Phase Compositions and Microwave Dielectric Properties of Na_1+xSrB₅O_9+0.5x Ceramics

Abstract

Microwave dielectric ceramics composed of Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) were synthesized via a traditional solid-state reaction approach. The effects of non-stoichiometric Na on the crystal structures, phase compositions, chemical bond characteristics, and microwave dielectric properties of the Na_1+xSrB₅O_9+0.5x ceramics were systematically studied. All Na_1+xSrB₅O_9+0.5x ceramics sintered at optimum temperatures consisted of a NaSrB₅O₉ solid-solution phase and a SrB₂O₄ phase. Appropriate excess Na could suppress the generation of the SrB₂O₄ phase, and the lowest content of the SrB₂O₄ phase was achieved at x = 0.075. The ε_r values of the Na_1+xSrB₅O_9+0.5x ceramics were primarily affected by the relative density and molecular polarization. The Q × f values showed a positive correlation with the lattice energy. The τ_f value was correlated to the SrB₂O₄ phase content, bond valence, and bond energy. Typically, the Na_1.075SrB₅O_9.0375 ceramic sintered at 825 °C possessed good microwave dielectric properties of ε_r = 5.61, Q × f = 31, 937 GHz, and τ_f = −3.09 ppm/°C, which are suitable for high-frequency, low-temperature co-fired ceramics (LTCCs) substrate applications.

1. Introduction

In recent years, significant advancements have been made in the development of millimeter-wave wireless communications. In order to facilitate the effective utilization of 5G communication, it is imperative to develop innovative microwave dielectric materials that can facilitate the miniaturization and integration of passive electronic components [1,2,3]. Low-temperature co-fired ceramic (LTCC) technologies play a critical role in enabling the miniaturization and integration of communication equipment [4,5,6]. To satisfy the demands of low-temperature co-fired ceramic (LTCC) technologies, microwave dielectric ceramics must be sintered at temperatures below 961 °C. Additionally, low permittivity (ε_r) values contribute to improved signal transmission speeds and reduced latencies, while high quality factor (Q × f) values mitigate losses and broaden the bandwidth. Finally, near-zero temperature coefficients of resonance frequency (τ_f) values ensure system stability.

The development of low-temperature synthetic microwave dielectric ceramics has predominantly centered around molybdates, phosphates, vanadates, borates, and glass–ceramics [7,8,9,10,11]. Of these, borate ceramics have received substantial attention in recent years owing to their low raw prices, variable chemical structures, excellent dielectric properties, and straightforward preparation processes. Liu et al. [12] reported that LiMBO₃ (M = Ca, Sr) ceramics could be densified at 800 °C with excellent dielectric properties (ε_r = 8.7, Q × f = 75,000 GHz, and τ_f = −150 ppm/°C and ε_r = 8.6, Q × f = 60,000 GHz, and τ_f = −39 ppm/°C) and could be chemically compatible with Ag. Zhou et al. [13] prepared dense Li₆B₄O₉ microwave dielectric ceramics at 640 °C with microwave dielectric properties of ε_r = 5.95, Q × f = 41,800 GHz, and τ_f = −72 ppm/°C, and a prototype patch antenna was fabricated by exploiting the compatibility of Li₆B₄O₉ with silver metallization using LTCC technology.

NaSrB₅O₉, a commonly studied borate due to its complex structural chemistry, has been utilized investigations of its photoluminescence properties [14,15,16]. Wu et al. [17] first reported the crystal structure of the NaSrB₅O₉ compound. The fundamental structural unit in NaSrB₅O₉ is the [B₅O₉]³⁻ anionic group, which is constructed from three [BO₃] triangles and two [BO₄] tetrahedra. The Na and Sr atoms are encircled by eight O atoms and form trigonal dodecahedra. In our previous work, we reported that NaSrB₅O₉-based ceramics densified at 800 °C exhibited remarkable microwave dielectric properties of ε_r = 5.67, Q × f = 49,824 GHz, and τ_f = −18.28 ppm/°C [18]. Thus, the second phase of SrB₂O₄ was formed in all ceramics sintered at various temperatures and could potentially be attributed to the evaporation of Na and B. Yang et al. [19] found that an excess of B can suppress the formation of the second phase of SrB₂O₄, resulting in improvements in the uniform microstructures of NaSrB_5+5xO_9+7.5x ceramics. Similarly, Na elements are prone to volatility during the sintering process. However, research on the non-stoichiometric effects of Na on the phase composition and properties of NaSrB₅O₉-based ceramics has not been reported yet.

In this study, the sintering behaviors, phase compositions, microstructures, and microwave dielectric properties of Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) ceramics fabricated via the solid-phase sintering method were thoroughly researched. The intrinsic mechanism responsible for the microwave dielectric properties was elucidated by utilizing the P-V-L bond theory.

2. Experimental Procedure

The analytical reagents, Na₂CO₃ (99.5%), SrCO₃ (99%), and H₃BO₃ (≥99.5%), were utilized in the traditional solid-state reaction method to fabricate Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) ceramics. The powders were weighed according to the aforementioned chemical formulae and mixed with ZrO₂ balls in a nylon jar for 4 h, using ethanol as the mixing medium. The resulting slurries were dried at 80 °C and pre-synthesized at 600 °C for 4 h to obtain the primary phase. The pre-synthesized powders were then re-milled for another 4 h and re-dried. The mixed powders were pressed into cylindrical samples with diameters of 10 mm and thicknesses of 6 mm, using a pressure of 150 MPa. A binder solution containing 5 wt.% of polyvinyl alcohol (PVA) was employed. The green samples were subsequently sintered at temperatures ranging from 750 °C to 850 °C for 4 h.

The phase compositions were analyzed via a powder X-ray diffractometer (Advanced D8, Bruker, Ettlingen, Germany) with CuKα radiation. GSAS and EXPGUI software were utilized to refine the diffraction data to ensure accuracy in determining the crystal structures. The total lattice energy, bond valence, and bond energy were calculated via the P-V-L bond theory [20]. In the case of binary crystals (A_mB_n), the lattice energy (U_total) of the ceramic was calculated as follows:

$$U_{total}=\sum U^{\mu }$$

(1)

$$U^{\mu }=U_c^{\mu }+U_i^{\mu }$$

(2)

$$U_c^{\mu }=2100·m·\frac{{\left(Z_{+}^{\mathsf{\mu }}\right)}^{1.64}}{{{(d}^{\mathsf{\mu }})}^{0.75}}·f_c^{\mathsf{\mu }}$$

(3)

$$U_i^{\mathsf{\mu }}=1270·\frac{\left(m+n\right)·Z_{+}^{\mathsf{\mu }}·Z_{-}^{\mathsf{\mu }}}{d^{\mathsf{\mu }}}·(1-\frac{0.4}{d^{\mathsf{\mu }}})·f_i^{\mathsf{\mu }}$$

(4)

where $U_c^{\mu }$ and $U_i^{\mu }$ represent the covalent and ionic lattice energies of the $\mu$ bond, respectively, and $Z_{+}^{\mu }$ and $Z_{-}^{\mu }$ are the valence states of the cations and anions that constitute the $\mu$ bonds, respectively.

The bond energy (E_T) of the ceramic can be obtained as follows:

$$E_T=\sum E_b^{\mu }$$

(5)

$$E_b^{\mu }=t_c{E}_c^{\mu }+t_i{E}_i^{\mu }$$

(6)

$$E_c^{\mu }=\frac{(r_{CA}+r_{CB})}{d^{\mu }}·{\left(E_{A-A}{E}_{B-B}\right)}^{1/2}$$

(7)

$$E_i^{\mu }=\frac{1389.088}{d^{\mu }}$$

(8)

where $E_c^{\mu }$ and $E_i^{\mu }$ represent the covalent and ionic parts of the bond energy, respectively, $t_c$ and $t_i$ represent the scale factors of the covalent and ionic parts, $r_{CA}$ and $r_{CB}$ are the covalent radii of the chemical bonds in A and B, respectively, and $E_{A-A}$ and $E_{B-B}$ are the homonuclear bond energies.

The bond valence (V) of the ceramic is calculated as follows:

$$V={\sum }_j{V}_{ij}/n$$

(9)

$$V_{ij}=\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{R_{ij}-d_{ij}}{b_0}\right)$$

(10)

where $V_{ij}$ is the bond valence of each bond, n is the number of bonds, $R_{ij}$ is the bond valence parameter (a fixed value), $d_{ij}$ is the bond length, and $b_0$ is a constant.

The microstructures of the samples were examined using scanning electron microscopy (SEM; S-3400 N. Hitachi, Tokyo, Japan). The Archimedes method was employed to determine the bulk densities of the ceramic samples. The microwave dielectric properties of the samples were evaluated using the Hakki–Coleman method [21] with a vector network analyzer (Agilent, N5244A, Santa Clara, CA, USA). Five specimens for each ceramic composition were tested, and the arithmetic means of the test results were taken. The resonance frequencies of the samples were measured at both 25 °C and 85 °C to estimate the temperature coefficients of the resonant frequencies (τ_f), which were determined as follows:

$${\tau }_f=\frac{f_{85}-f_{25}}{\left(85-25\right)}\times {10}^6 \left(\mathrm{p}\mathrm{p}\mathrm{m}/°\mathrm{C}\right)$$

(11)

where f₂₅ and f₈₅ were the TE01δ resonant frequencies at 25 °C and 85 °C, respectively.

3. Results and Discussion

The trend in the relative densities of the Na_1+xSrB₅O_9+0.5x microwave dielectric ceramics at different sintering temperatures is illustrated in Figure 1. The relative densities of ceramics with the same compositions initially increases and then decreases with an increase in the sintering temperature. When 0 ≤ x ≤ 0.05, the optimum sintering temperature for the Na_1+xSrB₅O_9+0.5x ceramics is 800 °C. When x ≥ 0.075, the optimum densification sintering temperature for the Na_1+xSrB₅O_9+0.5x ceramics increased from 800 °C to 825 °C, indicating that an excessive amount of Na can increase the optimum sintering temperature for the Na_1+xSrB₅O_9+0.5x ceramics. In addition, a suitable amount of Na can enhance the relative densities of the ceramics sintered at the optimum sintering temperature. Remarkably, the Na_1.1SrB₅O_9.05 ceramic sintered at 825 °C has the maximum relative density of 98.9%, which is higher than the maximum relative density of the NaSrB₅O₉ ceramic.

Figure 2a displays the XRD patterns of the Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) ceramics at the optimum sintering temperature. The diffraction peaks of all the samples match well with the standard cards for NaSrB₅O₉ (ICDD-PDF 00-056-0415, monoclinic, space group P2₁/c) and SrB₂O₄ (ICDD-PDF 00-015-0779, orthorhombic, space group Pbcn). In addition, the diffraction peak intensity of the second phase, SrB₂O₄, in all ceramics is relatively low, which implies that an excessive amount of Na can reduce the formation of the second phase, SrB₂O₄, to a certain extent.

Crystal structure refinements were performed on powder samples using GSAS software. The calculated patterns of all samples closely fit those of measured, indicating that the refinement results are credible. The pattern following the refinement of the Na_1+xSrB₅O_9+0.5x (x = 0.05) ceramics sintered at 800 °C is shown in Figure 2b. The lattice parameters and phase composition fractions are listed in

Table 1. Lattice and refinement data of Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) ceramics sintered at optimum temperatures.

x	Phase	a (Å)	b (Å)	c (Å)	V (Å3)	wt. %	Rwp	Rp	χ2
0	NaSrB5O9	6.4755	13.9231	8.0265	692.412	81.38	5.86%	4.36%	2.78
	SrB2O4	11.9770	4.3231	6.5811	340.714	18.62
0.025	NaSrB5O9	6.4957	13.9698	8.0489	698.873	82.81	1.93%	1.45%	2.808
	SrB2O4	12.0605	4.3581	6.6351	348.752	17.19
0.050	NaSrB5O9	6.5024	13.9818	8.0543	700.614	85.04	2.36%	1.85%	3.274
	SrB2O4	12.0267	4.3422	6.6080	345.084	14.96
0.075	NaSrB5O9	6.5030	13.9840	8.0561	700.976	90.95	1.88%	1.44%	2.845
	SrB2O4	12.0359	4.3450	6.6138	345.873	9.05
0.100	NaSrB5O9	6.5058	13.9907	8.0601	701.979	88.77	1.89%	1.34%	2.972
	SrB2O4	12.0488	4.3518	6.6235	347.299	11.23
0.125	NaSrB5O9	6.5009	13.9824	8.0537	701.465	87.16	2.24	1.56	3.276
	SrB2O4	12.0244	4.3448	6.6099	345.323	12.84

R_p—the reliability factor of patterns. R_wp—the reliability factor of weighted patterns. χ²—the goodness of fit indicator = chi.2.

. When 0 ≤ x ≤ 0.1, the unit cell volume of the NaSrB₅O₉ phase increases with an increase in x, probably due to the partial entry of Na+ ions into the interstitial sites, resulting in an enlargement of the unit cell volume of the NaSrB₅O₉ phase. When x continues to increase, the unit cell volume slightly decreases. It is noted that excessive Na can suppress the formation of the second phase, SrB₂O₄, and the minimum mass percentage of the SrB₂O₄ phase (content: 9.05 wt.%) was obtained at x = 0.075.

Figure 3 shows the microstructures of the Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) ceramics sintered at optimum temperatures. It can be seen that the grains of all samples are tightly arranged with each other, but irregular polygonal grains appear with the increase in the Na content. When x ≥ 0.05, the grain size increases, the grain boundaries become blurred, and the morphologies of the grains change in the samples. The number of nearly equiaxed grains decreases significantly, while the number of polygonal grains increases, and there are also abnormally large grains in Figure 3f.

In order to analyze the elemental compositions of the polygonal grains in the ceramic samples, EDS testing was conducted on the labeled grains in Figure 3c, and the results are shown in Figure 4. The EDS elemental analysis results indicate that the elements contained in the two types of grains (A and B) are the same, including Na, Sr, B, and O, and their atomic ratios are similar, indicating that they belong to the same solid-solution phase.

The ε_r values of the Na_1+xSrB₅O_9+0.5x ceramics at different sintering temperatures are shown in Figure 5a. The ε_r values of all compositions increase first and then decrease with the increase in sintering temperature, which agrees well with the variation trend of the relative densities of the ceramics, indicating that the relative density is the main factor for ε_r values.

To further discuss the influence of the Na content on the ε_r values of Na_1+xSrB₅O_9+0.5x ceramics sintered at optimum temperatures, the corrected dielectric constant (ε_rc) was obtained by correcting the measured dielectric constant (ε_r) of the ceramics for porosity, and the theoretical dielectric constant (ε_cal) and the actual molecular polarization (α_obs) were calculated based on the refined results, as shown in Figure 5b. The values were determined as follows [22,23,24]:

$${\epsilon }_{rc}={\epsilon }_r(1+1.5P)$$

(12)

$${\epsilon }_{cal}=\frac{3V_m+8\pi {\alpha }_{theo}}{3V_m-4\pi {\alpha }_{theo}}$$

(13)

$$\begin{gathered} {\alpha }_{theo}\left({Na}_{1+x}Sr{B}_5{O}_{9+0.5x}\right)=\left(1+x\right)\times \alpha \left({Na}^{+}\right)+\alpha \left({Sr}^{2+}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+5\alpha \left(B^{3+}\right)+\left(9+0.5x\right)\times \alpha \left(O^{2-}\right) \end{gathered}$$

(14)

$${\alpha }_{theo}\left(Sr{B}_2{O}_4\right)=\alpha \left({Sr}^{2+}\right)+2\alpha \left(B^{3+}\right)+4\alpha \left(O^{2-}\right)$$

(15)

$$\ln {\epsilon }_{cal}={\sum }_i^n{V}_i\ln {\epsilon }_i$$

(16)

where P is fractional porosity, V_m is the molecular volume, α_theo is the theoretical polarizability, and V_i represents the volume fraction of each phase: α(Na⁺) = 1.8 ų, α(Sr²⁺) = 4.24 ų, α(B³⁺) = 0.05 ų, and α(O²) = 2.01 ų [25].

The Clausius–Mosotti equation can be utilized to determine the observed ionic polarizability, which is calculated as follows [26]:

$${\alpha }_{obs}=\frac{3V({\epsilon }_r-1)}{4\pi ({\epsilon }_r+2)}$$

(17)

where V is the volume of the unit cell.

The trend in the variation of ε_r values is consistent with those of ε_rc and α_obs but inconsistent with that of ε_cal, indicating that relative density and molecular polarization are important factors influencing the ε_r values of Na_1+xSrB₅O_9+0.5x ceramics.

Figure 6 shows the Q × f values of Na_1+xSrB₅O_9+0.5x ceramics sintered at different temperatures. It can be seen that the Q × f values of Na_1+xSrB₅O_9+0.5x ceramics with the same composition first increase and then decrease with an increasing sintering temperature due to reductions in the extrinsic losses caused by decreases in pore and grain boundary defects. The maximum Q × f value is obtained at the optimal sintering temperature, after which the Q × f value decreases as the grain grows abnormally large. In addition, among all the compositions with excess Na, Na_1+xSrB₅O_9+0.5x (x = 0.05, Ts = 800 °C) shows the highest Q × f value of 38,453 GHz, indicating that excess Na will deteriorate the dielectric properties of ceramics.

In To further understand the variation in the Q × f values of Na_1+xSrB₅O_9+0.5x ceramics, the total lattice energies (U) and atomic packing densities of Na_1+xSrB₅O_9+0.5x ceramics were calculated. The atomic packing density is calculated as follows [27]:

$$\begin{gathered} Atom packing fraction= \frac{Volume of the atoms in the cell}{Volume of unit cell}\times Z \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{4\pi }{3}\times 4\times \frac{(1+x){\times r}_{Na}^3+r_{Sr}^3+5r_B^3+(9+0.5x){\times r}_O^3}{abc} \end{gathered}$$

(18)

where Z is the molecular number in a unit cell.

Typically, a higher lattice energy and atomic packing density lead to a reduction in the intrinsic loss and an enhanced quality factor of a ceramic material. As shown in Figure 6b, the variation trend of the Q × f values showed a positive correlation with U values and an inverse correlation with atomic packing density, implying that the lattice energy has a major impact on the Q × f value of a Na_1+xSrB₅O_9+0.5x ceramic. The larger lattice energy corresponds to a more stable crystal structure with a minimum intrinsic loss due to non-harmonic lattice vibration.

The τ_f values of microwave dielectric ceramics are influenced by their phase compositions, bond energies, and bond valences. Generally, a higher bond valence (V) and bond energy (E) correspond greater strengths of the chemical bonds and a smaller |τ_f| value. Figure 7 depicts the τ_f values, bond valences, and bond energies of Na_1+xSrB₅O_9+0.5x ceramics sintered at optimum temperatures. When x ≤ 0.05, the τ_f values slightly increase, which is mainly related to the reduction in the second phase, SrB₂O₄, content. When x = 0.075, the ceramic sintered at 825 °C exhibits the maximum τ_f value of −3.09 ppm/°C, which is correlated to the lower second phase content and increases in the bond valence and bond energy. However, as the x value further increases, the τ_f values decrease due to the increase in the second phase content.

Table 2. The sintering temperatures and microwave dielectric properties of some borate ceramics.

Compounds	S. T. (°C)	εr	Q × f (GHz)	τf (ppm/°C)	Ref.
CaAlB2O5.5	940	5.8	63,338	−29	[28]
Zn3B2O6	925	6.7	58,500	−58	[29]
(Zn0.95Ni0.05)3 B2O6	900	6.9	91,000	−55.6	[30]
LiBO2	640	5.3	18,200	−66.2	[31]
NaSrB5O9	850	5.67	49,824	−18.28	[17]
NaSrB5.35O9.525	825	5.68	57,173	−14.83	[18]
Na1.075SrB5O9.0375	825	5.61	31,937	−3.09	This work

lists the sintering temperatures and microwave dielectric properties of several borate ceramics. Generally, borate ceramics exhibit low sintering temperatures, low permittivity values, and high Q × f values, rendering them proficient for utilization in low-temperature co-fired ceramics. Compared to the CaAlB₂O_5.5 and Zn₃B₂O₆ systems, the NaSrB₅O₉ system exhibits a lower sintering temperature and a τ_f value closer to zero. In comparison to the LiBO₂ system, the NaSrB₅O₉ system has a higher Q × f value and a τ_f value that is closer to zero. Furthermore, the Na_1.075SrB₅O_9.0375 ceramic has a τ_f value that is closer to zero than the NaSrB₅O₉ ceramic. In this work, the Na_1.075SrB₅O_9.0375 ceramic exhibited a low densification temperature (825 °C), a near-zero τ_f value (−3.09 ppm/°C), a high Q × f value (31,937 GHz), and a low dielectric constant (5.61), making it suitable for LTCC applications.

4. Conclusions

Microwave dielectric ceramics composed of Na_1+xSrB₅O_9+0.5x (0 ≤ x ≤ 0.125) were synthesized via a traditional solid-state reaction approach. The samples sintered at optimum temperatures contained a Na_1+xSrB₅O_9+0.5x solid-solution phase and SrB₂O₄ phase. Excessive Na can suppress the formation of the second phase, SrB₂O₄, and the minimum mass percentage of the SrB₂O₄ phase (content: 9.05 wt.%) was obtained at x = 0.075. The ε_r values of the Na_1+xSrB₅O_9+0.5x ceramics were mainly related to the relative density and molecular polarization. The Q × f values showed a positive correlation with lattice energy. The τ_f value was dependent on the second phase content, bond valence, and bond energy. Temperature-stable microwave dielectric ceramics composed of Na_1.075SrB₅O_9.0375 were obtained at 825 °C and exhibited good microwave dielectric properties of ε_r = 5.61, Q × f = 31,937 GHz, and τ_f = −3.09 ppm/°C, which are suitable for high-frequency LTCC substrate applications.