Crystal structure, microwave dielectric properties, and dielectric resonant antenna studies of novel low-permittivity CoAl₂O₄ spinel ceramics

Abstract

CoAl₂O₄ spinel ceramics were prepared via a standard solid-state reaction method, and their crystal structure, microwave dielectric properties, and dielectric resonant antenna applications were systematically investigated in this study. X-Ray diffraction patterns and Raman spectra confirmed that CoAl₂O₄ belongs to the Fd-3 m space group with cubic crystal symmetry. ε_r and Qf values increased with the increasing sintering temperature, where an ever-improving microstructure was also observed from the scanning electron micrographs. The optimal microwave dielectric properties were achieved as follows: ε_r = 9.34, Qf = 30,500 GHz, and τ_f = −54 ppm/^°C. Moreover, a dielectric resonant antenna was designed and simulated to demonstrate the application prospects of CoAl₂O₄ ceramics towards microwave antennas. The CoAl₂O₄-based antenna resonating at 14.33 GHz exhibited a high return loss of −40.9 dB, a wide impedance bandwidth of 940 MHz, and an exceptionally high total efficiency of 96.6%. The remarkable antenna performances suggested that CoAl₂O₄ ceramics were promising candidates for wireless communication devices operating at the Ku-band, provided τ_f can be further tuned toward zero.

1 Introduction

Wireless communication technology is fundamental to how we live, work, and play in the increasingly digital world. This trend has been building for decades and came to a head during the COVID-19 pandemic, when millions of us have come to depend on networks for packaged goods, entertainment, work—and still expect nearly immediate gratification. To meet those needs, the operating frequency of communication is expanding to the millimeter-wave region to offer a more efficient, secure, and flexible network [1, 2]. Microwave dielectric ceramics are critical components in wireless communication devices owing to the merits of low cost, excellent dielectric properties, and good thermal conductivity [3, 4]. The dielectric permittivity (ε_r), quality factor (Qf), and temperature coefficient of resonant frequency (τ_f) are three fundamental parameters in evaluating microwave dielectric properties. For millimeter-wave applications, a low-permittivity (ε_r < 10) is preferred for high-speed signal transmission with minimum attenuation [5,6,7]. Moreover, high Qf and near-zero τ_f values are always desirable for satisfactory resonant frequency selectivity and temperature stableness, respectively.

Aluminates are promising low-ε_r candidates owing to the relatively low ionic polarizability of Al³⁺ (0.79 ų) [8]. Among these, spinels with the general formula of MAl₂O₄ (M = transition metals) have been extensively investigated owing to their easy preparation and low dielectric loss [9, 10]. Surendran et al. reported the microwave dielectric properties of ZnAl₂O₄ ceramics for the first time, where the optimal properties (ε_r = 8.5, Qf = 56,300 GHz, τ_f = −79 ppm/^°C) were obtained when sintered at 1425 °C [9]. Meanwhile, similar microwave dielectric properties with ε_r = 8.75, Qf = 68,900 GHz, and τ_f = −75 ppm/^°C were also obtained in MgAl₂O₄ ceramics [10]. On the other hand, the spinel structure is flexible to substitutions. Numerous cations and cation combinations can be accommodated to obtain extremely diversified spinel end-members [11, 12]. However, current studies on the dielectric properties of spinels are mainly focused on the most common Mg- and Zn-based compounds. Systematic studies on different spinel end-members are lacking in the literature.

Owing to the similar ionic radius of Co²⁺ (0.65 Å) and Mg²⁺ (0.67 Å), the substitution of Co²⁺ for Mg²⁺ has been widely conducted and confirmed effective in improving the sinterability and microwave dielectric properties. By partially substituting Mg with Co, Huang et al. reported that the (Mg_1-xCo_x)Ti₂O₄ ceramics possess much higher Qf values than the Mg-end member [13]. For Mg-based spinels, Tsai et al. reported a significant improvement of Qf value by forming (Mg_1-xCo_x)Al₂O₄ solid solutions as well [14]. Meanwhile, Tsai et al. reported similar low-ε_r values of around 9 in CoAl₂O₄ spinel ceramics as well [14], while a systematical investigation on their sintering behavior, structure, microwave dielectric properties and antenna applications is still lacking in the literature.

In this study, CoAl₂O₄ ceramics are prepared via a standard solid-state reaction method. The sintering behavior, crystal structure, microstructure are systematically investigated together with their effects on the microwave dielectric properties. Moreover, a CoAl₂O₄-based dielectric resonator antenna prototype is designed and simulated to further explore their antenna applications.

2 Experimental procedure

CoAl₂O₄ ceramics were prepared via a standard solid-state reaction method using high-purity CoO (99.99%) and Al₂O₃ (99.99%) powder as raw materials. First, the stoichiometrically weighted powder was ball-milled in ethanol media for 12 h. After drying, the mixture was sieved and then calcined at 1200 °C for 3 h. Next, the calcined powder was re-milled and then pressed into pellets with 12 mm in diameter and 5 mm in height. Finally, the green pellets were sintered at 1450–1550 °C for 3 h to obtain the dense CoAl₂O₄ ceramics.

The relative density of CoAl₂O₄ ceramics was evaluated using the Archimedes method. Room-temperature X-ray diffraction (XRD) patterns were collected using a Shimadzu XRD-700X diffractometer. The XRD data for Rietveld analysis was collected using the step-scan mode, with a step degree of 0.02° and a counting time of 2 s. The ceramic samples were carefully polished to a roughness of about 0.5 μm for Raman measurement. Room-temperature Raman spectra were recorded using an HR-800 LabRaman device (Jobin Yvon, Longjumeau, France). Ar⁺ ion laser with an output power of 20mW was used as the excitation source. The polished and thermal etched surfaces of CoAl₂O₄ ceramics were observed using an S-3400 (Hitachi, Tokyo, Japan) scanning electron microscopy (SEM). The thermal etching process was carried out at 50 °C lower than the sintering temperature for 0.5 h. The dimensions of the sintered CoAl₂O₄ ceramics were around 9.5 mm in diameter and 5 mm in height. The measured resonant frequency of the CoAl₂O₄ ceramics was around 11 GHz. The Qf value was evaluated by the resonant-cavity method [15], using a silver-coated cavity connected to an E8363B network analyzer (Agilent, Palo Alto, CA). ε_r and τ_f values were measured using the parallel-plate method [16]. The measurement of τ_f value was organized in the temperature range of 20–80 °C. The design and simulation of the dielectric resonant antenna were conducted using the commercially available Computer Simulation Technology (CST) software.

3 Result and discussion

Figure 1 shows the relative density of CoAl₂O₄ ceramics as a function of sintering temperature. CoAl₂O₄ ceramics exhibit a relatively large sintering temperature range, as dense ceramics with relative densities above 94.5% are achieved in the whole sintering temperature range. An abrupt increase of relative density from 94.7% at 1475 °C to 97.3% at 1500 °C is noticed and remains relatively stable with further increasing sintering temperature. On the other hand, CoAl₂O₄ spinels are commonly investigated as ceramic pigments owing to their intense blue color and peculiar optical properties [17, 18]. As shown in the inset of Fig. 1, the color of CoAl₂O₄ ceramics turns from navy blue at 1450 °C to dark blue at 1500 °C and 1550 °C, which further confirms the improvement of relative density with increasing sintering temperature.

Fig. 1

The relative density of CoAl₂O₄ ceramics as a function of sintering temperature. The inset shows an optical photograph of the sintered ceramics

Figure 2a shows the XRD patterns of CoAl₂O₄ ceramics sintered at various temperatures. All the diffraction patterns match well with the standard diffraction feature of CoAl₂O₄ (JCPDS card No. 44–0160), and the relevant indices of crystallographic planes are labeled. Furthermore, no apparent change of peak position and intensity is observed with the increasing temperature. Hence, monophasic CoAl₂O₄ ceramics have been successfully prepared in this study, and the crystal structure remains stable in the whole temperature range. To further explore the crystal structure, the XRD data of CoAl₂O₄ ceramics sintered at 1550 °C is refined based on the spinel structure with a space group of Fd-3 m. Figure 2b shows the measured and calculated diffraction profiles of CoAl₂O₄ ceramics. The refined atomic coordinates, thermal displacement parameters, and occupations are listed in Table 1.

Fig. 2

a The XRD patterns of CoAl₂O₄ ceramics sintered at various temperatures. b The measured (circles) and Rietveld refined (red line) XRD patterns of CoAl₂O₄ ceramics sintered at 1550 °C. The green short vertical lines mark the Brag peak positions

Table 1 The Wyckoff positions, refined atomic coordinates, thermal displacement parameters, and occupations for CoAl₂O₄ ceramics

The measured and calculated XRD patterns keep a good consistency, as confirmed by the flatness of the difference line (Yobs-Ycal). Moreover, the outstanding reliability factors (R_p = 0.839%, R_wp = 1.13%, R_exp = 0.73%, and χ² = 2.37) indicate that the adopted spinel structure is valid and the refined results are reliable. Based on the refined structural parameters, Fig. 3 demonstrates the crystal structure of CoAl₂O₄. There are two kinds of Wyckoff positions for cations, i.e., 8a (1/8, 1/8, 1/8) and 16d (1/2, 1/2, 1/2). The cations connect with the neighboring oxygen anions and form two types of oxygen polyhedrons (i.e., tetrahedron at 8a site and octahedron at 16d site). On the other hand, the structural formula of CoAl₂O₄ can also be expressed as ^IV(Co_1–xAl_x)^VI[Co_xAl_2–x]O₄, where ^IV() and ^VI[] represent the 8a and 16d site, respectively; x is called the inversion parameter [19, 20]. For normal spinels such as ZnAl₂O₄ and MgAl₂O₄, x equals 0. A value of x = 2/3 corresponds to a completely random cation distribution between 8a and 16d sites. The other spinels with x between 0 and 2/3 are denoted as largely normal spinels or between 2/3 and 1 (largely inverse spinels). According to the occupation results listed in Table 1, CoAl₂O₄ ceramics is a largely normal spinel with the calculated x value of 0.098. Co²⁺ has a strong preference for tetrahedral 8a site and Al³⁺ for octahedral 16d site, though the cation radius of Al³⁺ (0.535 Å) is smaller than that of Co²⁺ (0.65 Å).

Fig. 3

The crystal structure of CoAl₂O₄ spinel ceramics

On the other hand, Raman spectroscopy is a powerful tool in revealing information on the crystal structure, electronic structure, and lattice vibrations [21,22,23]. Figure 4 plots the Raman spectra of CoAl₂O₄ ceramics sintered at 1450 °C and 1550 °C, respectively. Both samples display similar Raman patterns with five obvious Raman active peaks. No apparent change of peak position and intensity is noticed, corresponding to the similar XRD patterns obtained at various sintering temperatures. For spinels, the irreducible representations that describe the vibration modes of each Wyckoff position can be written as follows [11, 24]:

$$ {\text{8a site}}:{\text{ F}}_{{{\text{1u}}}} \left( {{\text{IR}}} \right) + {\text{F}}_{{{\text{2g}}}} \left( {\text{R}} \right) $$

$$ {\text{16d site}}:{\text{ A}}_{{{\text{2u}}}} \left( {\text{S}} \right) + {\text{E}}_{{\text{u}}} \left( {\text{S}} \right) + {\text{F}}_{{{\text{2u}}}} \left( {\text{S}} \right) + {\text{2F}}_{{{\text{1u}}}} \left( {{\text{IR}}} \right) $$

$$ {\text{32e site}}:{\text{ A}}_{{{\text{1g}}}} \left( {\text{R}} \right) + {\text{A}}_{{{\text{2u}}}} \left( {\text{S}} \right) + {\text{E}}_{{\text{u}}} \left( {\text{S}} \right) + {\text{E}}_{{\text{g}}} \left( {\text{R}} \right) + {\text{2F}}_{{{\text{2g}}}} \left( {\text{R}} \right) + {\text{F}}_{{1}} \left( {\text{S}} \right) + {\text{F}}_{{{\text{2u}}}} \left( {\text{S}} \right) + {\text{2F}}_{{{\text{1u}}}} \left( {{\text{IR}}} \right) $$

Fig. 4

Raman spectra of CoAl₂O₄ ceramics sintered at 1450 °C and 1550 °C

where the (R) and (IR) denote Raman- and infrared-active vibrational modes, respectively. The rest modes marked with (S) are silent. Therefore, the Raman active modes of CoAl₂O₄ ceramics are 3F_2g + A_1g + E_g. Besides, the three 3F_2g modes are labeled as F_2g(1), F_2g(2), and F_2g(3) based on their wavenumbers.

The wavenumbers of the Raman active peaks are obtained via fitting the spectra using a Lorentz function, and the results are consistent with the previous works [25,26,27]. The F_2g(1) mode at 202 cm⁻¹ is assigned to the Co/Al-O₄ tetrahedron translation [25]. The position of E_g mode is reported to have a reasonable correlation with the cation radius at the 8a site [11]. Hence, the E_g mode at 409 cm⁻¹ is assigned to the symmetric bending motion of the oxygen atoms within the tetrahedron [26]. The F_2g(2) mode at 517 cm⁻¹ is attributed to the Co/Al-O asymmetric stretching vibration in the tetrahedral sites [11, 26]. The literature is inconsistent regarding the vibration assignment for the F_2g(3) mode at 629 cm⁻¹, which has been reported as either the anti-symmetric stretching mode of the tetrahedron unit or an asymmetric bending motion of the oxygen bonded to the tetrahedral cation [27, 28]. Previous studies on the wavenumber of A_1g mode demonstrate that the octahedral cation has a more significant effect than the tetrahedral cation [29, 30]. This justifies that the A_1g mode at 785 cm⁻¹ is related to the Co/Al-O stretching vibration in the octahedron.

Figure 5 shows the SEM images and corresponding grain size distributions of CoAl₂O₄ ceramics sintered at various temperatures. The microstructure is getting dense with the increasing sintering temperature. Besides, an apparent increase of grain size from 0.88 μm at 1450 °C to 5.10 μm at 1550 °C is also noticed. The improvement of microstructure is in good agreement with the variation of relative density and should be mainly attributed to the increased driving force of grain growth.

Fig. 5

SEM images of the polished and thermal etched surfaces of CoAl₂O₄ ceramics sintered at various temperatures, a 1450 °C, b 1500 °C, and c 1550 °C. d The corresponding grain size distributions and average grain size of CoAl₂O₄ ceramics

Figure 6 shows the microwave dielectric properties of CoAl₂O₄ ceramics as functions of sintering temperature. ε_r increases monotonously with the increasing sintering temperature, from 8.959.34 °C at 1450 °C to 9.34 °C at 1550 °C. The variation of ε_r is in good agreement with the relative density, indicating that ε_r should be mainly determined by the porosity (P). According to Alford et al. [31], the effect of porosity can be excluded using the following Eq. (1), and the porosity corrected values (ε_cor) are plotted in Fig. 6a. All the ε_cor values maintain at around 9.6, confirming that the porosity mainly dominates ε_r of the present ceramics.

$$ \varepsilon_{r} = \varepsilon_{cor} (1 - \frac{{3P(\varepsilon_{cor} - 1)}}{{2\varepsilon_{cor} + 1}}) $$

(1)

Fig. 6

The microwave dielectric properties (a) ε_r, (b) Qf, and (c) τ_f values of CoAl₂O₄ ceramics sintered at various temperatures

Qf value indicates a monotonous increase with the increasing sintering temperature, from 23,550 GHz at 1450 °C to 30,500 GHz at 1550 °C. Since no phase transformation is obtained as confirmed from the XRD patterns, the increase of Qf value should be mainly attributed to the optimization of microstructures as shown in the SEM images. The optimal Qf value of CoAl₂O₄ ceramics is lower than the normal spinels such as ZnAl₂O₄ (56,300 GHz) and MgAl₂O₄ (68,900 GHz). According to Tsai et al., the lower Qf value in CoAl₂O₄ ceramics should be attributed to the more random distributions of the cations occupying tetrahedral and octahedral sites, which could render the anharmonic phonon decay process in the ceramic crystal and degrade the quality factors [14]. The variation of τ_f value is insensitive to the sintering temperature, and all the values maintain at around −54 ppm/^°C. The negative τ_f value of the present ceramics poses difficulties for practical applications, which can be further optimized via forming composite ceramics with components having positive τ_f values, such as TiO₂ (τ_f =  + 460 ppm/^°C), CaTiO₃ (τ_f =  + 850 ppm/^°C) [32, 33]. The optimal microwave dielectric properties with ε_r = 9.34, Qf = 30,500 GHz, and τ_f = −54 ppm/^°C are obtained when sintered at 1550 °C.

A dielectric resonator antenna (DRA) consists of a block of ceramic (dielectric resonator) mounted on a metal surface (ground plane). DRA offers attractive features compared to microstrip patch antennas, including higher gain and efficiency, wider bandwidth, and easier excitation [34, 35].

A CoAl₂O₄-based DRA prototype is designed using the microstrip-slot coupling scheme. Figure 7 demonstrates the configuration of the proposed DRA, and the dimensions are listed in Table 2. A 40 × 40 × 1 mm FR4 substrate is pasted with copper foil (thickness: ~ 0.06 mm) on one side as conducting ground plane. A cylindrical CoAl₂O₄-based dielectric resonator (DR) with a diameter of 9.5 mm and height of 4.8 mm is placed over an etch slot in the ground plane. The fields of the microstrip line “leak” through the slot to excite the DR.

Fig. 7

Top and side view of the designed DRA using a microstrip-slot coupling scheme

Table 2 The dimensions of the designed rectangular DRA

Figure 8 shows the simulated antenna performances of the CoAl₂O₄-based DRA. The S₁₁ parameter is a measure of impedance mismatch and reflects how much power is reflected from the antenna. The minimum S₁₁ parameter is generally achieved at the resonant frequency. Meanwhile, for practical applications, the S₁₁ values should be lower than −10 dB in the whole operating frequency range [36, 37]. As shown in Fig. 8a, the designed DRA resonates at the Ku-band region, where an excellent S₁₁ of −40.9 dB is obtained at the resonant frequency of 14.33 GHz. Besides, a considerably large impedance bandwidth (the frequency range where S₁₁ is below −10 dB) of 940 MHz is also achieved, which surpasses those reported in microstrip patch antennas [1, 2, 38]. The voltage standing wave ratio (VSWR) is another indicator of impedance mismatch. The VSWR value at the resonant frequency should be close to unity for proper working [37]. As shown in Fig. 8b, the designed DRA exhibits an excellent VSWR of 1.03 at 14.33 GHz and is found to be less than 2 in the entire impedance bandwidth frequency range. Figure 8c shows the total efficiency of the DRA as a function of frequency, where a maximum value of 96.6% is obtained at the resonant frequency. The superior total efficiency surpasses the commercial antenna products (typically ranges from 20% to 70%) and indicates extensive application prospects [38, 39]. Finally, antenna gain is another critical parameter measuring the power radiated in a particular direction. Figure 8d demonstrates the three-dimensional (3D) polar plot of the radiation pattern, and the maximum gain is found to be 5.42 dB. A comparative table on the antenna performances is presented in Table 3. The comparative data suggests that the CoAl₂O₄-based DRA exhibits superior antenna properties, including S₁₁ parameters, bandwidth, and total efficiency, compared to the reported work.

Fig. 8

The simulated antenna performances a S₁₁ parameter, b VSWR, and c total efficiency of CoAl₂O₄-based DR antenna as functions of frequency. d The simulated 3D radiation patterns of CoAl₂O₄-based DR antenna

Table 3 Comparison of performances of recently reported antennas

4 Conclusions

In this study, single-phase CoAl₂O₄ ceramics have been successfully prepared via a standard solid-state reaction method. XRD and Raman results demonstrate that CoAl₂O₄ crystallizes in a largely normal spinel structure with a space group of Fd-3 m. The SEM images show an ever-optimizing microstructure with the increasing sintering temperature, which is beneficial to the improvement of ε_r and Qf values. The optimal microwave dielectric properties (ε_r = 9.34, Qf = 30,500 GHz, and τ_f = −54 ppm/^°C) are achieved when sintered at 1550 °C. A dielectric resonator antenna is designed using CoAl₂O₄ ceramics as the antenna element. The outstanding S₁₁ (−40.9 dB) and VSWR (1.03) values at the resonant frequency of 14.33 GHz indicate a good impedance matching. Moreover, the S₁₁ curve exhibits a large impedance bandwidth of 950 MHz, and the total efficiency at the resonant frequency is 96.6%. The excellent antenna performance suggests that CoAl₂O₄ ceramics have prospects of extensive applications in wireless communication devices operating at the Ku-band, provided τ_f can be further tuned toward zero.