Sintering behaviour, lattice energy and microwave dielectric properties of melilite-type BaCo2Si2O7 ceramics

A novel melilite-type compound BaCo2Si2O7 with monoclinic structure (C2/c) was prepared via solid-state reaction method. The correlations amongst microstructure, crystal structure, bond ionicity, lattice energy and microwave dielectric properties were systematically analyzed. The microwave dielectric properties of BaCo2Si2O7 ceramics were determined by extrinsic (pores) and intrinsic (lattice energy) factors. The dielectric constant (εr), quality factor (Q × f) and temperature coefficient of resonant frequency (τf) were dominated by the relative density and the lattice energies of Si–O and Ba–O bonds. Optimum microwave dielectric properties for BaCo2Si2O7 ceramics were obtained when sintered at 1060 °C for 3 h: εr = 9.26, Q × f = 31 135 GHz and τf = −92.05 ppm C−1.


Introduction
With the flourishment of 5G technology, millimeter-wave wireless communication has been leading the daily life of the general public [1]. High frequency is related to high transmission speed and short transmission distance; moreover, the number of devices, such as base station antennas, is considerably increased [2]. In addition to mobile communications, driverless cars have also generated rounds of discussion; meanwhile, vehicle radar is treated as the eye of the driverless cars, which also indicates the wide utilization of vehicle radar. The application of microwave dielectric ceramics for millimeter-wave devices, including dielectric antennae, resonators and filters, must be further studied [3].
In terms of traditional microwave wireless communication, microwave dielectric ceramics must present a high dielectric constant for devices miniaturization, a high quality factor to achieve excellent cross-coupling selectively and a near-zero temperature coefficient of resonant frequency to ensure the transmitted frequency [4,5]. However, dielectric constant must be as small as possible for millimeter-wave wireless communication. where λ 0 is the wavelength in a vacuum, λ is the wavelength in dielectric, ε r is the dielectric constant and c is the speed of light in a vacuum. The wavelength in a vacuum (λ 0 ) has reached the millimeter level for millimeterwave wireless communications; thus, high dielectric constant is not required for decreasing the wavelength (λ) in dielectric. Equation (2) reveals the significance of low dielectric constant on millimeter-wave wireless communications. High transmission speed (low time delay T PD ) plays a vital role in 5G communications. The velocity of light c is a constant, therefore, low dielectric constant is expected for low time delay T PD [1,6].
Silicates generally present a low dielectric constant due to the [SiO 4 ] tetrahedra and the strong Si-O bond, which contains approximately half of the covalent bond [7,8]. Many types of silicates, such as forsterite (Mg 2 SiO 4 ), cordierite (Mg 2 Al 4 Si 5 O 18 ), feldspar (BaAl 2 Si 2 O 8 ) and melilite (Ba 2 ZnSi 2 O 7 ), have been explored [9][10][11][12]. Previous work found that Ba 2 ZnSi 2 O 7 is also a ferroelectric, which render us to attach more attention to the melilite-type silicates [13]. As shown in figure 1( tetrahedra connect each other in the a-c plane, hence Ba 2 ZnSi 2 O 7 shows a layered structure, and Ba 2+ is located between the two layers. Except for Ba 2 ZnSi 2 O 7 , BaCo 2 Si 2 O 7 , which was firstly synthesized by by Adams in 1996, also belongs to melilite-type silicates ( figure 1(b)), the crystal structure and magnetic properties of BaCo 2 Si 2 O 7 were also investigated in the work [14]. Unlike Ba 2 ZnSi 2 O 7 , the [SiO 4 ] tetrahedra in BaCo 2 Si 2 O 7 connect with each other by corner sharing in a-b plane and form a [Si 2 O 7 ] 6− group [14]. [CoO 4 ] 2− tetrahedra then connect with each other in the a-c plane, and form a [CoO 4 ] 2− chain. The [CoO 4 ] 2− chain in a-c plane connects with the [Si 2 O 7 ] 6− group in a-b plane and forms a skeleton structure. Finally, polyhedral gap is filled by Ba 2+ . At present, considerable attention has been provided to the dielectric properties of Ba 2 ZnSi 2 O 7 type melilite, whilst studies on the dielectric properties of BaCo 2 Si 2 O 7 type melilite, especially the microwave dielectric properties, are unavailable. The rapid development of millimeter-wave communication motivated the exploration of new microwave dielectric ceramics with low dielectric constant. From the perspective of the relationship between crystal structure and dielectric properties, melilite-type BaCo 2 Si 2 O 7 ceramics may also have good microwave dielectric properties.
In this article, the BaCo 2 Si 2 O 7 ceramic was prepared through the solid-state reaction method. Bond ionicity and lattice energy were calculated based on the chemical bond theory. The relationships between microstructure, crystal structure, lattice energy and microwave dielectric properties were also systematically investigated for the first time.

Experimental procedure
BaCo 2 Si 2 O 7 ceramics were prepared by the conventional solid-state method using reagent grade BaCO 3 (99.8%), CoO (99.5%) and SiO 2 (99.5%) powders as raw materials [2]. Based on the chemical formula, the raw materials were weighed for ball milling in a polyethylene jar for 5 h using ZrO 2 balls with deionized water. After drying at 90°C, the mixtures were calcined in air at 1000°C for 3 h with a heating rate of 5°C min −1 . The powders were then uniaxially pressed into samples with dimensions of 12 mm in diameter and approximately 6 mm in height under a pressure of 150 MPa. The samples were sintered at 1020°C-1100°C for 3 h at a heating rate of 5°C min −1 , and then they were naturally cooled in the furnace. The pictorial representation of the experimental method is shown in figure 2. The bulk density of the sintered samples was measured by Archimedes' method [12]. The relative density ρ rel was obtained by: where ρ bul and ρ the are the bulk density and theoretical densities, respectively. The XRD data were obtained via x-ray diffraction (XRD, XRD-7000, Shimadzu, Kyoto, Japan) using CuKα radiation. Phase analysis was performed by Rietveld refinement by utilizing GSAS and EXPGUI software [15][16][17]. The microstructure of the BaCo 2 Si 2 O 7 samples was measured through the scanning electron microscope (SEM, Sirion 200, Netherlands). The ε r and the unloaded Q×f value was estimated at 12-14 GHz in the TE 011 mode by Hakki and Coleman method [18] using a network analyzer (Agilent E8362B, Agilent Technologies, USA) and parallel silver boards. The τ f value in the temperature range of 30°C to 80°C was calculated by equation (4): where f (T 1 ) and f (T 0 ) represent the resonant frequency at T 1 (80°C) and T 0 (30°C), respectively. Figure 3 shows the XRD patterns of BaCo 2 Si 2 O 7 ceramics sintered at different temperatures. All diffraction peaks are indexed by monoclinic BaCo 2 Si 2 O 7 (JCPDS#82-0184), and no second phase can be found. The relative intensity of the main diffraction peaks for BaCo 2 Si 2 O 7 sintered at 1100°C is lower than that of others. This finding indicates that this sintering temperature is detrimental to the crystallization of BaCo 2 Si 2 O 7 ceramics. Table 1 and figure 4 show the results of the Rietveld refinement for BaCo 2 Si 2 O 7 ceramics that belong to the C2/c (15) space group. The structure parameters and bond lengths are presented in table 1 and S1 is available online at stacks.iop.org/MRX/6/126322/mmedia.  sintered at different temperatures. The bulk densities linearly increase and reach the maximum value at approximately 1080°C. Despite few closed pores on the fracture surface (figure 5(e)), the bulk density starts to decrease after reaching the maximum value. This phenomenon may be due to the abnormal grain growth at substantially high sintering temperatures.

Results and discussion
In order to reveal the relationships between crystal structure and microwave dielectric properties, the bond ionicity and lattice energy must be calculated based on Phillips-Van Vechten-Levine (P-V-L) theory, which was developed at the end of the 1960 s to 1973 s and finally generalized by Zhang in recent years [19][20][21][22][23][24][25]. According to the P-V-L theory [25], the complex crystals BaCo 2 Si 2 O 7 could be decomposed into binary crystals, and the sub-chemical formula was written as follows: The dielectric constant represents the polarization ability of materials under the electric field [26]. At microwave frequency, the polarization is dominated by electron displacement polarization and ionic displacement polarization. Thus, neglecting extrinsic factor, such as pores and the second phase, the dielectric constant can be determined by the ionic displacement polarization and calculated based on the P-V-L theory [27,28]. Table 2 Figure 6 shows the dielectric constant, relative density and weighted average bond ionicity of BaCo 2 Si 2 O 7 sintered at different temperatures. The weighted average bond ionicity of BaCo 2 Si 2 O 7 initially decreases and then linearly increases. However, these conditions do not show any relevance with dielectric constant. The dielectric constant and relative density increase to their maximum value at 1060°C-1080°C, maintaining the maximum value or demonstrating a slight decrease. The correlation between dielectric constant and relative density shows that the dielectric constant of BaCo 2 Si 2 O 7 ceramics sintered at the different temperatures is determined by the extrinsic factor (relative density). The low maximum relative density (approximately 96.6%) proves the poor sinterability of BaCo 2 Si 2 O 7 ceramics (figure 5).
Quality factor represents the dielectric loss of microwave dielectric ceramics, which can be affected by extrinsic and intrinsic losses. The extrinsic loss is affected by pores, the second phase, and grain boundary, whilst the intrinsic loss originates from anharmonic lattice vibration [29]. Numerous works confirmed that lattice energy largely affects quality factor [28,30,31]. Table 3 and S3 shows the lattice energy of BaCo 2 Si 2 O 7 ceramics sintered at the different temperatures. The total lattice energy of Si-O bonds (ΣU(Si-O)) is approximately 33 000 KJ mol −1 , which is around 76% of the lattice energy of BaCo 2 Si 2 O 7 (U cal ). Figure 7 shows the quality factor and the lattice energies of Si-O bonds and BaCo 2 Si 2 O 7 sintered at different temperatures. Quality factor and lattice energy increase to their maximum value at 1060°C and then decrease. The quality factor for the extrinsic part is mainly dominated by pores (relative density) for BaCo 2 Si 2 O 7 ceramics, which can be proven from the microstructure evolution in figure 5 and the variation of relative density in figure 6. The quality factor for the intrinsic part is determined by the lattice energy of BaCo 2 Si 2 O 7 (U cal ), particularly that of Si-O bonds. High bond energy indicates high bond strength, which stabilizes the structure and decreases the anharmonic lattice vibration [32]. Thus, the lattice energy of Si-O bonds plays a dominant role in the intrinsic dielectric loss. The variation of ΣU(Ba-O) presents an opposite trend with the quality factor, but the value of ΣU(Ba-O) is too low to have an apparent effect on quality factor when compared with that of the ΣU(Si-O).  Usually, the system with high lattice energy possesses a small |τ f | value, but the variation of τ f values present an opposite trend compared with that of the lattice energy of BaCo 2 Si 2 O 7 (figures 7 and 8). The τ f is defined as follows [29]:    where α L is the linear thermal expansion coefficient, which is approximately 10 ppm C −1 for oxide ceramics [33]. The first term A mostly contributes to the temperature coefficient of dielectric constant (τ ε ), which represents the temperature dependence of the ionic polarizability [29]. The total ionic polarizability for Ba 2+ , Co 2+ and Si 4+ in BaCo 2 Si 2 O 7 is 6.4, 3.3 and 1.74 Å 3 , respectively [34]. Ba 2+ exhibits the largest ionic polarizability, which is larger than the sum of all Co 2+ and Si 4+ . The lattice energy for BaCo 2 Si 2 O 7 ceramics is mainly attributed to Si-O bonds, but ionic polarizability is mainly contributed by Ba 2+ . Therefore, Si-O bond largely influences quality factor, but slightly affects dielectric constant and temperature coefficient of resonant frequency. Unlike Si-O bond, the Ba-O bond largely influences dielectric constant and temperature coefficient of resonant frequency, but slightly affects quality factor due to the low lattice energy (ΣU(Ba-O)), high bond ionicity (Af i (Ba-O)) and large ionic polarizability of Ba 2+ . Figure  ] polyhedra also decreases. Thus, the ionic polarizability of Ba 2+ is susceptible to temperature, which increases the first term A in equation (5), and then the τ ε decreases and τ f increases. In summary, the τ f value of BaCo 2 Si 2 O 7 ceramics sintered at the different temperatures is highly dependent on the lattice energy of Ba-O bond.

Conclusions
BaCo 2 Si 2 O 7 microwave dielectric ceramics with low dielectric constant have been prepared by the solid statereaction method. At increasing the sintering temperature from 1020°C to 1060°C, the interconnected pores change into closed pores and are trapped in the grains. At sintering temperatures higher than 1080°C, abnormal grain growth emerges, and the bulk density decreases. The dielectric constant of BaCo 2 Si 2 O 7 ceramics increases with relative densities, but the weighted average bond ionicity of BaCo 2 Si 2 O 7 does not show any relevance with the dielectric constant. This finding indicates that the extrinsic factor plays a dominant role in dielectric constant. Quality factor is affected by both extrinsic and intrinsic factors. For the extrinsic part, the quality factor is mainly dominated by pores (relative density) of BaCo 2 Si 2 O 7 ceramics. For intrinsic part, the quality factor is determined by the lattice energy, especially that Si-O bonds. The quality factor, lattice energy (U cal ) and