Temperature coefficient of permittivity and loss tangent at selected frequency (reprinted with permission from Ref. [39]).
Abstract
High-temperature microwave-absorbing materials are in great demand in military and aerospace vehicles. The high-temperature dielectric behavior of multilayer Cf/Si3N4 composites fabricated by gelcasting has been intensively investigated at temperature coverage up to 800°C in the X-band (8.2–12.4 GHz). Experimental results show that the permittivity of Si3N4 matrix exhibits excellent thermo-stability with temperature coefficient lower than 10−3°C−1. Taking temperature-dependent polarized bound charge and damping coefficient into consideration, a revised dielectric relaxation model with Lorentz correction for Si3N4 ceramics has been established and validated by experimental results. Besides, a general model with respect to permittivity as a function of temperature and frequency has been established with the help of nonlinear numerical analysis to reveal mechanisms of temperature-dependent dielectric responses in Cf/Si3N4 composites. Temperature-dependent permittivity has been demonstrated to be well distributed on circular arcs with centers actually kept around the real ( ε ′ ) axis in the Cole-Cole plane. Furthermore, space charge polarization and relaxation are discussed. These findings point to important guidelines to reveal the mechanism of dielectric behavior for carbon fiber functionalized composites including but not limited to Cf/Si3N4 composites at high temperatures, and pave the way for the development of high-temperature radar absorbing materials.
Keywords
- high temperature
- microwave-absorbing material
- dielectric
- relaxation
1. Introduction
Wireless electronic devices and communication instruments have found wide application in our daily life. Their efficient operation depends strongly on transmission behavior of alternating electromagnetic wave with frequency ranging from kilohertz (KHz) to gigahertz (GHz), and vice versa, are very sensitive to interference from external electromagnetic wave. Driven by the demand for both adequate interference rejection and controlled radiation, more and more efforts have been devoted to high-performance electromagnetic compatibility/interference (EMC/EMI) materials. As we all know, the propagation behavior of electromagnetic wave when encountering a material could be divided into three types in principle: reflection, absorption, and transmission. As typical EMI materials, metals or materials with high electrical conductivity could prevent external electromagnetic wave from penetration due to the large amount of free electrons. Last decades have witnessed intensive efforts toward exploring lightweight and cost-effective electromagnetic interference (EMI) materials with adequate shielding effectiveness [1, 2, 3, 4, 5], involving carbonaceous fillers-enabled polymers, novel lightweight metal composites, etc.
However, the primary function of EMI shielding is to reflect radiation using charge carriers that interact directly with incident electromagnetic field, and the back-radiation would in turn affect the surrounding environment and devices. What is more, the reflected radiation may also be caught by radar observation systems and lead to exposure of moving trace, which is extremely undesirable from the defense-oriented point of view. As a result, electromagnetic wave-absorbing materials with reduced reflection on the surface as well as enhanced internal attenuation are more favorable candidates for EMI shielding, especially in the GHz range. Polymers modified by carbon nanomaterials (e.g., carbon nanotubes [6, 7, 8], carbon nanofibers [9, 10], graphene [11, 12], etc.), metal powders [13, 14], and ferrite [15] have been demonstrated to be excellent microwave-absorbing/shielding materials especially in the X-band (8.2–12.4 GHz) [16, 17], and have achieved successful application [18, 19, 20]. However, due to their inferior temperature stability and mechanical properties, their application is limited toward application under high temperature. For example, the temperature on the windward side of high-speed aircraft (>3 Ma) could reach up to 1000°C due to the aerodynamic heating effect. As a result, ceramics and their derivative architecture (r-GOs/SiO2, CNT/SiO2, ZnO/ZrSiO4, SiC
In this chapter, we mainly focus on the microwave dielectric responses in laminate-structure or multilayer-structure C
2. Experiments
2.1 Preparation of multilayer Cf /Si3N4 composites
Commercially available carbon fibers (T700, 12 K, TohoTenax Inc., Japan) were used as starting materials in this work. In order to avoid damage at high-temperature sintering, pyrolytic carbon(PyC)/SiC dual-coating on carbon fibers was prepared by chemical vapor deposition based on Methyltrichlorosilane (MTS)-H2-Ar system at 1150°C. The powder mixture of 85 wt% α-Si3N4 (purity > 93%, d50 = 0.5 μm, Beijing Unisplendor Founder High Technology Ceramics Co. Ltd., China), 5 wt% Al2O3, and 10 wt% Y2O3 was mixed with solvent-based acrylamide-N,N′-methylenebisacrylamide (AM-MBAM) system, and consolidated via gelcasting and pressureless-sintering route (as illustrated in Figure 1). Details of the multilayer C
2.2 High-temperature electromagnetic measurements
In order to evaluate the high-temperature permittivity, specimens with the size of 22.86 × 10.16 × 1.5 mm3 were polished and determined in X-band through the wave-guide method with a vector network analyzer (Agilent N5230A, USA). As shown in Figure 2, the as-prepared Si3N4 ceramic sample was heated by an inner heater with a ramp rate of 10°C/min up to 800°C in air. For accuracy of measurement, the device was carefully calibrated with the through-reflect-line (TRL) approach, and a period of 10 min was applied to guarantee system stability at each evaluated temperature.
3. Microwave dielectric properties
3.1 Structure of multilayer Cf /Si3N4 composites
The optical image of cross-section of multilayer C
3.2 Room-temperature dielectric properties of multilayer Cf /Si3N4 composites
According to the classical transmission line theory, microwave complex permittivity (
However, both the real permittivity and imaginary permittivity of C
and
where
The enhanced microwave-absorbing performance could be mainly attributed to polarization relaxation. As we know, there exists migration of free electrons inside the electro-conductive carbon fibers, as well as charge accumulation at interfaces between short carbon fibers and insulated matrix when subjected to external electric field. As a result, the chopped carbon fibers are more inclined to be equivalent to micro-dipoles. With increase of frequency, the orientation of these dipoles could not keep up with change of electric field gradually, resulting in the real part of permittivity (
For a deep-seated investigation of frequency-dependent dielectric responses of multilayer C
According to the circuit theory knowledge, the relationship between permittivity and frequency
where
3.3 High-temperature dielectric behaviors of Si3N4 ceramics
Due to the fact that there will inevitably be some variation of electromagnetic performance or even the mechanical property of materials served in high-temperature condition, the dielectric property would be supposed to dynamically change with temperature. How and to what extent does the permittivity dynamically change with temperature (increase or decrease)? All these are quite critical in parameter modification strategy for improving the accuracy of radar detection and guidance. Consequently, it is of utmost importance to explore the evolution of dielectric properties of Si3N4 ceramics used in high-temperature circumstances. Three-dimensional (3D) plots of the effect of temperature on permittivity of Si3N4 ceramics over X-band are shown in Figure 8. Clearly, the real permittivity (
Herein, temperature coefficient
where
Temperature (°C) |
|
|
||
---|---|---|---|---|
8.2 GHz | 12.4 GHz | 8.2 GHz | 12.4 GHz | |
25 | 0.46 | 0.45 | 2.08 | 2.84 |
100 | 0.22 | 0.93 | 1.79 | 3.11 |
200 | 0.45 | 0.031 | 2.83 | 4.83 |
300 | 1.04 | 1.02 | 3.02 | 3.91 |
400 | 0.16 | 1.31 | 2.87 | 4.89 |
500 | 0.40 | 1.11 | 4.98 | 6.92 |
600 | 0.97 | 1.70 | 4.68 | 5.97 |
700 | 1.16 | 1.94 | 3.49 | 4.34 |
It should be noted that the real permittivity increases slightly with frequency increase, which is contrary to the ordinary frequency dispersion effect described by the Debye model [49, 50, 51, 52, 53, 54, 55]. In order to further expound this peculiar frequency dispersion characteristic, it is essential to explore the details of electronic polarizing processing of Si3N4 ceramics. Considering the covalent bonding, the electronic polarization in Si3N4 ceramics mainly results from the bound charge’s displacement deviated from the equilibrium position. The motion equation of bound charge driven by an external electric field
where
where
where
It can be clearly seen that the dielectric constant gradually increases as temperature increased, starting from room temperature to 800°C, and results show that the real permittivity is well distributed on the predicted curves with coefficient of determination (
3.4 High-temperature dielectric behaviors of multilayer Cf /Si3N4 composites
The evolution of
It should also be noted here that the lattice vibration also enhances with temperature rise, corresponding to the enhancement of scattering effect on migration of electrons. Fortunately, the energy of lattice vibration, which is described by phonons, is so small [68] that the scattering effect on electron migration could be neglected reasonably.
Attenuation coefficient is a quantity that characterizes how easily a material can be penetrated by incident microwave. A large attenuation coefficient means that the beam is quickly “attenuated” (weakened) as it passes through the material. The intrinsic attenuation coefficient of multilayer C
3.5 Modeling of temperature-dependent dielectric responses for Cf /Si3N4 composites
As explicated in Section 3.2, the dielectric responses for multilayer C
where
As expected, the measured results at each evaluated temperature agree quite well with the theoretical curve with coefficient of determination (R2) above 0.98. These observed results suggest that both
where
where
We finally obtain the relationship between
Eq. (15) suggests that the locus of the permittivity in the (
In addition, it is important to highlight some additional details. Firstly, the y-coordinates of fitted circular centers remain so small (~10−3) that Eq. (12) would be reduced to the classical Debye expression. From this point of view, the electronic polarization of short carbon fibers still follows the classic Debye relaxation process. Besides, the effects of temperature and electromagnetic interaction between neighboring short carbon fibers on relaxation time could be neglected reasonably.
Relaxation time also is one of key factors to analyze the dielectric behaviors for composites. After leaving out the effect of
It can be clearly seen from Eq. (16) that the real and imaginary parts of permittivity in (
4. Conclusion
In this chapter, microwave dielectric properties of multilayer C
Acknowledgments
The authors would like to acknowledge the generous funding from the National Key Research and Development Program of China (Grant No. 2017YFA0204600), the State Key Development Program for Basic Research of China (Grant No. 2011CB605804), and the National Natural Science Foundation of China (Grant No. 51802352).
Conflict of interest
The authors declared that they have no conflicts of interest to this work.
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