Crystal Structure, Infrared Spectra, and Microwave Dielectric Properties of Ce2(Zr0.94Sn0.06)3(MoO4)9 Ceramics With Low Sintering Temperature

Tian, Huanrong; Liu, Xin; Yang, Yaokang; Wu, Haitao; Zhang, Zhiliang

doi:10.3389/fmats.2020.00145

ORIGINAL RESEARCH article

Front. Mater., 22 May 2020
Sec. Ceramics and Glass
Volume 7 - 2020 | https://doi.org/10.3389/fmats.2020.00145

Crystal Structure, Infrared Spectra, and Microwave Dielectric Properties of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ Ceramics With Low Sintering Temperature

Huanrong Tian¹

Xin Liu¹

Yaokang Yang¹

Haitao Wu¹^*

Zhiliang Zhang²^*

¹School of Materials Science and Engineering, University of Jinan, Jinan, China
²State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China

Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ (CZSM) ceramics were synthesized via a traditional solid-state method. The effects of Sn-substitution on phase composition, microstructure, and microwave dielectric properties as a function of sintering temperature were discussed. The XRD results indicated that all the samples exhibited a single phase. The chemical bonds of CZSM ceramics were calculated based on P-V-L theory, which could be used to evaluate the relationship between structure and microwave dielectric properties. The tendency of dielectric constant was depended on the theoretical dielectric polarizability and bond ionicity. Moreover, the improvement of Q·f value was ascribed to the increase of packing fraction. The reduced τ_f value could be explained by decrease of the bond energy, enhanced the co-efficient of thermal expansion and increase of bond valence (V_Zr(Sn)). The complex permittivity values were obtained from infrared reflectivity spectra. The dielectric permittivity and loss were 10.92 and 3.08 × 10⁻⁴, respectively, which agreed well with the measured value. Typically, the optimal microwave dielectric properties of ε_r = 10.35, Q·f = 59,660 GHz (at 9.70 GHz), and τ_f = −7.52 ppm/°C were achieved in CZSM ceramics sintered at 800°C for 6 h.

Introduction

Owing to the characteristics of light weight, low cost, and high performance, the microwave dielectric ceramics have been widely used as filters, waveguides, resonators, substrates, and waveguides (Cava, 2001; Reaney and Iddles, 2006; Li et al., 2018; Chen et al., 2019; Cheng et al., 2019; Wu et al., 2019). Currently, 5th generation mobile communication systems have received increasing attention (Zhou et al., 2017; Pang and Zhou, 2019; Bafrooei et al., 2020; Lin et al., 2020). To meet the microwave devices applied at millimeter wave, new materials and technologies are required. As a new ceramic fabrication technology, the low temperature co-firing ceramics (LTCC) technology have been intensively studied, it provide the platform for fabrication of three-dimensional ceramic modules (Yu et al., 2015; Sebastian et al., 2016; Guo et al., 2019; Hsiang et al., 2019; Song et al., 2020). Materials in this discipline require a low sintering temperature to co-fire with electrode material and suitable properties: a low dielectric constant (ε_r) to avoid the signal delay, a high quality factor (Q·f) for better selectivity at higher frequencies and a near-zero temperature coefficient of resonant frequency (τ_f) for the frequency stability (Song et al., 2018; Lin et al., 2020). Therefore, it is essential to develop the microwave materials with low permittivity and high Q·f value.

Recently, Mo-based dielectric ceramics have been widely reported owing to low sintering temperature (<960°C) and good microwave dielectric properties (Choi et al., 2007; Pang et al., 2011; Surjith and Ratheesh, 2013; Zhang et al., 2015, 2019; Liu and Zuo, 2017, 2018; Tao et al., 2019; Xing et al., 2019; Zhang and Wu, 2019; Zheng et al., 2020). Among these excellent materials, the Ce₂Zr₃(MoO₄)₉ ceramic was regarded as candidate for LTCC materials applications due to low sintering temperature and near-zero τ_f value (Tao et al., 2019). However, the Ce₂Zr₃(MoO₄)₉ ceramics exhibited a higher dielectric losses, some strategies should be adopted in this paper. A large of studies for improving microwave dielectric properties have been carried out via Sn⁴⁺ ions substitution (Yang et al., 2009; Ma et al., 2013; Li et al., 2019). For instance, when x value increased from 0.0 to 0.6, the quality factor of Ca(Sn_1−xSi_x)O₃ (x = 0.5–1.0) ceramics increased from 16,000 to 63,000 GHz (Ma et al., 2013). The optimal microwave dielectric properties of Mg₂(Ti_0.8Sn_0.2)O₄ ceramics with ε_r = 12.18, Q·f = 170,130 GHz, and τ_f = −53.1 ppm/°C (Li et al., 2019). Thus, Sn⁴⁺ ions substitution was taken to improve Q·f value of Ce₂Zr₃(MoO₄)₉ ceramics in this work. The Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ (CZSM) ceramics were successfully prepared. The phase composition, sintering characteristics, microstructure, and dielectric properties of CZSM ceramics were investigated scientifically. Infrared reflectivity spectra (IR) and chemical bonds theory of complex crystals were adopted as useful tools to analyze the effect of intrinsic factor on microwave dielectric properties of CZSM ceramics.

Experimental

The reagent grade CeO₂ (99.9%, Macklin, China), ZrO₂ (99.99%, Macklin, China), SnO₂ (99.95%, Aladdin, China), and MoO₃ (99.95%, Aladdin, China) powders were used to fabricate CZSM ceramics by the traditional solid-state method. Based on the chemical formula, the raw materials were mixed by zirconia balls for 24 h with absolute ethanol as media. After drying at a temperature 80°C, the slurries were calcined at 700°C for 2 h. Then, the pre-sintered powders were crushed and re-milled for 24 h. Subsequently, 12 wt.% PVA added to the mixture, and the powders were pressed into pellets (10 mm in diameter and 6 mm in height). Finally, all the samples were sintered at 650–850°C for 6 h in air.

XRD was applied to examine the phase compositions of the sintered samples with Cu Kα radiation (D8 Advance, Bruker Co., Germany). The structure parameters and cell volume were obtained from refinement of XRD data using FullProf program. The microstructures of sintered samples were observed using SEM (FEI Co., United States) coupled with EDS. The ε_r value at microwave frequencies (13–15 GHz) and the Q·f value at microwave frequencies (9–11 GHz) were measured using the network analyzer (N5234A, Agilent Co., USA) (Hakki and Coleman, 1960; Courtney, 1970). The τ_f value was calculated using Equation (1):

\begin{array}{l} τ f = \frac{f_{2} - f_{1}}{f_{1} (T_{2} - T_{1})} \times 10^{6} (p p m /^{°} C) & (1) \end{array}

where f₁ and f₂ are the resonant frequencies at the measuring temperatures T₁ (25°C) and T₂ (85°C), respectively. The apparent density was measured via the Archimedes method, and the theoretical density can be obtained through Equation (2).

\begin{array}{l} ρ_{t h e o r y} = \frac{Z A}{V_{c} N_{A}} & (2) \end{array}

where A, Z, and N_A are the atomic weight, number of atom in unit cell and volume of unit cell, respectively. The relative density was calculated by Equation (3):

\begin{array}{l} ρ_{r e l a t i v e} = \frac{ρ_{a p p a r e n t}}{ρ_{t h e o r y}} \times 100 % & (3) \end{array}

Results and Discussion

Figure 1 presented the XRD patterns of CZSM ceramics sintered between 650–850°C. It was observed that all of diffraction patterns match well with the Pr₂Zr₃(MoO₄)₉ (PDF#51-1851) phase, with no secondary phase detected. It indicated that all of sintered samples formed single phase solid solution, which belongs to trigonal system with R-3c (167) space group. To determinate its structure, refinement of the XRD data were conducted using FullProf program with Rietveld's method. The Nd₂Zr₃(MoO₄)₉ (ICSD File No. 92600) was used as starting structural model. The refinement pattern of samples sintered at range of 650–850°C, as shown in Figure 2. The main crystallographic parameters and reliability factors of R_wp, R_p, and χ² for samples are summarized in Table 1. The R_wp, R_p, and χ² values were found to be in the range of 9.5–10.9, 7.2–8.6%, and 1.8–2.5, respectively. The value χ² were smaller to ensure the reliability of refinement. With the increasing sintering temperature, the a and b gradually increased from 9.8251 to 9.8269 Å, and c increased from 58.8278 to 58.8434 Å, which resulted in V_m increased from 4918.02 Å³ at 650°C to 4921.14 Å³ at 800°C. Figure 3 presented crystal structure of CZSM ceramics. It can be seen that the Ce, Zr(1), Zr(2), Mo(1), and Mo(2) atoms are nearest neighbors to 9, 6, 6, 4, and 4 oxygen atoms, respectively. The [CeO₉] occupying the large cavities of the structure, the [CeO₉] and [ZrO₆] were connected by [MoO₄] at the structure.

FIGURE 1

Figure 1. XRD patterns of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 650–850°C.

FIGURE 2

Figure 2. Rietveld refinement of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 650–850°C.

TABLE 1

Table 1. The refinement parameters, theoretical densities and relative densities of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics fired at 650–800°C.

FIGURE 3

Figure 3. The schematic of the crystal structure for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics.

Figure 4 illustrated the curves of the apparent and relative density of CZSM samples sintered at 650–850°C. The apparent densities increased from 3.50 g/cm³ to the maximum value of 3.90 g/cm³ with increasing sintering temperature. The relative density have same tendency as apparent density, a high relative density (>94%) was achieved at 750–850°C. Typical SEM images of CZSM ceramics sintered at different temperature were shown in Figures 5A–E. Grain boundaries were evident in all the samples, indicating that crystalline grains grew well in these samples. Moreover, the grain size increased from 1.93 to 3.19 μm and the pores gradually decreased with the increase of sintering temperature. The result of EDS about grain from samples sintered at 800°C was presented in Figure 5F. The ratio of Ce, Zr, Sn, Mo, and O atom were 3.93, 6.56, 0.34, 18.50, and 70.67%, respectively, which was corresponded to theoretical composition of CZSM ceramic.

FIGURE 4

Figure 4. Apparent and relative density of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics as a function of sintering temperature.

FIGURE 5

Figure 5. Typical SEM micrographs of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics fired at (A) 650°C, (B) 700°C, (C) 750°C, (D) 800°C, (E) 850°C, and (F) EDS analysis about grain selected randomly from the sample sintered at 800°C.

The curves of microwave dielectric properties for CZSM samples were shown in Figure 6. The dielectric constant (ε_r) increased and reached maximum value of 10.47 as the temperature shifted from 650 to 750°C, and then kept stable with further increasing sintering temperature. In addition, the tendency of the ε_r value was corresponded to the density when sintering temperature at 650–800°C, suggesting that dielectric constant was closely related to the density in lower temperature. As we all know, apart from the extrinsic factors like density and phase composition, the ε_r also affected by the intrinsic factors such as polarizability and bond ionicity (Bi et al., 2018; Manan et al., 2018; Zhang et al., 2019). The XRD result suggesting the single phase ceramics was formed. Thus, the ε_r value of CZSM ceramics were mainly determined by polarizability and bond ionicity when the sample was compact. The theoretical dielectric polarizability (α_theo.) and observed dielectric polarizability (α_obs.) were calculated through Equations (4) and (5), respectively.

\begin{array}{l} α_{t h e o .} = α (C e_{2} {(Z r_{0.94} S n_{0.06})}_{3} {(M o O_{4})}_{9}) \\ = 2 α (C e^{3 +}) + 2.82 α (Z r^{4 +}) + 0.18 α (S n^{4 +}) + 9 α (M o^{6 +}) + 36 α (O^{2 +}) & (4) \end{array}

\begin{array}{l} α_{o b s .} = \frac{1}{b} V_{m} \frac{ε - 1}{ε + 2} & (5) \end{array}

where α(Ce³⁺) = 6.15 Å³, α(Zr⁴⁺) = 3.25 Å³, α(Sn⁴⁺) = 2.83 Å³, α(O²⁺) = 2.01 Å³ was reported by Shannon et al. and α(Mo⁶⁺) = 3.28 Å³ is calculated by Choi et al. (Shannon, 1993; Choi et al., 2007). Moreover, V_m is the molar volume and b is a constant value (4π/3), respectively. The results were listed in Table S1. The α_theo. value (123.85 Å³) lower than the Ce₂Zr₃(MoO₄)₉ ceramics (123.93 Å³), which could be attributed to the smaller polarizability of Sn⁴⁺:α(Sn⁴⁺) = 2.83 Å³ < α(Zr⁴⁺) = 3.25 Å³ (Tao et al., 2019). Besides, the tendency of ε_r value was similar to the α_theo. value and α_obs. value, indicating that the reduced ε_r value was strongly dependent on the decrease of polarizability.

FIGURE 6

Figure 6. Curves of microwave dielectric properties as a function of sintering temperature for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics in the temperature range from 650 to 850°C.

Moreover, the quality factor(Q·f) increased from 24,410 to 59,660 GHz, and then declined slightly with further increasing sintering temperature, the maximum of the Q·f was 59,660 GHz at 800°C. In general, the dielectric losses are composed of intrinsic losses (lattice vibration) and extrinsic losses (grain size and impure phase). The grain size showed upward tendency with increasing sintering temperature, it was similar to the variation of Q·f value. Therefore, the increased grain size was important for improvement of the Q·f value (Yang et al., 2002, 2019; Ichinose and Shimada, 2006). In order to investigate the effect of the intrinsic factors, the packing fraction has been calculated by Equation (6).

\begin{array}{l} p a c k i n g f r a c t i o n (%) = \frac{v o l u m e o f t h e a t o m s i n t h e c e l l}{v o l u m e o f u n i t c e l l} \times Z & (6) \end{array}

where Z is the number of molecules per cell. Kim et al. reported the effective ionic size (Kim et al., 2010). The results indicated that the smaller ions size of Sn⁴⁺ (0.69 Å) substitution to Zr⁴⁺ (0.72 Å) lead to the higher packing fraction (47.84 > 47.74%). Thus, the improvement of Q·f value was ascribed to the increase of packing fraction. Furthermore, it suggested that the Sn⁴⁺ ions substitution could improve the quality factor of Ce₂Zr₃(MoO₄)₉ ceramics.

The temperature co-efficient of resonant frequency (τ_f) of CZSM ceramics sintered at different temperatures from 650 to 850°C was shown in Figure 6. It can be seen that the saturation value of τ_f = −7.52 ppm/°C was obtained when sintered at 800°C and kept stable at 700–850°C. The temperature coefficient of resonant frequency was associated with bond valence (Yoon et al., 2003; Cai et al., 2015). Therefore, the bond valence of [Zr(Sn)O₆] octahedra can be obtained by Equations (7) and (8).

\begin{array}{l} V_{i} = \sum_{j} v_{i j} & (7) \end{array}

\begin{array}{l} v_{i j} = exp [\frac{(R_{i j} - d_{i j})}{b}] & (8) \end{array}

where V_ij represent the sum of all the bond valences, R_ij is the bond valence parameter, d_ij is the length of the bond between atoms i and j, and b is an constant equal to 0.37. The results of bond valence were listed in Table S1. The bond valence (V_Zr(Sn)) increased from 8.92 to 9.17 with the Sn⁴⁺ substitution, and the τ_f value correlated to the change of bond valence (V_Zr(Sn)) (Tao et al., 2019). It indicated that the decline of τ_f value was related to the increase of bond valence (V_Zr(Sn)).

Figure 7 showed the microwave dielectric properties of Mo-based dielectric ceramics with low dielectric constant, and the parameters were summarized in Table S2 (Choi et al., 2007; Pang et al., 2011; Surjith and Ratheesh, 2013; Zhang et al., 2015, 2019; Liu and Zuo, 2017, 2018; Tao et al., 2019; Xing et al., 2019; Zhang and Wu, 2019; Zheng et al., 2020). The CZSM ceramics possessed excellent microwave dielectric properties and low sintering temperature in this system. It suggests that they have potential for exploitation in LTCC technology. Certainly, it is necessary to study the relationship between structure and microwave dielectric properties. Thus, the bond ionicity, lattice energy, bond energy, and coefficients of thermal expansion were calculated to investigate the relationships between chemical bond and dielectric properties of the CZSM ceramic. Based on P-V-L theory, the complex crystals CZSM were decomposed into the sum of binary crystals as Equation (9) (Xue and Zhang, 1996; Wu et al., 1998; Yang et al., 2019):

\begin{array}{l} C e_{2} {(Z r_{0.94} S n_{0.06})}_{3} {(M o O_{4})}_{9} = C e_{2} Z r / S n (1) Z r / S n {(2)}_{2} M o {(1)}_{6} M o {(2)}_{3} \\ O {(1)}_{6} O {(2)}_{6} O {(3)}_{6} O {(4)}_{6} O {(5)}_{6} O {(6)}_{6} \\ = C e_{2 / 3} O {(1)}_{3} + C e_{2 / 3} O {(2)}_{3} + C e_{2 / 3} O {(6)}_{3} \\ + Z r / S n (1) O {(4)}_{3} + Z r / S n (2) O {(3)}_{3} + Z r / S n (2) O {(5)}_{3} \\ + M o {(1)}_{3 / 2} O {(1)}_{3} + M o {(1)}_{3 / 2} O {(2)}_{3} + M o {(1)}_{3 / 2} O {(3)}_{3} \\ + M o {(1)}_{3 / 2} O {(4)}_{3} + M o {(2)}_{3 / 2} O {(5)}_{3} + M o {(2)}_{3 / 2} O {(6)}_{3} & (9) \end{array}

Equation (10) indicated that the dielectric constant can be predicted by bond ionicity (Batsanov, 1982).

\begin{array}{l} ε_{r} = \frac{n^{2} - 1}{1 - f_{i}} + 1 & (10) \end{array}

where n is the refractive index. The bond ionicity were calculated using the Equations (11)–(13) (Xue and Zhang, 1996; Wu et al., 1998).

\begin{array}{l} {f_{i}}^{μ} = \frac{{(C^{μ})}^{2}}{{(E_{g}^{μ})}^{2}} = \frac{{(C^{μ})}^{2}}{{(E_{h}^{μ})}^{2} + {(C^{μ})}^{2}} & (11) \end{array}

\begin{array}{l} {(E_{h}^{μ})}^{2} = \frac{39.74}{{(d^{μ})}^{2.48}} & (12) \end{array}

\begin{array}{l} C^{μ} = 14.4 b^{μ} e x p (- k_{s}^{μ} r_{0}^{μ}) [\frac{{(Z_{A}^{μ})}^{*}}{r_{0}^{μ}} - (n / m) \frac{{(Z_{B}^{μ})}^{*}}{r_{0}^{μ}}] & (13) \end{array}

\begin{array}{l} k_{s}^{μ} = {(4 k_{F} / π α_{B})}^{1 / 2} & (14) \end{array}

\begin{array}{l} r_{0}^{μ} = \frac{1}{2} d^{μ} & (15) \end{array}

where $E_{g}^{μ}$ is the average energy gap, and it can be separated into homopolar $E_{h}^{μ}$ and heteropolar c^μ parts. The exp(- $k_{s}^{μ} r_{0}^{μ}$ ) is Thomas-Fermi prescreening factor, and it was calculated through Equations (14) and (15) (Levine, 1973). The f_i value of CZSM ceramics were shown in Figure 8, and the results were listed in Table 2. Decreasing sequence of f_i was f_i (Ce-O)> f_i (Zr/Sn-O)> f_i (Mo-O), the largest f_i value of 85.64% was obtained in Ce-O bond. Besides, the average of f_i (Ce-O) value decreased from 85.18 to 85.14% with the Sn⁴⁺ doped shifted from 0 to 0.06. The tendency of the ε_r value was consisted with the variation of f_i (Ce-O) value. It indicated that the reduced ε_r value was mainly dominated by the degressive bond ioniticy of Ce-O bond.

FIGURE 7

Figure 7. (A) Quality factors (Q·f) and (B) the temperature coefficient of resonant frequency (τ_f) of Mo-based microwave dielectric ceramics with a low dielectric constant.

TABLE 2

Table 2. Band ionicity f_i, lattice energy U, bond energy E, and coefficient of thermal expansion α of each bond for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramic sintered at 800°C.

FIGURE 8

Figure 8. Bond ionicity for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 800°C.

The dielectric loss can be control by the binding ability between cation and oxygen ion, high binding energy corresponds to low intrinsic loss. Thus, lattice energy of CZSM ceramics can be calculated by Equations (16)–(18) (Xue and Zhang, 1996; Wu et al., 1998).

\begin{array}{l} U = \sum_{μ} (U_{b i}^{μ} + U_{b c}^{μ}) & (16) \end{array}

\begin{array}{l} U_{b i}^{μ} = 1270 \frac{(m + n) Z_{+}^{μ} Z_{-}^{μ}}{d^{μ}} (1 - \frac{0.4}{d^{μ}}) f_{i}^{μ} & (17) \end{array}

\begin{array}{l} U_{b c}^{μ} = 2100 m \frac{{(Z_{+}^{μ})}^{1.64}}{{(d^{μ})}^{0.75}} f_{c}^{μ} & (18) \end{array}

where the lattice energy $U_{b}^{μ}$ can be separated into covalent $U_{b c}^{μ}$ and ionic $U_{b t}^{μ}$ parts. According to Figure 9, the sequence of U (Mo-O)>U (Zr/Sn-O)>U (Ce-O) suggested that Mo-O bond play a vital role in enhancing the stability of ionic crystals.

FIGURE 9

Figure 9. Lattice energy for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 800°C.

What's more, the τ_f should be considered for realistic application of microwave dielectric ceramic. High bond energy could lead to a small absolute τ_f value. Hence, the bond energy can be obtained by Equations (19)–(21) (Sanderson, 1968, 1971, 1983):

\begin{array}{l} E_{b}^{μ} = t_{c} E_{c}^{μ} + t_{i} E_{i}^{μ} & (19) \end{array}

\begin{array}{l} E_{i}^{μ} = \frac{33200}{d^{μ}} & (20) \end{array}

\begin{array}{l} E_{c}^{μ} = \frac{r_{c A} + r_{c B}}{d^{μ}} {(E_{A - A} E_{B - B})}^{1 / 2} & (21) \end{array}

where r_cA and r_cB are the covalent radii of atom A and atom B; t_i and t_c are ionic and covalent proportional coefficient of an individual bond μ. The bond energy E_A−A and E_B−B can be referred to handbook (Luo, 2007). What's more, S_A and S_B are the electronegativities of A and B atoms. Figure 10 illustrated bond energy of different bond type for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics. The bond energy of Mo-O bond was larger than others, it suggested that Mo-O bond provided major contribution to the structural stability of CZSM ceramics. Compared with the Ce₂Zr₃(MoO₄)₉ ceramic, the bond energy of Mo-O bond declined from 574.8383 to 568.7162 KJ/mol. Meanwhile, the τ_f value was positively correlated with the change of bond energy (E_Mo−O). It suggested that the downward trend τ_f value could be explained by the decrease of bond energy (E_Mo−O).

FIGURE 10

Figure 10. Bond energy of different bond type for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 800°C.

The τ_f value was negatively related to the coefficients of thermal expansion, which can be obtained via Equation (22). Thus, the coefficients of thermal expansion were calculated based on P-V-L theory (Hakki and Coleman, 1960; Courtney, 1970; Xing et al., 2019).

\begin{array}{l} τ_{f} = - (\frac{τ_{ε}}{2} + α) & (22) \end{array}

where τ_ε is temperature coefficient of the dielectric constant. The average values of Ce-O, Mo-O, and Zr/Sn-O bond were 10.0908 × 10⁻⁶ K⁻¹, −0.3333 × 10⁻⁶ K⁻¹ and 3.3463 × 10⁻⁶ K⁻¹, respectively. In addition, The Mo-O bonds had a positive effect on τ_f value due to α_Mo−O value was negative. The α_Mo−O value increased from −0.3575 × 10⁻⁶ K⁻¹ to −0.3333 × 10⁻⁶ K⁻¹ because of the Sn⁴⁺ substitution for Zr⁴⁺. The higher α_Mo−O value result in large absolute value. Hence, the reduced τ_f value was associated with enhanced the thermal expansion coefficient (α_Mo−O).

IR reflectivity spectra of CZSM ceramics was exhibited in Figure 11. Based on the classical harmonic oscillator model, the infrared spectra were fitted with 24 internal modes, which were listed in Table 3 (Petzelt and Kamba, 2003). ε^* (ω) (the complex dielectric permittivity) and R (ω) (the complex reflectivity) were calculated by Equations (23) and (24) (Wakino et al., 1986; Li et al., 2016; Tang et al., 2019; Guo et al., 2020). Furthermore, the tan δ (dielectric loss tangent) can be obtained through Equation (25).

\begin{array}{l} ε^{*} (ω) = ε_{\infty} + \sum_{j = 1}^{n} \frac{{ω_{p j}}^{2}}{{ω_{o j}}^{2} - ω^{2} - j γ_{j} ω} & (23) \end{array}

\begin{array}{l} R (ω) = {| \frac{1 - \sqrt{ε^{*} (ω)}}{1 + \sqrt{ε^{*} (ω)}} |}^{2} & (24) \end{array}

\begin{array}{l} t a n δ = \frac{ε^{″}}{ε^{'}} = \frac{\sum_{j = 1}^{n} Δ ε_{j} (γ_{j} ω) / ω_{o j}^{2}}{ε_{\infty} + \sum_{j = 1}^{n} Δ ε_{j}} & (25) \end{array}

where ε_∞ is dielectric constant by electronic polarization, n is the number of transverse phonon modes, ω_pj, ω_oj, and γ_j are plasma frequency, transverse frequency and damping factors of the j-th Lorentz oscillator, respectively.

FIGURE 11

Figure 11. Measured (black line) and fitted (red circle) infrared reflectivity spectra of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 800°C.

TABLE 3

Table 3. Phonon parameters obtained from the fitting of the infrared spectra of Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramic sintered at 800°C.

Figure 12 presented the complex permittivity of CZSM ceramics sintered at 800°C. The extrapolated dielectric permittivity and loss were 10.92 and 3.08 × 10⁻⁴, respectively. It can be seen that the calculated permittivity was slightly higher than the measured permittivity, the measured and calculated dielectric losses of CZSM ceramic were comparable with the same order of magnitudes. Therefore, the major dielectric contribution of the CZSM ceramics was in microwave region, and related to the absorptions of phonon oscillation.

FIGURE 12

Figure 12. The real and imaginary parts of the complex permittivity for Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ ceramics sintered at 800°C (black points are measured value at microwave region).

Conclusion

Ce₂(Zr_0.94Sn_0.06)₃(MoO₄)₉ (CZSM) microwave dielectric ceramics were successfully prepared. The XRD patterns demonstrated that all samples displayed a single phase. The SEM results indicated that nearly compact structure can be obtained sintered at 750–850°C. Subsequently, the dependence of microwave dielectric properties on intrinsic factors was evaluated based on P-V-L theory. The decrease of dielectric constant was mainly dominated by the decline of polarizability and bond ioniticy of Ce-O bond. The improvement of quality factor was dependent on enhanced packing fraction. In addition, the reduced temperature coefficient of resonant frequency was related to the increase of thermal expansion coefficient and decrease of bond energy (E_Mo−O). The complex permittivity values were obtained by infrared spectra, which agreed well with the measured value. The CZSM ceramic sintered at 800°C exhibited an optimum microwave dielectric properties of ε_r = 10.35, Q·f = 59,660 GHz (at 9.70 GHz) and τ_f = −7.52 ppm/°C.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation, to any qualified researcher.

Author Contributions

HT: methodology, investigation, data curation, visualization, writing-original draft, and writing-review and editing. XL: investigation, validation, methodology, software and formal analysis. YY: software, validation, writing-review and editing. HW and ZZ: conceptualization, resources, writing-review and editing, project administration, supervision, and funding acquisition.

Funding

This work was supported by the National Natural Science Foundation of China (No. 51972143).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmats.2020.00145/full#supplementary-material

References

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