Evolution of Phase Transformation on Microwave Dielectric Properties of BaSi_xO_1+2x Ceramics and Their Temperature-Stable LTCC Materials

Abstract

BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) and LiF-doped BaSi_1.63O_4.26 ceramics were prepared by using a traditional solid-state method at the optimal sintering temperatures. The evolution of phase compositions of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9) ceramics was revealed. The coexistence of Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases was obtained in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics. The BaSi₂O₅ phase appeared inBaSi_xO_1+2x (1.68 ≤ x ≤ 1.90) ceramics. At 1.68 ≤ x ≤ 1.69, only BaSi₂O₅ and Ba₃Si₅O₁₃ phases existed. With the further increase in x, the Ba₅Si₈O₂₁ phase appeared, and BaSi₂O₅, Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases coexisted in BaSi_xO_1+2x (1.70 ≤ x ≤ 1.90) ceramics. The phase compositions of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were controlled by the ratio of Ba:Si. The BaSi_xO_1+2x (x = 1.68) ceramics with 98.15 wt% Ba₃Si₅O₁₃ and 1.85 wt% BaSi₂O₅ phases exhibited a negative τ_f value (−37.53 ppm/°C), and the good microwave dielectric properties of ε_r = 7.51, Q × f = 13,038 GHz and τ_f = +3.95 ppm/°C were obtained for BaSi_1.63O_4.26 ceramics with 70.05 wt% Ba₅Si₈O₂₁ and 29.95 wt% Ba₃Si₅O₁₃ phases. The addition of LiF sintering aids were able to reduce the sintering temperatures of BaSi_1.63O_4.26 ceramics to 800 °C. The phase composition of BaSi_1.63O_4.26 ceramics was affected by the sintering temperature, and the coexistence of Ba₅Si₈O₂₁, Ba₂Si₃O₈, BaSi₂O₅ and SiO₂ phases was achieved in BaSi_1.63O_4.26-3 wt% LiF ceramics. The BaSi_1.63O_4.26-3 wt% LiF ceramics sintered at 800 °C exhibited dense microstructures and excellent microwave dielectric properties (ε_r = 7.10, Q × f = 12,463 GHz and τ_f = +5.75 ppm/°C), and no chemical reaction occurred between BaSi_1.63O_4.26-3 wt% LiF ceramics and the Ag electrodes, which indicates their potential for low-temperature co-fired ceramic (LTCC) applications.

1. Introduction

The rapid development of telecommunication has promoted the high demand for multi-layer devices and microwave dielectric ceramics [1,2,3,4,5]. Barium silicates with excellent luminescence and dielectric properties are widely used in optical glasses and microwave dielectric ceramics [6,7,8,9,10,11,12]. The low cost and free of variable valence elements of barium silicates indicated their great application potential, especially in communication applications [13,14]. The Si–O bond was also strong because it is approximately 55% covalent and 45% ionic [15,16,17]. Barium silicates with high contents of SiO₄ tetrahedra and Si–O bonds demonstrated their low permittivity (ε_r < 15) and high-quality factor (Q × f), which attracted considerable attention regarding microwave dielectric materials [18,19,20,21,22]. However, 13 crystalline phases were known in the BaO–SiO₂ system [23], which indicates that the complex phase compositions might exist in barium silicates. Ambiguous phase compositions might limit the application of barium silicates in microwave dielectric materials.

The microwave dielectric properties of barium silicates were first reported by Wen Lei et al. [9], and a BaSi₂O₅ ceramic with excellent microwave dielectric properties (ε_r = 6.7, Q × f = 59,500 GHz and τ_f = −28.0 ppm/°C) was synthesised through sintering at 1250 °C. Enzhu Li et al. pointed out that the synthesis temperature of a single-phase BaSi₂O₅ ceramic was more than 1100 °C, and the coexistence of BaSi₂O₅, Ba₅Si₈O₂₁ (BaSi_1.6O_4.2) and SiO₂ phases was identified in BaSi₂O₅ ceramics. The Ba₅Si₈O₂₁ phases existed in BaSi₂O₅-2 wt% Li₂O–B₂O₃–CaO–CuO glass ceramics when their sintering temperature was below 800 °C, which means that the Ba₅Si₈O₂₁ phase was easier to synthesise than the BaSi₂O₅ phase [10]. A single-phase BaSi₂O₅ ceramic sintered at 1225 °C was prepared by Yun Zhang [11]. The Ba₅Si₈O₂₁ ceramic with a stable phase composition and novel positive temperature coefficient of the resonance frequency (τ_f) was used as a τ_f regulator to control the negative τ_f values of many low-ε_r microwave dielectric ceramics [12]. The Ba₅Si₈O₂₁ ceramics always exhibited the Ba₅Si₈O₂₁ phase at a high sintering temperature (above 800 °C). However, the Ba₃Si₅O₁₃ (BaSi_1.667O_4.334) ceramic, as an intermediate compound between Ba₅Si₈O₂₁ (BaSi_1.6O_4.2) and BaSi₂O₅, exhibited the highest structural and topological complexity in barium silicates [8]. The Ba₃Si₅O₁₃ (BaSi_1.667O_4.334) ceramics sintering at different temperatures exhibited the opposite τ_f values (+37.0 ppm/°C sintering at 1200 °C and −36.0 ppm/°C sintering at 1250 °C) and different phase compositions (Ba₅Si₈O₂₁ and BaSi₂O₅ phases sintered at 1200 °C and Ba₃Si₅O₁₃ phase sintered at 1250 °C) [9]. Toshihiro Moriga et al. pointed out that Ba₃Si₅O₁₃ single-phase ceramics sintered at 1000 °C could be synthesised at stoichiometric ratios [7]. The small difference in the Ba:Si ratios of the Ba₅Si₈O₂₁, Ba₃Si₅O₁₃ and BaSi₂O₅ phases caused difficulty in synthesizing Ba₃Si₅O₁₃ ceramics.

Considering the excellent application potential of barium silicate ceramics in LTCC technology, the variation in the phase compositions of BaSi_xO_1+2x ceramics with stoichiometric ratios and sintering temperatures needs to be investigated. This study aimed to clarify the phase compositions of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9) ceramics with different stoichiometric ratios and investigate the evolution of their phase compositions on microwave dielectric properties. Simultaneously, high-performance BaSi_xO_1+2x-based LTCC materials with LiF doped were prepared.

2. Materials and Methods

BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9)- and LiF-doped BaSi_xO_1+2x ceramics were prepared using the solid reaction method. BaCO₃ (99.9%), SiO₂ (99.9%) and LiF (99.9%) were weighed according to the stoichiometric formulation of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9) and ground in deionised water for 5 h. After drying, BaSi_xO_1+2x-prepared powders were calcined at 1050 °C for 5 h to obtain barium silicates. After being re-milled for 5 h and dryed, the as-prepared powders together with 8 wt% PVA were pressed into cylindrical samples. The BaSi_xO_1+2x samples were then sintered at 1300–1325 °C for 5 h. The BaSi_xO_1+2x calcined powders and LiF were weighed according to the mass percentage formulation of BaSi_xO_1+2x-y wt% LiF (1 ≤ y ≤ 3), which were sintered at 800–1025 °C for 3 h.

The sintered samples of BaSi_xO_1+2x and BaSi_xO_1+2x-y wt% LiF (1 ≤ y ≤ 3) ceramics were broken up and ground into powders. The phase and crystal structure of powders were obtained using an X-ray diffractometer (X’Pert PRO). The Rietveld refinement of samples was conducted via Fullprof software [24]. The polished surfaces of samples were observed via scanning electron microscopy (SEM; Sirion 200) after thermal etching. The microwave dielectric properties of as-sintered BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9) and BaSi_xO_1+2x-y wt% LiF (1 ≤ y ≤ 3) ceramics were measured in the range of 10–14 GHz by employing the Hakki–Coleman methods with a network analyser (Keysight E5063A) [25].

3. Results

The BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics at the optimal sintering temperature (T_sint) were broken up and ground into powders for X-ray analysis. As shown in Figure 1a, the optimal sintering temperature of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics was between 1300 and 1325 °C. Only Ba₅Si₈O₂₁ phase seemed to exist in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.62) ceramics, and the BaSi_xO_1+2x (1.66 ≤ x ≤ 1.67) ceramics exhibited the Ba₃Si₅O₁₃ single phase. The evident coexistence of Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases was observed in BaSi_xO_1+2x (1.63 ≤ x ≤ 1.65) ceramics. As illustrated in Figure 1c, the Ba₃Si₅O₁₃ single phase existed in the BaSi_xO_1+2x (x = 1.68) ceramics, and the obvious coexistence of Ba₃Si₅O₁₃ and BaSi₂O₅ phases was observed in the BaSi_xO_1+2x (1.69 ≤ x ≤ 1.90) ceramics. However, the similar XRD patterns between Ba₃Si₅O₁₃ and Ba₅Si₈O₂₁ phases caused difficulty in distinguishing the phase compositions of BaSi_xO_1+2x ceramics. The enlarged XRD patterns of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.9) ceramics at a 20°–30° scanning range can be seen in Figure 1b,d, along with the evolution of the main XRD peaks. The evident Ba₃Si₅O₁₃ second phase existed in BaSi_xO_1+2x (x = 1.62) ceramics, and the content of the Ba₃Si₅O₁₃ phase in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics increased gradually with the rise in x. In the BaSi_xO_1+2x (x = 1.67) ceramics, the Ba₅Si₈O₂₁ second phase was present. The single-phase Ba₃Si₅O₁₃ ceramics might be seen in the BaSi_xO_1+2x (x = 1.68) ceramics (Figure 1d). With the further increase in x, the intensity of the XRD patterns of the BaSi₂O₅ and Ba₃Si₅O₁₃ phases gradually rose and decreased, respectively. The evident Ba₅Si₈O₂₁ phase also existed in BaSi_xO_1+2x (1.80 ≤ x ≤ 1.85) ceramics, which indicates the complex evolution of the phase compositions of BaSi_xO_1+2x (1.68 ≤ x ≤ 1.90) ceramics. Moreover, the Ba₃Si₅O₁₃ ceramics were able to be synthesised via sintering at 1325 °C.

The Rietveld refinement of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics was conducted for quantitative analysis via phase composition. The results of the Rietveld refinement are shown in

Table 1. The lattice parameters and Rietveld discrepancy factors of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics sintered at their densification temperatures.

Compositions	Phase Compositions		Lattice Parameter of Main Phase					Rietveld Discrepancy Factors
	Main Phase (wt%)	Second Phase (wt%)	a (Å)	b (Å)	c (Å)	β (°)	V (Å3)	Rwp (%)	Rp (%)	χ2
x = 1.61	Ba5Si8O21 (95.87)	Ba3Si5O13 (4.13)	32.702	4.698	13.899	98.157	2113.719	16.2	12.9	5.8
x = 1.62	Ba5Si8O21 (81.66)	Ba3Si5O13 (18.34)	32.723	4.701	13.892	98.211	2115.226	14.5	11.5	4.8
x = 1.63	Ba5Si8O21 (70.05)	Ba3Si5O13 (29.95)	32.741	4.703	13.886	98.299	2115.890	16.5	12.8	6.1
x = 1.64	Ba5Si8O21 (57.21)	Ba3Si5O13 (42.79)	32.730	4.701	13.898	98.189	2116.584	16.7	13.1	6.7
x = 1.65	Ba3Si5O13 (72.70)	Ba5Si8O21 (27.30)	20.196	4.710	13.866	98.697	1303.919	15.7	12.1	5.3
x = 1.66	Ba3Si5O13 (85.75)	Ba5Si8O21 (14.25)	20.199	4.710	13.858	98.657	1303.376	13.7	10.4	4.2
x = 1.67	Ba3Si5O13 (91.27)	Ba5Si8O21 (8.73)	20.208	4.710	13.854	98.639	1303.641	13.6	10.8	3.7
x = 1.68	Ba3Si5O13 (98.15)	BaSi2O5 (1.85)	20.213	4.712	13.856	98.617	1304.856	14.2	10.9	4.4
x = 1.69	Ba3Si5O13 (96.99)	BaSi2O5 (3.01)	20.212	4.711	13.855	98.620	1304.388	14.0	10.9	4.0
x = 1.70	Ba3Si5O13 (92.64)	BaSi2O5 (4.68) Ba5Si8O21 (2.68)	20.210	4.711	13.853	98.617	1304.110	14.5	11.0	5.0
x = 1.75	Ba3Si5O13 (67.58)	BaSi2O5 (26.83) Ba5Si8O21 (5.59)	20.213	4.712	13.854	98.611	1304.643	13.7	10.7	4.9
x = 1.8	BaSi2O5 (41.79)	Ba3Si5O13 (41.34) Ba5Si8O21 (16.87)	4.633	7.689	13.515	—	481.480	13.7	10.6	5.2
x = 1.85	BaSi2O5 (61.07)	Ba3Si5O13 (26.28) Ba5Si8O21 (12.65)	4.634	7.688	13.524	—	481.766	14.0	11.0	5.2
x = 1.9	BaSi2O5 (71.12)	Ba3Si5O13 (28.36) Ba5Si8O21 (0.52)	4.635	7.688	13.527	—	482.064	11.9	9.3	3.8

, and the calculated XRD patterns of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics matched the measured XRD patterns well (Figure 2). Therefore, the fitting content of phase compositions was accurate. As shown in Table 1, the Ba₅Si₈O₂₁ main phase and Ba₃Si₅O₁₃ second phase existed in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.64) ceramics. The main phase in BaSi_xO_1+2x (1.65 ≤ x ≤ 1.67) ceramics changed from the Ba₅Si₈O₂₁ to Ba₃Si₅O₁₃ phase. Moreover, the Ba₅Si₈O₂₁ second phase changed to the BaSi₂O₅ phase in the BaSi_xO_1+2x (x = 1.68) ceramics. The BaSi_xO_1+2x (x = 1.68) ceramics with 98.5 wt% Ba₃Si₅O₁₃ and 1.85 wt% BaSi₂O₅ was synthesised, and the BaSi₂O₅-Ba₃Si₅O₁₃ system could be obtained in BaSi_xO_1+2x (1.68 ≤ x ≤ 1.69) ceramics. With the further increase in x, the other Ba₅Si₈O₂₁ second phase appeared in BaSi_xO_1+2x (1.7 ≤ x ≤ 1.90) ceramics, and the content of the BaSi₂O₅ phase increased gradually. Lastly, the results of the Rietveld refinement indicated that the coexistence of the Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases were obtained in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics (Ba₅Si₈O₂₁–Ba₃Si₅O₁₃ system), and the Ba₃Si₅O₁₃ single-phase ceramics could be synthesised in BaSi_xO_1+2x (1.67 < x < 1.68) ceramics. The phase compositions of the BaSi_xO_1+2x ceramics was significantly affected by the ratio of Ba:Si.

As shown in Figure 3 and S1, the thermally etched SEM and EDS map scanning images of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were obtained. The dense and smooth microstructures of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were observed. Only the grains of barium silicates were observed in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics. However, the similar monoclinic structure and elemental composition caused difficulty in distinguishing the grains of Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ based on Figure 3 and S1. In Figure 3e, the EDS results of Spots A and B indicated that the strip-shaped (Spot B) and large (Spot A) grains were Ba₃Si₅O₁₃ and BaSi₂O₅, respectively. The Ba₃Si₅O₁₃ second phase can be observed in Figure 3f. With the increase in x, the content of strip-shaped grains decreased gradually and the average grain sizes increased, which implies that the content of BaSi₂O₅ rose gradually.

The microwave dielectric properties of the BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics sintered at the optimal temperature were obtained, as shown in Table S1 (see Supplementary materials) and Figure 4 and Figure 5. As shown in Figure 4a, the relative density (ρ_rel) and experimental relative permittivity (ε_r-exp) of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics fluctuated with the increase in x, and all BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics exhibited high ρ_rel (>95%) except th BaSi_xO_1+2x (x = 1.75) ceramics. Therefore, ρ_rel might have little effect on themicrowave dielectric properties of BaSi_xO_1+2x ceramics. In the BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics, the BaSi_xO_1+2x (x = 1.67) ceramics with a 91.27 wt% Ba₃Si₅O₁₃ phase exhibited the largest ε_r-exp value, and a low ε_r-exp (7.33) was obtained in BaSi_xO_1+2x (x = 1.61) ceramics with a 95.87 wt% Ba₅Si₈O₂₁ phase, which was attributed to the low ε_r-exp value (7.3) of Ba₅Si₈O₂₁ ceramics [9]. In BaSi_xO_1+2x (1.68 ≤ x ≤ 1.90) ceramics, ε_r-exp decreased from 7.49 to 6.94, and the BaSi_xO_1+2x (x = 1.90) ceramics with a 71.12 wt% BaSi₂O₅ phase exhibited the lowest ε_r-exp value. For multi-phase ceramics, ε_r could be calculated using the Lichtenecker empirical rule [26,27,28].

$$ln {\epsilon }_{r-cal}=V_1 ln {\epsilon }_{r-1}+V_2 ln {\epsilon }_{r-2}+V_3 ln {\epsilon }_{r-3}$$

(1)

where ε_r-cal represents the calculated relative permittivity; V₁, V₂ and V₃ are the volume fraction of phases 1, 2 and 3; and ε_r-1, ε_r-2 and ε_r-3 are the ε_r-exp values of Ba₅Si₈O₂₁, Ba₃Si₅O₁₃ and BaSi₂O₅ ceramics [9], respectively. The ε_r-cal of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics increased initially and then decreased, and the variation tendency of the ε_r-exp values was similar to ε_r-cal with x (Figure 4a). This finding implies that phase compositions significantly affected the ε_r-exp values for BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics. Moreover, the BaSi_xO_1+2x (x = 1.66) ceramics exhibited lower ε_r-exp (7.57) than BaSi_xO_1+2x (x = 1.64, 1.65, 1.67) ceramics, which was attributed to their low ρ_rel. The BaSi_xO_1+2x (x = 1.80) ceramics exhibited larger ρ_rel and ε_r-exp than BaSi_xO_1+2x (x = 1.75) ceramics. Thus, the effect of ρ_rel on the ε_r-exp of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics cannot be neglected.

Figure 4b shows the Q × f values of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics. The BaSi_xO_1+2x (1.68 ≤ x ≤ 1.90) ceramics exhibited higher Q × f values than BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics, and the BaSi_xO_1+2x (x = 1.90) ceramics with 71.12 wt% BaSi₂O₅ phase exhibited high Q × f value (22,563 GHz), which was attributed to the high Q × f value of BaSi₂O₅ ceramics [9]. Moreover, the low Q × f value of BaSi_xO_1+2x (x = 1.80) ceramics was obtained at 1.68 ≤ x ≤ 1.90. This result indicates that the largest harmful inner stress at the two-phase interface was obtained in BaSi_xO_1+2x (x = 1.80) ceramics with 41.79 wt% BaSi₂O₅ phase, 41.34 wt% Ba₃Si₅O₁₃ phase and 16.87 wt% Ba₅Si₈O₂₁ phase. The inner stress at the two-phase interface could not be neglected in multiphase BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics. The BaSi_xO_1+2x (x = 1.61) ceramics with minimal Ba₃Si₅O₁₃ phase (4.13 wt%) exhibited lower Q × f value (13,062 GHz) than Ba₅Si₈O₂₁ single-phase ceramics (16,700 GHz) due to the existence of inner stress at the two-phase interface. The Q × f value of BaSi_xO_1+2x (x = 1.68) ceramics with a 98.15 wt% Ba₃Si₅O₁₃ phase was higher than that of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.67) ceramics, which means that Ba₃Si₅O₁₃ ceramics might exhibit higher Q × f value than Ba₅Si₈O₂₁ ceramics.

The τ_f-exp values of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were obtained, as shown in Figure 5a. At 1.61 ≤ x ≤ 1.67 (Ba₅Si₈O₂₁-Ba₃Si₅O₁₃ system), the τ_f-exp values changed from +24.20 ppm/°C to −29.40 ppm/°C, and the BaSi_xO_1+2x (x = 1.63 and 1.64) ceramics exhibited near-zero τ_f-exp values. At 1.68 ≤ x ≤ 1.90, the τ_f-exp values of the BaSi_xO_1+2x ceramics fluctuated with x, and the small |τ_f-exp| value was obtained at x = 1.80. For multi-phase ceramics, τ_f-cal could be calculated using Lichtenecker’s empirical rule [26,27,28].

$${\tau }_{f-cal}=V_1{\tau }_{f1}+V_2{\tau }_{f2}+V_3{\tau }_{f3}$$

(2)

where τ_f-cal represents the calculated τ_f; V₁, V₂ and V₃ are the volume fractions of phases 1, 2 and 3, respectively; and τ_f1, τ_f2 and τ_f3 are the τ_f values of Ba₅Si₈O₂₁, Ba₃Si₅O₁₃ and BaSi₂O₅ ceramics [9], respectively. τ_f-cal agreed well with the τ_f-exp in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics, and τ_f-exp, τ_f-cal and content of Ba₅Si₈O₂₁ phase of the BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics with x displayed a similar trend. Therefore, the content of the Ba₅Si₈O₂₁ phase significantly affected the τ_f-exp of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics. At 1.65 ≤ x ≤ 1.75, the BaSi_xO_1+2x ceramics with the Ba₃Si₅O₁₃ main phase exhibited negative τ_f-exp values. Therefore, the present study confirmed the negative τ_f value of Ba₃Si₅O₁₃ ceramics, which was controversial in a previous work [9]. Ba₅Si₈O₂₁, as a new τ_f compensator, successfully adjusted the negative τ_f-exp value of Ba₃Si₅O₁₃ to near zero (+3.95 ppm/°C and −7.25 ppm/°C) in the BaSi_xO_1+2x (x = 1.63, 1.64) ceramics.

In accordance with Formula (3) [29,30], the τ_f related to α_L and τ_ε and α_L can be seen in Figure 5b.

$${\tau }_f=-\left({\alpha }_L+\frac{1}{2}{\tau }_{\epsilon }\right)$$

(3)

with the increase in measured temperature, the length of BaSi_xO_1+2x (x = 1.63) ceramics increased gradually, and the average linear thermal expansion coefficient (CTE in Figure 5b) at 25–750 °C is 10.1 ppm/°C. The dependence of ε_r on temperature for BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics is shown in Figure 6, and the fitting τ_ε values at 30–125 °C and 1 MHz were obtained. The negative τ_ε values were obtained in BaSi_xO_1+2x (1.61 ≤ x ≤ 1.64) ceramics, and BaSi_xO_1+2x (1.66 ≤ x ≤ 1.90) ceramics exhibited positive τ_ε values. At 1.61 ≤ x ≤ 1.64, the negative τ_ε values increased gradually to near zero, and BaSi_xO_1+2x (x = 1.64) ceramics exhibited a near-zero τ_ε value (−2.9 ppm/°C). At 1.66 ≤ x ≤ 1.90, the small τ_ε value was obtained in BaSi_xO_1+2x (x = 1.80) ceramics. According to the τ_f–ε_r relationship, a similar variation in the τ_ε and τ_f values of the BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics was observed as x increased, which indicates that the measured τ_f-exp values using the Hakki–Coleman method were exacted. The measured α_L (10.1 ppm/°C) and τ_ε (−15.4 ppm/°C) values of BaSi_xO_1+2x (x = 1.63) ceramics also confirmed their near-zero τ_f-exp value.

At high T_sint (≥1300 °C), the phase compositions of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were revealed in this work. However, the phase compositions of barium silicates were sensitive to T_sint, and the complex phase transformation of barium silicates existed with the change in T_sint, especially Ba₅Si₈O₂₁, Ba₃Si₅O₁₃ and BaSi₂O₅ ceramics [9,10]. Thus, the phase transformation of BaSi_xO_1+2x ceramics with the change in T_sint must be clarified. The BaSi_xO_1+2x (x = 1.63) ceramics sintered at 1300 °C presented the coexistence of Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases and exhibited good microwave dielectric properties. As shown in Figure 7, the XRD patterns of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were obtained. The coexistence of Ba₅Si₈O₂₁ and BaSi₂O₅ phases was obtained in BaSi_1.63O_4.26-1 wt% LiF ceramics sintered at 1025 °C, and the Ba₃Si₅O₁₃ second phase of BaSi_1.63O_4.26 ceramics sintered at 1300 °C was inhibited. However, the new Ba₂Si₃O₈ and SiO₂ second phases appeared in BaSi_1.63O_4.26-1 wt% LiF ceramics when T_sint = 925 °C, which implies that the Ba₂Si₃O₈ and SiO₂ phase can transform into BaSi₂O₅ phases at T_sint = 1025 °C. With the increase in the content of LiF, the T_sint of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics decreased gradually. The coexistence of Ba₅Si₈O₂₁, Ba₂Si₃O₈, BaSi₂O₅ and SiO₂ phases was observed in BaSi_1.63O_4.26-y wt% LiF (y = 2, 3) ceramics sintered at 925 and 800 °C.

Figure S2 and

Table 2. The lattice parameters and Rietveld discrepancy factors of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics sintered at their densification temperatures.

Compositions	Phase Compositions		Lattice Parameter of Main Phase					Rietveld Discrepancy Factors
	Main Phase (wt%)	Second Phase (wt%)	a (Å)	b (Å)	c (Å)	β (°)	V (Å3)	Rwp (%)	Rp (%)	χ2
y = 1	Ba5Si8O21 (74.39)	BaSi2O5 (25.61)	32.687	4.694	13.877	98.276	2106.951	12.0	9.1	3.9
y = 2	Ba5Si8O21 (84.51)	Ba2Si3O8 (13.14) BaSi2O5 (1.10) SiO2 (1.25)	32.699	4.699	13.900	98.155	2114.038	18.3	14.5	7.6
y = 3	Ba5Si8O21 (68.69)	Ba2Si3O8 (15.55) BaSi2O5 (13.70) SiO2 (2.06)	32.697	4.697	13.898	98.159	2112.718	16.0	12.6	6.5

show the results of Rietveld refinement. The calculated XRD patterns of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics matched the measured XRD patterns well (Figure S2). The phase compositions of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were observed, as shown in Table 2. The BaSi_1.63O_4.26-1 wt% LiF ceramics with 74.39 wt% Ba₅Si₈O₂₁ and 25.61 wt% BaSi₂O₅ phases was obtained. The decrease in T_sint induced the appearance of the Ba₂Si₃O₈ second phase, and 84.51 wt% and 68.69 wt% Ba₅Si₈O₂₁ phases were obtained in BaSi_1.63O_4.26-y wt% LiF (y = 2, 3) ceramics. The Ba₃Si₅O₁₃ phase could not be obtained in BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics with low T_sint (≤1025 °C), which means that Ba₃Si₅O₁₃ phase can only be synthesised at high T_sint (≥1300 °C). The Ba₅Si₈O₂₁, Ba₂Si₃O₈ and BaSi₂O₅ phases can be synthesised at low T_sint (≤925 °C). In summary, the Ba₅Si₈O₂₁ phase was the most stable phase of barium silicates, and the phase compositions of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were related to T_sint.

The thermally etched SEM images of BaSi_1.63O_4.26-3 wt% LiF and BaSi_1.63O_4.26-3 wt% LiF-Ag electrode ceramics were obtained, as shown in Figure 8. Dense and smooth microstructures were observed in BaSi_1.63O_4.26-3 wt% LiF ceramics. The evident small SiO₂ second phase existed at the grain boundary, as shown in Figure 8 and S3. No LiF or liquid phases existed, and complex phase compositions could not be clarified via SEM images. As shown in Figure 8b, the surface of BaSi_1.63O_4.26-3 wt% LiF ceramics could be well combined with Ag electrodes, which indicates that it is well able be co-fired with Ag electrodes at 800 °C.

The evolution of the phase compositions and sintering characteristic of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics on microwave dielectric properties was investigated. As shown in

Table 3. The optimal sintering temperature, relative density and microwave dielectric properties of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics.

Compositions	Tsint (°C)	ρrel (%)	εr-exp	Q × f (GHz)	τf (ppm/°C)	τf-cal (ppm/°C)
y = 1	1025	96.5	7.42	14,252	+8.37	+11.00
y = 2	950	95.2	7.21	12,913	+11.90	+16.20
y = 3	800	94.4	7.10	12,463	+5.75	+6.12

, with the addition of a LiF sintering aid, the optimal T_sint of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were able to be reduced to less than 1025 °C. At the optimal sintering temperatures, the ρ_rel of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics decreased from 96.5% (y = 1) to 94.4% (y = 3), and the addition of a LiF sintering aid [31] and the decrease in sintering temperature caused a reduction in ρ_rel. The ε_r-exp and Q × f values decreased gradually, and the τ_f-exp values fluctuated with x. The decrease in ε_r-exp and Q × f values was mainly attributed to the decline in ρ_rel. According to Formula (2), the τ_f-cal values of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were calculated, and similar variations in τ_f-exp, τ_f-cal and the content of the Ba₅Si₈O₂₁ phase of the BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were observed as y increased. The τ_f-exp values of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were significantly affected by the content of the Ba₅Si₈O₂₁ phase, and the near-zero τ_f-exp value (+5.75 ppm/°C) was obtained in BaSi_1.63O_4.26-3 wt% LiF ceramics with 68.69 wt% Ba₅Si₈O₂₁, 15.55 wt% Ba₂Si₃O₈, 13.70 wt% BaSi₂O₅ and 2.06 wt% SiO₂ phases.

4. Conclusions

BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) and BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics were synthesised, and the evolution of their phase compositions was investigated. The two-phase system of Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ was obtained at 1.61 ≤ x ≤ 1.67, and no other second phase existed. At 1.67 ≤ x ≤ 1.69, the content of Ba₃Si₅O₁₃ phase was more than 90 wt%. The Ba₅Si₈O₂₁ second phase could be inhibited in BaSi_xO_1+2x (1.68 ≤ x ≤ 1.69) ceramics, and the other BaSi₂O₅ phase was induced. At 1.70 ≤ x ≤ 1.90, the excessive Si element content of BaSi_xO_1+2x ceramics caused the appearance of the Ba₅Si₈O₂₁ second phase, and the coexistence of BaSi₂O₅, Ba₅Si₈O₂₁ and Ba₃Si₅O₁₃ phases was observed. Therefore, the phase compositions of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics sintered at high temperature (≥1300 °C) were significantly controlled by the ratio of Ba:Si. The ε_r-exp and Q × f values of BaSi_xO_1+2x (1.61 ≤ x ≤ 1.90) ceramics were mainly affected by the phase compositions and ρ_rel, and the τ_f-exp values were controlled via the content of the Ba₅Si₈O₂₁ phase with a positive τ_f value. The near-zero τ_f-exp value (+3.95 ppm/°C) was obtained at x = 1.63. Moreover, the LiF sintering aids were able to reduce the sintering temperature of BaSi_1.63O_4.26 ceramics, and the low sintering temperature (800 °C) was obtained in BaSi_1.63O_4.26-y wt% LiF (y = 3) ceramics. When sintering temperature was less than 1025 °C, the Ba₃Si₅O₁₃ phase of BaSi_1.63O_4.26 ceramics was inhibited and the Ba₂Si₃O₈, BaSi₂O₅ and SiO₂ appeared. The content of phases could be affected by the sintering temperature, which shows that the phase compositions of BaSi_xO_1+2x ceramics were related to their sintering temperature. The development of microwave dielectric properties of BaSi_1.63O_4.26-y wt% LiF (1 ≤ y ≤ 3) ceramics strongly relied on their phase compositions, and microwave dielectric properties (ε_r = 7.10, Q × f = 12,463 GHz, and τ_f = +5.75 ppm/°C) were obtained in BaSi_1.63O_4.26-3 wt% LiF ceramics.