Evolution of Phase Transformation on Microwave Dielectric Properties of BaSi x O 1+2 x Ceramics and Their Temperature-Stable LTCC Materials

: BaSi x O 1+2 x (1.61 ≤ x ≤ 1.90) and LiF-doped BaSi 1.63 O 4.26 ceramics were prepared by using a traditional solid-state method at the optimal sintering temperatures. The evolution of phase compositions of BaSi x O 1+2 x (1.61 ≤ x ≤ 1.9) ceramics was revealed. The coexistence of Ba 5 Si 8 O 21 and Ba 3 Si 5 O 13 phases was obtained in BaSi x O 1+2 x (1.61 ≤ x ≤ 1.67) ceramics. The BaSi 2 O 5 phase appeared inBaSi x O 1+2 x (1.68 ≤ x ≤ 1.90) ceramics. At 1.68 ≤ x ≤ 1.69, only BaSi 2 O 5 and Ba 3 Si 5 O 13 phases existed. With the further increase in x , the Ba 5 Si 8 O 21 phase appeared, and BaSi 2 O 5 , Ba 5 Si 8 O 21 and Ba 3 Si 5 O 13 phases coexisted in BaSi x O 1+2 x (1.70 ≤ x ≤ 1.90) ceramics. The phase compositions of BaSi x O 1+2 x (1.61 ≤ x ≤ 1.90) ceramics were controlled by the ratio of Ba:Si. The BaSi x O 1+2 x ( x = 1.68) ceramics with 98.15 wt% Ba 3 Si 5 O 13 and 1.85 wt% BaSi 2 O 5 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 1.63 O 4.26 ceramics with 70.05 wt% Ba 5 Si 8 O 21 and 29.95 wt% Ba 3 Si 5 O 13 phases. The addition of LiF sintering aids were able to reduce the sintering temperatures of BaSi 1.63 O 4.26 ceramics to 800 ◦ C. The phase composition of BaSi 1.63 O 4.26 ceramics was affected by the sintering temperature, and the coexistence of Ba 5 Si 8 O 21 , Ba 2 Si 3 O 8 , BaSi 2 O 5 and SiO 2 phases was achieved in BaSi 1.63 O 4.26 -3 wt% LiF ceramics. The BaSi 1.63 O 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 1.63 O 4.26 -3 wt% LiF ceramics and the Ag electrodes, which indicates their potential for low-temperature co-ﬁred ceramic (LTCC) applications.

The microwave dielectric properties of barium silicates were first reported by Wen Lei et al. [9], and a BaSi 2 O 5 ceramic with excellent microwave dielectric properties (ε r = 6.7,Q × f = 59,500 GHz and τ f = −28.0ppm/ • C) was synthesised through sintering at 1250 • C. Enzhu Li et al. pointed out that the synthesis temperature of a single-phase BaSi 2 O 5 ceramic was more than 1100 • C, and the coexistence of BaSi 2 O 5 , Ba 5 Si 8 O 21 (BaSi 1.6 O 4.2 ) and SiO 2 phases was identified in BaSi 2 O 5 ceramics.The Ba 5 Si 8 O 21 phases existed in BaSi 2 O 5 -2 wt% Li 2 O-B 2 O 3 -CaO-CuO glass ceramics when their sintering temperature was below 800 • C, which means that the Ba 5 Si 8 O 21 phase was easier to synthesise than the BaSi 2 O 5 phase [10].A single-phase BaSi 2 O 5 ceramic sintered at 1225 • C was prepared by Yun Zhang [11].The Ba 5 Si 8 O 21 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 Ba 5 Si 8 O 21 ceramics always exhibited the Ba 5 Si 8 O 21 phase at a high sintering temperature (above 800 • C).However, the Ba 3 Si 5 O 13 (BaSi 1.667 O 4.334 ) ceramic, as an intermediate compound between Ba 5 Si 8 O 21 (BaSi 1.6 O 4.2 ) and BaSi 2 O 5 , exhibited the highest structural and topological complexity in barium silicates [8].The Ba 3 Si 5 O 13 (BaSi 1.667 O 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 (Ba 5 Si 8 O 21 and BaSi 2 O 5 phases sintered at 1200 • C and Ba 3 Si 5 O 13 phase sintered at 1250 • C) [9].Toshihiro Moriga et al. pointed out that Ba 3 Si 5 O 13 single-phase ceramics sintered at 1000 • C could be synthesised at stoichiometric ratios [7].The small difference in the Ba:Si ratios of the Ba 5 Si 8 O 21 , Ba 3 Si 5 O 13 and BaSi 2 O 5 phases caused difficulty in synthesizing Ba 3 Si 5 O 13 ceramics.
Considering the excellent application potential of barium silicate ceramics in LTCC technology, the variation in the phase compositions of BaSi x O 1+2x ceramics with stoichiometric ratios and sintering temperatures needs to be investigated.This study aimed to clarify the phase compositions of BaSi x O 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 x O 1+2x -based LTCC materials with LiF doped were prepared.
The sintered samples of BaSi x O 1+2x and BaSi x O 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 x O 1+2x (1.61 ≤ x ≤ 1.9) and BaSi x O 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].

Results
The BaSi x O 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 x O 1+2x (1.61 ≤ x ≤ 1.67) ceramics was between 1300 and 1325 (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 Ba 3 Si 5 O 13 second phase existed in BaSi x O 1+2x (x = 1.62) ceramics, and the content of the Ba 3 Si 5 O 13 phase in BaSi x O 1+2x (1.61 ≤ x ≤ 1.67) ceramics increased gradually with the rise in x.In the BaSi x O 1+2x (x = 1.67) ceramics, the Ba 5 Si 8 O 21 second phase was present.The single-phase Ba 3 Si 5 O 13 ceramics might be seen in the BaSi x O 1+2x (x = 1.68) ceramics (Figure 1d).With the further increase in x, the intensity of the XRD patterns of the BaSi 2 O 5 and Ba 3 Si 5 O 13 phases gradually rose and decreased, respectively.The evident Ba 5 Si 8 O 21 phase also existed in BaSi x O 1+2x (1.80 ≤ x ≤ 1.85) ceramics, which indicates the complex evolution of the phase compositions of BaSi x O 1+2x (1.68 ≤ x ≤ 1.90) ceramics.Moreover, the Ba 3 Si 5 O 13 ceramics were able to be synthesised via sintering at 1325  2).Therefore, the fitting content of phase compositions was accurate.As shown in Table 1, the Ba 5 Si 8 O 21 main phase and Ba 3 Si 5 O 13 second phase existed in BaSi x O 1+2x (1.61As shown in Figure 3 and S1, the thermally etched SEM and EDS map scanning images of BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics were obtained.The dense and smooth microstructures of BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics were observed.Only the grains of barium silicates were observed in BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics.However, the similar monoclinic structure and elemental composition caused difficulty in distinguishing the grains of Ba 5 Si 8 O 21 and Ba 3 Si 5 O 13 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 Ba 3 Si 5 O 13 and BaSi 2 O 5 , respectively.The Ba 3 Si 5 O 13 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 BaSi 2 O 5 rose gradually.The microwave dielectric properties of the BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics sintered at the optimal temperature were obtained, as shown in Table S1 (see Supplementary materials) and Figures 4 and 5.As shown in Figure 4a, the relative density (ρ rel ) and experimental relative permittivity (ε r-exp ) of BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics fluctuated with the increase in x, and all BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics exhibited high ρ rel (>95%) except th BaSi x O 1+2x (x = 1.75) ceramics.Therefore, ρ rel might have little effect on themicrowave dielectric properties of BaSi x O 1+2x ceramics.In the BaSi x O 1+2x (1.61 ≤ x ≤ 1.67) ceramics, the BaSi x O 1+2x (x = 1.67) ceramics with a 91.27 wt% Ba 3 Si 5 O 13 phase exhibited the largest ε r-exp value, and a low ε r-exp (7.33) was obtained in BaSi x O 1+2x (x = 1.61) ceramics with a 95.87 wt% Ba 5 Si 8 O 21 phase, which was attributed to the low ε r-exp value (7.3) of Ba 5 Si 8 O 21 ceramics [9].In BaSi x O 1+2x (1.68 ≤ x ≤ 1.90) ceramics, ε r-exp decreased from 7.49 to 6.94, and the BaSi x O 1+2x (x = 1.90) ceramics with a 71.12 wt% BaSi 2 O 5 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].
where ε r-cal represents the calculated relative permittivity; V 1 , V 2 and V 3 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 Ba 5 Si 8 O 21 , Ba 3 Si 5 O 13 and BaSi 2 O 5 ceramics [9], respectively.The ε r-cal of BaSi x O 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       At high Tsint (≥1300 °C), the phase compositions of BaSixO1+2x (1.61 ≤ x ≤ 1.90) ceramics were revealed in this work.However, the phase compositions of barium silicates were sensitive to Tsint, and the complex phase transformation of barium silicates existed with the change in Tsint, especially Ba5Si8O21, Ba3Si5O13 and BaSi2O5 ceramics [9,10].Thus, the phase transformation of BaSixO1+2x ceramics with the change in Tsint must be clarified.The where τ f-cal represents the calculated 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.
with the increase in measured temperature, the length of BaSi  At high Tsint (≥1300 °C), the phase compositions of BaSixO1+2x (1.61 ≤ x ≤ 1.90) ceramics were revealed in this work.However, the phase compositions of barium silicates were sensitive to Tsint, and the complex phase transformation of barium silicates existed with the change in Tsint, especially Ba5Si8O21, Ba3Si5O13 and BaSi2O5 ceramics [9,10].Thus, the phase transformation of BaSixO1+2x ceramics with the change in Tsint must be clarified.The BaSixO1+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 BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics were obtained.The coex- Figure S2 and Table 2 show the results of Rietveld refinement.The calculated XRD patterns of BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics matched the measured XRD patterns well (Figure S2).The phase compositions of BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics were observed, as shown in Table 2.The BaSi1.63O4.26-1wt% LiF ceramics with 74.39 wt% Ba5Si8O21 and 25.61 wt% BaSi2O5 phases was obtained.The decrease in Tsint induced the appearance of the Ba2Si3O8 second phase, and 84.51 wt% and 68.69 wt% Ba5Si8O21 phases were obtained in BaSi1.63O4.26-ywt% LiF (y = 2, 3) ceramics.The Ba3Si5O13 phase could not be obtained in BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics with low Tsint (≤ 1025 °C), which means that Ba3Si5O13 phase can only be synthesised at high Tsint (≥ 1300 °C).The Ba5Si8O21, Ba2Si3O8 and BaSi2O5 phases can be synthesised at low Tsint (≤ 925 °C).In summary, the Ba5Si8O21 phase was the most stable phase of barium silicates, and the phase compositions of BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics were related to Tsint.The thermally etched SEM images of BaSi1.63O4.26-3wt% LiF and BaSi1.63O4.26-3wt% LiF-Ag electrode ceramics were obtained, as shown in Figure 8. Dense and smooth microstructures were observed in BaSi1.63O4.26-3wt% LiF ceramics.The evident small SiO2 second phase existed at the grain boundary, as shown in Figures 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 BaSi1.63O4.26-3wt% 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 BaSi1.63O4.26-ywt% LiF (1 ≤ y ≤ 3) ceramics on microwave dielectric properties was investigated.As shown in Table 3, with the addition of a LiF sintering aid, the optimal Tsint of BaSi1.63O4.26ywt% LiF (1 ≤ y ≤ 3) ceramics were able to be reduced to less than 1025 °C.At the optimal sintering temperatures, the ρrel of BaSi1.63O4.26-ywt% 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]   The evolution of the phase compositions and sintering characteristic of BaSi 1.63 O 4.26y wt% LiF (1 ≤ y ≤ 3) ceramics on microwave dielectric properties was investigated.As shown in Table 3, with the addition of a LiF sintering aid, the optimal T sint of BaSi 1.63 O 4.26y 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 1.63 O 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 1.63 O 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 Ba 5 Si 8 O 21 phase of the BaSi 1.63 O 4.26 -y wt%
and V 3 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 Ba 5 Si 8 O 21 , Ba 3 Si 5 O 13 and BaSi 2 O 5 ceramics [9], respectively.τ f-cal agreed well with the τ f-exp in BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics, and τ f-exp , τ f-cal and content of Ba 5 Si 8 O 21 phase of the BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics with x displayed a similar trend.Therefore, the content of the Ba 5 Si 8 O 21 phase significantly affected the τ f-exp of BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics.At 1.65 ≤ x ≤ 1.75, the BaSi x O 1+2x ceramics with the Ba 3 Si 5 O 13 main phase exhibited negative τ f-exp values.Therefore, the present study confirmed the negative τ f value of Ba 3 Si 5 O 13 ceramics, which was controversial in a previous work [9].Ba 5 Si 8 O 21 , as a new τ f compensator, successfully adjusted the negative τ f-exp value of Ba 3 Si 5 O 13 to near zero (+3.95 ppm/ • C and −7.25 ppm/ • C) in the BaSi x O 1+2x (x = 1.63, 1.64) ceramics.

Figure 6 . 12 Figure 7 .
Figure 6.Temperature and frequency dependences of relative permittivity for BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics.At high T sint (≥1300 • C), the phase compositions of BaSi x O 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

Figure S2 and Table 2
Figure S2 and Table 2 show the results of Rietveld refinement.The calculated XRD patterns of BaSi 1.63 O 4.26 -y wt% LiF (1 ≤ y ≤ 3) ceramics matched the measured XRD patterns well (Figure S2).The phase compositions of BaSi 1.63 O 4.26 -y wt% LiF (1 ≤ y ≤ 3) ceramics were observed, as shown in Table 2.The BaSi 1.63 O 4.26 -1 wt% LiF ceramics with 74.39 wt% Ba 5 Si 8 O 21 and 25.61 wt% BaSi 2 O 5 phases was obtained.The decrease in T sint induced the appearance of the Ba 2 Si 3 O 8 second phase, and 84.51 wt% and 68.69 wt% Ba 5 Si 8 O 21 phases were obtained in BaSi 1.63 O 4.26 -y wt% LiF (y = 2, 3) ceramics.The Ba 3 Si 5 O 13 phase could not be obtained in BaSi 1.63 O 4.26 -y wt% LiF (1 ≤ y ≤ 3) ceramics with low T sint (≤1025 • C), which means that Ba 3 Si 5 O 13 phase can only be synthesised at high T sint (≥1300 • C).The Ba 5 Si 8 O 21 , Ba 2 Si 3 O 8 and BaSi 2 O 5 phases can be synthesised at low T sint (≤925 • C).In summary, the Ba 5 Si 8 O 21 phase was the most stable phase of barium silicates, and the phase compositions of BaSi 1.63 O 4.26 -y wt% LiF (1 ≤ y ≤ 3) ceramics were related to T sint .

Figure 8 .
Dense and smooth microstructures were observed in BaSi 1.63 O 4.26 -3 wt% LiF ceramics.The evident small SiO 2 second phase existed at the grain boundary, as shown in Figures 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 1.63 O 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. Crystals 2023, 13, x FOR PEER REVIEW 10 of 12
• C.Only Ba 5 Si 8 O 21 phase seemed to exist in BaSi x O 1+2x (1.61 ≤ x ≤ 1.62) ceramics, and the BaSi x O 1+2x (1.66 ≤ x ≤ 1.67) ceramics exhibited the Ba 3 Si 5 O 13 single phase.The evident coexistence of Ba 5 Si 8 O 21 and Ba 3 Si 5 O 13 phases was observed in BaSi x O 1+2x (1.63 ≤ x ≤ 1.65) ceramics.As illustrated in Figure 1c, the Ba 3 Si 5 O 13 single phase existed in the BaSi x O 1+2x (x = 1.68) ceramics, and the obvious coexistence of Ba 3 Si 5 O 13 and BaSi 2 O 5 phases was observed in the BaSi x O 1+2x (1.69 ≤ x ≤ 1.90) ceramics.However, the similar XRD patterns between Ba 3 Si 5 O 13 and Ba 5 Si 8 O 21 phases caused difficulty in distinguishing the phase compositions of BaSi x O 1+2x ceramics.The enlarged XRD patterns of BaSi x O 1+2x • C. The Rietveld refinement of BaSi x O 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, and the calculated XRD patterns of BaSi x O 1+2x (1.61 ≤ x ≤ 1.90) ceramics matched the measured XRD patterns well (Figure

85 wt% BaSi 2 O 5 was synthesised, and the BaSi 2 O 5 -Ba 3 Si 5 O 13 system could be obtained in BaSi x O 1+2x (1.68 ≤ x ≤ 1.69) ceramics. With the further increase in x, the other Ba 5 Si 8 O 21 second phase appeared in BaSi x O 1+2x (1.7 ≤ x ≤ 1.90) ceramics, and the content of the BaSi 2 O 5 phase increased gradually. Lastly, the results of the Rietveld refinement indicated that the coexistence of the Ba 5 Si 8 O 21 and Ba 3 Si 5 O 13 phases were obtained in BaSi x O 1+2x
≤ x ≤ 1.64) ceramics.The main phase in BaSi x O 1+2x (1.65 ≤ x ≤ 1.67) ceramics changed from the Ba 5 Si 8 O 21 to Ba 3 Si 5 O 13 phase.Moreover, the Ba 5 Si 8 O 21 second phase changed to the BaSi 2 O 5 phase in the BaSi x O 1+2x (x = 1.68) ceramics.The BaSi x O 1+2x (x = 1.68) ceramics with 98.5 wt% Ba 3 Si 5 O 13 and 1.(1.61≤ x ≤ 1.67) ceramics (Ba 5 Si 8 O 21 -Ba 3 Si 5 O 13 system), and the Ba 3 Si 5 O 13 single-phase ceramics could be synthesised in BaSi x O 1+2x (1.67 < x < 1.68) ceramics.The phase compositions of the BaSi x O 1+2x ceramics was significantly affected by the ratio of Ba:Si.

Table 2 .
The lattice parameters and Rietveld discrepancy factors of BaSi 1.63 O 4.26 -y wt% LiF (1 ≤ y ≤ 3) ceramics sintered at their densification temperatures.The thermally etched SEM images of BaSi 1.63 O 4.26 -3 wt% LiF and BaSi 1.63 O 4.26 -3 wt% LiF-Ag electrode ceramics were obtained, as shown in