosphere. The obtained Si₃N₄ ceramics were cut into annular discs (inner diameter b, outer diameter c and height h were 7, 19, and 2 mm, respectively) and square discs (22 mm × 10 mm × 2 mm).

For the preparation of Co/Si₃N₄ composites, the Si₃N₄ discs were soaked in the 1.5 mol L⁻¹ Co(NO₃)₂ ethanol solution for 30 min under a vacuum environment. The impregnated discs were dried in an oven at 80 °C for 2 h, and calcined at 400 °C for 30 min in air. Then the as-achieved discs were reduced at 500 °C for 2 h in hydrogen atmosphere to get the Co/Si₃N₄ composites. After repeating impregnation–calcination process, the composites with cobalt content of 8 wt% (1.7 vol%), 13 wt% (3.2 vol%), 20 wt% (5.4 vol%), 27 wt% (8.0 vol%) and 35 wt% (11.6 vol%) were prepared, and referred to as Co8, Co13, Co20, Co27 and Co35, respectively.

2.3. Characterization

X-ray diffractometer (XRD) patterns of the Co/Si₃N₄ composites were obtained over 2θ range of 10–80° at a scanning speed of 8° min⁻¹ using Rigaku Dmax-rc diffractometer (Tokyo, Japan) with CuKα radiation. A field emission scanning electron microscope (FESEM) (Hitachi SU-70, Tokyo, Japan) was employed to observe the fracture surface morphologies of Co/Si₃N₄ composites. The electromagnetic properties of the Co/Si₃N₄ composites were characterized by using Agilent E4991A Precision Impedance Analyzer at room temperature. The alternating current conductivity (σ_ac), reactance (Z′′) and complex permittivity (ε′ and ε′′) were measured using the dielectric test fixture of 16453A under ac voltage 100 mV. The parameters of complex permittivity and the real part of ac conductivity were determined by the following formula:¹⁷where d is the sample thickness, C is the capacitance, A is the electrode plate area, R is resistances, ε₀ is the absolute permittivity of free space (8.85 × 10⁻¹² F m⁻¹), and f is the frequency. The 16454A test fixture was used to measure the complex permeability μ*, under ac current of 100 mA. The permeability μ* was calculated by the following formula:²¹where L and L₀ are the self-inductance of the test fixture with and without sample mounted, Z* is the complex impendence of test fixture with sample mounted, ω is the angular frequency, μ₀ is the permeability of free space (4π × 10⁻⁷ N A⁻²), b, c and h are the inner diameter, outer diameter and thickness of the sample.

3. Results and discussion

3.1. Phase and microstructure characterization

The XRD patterns of the Co/Si₃N₄ composites are shown in Fig. 2. It is shown that, all of the composites are composed of β-Si₃N₄, Co, α-Si₃N₄ and Si₂N₂O, indicating that the low-temperature preparation process can avoid deleterious reactions between cobalt and silicon nitride. The intensity of cobalt peaks increases in the composites with increasing cobalt content.

Fig. 2 The XRD patterns of Co/Si₃N₄ composites with different cobalt contents.

Fig. 3 shows the FESEM images of composites with different cobalt contents. We can see that the cobalt particles randomly distributed in porous Si₃N₄ matrixes, and the cobalt particle size was gradually enlarged with the increase of cobalt content, leading to the interconnection of the particles and the formation of cobalt networks.

Fig. 3 FESEM images of Co/Si₃N₄ composites with different cobalt contents: (a) Co8, (b) Co13, (c) Co27 and (d) Co35.

3.2. Conduction behavior and reactance

Frequency dependences of ac conductivity (σ_ac) for composites with different cobalt contents are shown in Fig. 4. We can see that σ_ac increases with increasing metal content. The frequency dispersion characteristic of σ_ac for Co8 sample differs from the other samples', indicating that a percolation behavior appears because of the formation of conductive networks in the composites, and the percolation threshold is between 8 wt% (1.7 vol%) and 13 wt% (3.2 vol%). The σ_ac spectrum of the Co8 sample has a direct current (dc) conductivity (σ_dc) plateau in the low frequency region and exhibits conductivity dispersions at the higher frequencies. The high frequency part of σ_ac–f relationship obeys the formula σ_ac ∝ (2πf)ⁿ (0 < n < 1), indicating a hopping conduction behavior.³⁴ In the composites above the percolation threshold, the formation of continuous conductive pathways (shown in Fig. 5) for facilitating electron transfer leads to the conductive mechanism changing from hopping conduction to metal-like conduction, and the σ_ac decreases with increasing the frequency due to skin effects.

Fig. 4 Frequency dependences of ac conductivity for composites with different cobalt contents.

Fig. 5 The SEM and EDX-mapping images of Co35 sample. The red part is cobalt conductive pathways and the green part is Si₃N₄ matrix.

Fig. 6 shows frequency dependence of reactances (Z′′) for the composites with different cobalt contents. In external electric field, the composites can be simulated by a circuit with electronic elements, resistance R, capacitance C and inductor L.³⁵ The reactance of Co8 sample is negative (Z′′ < 0) in the whole test frequency range, meaning a lag of the voltage phase behind the current phase. Hence the composites are regarded as the combinations of resistor R and capacitor C, manifesting a capacitive behavior.³⁶ For the Co35 sample, the current loops are induced under the action of high frequency electric field due to the formation of conductive network, so the inductor L is introduced into the composite, leading to an inductive character (Z′′ > 0). There is a shift for Z′′ from positive to negative in Co13, Co20 and Co27 samples (inset of Fig. 6), which indicates that an inductive–capacitive transition appears with increasing the frequency. The similar transition is also observed in the metal–alumina composites.^22,23,27

Fig. 6 Frequency dependence of reactances for the composites with different cobalt contents.

3.3. Dielectric property

The frequency dispersions of permittivity (ε′ and ε′′) for the composites with different cobalt contents are presented in Fig. 7.

Fig. 7 Frequency dependence of permittivity for Co/Si₃N₄ composites with different cobalt contents.

As shown in Fig. 7a, the ε′ of Co8 sample is positive in the whole test frequency band. For the composites Co13, Co20 and Co27, the negative ε′ is obtained at the low frequencies, which results from the plasma oscillation of free electrons in cobalt networks,^22,25 and a shift for ε′ from negative to positive is observed (inset of Fig. 7a). As can be noted, those switching frequencies correspond well to the frequency points of the positive–negative transitions for Z′′ (Fig. 4a). As discussed above, these composites beyond percolation threshold can be equivalent to the circuit consisting of resistance R, inductance L and capacitance C, so LC resonances will take place when Z′′ becomes zero.²⁶ When the cobalt content increases from 13 wt% to 27 wt%, the inductance L increases because of enhanced interconnectivity of cobalt particles, and the capacitance C also gets larger due to the increase of cobalt–silicon nitride interface, so the LC resonance frequency (f = 1/[2π(LC)^1/2]) moves to the lower frequency (from 400 MHz to 160 MHz). When the cobalt content is further increased to 35 wt%, the negative ε′ is observed in the entire frequency region. This plasma-like negative permittivity behavior is well described by the Drude model:³⁷

where ω_P (ω_P = 2πf_P) is the angular plasma frequency, ω (ω = 2πf) is the angular frequency of the electric field, ω_τ (ω_τ = 2πf_τ) is the collision frequency, ε₀ is the permittivity of a vacuum (8.85 × 10⁻¹² F m⁻¹), n_eff is the effective concentration of delocalized electrons, m_eff is the effective weight of an electron, and e is the electron charge (1.6 × 10⁻¹⁹ C). The fitted ε′–f curve using the Drude model (solid line in Fig. 7a), is in agreement with the experimental data of Co35 sample, suggesting the effective f_P is 3.8 GHz. The ε′′ (Fig. 7b) increases with higher Co content owing to the increase of polarization loss and leakage conductance loss.¹⁶ As mentioned above, the negative permittivity region is closely related to the cobalt content, and tunable negative permittivity property can be achieved by adjusting the composites' composition and microstructures.

3.4. Magnetic property

Fig. 8 shows frequency dependence of permeability (μ′ and μ′′) for Co/Si₃N₄ composites with different cobalt contents. As shown in Fig. 8a, we can find that the μ′ spectrum of Co8 sample shows small frequency dispersion in the measurement frequency range, but for the other samples, the μ′ markedly decreases with the frequency increasing, then to the negative at the high frequency (above 550 MHz). During the permeability measurements, large quantities of current loops are induced in the composites above percolation threshold under high-frequency electromagnetic field, so an extra electromagnetic field derived from current loops resists external electromagnetic field,³⁸ leading to the decrease of μ′. Meanwhile, the magnetic resonance (the domain wall motion and gyromagnetic spin rotation) of ferromagnetic cobalt particles can also contribute to the decrease of μ′, and the domain wall motion generally makes greater contribution to the decrease of μ′ than that of gyromagnetic spin rotation at relatively low frequency.^17,23,38,39 Hence, the occurrence of negative μ′ behavior should result from the effect of diamagnetic responses and magnetic resonances. With increasing cobalt content, the diamagnetic response and magnetic resonance will be enhanced due to the improvement of metallic network and the increase of cobalt particle size, respectively.^23,40,41 This indicates that the composite with higher cobalt content has the lower μ′ and broader negative μ′ region (inset of Fig. 8a). As shown in Fig. 8b, the magnetic loss peaks corresponding to the rapid decrease of μ′ with frequency are observed in Co13 and Co20 samples. For the Co27 and Co35 samples, the stronger diamagnetic responses will lead to the fast decrease of μ′ at lower frequencies, so the magnetic loss peaks will appear at lower frequencies, which are exceeding the tested frequency range.⁴²

Fig. 8 Frequency dependence of permeability for Co/Si₃N₄ composites with different cobalt contents.

4. Conclusions

In this work, the cobalt particles were loaded into the porous Si₃N₄ matrix by a facile impregnation–calcination process at low temperature. Near the percolation threshold (between 1.7 vol% and 3.2 vol%), the conductive mechanism of composites varied from hopping conduction to metal-like conduction due to the formation of conductive cobalt networks. In the composites above the percolation threshold, the plasma oscillation of conduction electrons in cobalt network leads to the negative permittivity, and the negative permeability is mainly attributed to the diamagnetic responses of conductive cobalt network. The frequency regions and magnitudes of such negative electromagnetic parameters are found to be highly dependent on the cobalt content. For the composites with cobalt content of 35 wt%, double negative properties are realized in the frequency range from 550 MHz to 1 GHz. The realization of tunable negative parameters for the Co/Si₃N₄ composites determines their potential applications in antennas, electromagnetic shielding and band-pass filter.

Acknowledgements

Zi-dong Zhang and Chuan-bing Cheng, these authors contributed equally to this work and should be considered co-first authors. The authors acknowledge the supports of National Natural Science Foundation of China (Grant No. 51172131), Natural Science Foundation of Shandong Province (BS2015CL020), China Postdoctoral Science Foundation (2014M561925), and the Fundamental Research Funds of Shandong University (FRFSDU-2014GN002).

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Footnote

† These authors contributed equally to this work.

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