Low-temperature sintering and microwave dielectric properties of CaMg1−xLi2xSi2O6 (x = 0−0.3) ceramics

In this study, low-temperature fired CaMg1−xLi2xSi2O6 microwave dielectric ceramics were prepared via the traditional solid-state reaction method. In this process, 0.4 wt% Li2CO3-B2O3-SiO2-CaCO3-Al2O3 (LBSCA) glass was added as a sintering aid. The results showed that ceramics consisted of CaMgSi2O6 as the main phase. The second phases were CaSiO3 always existing and Li2SiO3 occurring at substitution content x > 0.05. Li+ substitution effectively lowered sintering temperature due to 0.4 wt% LBSCA and contributed to grain densification, and the most homogeneous morphology could be observed at x = 0.05. The effects of relative density, the second phase, and ionic polarizability on dielectric constant (εr) were investigated. The quality factor (Q × f) varied with packing fraction that concerned the second phase. Moreover, the temperature coefficient of the resonant frequency (τf) was influenced by MgO6 octahedral distortion and bond valence. Excellent dielectric properties of the CaMg1−xLi2xSi2O6 ceramic was exhibited at x = 0.05 with εr = 7.44, Q × f = 41,017 GHz (f = 15.1638 GHz), and τf = −59.3 ppm/°C when sintered at 900 °C. It had a good application prospect in the field of low-temperature co-fired ceramic (LTCC) substrate and devices.


Introduction 
Microwave dielectric ceramics constitute key materials used in microwave band communication (mainly from 300 MHz to 300 GHz). With the rapid development of information technology, microwave dielectric ceramics with low dielectric constant ( r ), high quality factor (Q × f ) value, and near-zero temperature coefficient of

Experimental
The CaMg 1-x Li 2x Si 2 O 6 (x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3) ceramics were synthesized via the solid-state reaction method with highly pure raw materials: CaCO 3 (99%, Ke-Long Co., Ltd., Chengdu, China), MgO (98%, Ke-Long Co., Ltd., Chengdu, China), Li 2 CO 3 (99.9%, Aladdin, Shanghai, China), and SiO 2 (99.9%, Aladdin, Shanghai, China). Different compositions of the ceramics were weighed according to the stoichiometric formula. The mixed raw powders were milled with zirconia balls and distilled water in nylon containers for 12 h. The slurries were subsequently dried in air for 24 h and calcinated at 900 ℃ for 3 h. Following, the pre-sintered powders were re-milled with 0.4 wt% LBSCA glass for 6 h and dried for 24 h. The LBSCA glass was obtained through the quenching method. Following weighing at the molar ratio of Li 2 CO 3 :B 2 O 3 :SiO 2 :CaCO 3 :Al 2 O 3 =52:31.06:11.99: 2.25:2.25, the mixed analytical grade raw powder was ball-milled with ethanol for 48 h, dried at 40 ℃ or lower, and melted in alumina crucible at 1000 ℃ for 2 h. Next, the alumina crucible was instantly removed from the furnace, and the molten glass was quenched in cold distilled water [29]. The crushed glass powder was added to the pre-sintered powders. The second-milled powder with LBSCA glass was mixed with 10 wt% PVA to obtain granulations that were squashed into cylinders of 12 mm in diameter and 6 mm in thickness. Sintering of these cylinders was achieved at the temperatures of 875, 900, and 925 ℃.
In order to obtain the microwave dielectric properties of the ceramics, the network analyzer based on Hakki-Coleman resonator method was used, while the τ f value could be calculated according to Eq. (1). The microstructure images of the polished and thermally etched surfaces were observed via scanning electron microscopy (SEM: Versa3D; FEI, USA). Moreover, the bulk density was calculated via the Archimedes principle. Regarding the crystal phase compositions of the CaMg 1-x Li 2x Si 2 O 6 ceramics, they were identified via X-ray diffraction (XRD: MinFlex 600; Rigaku, Japan), while crystal structure refinement could be obtained via the XRD diffraction data input to Fullprof software. Refined results were applied to draw the crystal structure charts with VESTA software. The τ f (ppm/ ℃ ) values were calculated according to the following equation:

Results and discussion
The phase composition was confirmed through XRD patterns, as presented in Fig. 1(a), when the CaMg 1-x Li 2x Si 2 O 6 ceramics were sintered at 900 ℃. It could be observed that the main phase CaMgSi 2 O 6 (PDF#11-0654) and the second phase CaSiO 3 (PDF#27-1064) always existed indifferently to x (0-0.3) variation. When x ≥ 0.1, another second phase, Li 2 SiO 3 (PDF#29-0829) appeared. The unexpected phase CaSiO 3 of wollastonite structure was generated through the following reaction (Eq. (2)), due to low calcination temperature (900 ℃ ) and the same sintering temperature. This signified that the raw materials had not completely reacted at a calcination temperature of 900 ℃. Besides, the formation of Li 2 SiO 3 was due to the reaction (Eq. (3)) of SiO 2 and Li 2 CO 3 within the raw powder. From these results, it could be initially determined that lower than 0.2 solid solubility of Li + occurred in the lattice of CaMgSi 2 O 6 phase. The presence of three crystal phases would definitely affect the microwave dielectric properties of the ceramics. Figure 1(b) shows the amplification of diffraction peaks (2 2 1) and (3 1 0). The diffraction peaks shifted nonlinearly with the doping amount, which had a close relationship with the unit cell parameters.
L i 2 CO 3 + SiO 2 → Li 2 SiO 3 + CO 2 ↑ (3) In order to further analyze the relationship between microstructure, phase composition, and microwave dielectric properties of the ceramics, XRD data of the CaMg 1-x Li 2x Si 2 O 6 samples sintered at 900 ℃ were refined with the Fullprof software. The theoretical models were monoclinic CaMgSi 2 O 6 (a = 9.7397 Å, b = 8.9174 Å, and c = 5.2503 Å), triclinic CaSiO 3 (a = 7.9400 Å, b = 7.3200 Å, and c = 7.0700 Å), and orthorhombic Li 2 SiO 3 (a = 9.3600 Å, b = 5.3950 Å, and c = 4.6750 Å). The refined plots of XRD patterns are exhibited in Figs. 2(a)-2(g) (0 ≤ x ≤ 0.3), which indicated that the calculated patterns (Y cal ) fitted well with the observed patterns (Y obs ). The reliability factors (R p , R wp , R exp , and χ 2 (> 0) are the profile factor, weighted profile factor, expected weighted profile factor, and reduced chi-square, respectively) in Table 1 could also help explain that structural information, such as lattice parameters of CaMgSi 2 O 6 phase summarized from the refinement results, was credible. Figure 3 and Table 1 demonstrate that the weight fraction of CaSiO 3 , the lattice parameters (especially a and c), and the unit cell volume (V) shared the same trend as x increased. The fact proved that the content of Li + substitution, as well as the CaSiO 3 phase, influenced the lattice structure, which eventually affected the microwave dielectric properties. However, the diffraction peaks shifted and the unit cell volume changed inconsistently, even in the opposite trend. Besides, the refinement results of XRD data could be applied in crystal structure drawings of the three phases of the CaMg 1-x Li 2x Si 2 O 6 ceramics with VESTA software, as presented in Figs. 4(a)-4(c). The performance of the synthesized ceramics would be affected by the three different structures synergistically and these would be discussed further. Moreover, the diffraction peak intensities (Fig. 2) and the content of CaMgSi 2 O 6 phase (Fig. 3) demonstrated the same tendency when Li + substitution content increased. The microwave dielectric properties influenced by crystal structure features and the second phase could be investigated via V, bond valence, oxygen octahedron distortion calculated from bond length, and the mixture rules.
Figures 5(a)-5(g) present the morphologies of the CaMg 1-x Li 2x Si 2 O 6 ceramic samples sintered at 900 ℃. When x = 0, the component was porous and the grain size was small, due to insufficiently high sintering temperature. Minor changes existed from Figs. 5(b) to 5(g), i.e., x value was in the interval of 0.05-0.3, considering the porosity and grain size. While when x = 0.05, the ceramic demonstrated good homogeneity in relative terms. In contrast, it was presented that the largest bulk density arises at x = 0.1 in the latter Fig. 6(b), which corresponded well with the SEM images. The enhancement of bulk density could be attributed to O vacancies due to Eq. (4): The generation of vacancy defects was conducive to ion diffusion and promoted the sintering [30]. However, the grain size distribution became gradually uneven as x value increased, accompanied with the occurrence of blurred grain boundaries. This could be originated from the portion increase of the second phases and the cell volume of CaMgSi 2 O 6 main phase. The appearance of pores might be due to the Li + volatilization [28]. Undoubtedly, Li + substitution could contribute to sintering temperature reduction and densification improvement of the CaMg 1-x Li 2x Si 2 O 6 ceramics, which would lead to significant influences on microwave dielectric properties.
The Q × f values of the samples are presented in Fig. 7(a). Regardless of sintering temperatures, Q × f www.springer.com/journal/40145 values reached the optimal values at x = 0.05, where the main phases occupied the dominant positions. As known, the quality factor is primarily determined by the structure and composition of the ceramic material itself. The loss due to crystal structure characteristics constitutes an intrinsic loss, while the losses caused by nonintegrity, such as the second phase, impurities, pores, cracks, and grain boundaries are called extrinsic losses [31]. In this study, no pure CaMgSi 2 O 6 phase existed in the samples, and the highest weight fraction (Fig. 3) and peak intensity (Fig. 2) of CaMgSi 2 O 6 were reached at x = 0.05. Consequently, the Q × f value was severely affected by both the second phase and the crystallinity simultaneously. Moreover, the packing fraction is an    In particular, the packing fraction depicted in Fig. 7(b) was the sum of the products of the packing fraction of each phase and its volume fraction, implying that packing fraction here took the second phase into account. Therefore, it was explained again that the impact of the second phase on the Q × f value was high. The (Q × f) theo values calculated from the mixture rule [33]: where i V  and (Q × f ) i are the volume fraction and Q × f of each phase, respectively (the Q × f values of CaSiO 3 and Li 2 SiO 3 were 25,398 GHz [34] and 9849 GHz [35], respectively), were in the same trend as the measured ones when combining Figs. 7(a) and 7(b). And the measured values were smaller than those of the theoretical ones, confirming the effect of the second phase on the Q × f value. Moreover, the effect of relative density on Q × f value could be ignored when 0.05 ≤ x ≤ 0.3. The relative density values of the ceramics sintered at 900 ℃ were above 94%; the highest Q × f value did not occur at the largest density. Therefore, it could be easily deduced that the intrinsic loss had an equal impact on the Q × f value to extrinsic loss, and moderate substitution content of Li + could decrease the sintering temperature not at the cost of sacrificing the quality factor. Figure 6(a) presents the variations in dielectric constant with x value at three different sintering temperatures: 875, 900, and 925 ℃. At any sintering temperature in the experiment, the maximum ε r was obtained at x = 0.1. In general, ε r is related to relative density, the second phase, and ionic polarizability. Figure 6(b) presents the relationship between ε r , relative density, and bulk density of samples sintered at 900 ℃ . The relative density (ρ) was calculated www.springer.com/journal/40145 through Eq. (7). The theoretical density (ρ theo ) was decided via Eq. (8) [16] where ρ bulk represents the bulk density; 1 2 3 4 , , , , , , , W W W and 4 W represent the theoretical density and weight fraction of CaMgSi 2 O 6 phase, CaSiO 3 phase, Li 2 SiO 3 phase, and LBSCA glass, respectively; for LBSCA glass, ρ 4 = 2.36 g/cm 3 [29]. The microwave dielectric constants of CaMg 1-x Li 2x Si 2 O 6 samples were consistent with the trends of ρ. Meanwhile, the influence of porosity on ε r (ε rc ) could be obtained according to Eq. (9): where p represents porosity that is opposite to the relative density and ε rc is the dielectric constant corrected by the porosity. The results are listed in Table  2. When combined with the relative density, it was indicated that ε r was severely affected by ρ and the porosity as Li + substitution content increased. Moreover, the observed and theoretical ionic polarizability,  obs and  theo , could be calculated through Clausius-Mosotti equation: Eqs. (10) and (11), which was based on the oxide additivity rule [36], and ionic polarizabilities of cations and oxygen were reported by Shannon [37]. The error between  obs and  theo () was calculated by Eq. (12).
where b is a constant of 4/3. The calculation results of samples sintered at 900 ℃ are presented in Table 2.
In Fig. 6(c), both ε r and  obs increased first and consequently decreased with x.  theo increased linearly with x, as attributed to the 2 mol Li + (1.2 Å 3 ) substitution for 1 mol Mg 2+ (1.32 Å 3 ). The  is low, as listed in Table 2, facilitating the reliability of the  obs . Besides,  obs was obtained only through the data of CaMgSi 2 O 6 main phase and it produced consonance well with ε r , when the weight fraction of the second phase increased with x value. More importantly, combined with the mixture rule: where ε ri represents dielectric constant of each phase (ε r (CaSiO 3 ) = 6.69 [34], ε r (Li 2 SiO 3 ) = 7.7 [35]), it could be inferred that ε r was affected by more ionic polarizability and ρ than the second phase combined with the above analysis.
In general, the  f value is determined by the linear expansion coefficient ( 1 ) and the temperature coefficient of dielectric constant (  ) as presented in Eq. .
where  1 is an empirical constant of approximately 10 ppm/℃. Consequently,  f was mainly affected by   , which was closely related to the oxygen polyhedral distortion (MgO 6 octahedral distortion in CaMgSi 2 O 6 system). The octahedral distortion () could be calculated via Mg-O bond length, obtained through XRD refinement results, according to Eq. (15). The bond valence, through which the bond strength could be evaluated, V i of atom i was the sum of all valences v ij from i, calculated via Eqs. (16) and (17) [38].  = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 [39,40]. All bond length information and the calculated results are presented in Table 3. As presented in Fig. 8,  f and  of cylinders sintered at 900 ℃ exhibited the same tendency as x value increased, except the porous samples of x = 0, which was due to insufficient sintering. The results well agreed with Lai et al. [41,42], which implied that the dependence of  f value on  was high. Besides, the curve of total bond valence (V total ) presented in Fig. 8 also corresponded well with the one of  f value, which could be explained by the result that higher bond valence results in lower | f | [43,44]. These phenomena in turn illustrated that although the second phases of CaSiO 3 and Li 2 SiO 3 were observed, the structural characteristics played an important role in  f .

Conclusions
In this study, the effects of Li + substitution for Mg 2+ on the microwave dielectric properties and microstructure, and the correlation between performance and structure of the CaMg 1-x Li 2x Si 2 O 6 ceramics sintered at 875, 900, and 925 ℃ with 0.4 wt% LBSCA as sintering aid, were investigated. The phase compositions detected from the XRD patterns, which were composed of at least two phases (CaMgSi 2 O 6 and CaSiO 3 existed when x varied from 0 to 0.3, and Li 2 SiO 3 occurred since x exceeded 0.05), were confirmed by the Rietveld refinement results. SEM micrographs demonstrated that welluniform morphologies were observed at x = 0.05. The optimal Q × f value was reached where the fraction of the second phase was the lowest, indicating that the Q × f value was highly influenced by the second phase, V, and the packing fraction, but the relative density had much less effect on the Q × f value. The ε r was not only affected by the relative density, but also was affected by the ionic polarizability, which was closely Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.