Crystal structure and enhanced microwave dielectric properties of the Ce2[Zr1−x(Al1/2Ta1/2)x]3(MoO4)9 ceramics at microwave frequency

Abstract: Dense microwave dielectric ceramics of Ce₂[Zr_1−x(Al_1/2Ta_1/2)_x]₃(MoO₄)₉ (CZMAT) (x = 0.02–0.10) were prepared by the conventional solid-state route. The effects of (Al_1/2Ta_1/2)⁴⁺ on their microstructures, sintering behaviors, and microwave dielectric properties were systematically investigated. On the basis of the X-ray diffraction (XRD) results, all the samples were matched well with Pr₂Zr₃(MoO₄)₉ structures, which belonged to the space group R3¯c">R3¯cR3¯c. The lattice parameters were obtained using the Rietveld refinement method. The correlations between the chemical bond parameters and microwave dielectric properties were calculated and analyzed by using the Phillips—Van Vechten—Levine (P—V—L) theory. Excellent dielectric properties of Ce₂[Zr_0.94(Al_1/2Ta_1/2)_0.06]₃(MoO₄)₉ with a relative permittivity (ε_r) of 10.46, quality factor (Q × f) of 83,796 GHz, and temperature coefficient of resonant frequency (τ_f) of −11.50 ppm/°C were achieved at 850 °C.

Keywords: microwave dielectric ceramics; Ce₂[Zr_1−x(Al_1/2Ta_1/2)_x]₃(MoO₄)₉ (CZMAT); Phillips–Van Vechten–Levine (P–V–L) theory; low sintering temperature

1 Introduction

With the rapid growth of wireless communication industry, microwave dielectric ceramics are widely studied for their use in global positioning system (GPS) patch antennas, resonators in filters or oscillators at microwave frequencies in radar detectors, and mobile telephones ^[1–3]. The important characteristics required for excellent microwave dielectric ceramics are high-quality factor (Q × f ) for the enhancement of frequency selectivity, low dielectric constant (ɛ_r) for fast signal speed, and near-zero temperature coefficient of resonant frequency (τ_f) to improve the stability of the frequency against temperature change ^[4–6]. It is difficult to balance these three parameters of microwave dielectric properties. To meet the development requirements of the communication technology, it is necessary to explore the novel microwave dielectric ceramics with excellent dielectric properties, such as Eu₂TiO₅, Ba₂CuGe₂O₇, Y2MgTiO6, and CaAl₂O₄ ^[7–10]. In addition, researchers focused on the improvement of the microwave dielectric properties through ion substitution and the use of composite ceramics ^[11–16]. For instance, the crystal structure and dielectric properties of Ti⁴⁺-substituted CaSnSiO₅ ceramics were investigated by Du et al. [11]. Yang et al. ^[12] reported the trirutile-type Co_0.5Ti_0.5TaO₄ ceramics with a ɛ_r of 40.69, Q × f of 17,291 GHz, and τf of 114.54 ppm/℃. A temperature-stable CaSnSiO₅–K₂MoO₄ composite microwave ceramic was prepared through the cold sintering process ^[13]. 

Rare-earth molybdate (Ln₂Zr₃(MoO₄)₉) ceramics have attracted great attention recently due to their low dielectric loss and sintering temperature ^[17,18]. Tao et al. ^[19] reported that the Ce₂Zr₃(MoO₄)₉ ceramics with performance parameters of Q × f = 19,062 GHz, ε_r = 10.69, and τ_f = −1.29 ppm/℃ were attained at 575 ℃. Moreover, Shi et al. ^[20] improved Q × f value by the partial replacement of Mo⁶⁺ by W⁶⁺ ions in Ce₂Zr₃(MoO₄)₉ ceramic. The effect of Ti⁴⁺ doping on Ce₂Zr₃(MoO₄)₉ ceramic properties was analyzed ^[21]. The substitution of complex ions for divalent or tetravalent ions was recently investigated as an alternative approach to increase the Q × f value of dielectric materials ^[22]. Improved Q × f values were obtained when (Mg_1/3Sb_2/3)⁴⁺ substituted the Zr-site of Ce₂Zr₃(MoO₄)₉ ceramics ^[23]. Hence the high Q × f values can be obtained not only by the substitution of the tetravalent cations at the Zr-sites, but also by the isovalent substitution of combinations of aliovalent cations. With reference to Ce₂[Zr_1−x(Mg_1/3Sb_1/3)_x]₃(MoO₄)₉ ceramics, we wonder if the Al³⁺ can be used. Considering that Sb⁵⁺ (0.60 Å) and Ta⁵⁺ (0.64 Å) ions possess a similar ionic radius at the same coordination number (CN = 6), Ta⁵⁺ was introduced to form (Al_1/2Ta_1/2)⁴⁺ to replace Ti⁴⁺. 

In the present work, the effect of substituting (Al_1/2Ta_1/2)⁴⁺ for the Zr-sites on the microwave dielectric properties of Ce₂[Zr_1−x(Al_1/2Ta_1/2)_x]₃(MoO₄)₉ (CZMAT) ceramics was investigated. Microstructure and sintering behaviors of the CZMAT ceramics were determined using the X-ray diffraction (XRD) and the scanning electron microscopy (SEM). The lattice parameters of CZMAT ceramics were obtained via the Rietveld refinement method. To investigate the relationship between the dielectric properties and chemical bond characteristics, the chemical bond theory was used to calculate the bond ionicity, bond energy, lattice energy, and coefficient of thermal expansion. 

2 Experimental 

High-purity powders CeO₂ (99.9%, Macklin), Al₂O₃ (99.09%, Macklin), Ta₂O₅ (99.5%, Macklin), ZrO₂ (99.99%, Aladdin), and MoO₃ (99.95%, Aladdin) were weighted accurately based on the formula of CZMAT. The mixed powders were ball-milled with ZrO₂ balls and ethanol media for 24 h. The oven-dried slurry was pre-sintered for 2 h in a muffle furnace and ball-milled for 24 h. Afterward, the oven-dried slurry was admixed with 10 wt% paraffin, pressed into a cylindrical billet (10 mm stainless steel die, 6 MPa), and sintered at 775—875 ℃ for 6 h. 

The crystal structures were confirmed by XRD (Model D/MAX-B, Rigaku Co.) with Cu Kα radiation (working at 40 kV and 40 mA) in the 2θ range of 5°–80°. The microstructure was observed by the scanning electron microscope (FeSEM Quanta 250, FEI Co.). The apparent densities of specimens were analyzed using the Archimedes method (Mettler Toledo, XS64). To obtain the lattice parameters of the specimens, the XRD data were analyzed by FULLPROF program on the basis of Rietveld refinements. A network analyzer (Agilent Co., N5234A) was used to obtain the ɛ_r and Q × f of samples with the TE_01δ method at microwave frequency. The τ_f values are obtained by Eq. (1) as follows: 

where f₂₅ and f₈₅ represent resonant frequencies at 25 and 85 ℃, respectively.

3 Results and discussion 

The XRD patterns of the CZMAT ceramics sintered at optimal temperatures are exhibited in Fig. 1(a). All the diffraction peaks match well with the Pr₂Zr₃(MoO₄)₉ standard pattern (PDF# 51-1851), and no secondary phase was detected, thereby suggesting that the Pr₂Zr₃(MoO₄)₉-like crystal structure with a R^▔3c space group is formed. The crystal structure of the CZMAT ceramics does not change with increasing (Al_1/2Ta_1/2)⁴⁺. The magnified results in the 2θ range of 22.4°–22.8° are plotted in Fig. 1(b). The diffraction peaks (119) slightly shift to a higher angle with the augmentation of (Al_1/2Ta_1/2)⁴⁺, because the ionic radius of Zr⁴⁺ (0.72 Å) is longer than that of (Al_1/2Ta_1/2)⁴⁺ (0.64 Å), which corresponds with the decrease of the unit cell volume based on Bragg’s diffraction law.

Fig. 1 XRD patterns of CZMAT ceramics sintered at 850 ℃ and the details in the range of 22.4°–22.8°. 

In addition, the FULLPROF software was used to obtain structural parameters, such as lattice parameters, bond length, and unit cell volumes. The refined results are shown in Table 1 and Fig. 2. The Rwp, Rp, and χ² values are obtained in the range of 9.26%–10.5%, 7.04%–7.89%, and 1.60–2.16, respectively, indicating that they are acceptable and accurate. The variations of a, b, c, and V_m are presented in Fig. 3. The a-axis, b-axis, and V_m linearly decrease, whereas the c-axis fluctuates slightly between 58.89 and 58.86 Å. The decline of unit cell parameters can be attributed to the ionic radius mismatch between Zr⁴⁺ and (Al_1/2Ta_1/2)⁴⁺ ions. The occupations and the refined atomic positions of CZMAT ceramics are displayed in Table 2. In this structure, Ce, Zr(1), Zr(2), Mo(1), Mo(2), and O atoms occupy the 12c, 6b, 12c, 36f, 18e, and 36f Wyckoff positions, respectively. The schematic illustration of CZMAT ceramics is presented in Fig. 4. The coordination number of Ce, Zr(AlTa), and Mo atoms are 9, 6, and 4, respectively. The crystal structure of ceramics is composed of [CeO₉], [Zr(AlTa)O₆], and [MoO₄] polyhedra with common vertex angle. 

Table 1 Refinement parameters of CZMAT ceramics sintered at 850 ℃

Fig. 2 Rietveld refinement patterns of CZMAT ceramics sintered at 850 ℃. 

Fig. 3 Lattice parameters (a, b, and c) and unit cell volume (Vm) of CZMAT ceramics as a function of the substitution amount of (Al_1/2Ta_1/2)⁴⁺. 

Table 2 Refined atomic positions of CZMAT ceramics 

Fig. 4 Schematic illustration of CZMAT ceramics. 

SEM microphotographs of CZMAT ceramic sintered at 850 ℃ are shown in Fig. 5. The dense microstructure and unambiguous grain boundary of the samples is obtained. The grain size increases slightly, and the grain boundary fraction decreases with the content of (Al_1/2Ta_1/2)⁴⁺ substitution. All grain boundaries are straight, and the angle of grain boundary is close to 120°, which indicates that the ceramic reaches a dense microstructure. For x = 0.02–0.10, the grain size increases gradually, indicating that the (Al_1/2Ta_1/2)⁴⁺ ion can increase the grain size of CZMAT ceramics. 

Fig. 5 SEM microphotographs of the CZMAT ceramics sintered at 850 ℃ for 6 h: (a) x = 0.02, (b) x = 0.04, (c) x = 0.06, (d) x = 0.08, and (e) x = 0.10.

The diametric shrinkage ratio was used to analyze the sintering behaviors of the CZMAT ceramics. Figure 6(a) shows the diametric shrinkage ratio curves of CZMAT ceramics sintered at 775–875 ℃. The diametric shrinkage ratio of CZMAT ceramic increases, reaches the maximum value at 850 ℃, and then decreases slightly. The increase of diametric shrinkage ratio can be attributed to the pore elimination. A higher sintering temperature will accelerate the growth of crystal grains, and the pores will not be discharged in time, thereby resulting in a sample with poor densification. The apparent density of the CZMAT ceramics is illustrated in Fig. 6(b). The apparent density of CZMAT ceramic is obtained by using the Archimedes method. The apparent density of CZMAT ceramic increases with sintering temperature and then decreases slightly; this trend is consistent with that of the diametric shrinkage ratio. 

Fig. 6 (a) Diametric shrinkage ratio of CZMAT ceramics as a function of sintering temperature; (b) apparent density of CZMAT ceramics as a function of sintering temperature.

Figure 7 illustrates the ε_r and Q × f values of CZMAT ceramics as a function of sintering temperature. As shown in Fig. 7(a), the ε_r of each composition increases initially due to the disappearance of pores and then decreases slightly. For x = 0.04, 0.06, 0.08, and 0.10, the ɛr values of samples reach the maximum (10.45, 10.53, 10.52, and 10.47, respectively) at 825 ℃. For x = 0.02, the maximum ε_r value (10.61) is obtained at 850 ℃. The variation in dielectric constant is consistent with the density, suggesting that density serves as the main extrinsic factor of ɛr. The Q × f of CZMAT ceramics as a function of the sintering temperature is displayed in Fig. 7(b). Q × f values increase with the sintering temperature and then decrease slightly. The optimal values are obtained at 850 ℃. Densification and a relatively uniform microstructure are the main reasons for optimizing the quality factor; the decline of Q × f values at a higher sintering temperature can be attributed to intrinsic loss ^[24,25]. 

Fig. 7 (a) ɛr values of CZMAT ceramics as a function of sintering temperature; (b) Q × f values of CZMAT ceramics as a function of sintering temperature. 

In recent years, Mo-based microwave dielectric ceramics were studied in depth, as shown in Fig. 8 ^{[10,17–21,26–32]}. Most Mo-based microwave dielectric ceramics have Q × f in the range of 20,000–80,000 GHz. New double molybdates of lanthanides and transition metal zirconium (Ln₂O₃–ZrO₂–MoO₃ systems) have attracted great attention due to the excellent microwave dielectric properties. Several studies have focused on the microwave dielectric properties of Ln₂Zr₃(MoO₄)₉ (Ln = La, Ce, Nd, Sm). Liu and Zuo ^[17] reported that Ln₂Zr₃(MoO₄)₉ (Ln = Sm, Nd) ceramics exhibited properties of ε_r = 11.0, Q × f = 74,012 GHz, and τ_f = −45.3 ppm/℃ at sintering temperature of 875 ℃ for Ln = Sm and ε_r = 10.8, Q × f = 58,942 GHz, and τ_f = −40.9 ppm/℃ at the sintering temperature of 850 ℃ for Ln = Nd. In particular, Ce₂Zr₃(MoO₄)₉ ceramics with Q × f = 19,062 GHz were prepared by the traditional solid-state method ^[19]. In this study, excellent Q × f of 83,796 GHz was obtained in Ce₂[Zr_0.94(Al_1/2Ta_1/2)_0.06]₃(MoO₄)₉ ceramic. The dielectric properties of Ce₂Zr₃(MoO₄)₉ ceramics can be optimized efficiently by doping (Al_1/2Ta_1/2)⁴⁺ at Zr-site ions. This study enriched the microwave dielectric systems. The CZMAT ceramic with low-temperature and high-quality factors is a good candidate for passive communication devices. 

Fig. 8 Q × f with ε_r of Mo-salt microwave dielectric ceramics. 

In general, the microwave dielectric properties are associated with the extrinsic factors. The extrinsic factors include grain boundaries, pores, abnormal grains, defect, and dislocation, which are the main factors that produce the dielectric loss. The intrinsic factors need to be investigated in detail because of the dense microstructures and no secondary phases ^[33]. The dense microstructures of the CZMAT ceramic are observed at 850 ℃. The observed (α_obs.) and theoretical (α_theo.) dielectric polarizability values are the microscopic parameters that can be used to evaluate the structural dependence of ε_r. According to the Clausiuse–Mosotti equation and the additive rule of dielectric polarizability, αo_bs. and α_theo. can be evaluated by Eqs. (2) and (3): 

where α (Ce³⁺), α (Zr⁴⁺), α (Al³⁺), α (Ta⁵⁺), and α (O²⁻) are the ion polarizability values, which were obtained by Shannon and Rossman ^[34]. The value of α (Mo⁶⁺) was obtained by Choi et al. ^[35]. b is 4π/3, and V_m represents the unit cell volume. The values of α_theo. and α_obs. of CZMAT ceramics are shown in Fig. 9. The values of α_theo. and αobs. decrease gradually with the increase of x. The discrepancy between α_theo. and α_obs. can be explained by the atomic vibration and polyhedral distortion. 

Fig. 9 ɛ_r, α_theo., and α_obs. of CZMAT ceramics as a function of x.

The relationship between property and structure of dielectric materials, which are composed of complex oxide crystals, is worth analyzing and exploring. Any complex crystal can be decomposed into multiple binary crystals on the basis of the P–V–L theory. Hence, the chemical bond parameters of an individual bond can be calculated. The bond equation of CZMAT ceramics is shown in Eq. (4). 

The effective valence electron number, which is an important intermediate parameter in the calculation of bond parameters, can be calculated by using Eqs. (5)–(9) as follows: 

where A and B represent the cation and anion, respectively. (Z^μ_A)^* and (Z^μ_B)^* are the effective numbers of valence electrons of cation and anion, respectively. (Z^μ_A)^* and (Z^μ_B)^* are the valence states of cation and anion, respectively. (q^μ_A)^* and (q^μ_B)^* are are the effective charge of valence electrons of cation and anion, respectively. P^μ_A and P^μ_B are the valence states of cation and anion, respectively.  (n^μ_B)^*  represents the effective number of valence electrons of an individual bond μ. N^μ_cA and N^μ_cB are the coordination numbers of cation and anion, respectively. 

The coordination and charge distributions of various ions in CZMAT ceramics are illustrated in Fig. 10. The coordination numbers of Ce, Zr(AlTa), Mo, and O atoms are 9, 6, 4, and 2, respectively. The valence of cations is expressed as P_Ce = +3, P_Zr(AlTa) = +4, and P_Mo = +6, whereas the valence of the oxygen ion is expressed as Eq. (4). The valences in the Ce−O, Zr(AlTa)−O, and Mo−O bonds are P_O−Ce = −2/3, P_O−Zr(AlTa) = −4/3, and P_O−Mo = −3, respectively. On the basis of Eqs. (5) and (6), the effective valence electron number of cations are 3, 4, and 6, whereas the effective valence electron numbers of oxygen ion in the Ce−O, Zr(AlTa)−O, and Mo−O bonds are 2, 4, and 9, respectively. Figure 10 shows that the effective valence electron numbers in the Ce−O bond, Zr(AlTa)−O bond, and Mo−O bond are 4/3, 8/3, and 6, respectively.

Fig. 10 Coordination and charge distribution of various ions in CZMAT ceramics.

According to the P–V–L theory, the ε_r can be predicted using bond ionicity ^[36]. ε_r and bond ionicity f^μ_i can be estimated by Eqs. (10) and (11) as follows: 

where C^µ represents the heteropolar part, n₀ represents the refractive index, and E^μ_g represents the average energy gap. 

Table 3 lists the bond ionicity of individual bonds, and the calculation process has been described in previous works. In addition, ε_r and f_{i(Zr(AlTa)–O(4))} as a function of the content of (Al_1/2Ta_1/2)⁴⁺ substitution are shown in Fig. 11. The εr values of CZMAT ceramics fluctuate slightly between 10.42 and 10.61 with the increase of (Al_1/2Ta_1/2)⁴⁺. The same trend is observed in f_{i(Zr(AlTa)–O(4))}, indicating that the Zr(AlTa)–O(4) bond ionicity is an important factor of the dielectric constant. 

Table 3 Bond iconicity fi of CZMAT ceramics sintered at densification temperature for 6 h (Unit: %)

Fig. 11 ɛ_r and the Zr(AlTa)–O(4) bond ionicity of CZMAT ceramics as a function of x. 

The physical properties are predicted by lattice energy, and the stability of materials is positively associated with lattice energy. The lattice energy U can be 
expressed as Eq. (12): 

where U^μ_bi and U^μ_bc represent ionic and covalent energy parts, respectively. The lattice energy U of CZMAT ceramics is presented in Table 4. U_(Ce–O(1)) values and Q × f as a variation of (Al_1/2Ta_1/2)⁴⁺ substitution are exhibited in Fig. 12. The variation of Q × f is consistent with that of U_(Ce–O(1)), thereby indicating that Q × f is influenced by U_(Ce–O(1)). For x = 0.06, superior performances are obtained (ɛ_r = 10.46, Q × f = 83,796 GHz, and τ_f = −11.50 ppm/℃), indicating that the Q × f of Ce₂[Zr_0.94(Al_1/2Ta_1/2)_0.06]₃(MoO₄)₉ ceramics is greatly improved compared with that of Ce₂Zr₃(MoO₄)₉ (Q × f = 19,062 GHz). 

Table 4 Lattice energy Uof CZMAT ceramics sintered at densification temperature for 6 h (Unit: kJ/mol)

Fig. 12 Q × f and the Ce–O(1) lattice energy of CZMAT ceramics as a function of the value of x. 

τ_f plays a crucial role in dielectric materials. It symbolizes the resistance of materials to temperature changes in service. In addition, it is related to structural characteristics, such as bonding types, chemical properties of ions, distance between anions, and the temperature coefficients of the relative permittivity ^[37−39]. The relationships among τ_f, τ_ɛ, and α are illustrated in Eq. (13). α and τ_ɛ are the coefficient of thermal expansion and the temperature coefficient of dielectric constant, respectively.

The α values of Ce–O, Zr/AlTa–O, and Mo–O bonds are explored quantitatively, as shown in Table 5. The calculation process used has been described in Ref. ^[23]. Obviously, the average α value of Mo–O bonds is negative, thereby indicating that the α value of Mo–O bonds is also an important factor of τ_f. A strong relationship was reported between bond energy E and τ_f. A smaller |τ_f| corresponded to higher bond energy values. The E values (Table 6) of an individual bond μ can be calculated by using Eqs. (14) and (15). The variation of τ_f and bond ionicity E_(Mo–O) along with x is exhibited in Fig. 13. The maximum value (−8.96 ppm/℃) of τ_f is shown at x = 0.04. The same trend is observed between τ_f and E_(Mo–O), indicating that E_(Mo–O) is a primary intrinsic factor of τ_f. 

where E_μ is the bond energy for the type μ bond, which is composed of nonpolar covalence energy E_c^μ and complete ionicity energy E_i^μ parts; t_c and t_i are covalent and ionic blending coefficients, respectively; r_cA and r_cB are the covalent radii; and E_A–A and E_B–B are the homonuclear bond energies.

Fig. 13 τ_f and the MoO bond energy of CZMAT ceramics as a function of the value of x. 

Table 5 Coefficients of thermal expansion αof CZMAT ceramics sintered at densification temperature for 6 h  (Unit: 10^-6 K^-1)

Table 6 Bond energies E of CZMAT ceramics sintered at densification temperature for 6 h (Unit: kJ/mol) 

4 Conclusions 

Dense microwave dielectric ceramics of CZMAT (x = 0.02–0.10) were prepared by the conventional solid-state route. The sintered samples belong to the trigonal structure with the R^▔3c space group identified by the XRD. According to the results of SEM, the dense ceramics were obtained at 850 ℃. The lattice parameters of the samples were obtained by the Rietveld refinement method. Based on the chemical bond theory, the microwave dielectric properties were investigated. The optimum dielectric performance of ɛ_r = 10.46, Q × f = 82,189 GHz, and τ_f = −12.74 ppm/℃ for Ce₂[Zr_0.94(Al_1/2Ta_1/2)_0.06]₃(MoO₄)₉ ceramic was obtained at 850 ℃. 

Reference: Omitted