Effects of (Mg1/3Sb2/3)4+ substitution on the structure and microwave dielectric properties of Ce2Zr3(MoO4)9 ceramics

Abstract: Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics were prepared by the traditional solid-state method. A single phase, belonging to the space group of R3c , was detected by using X-ray diffraction at the sintering temperatures ranging from 700 to 850 ℃. The microstructures of samples were examined by applying scanning electron microscopy (SEM). The crystal structure refinement of these samples was investigated in detail by performing the Rietveld refinement method. The intrinsic properties were calculated and explored via far-infrared reflectivity spectroscopy. The correlations between the chemical bond parameters and microwave dielectric properties were calculated and analyzed by Phillips–van Vechten–Levine (P–V–L) theory. Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics with excellent dielectric properties were sintered at 725 ℃ for 6 h (εr = 10.37, Q×f = 71,748 GHz, and τf = −13.6 ppm/℃, εr is the dielectric constant, Q×f is the quality factor, and τf is the temperature coefficient of resonant frequency). 

Keywords: crystal structure; Phillips–van Vechten–Levine (P–V–L) theory; microwave dielectric property; (Mg1/3Sb2/3) doping 

1 Introduction

It is well-known that dielectric materials have developed rapidly in the past decades. Microwave dielectric ceramics have sprung up in the communication industry and received widely attentions. It is required to have a high-quality factor (Q×f), a moderate dielectric constant (εr), and a near-zero temperature coefficient of resonant frequency (τf) to meet the demands of applications [1,2]. Recently, researchers focused on novel microwave dielectric ceramics. At the same time, some researchers have widely investigated the substitution of cationic and composite ceramics to improve the dielectric properties of microwave dielectric materials [3–5]. In addition, high cost limits the application of these ceramics, and consequently it is required to reduce their sintering temperatures. The low temperature co-fired ceramic (LTCC) [6–8] technology has become a common method due to its simplicity and high efficiency. Hence, LTCC technology is becoming more and more important in practical applications. 

In recent years, Mo-based microwave dielectric ceramics have been studied in depth as shown in Table 1 [9–13]. Many microwave dielectric ceramic systems have been developed, but their properties are not optimistic. The performance (Q×f = 19,062 GHz) of Ce2Zr3(MoO4)9 ceramic was investigated [12]. In order to improve Q×f of Ce2Zr3(MoO4)9 ceramics, doping (Mg1/3Sb2/3)4+ at Zr-sites was reported in this work. The crystal structure and the sintering behavior of samples were discussed in detail. Also, the relationship between the dielectric properties and the structure of samples was explored scientifically by far infrared reflectivity spectrum and the Phillips–van Vechten–Levine (P–V–L) theory. 

Table 1 Summarized microwave dielectric properties of Mo-based microwave dielectric ceramics

2 Experimental

Highly pure powders of CeO2, ZrO2, MoO3, MgO, and Sb2O5 were weighed accurately based on the stoichio-metric composition of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10). The mixed powders were continuously rotated for 24 h with ethanol media and ZrO2 balls. Mixtures were oven-dried at 80 ℃ and pre-sintered at 700 ℃ for 2 h, and after that, ball milled and dried again under the same condition as above. Subsequently, the combination of powders and 10 wt% paraffin passed through a 60-mesh sieve, and a certain size of the cylinders (length≈6 mm, diameter≈10 mm) was pressed at 200 MPa. Those pressed cylinders were sintered from 700 to 850 ℃ for 6 h. 

Phase identification of sintered pellets was analyzed using a X-ray diffraction (D8 Advance, Bruker Co., Germany) with Cu Kα radiation and refined lattice parameters were obtained using a FULLPROF program to explore structure. The surface microstructures of specimens were observed by using a QUANTA 250FEG type scanning electron microscope (SEM, FEI Co., USA), equipped with the energy dispersive spectrometer (EDS). The apparent densities of specimens were analyzed using Archimedes method. The infrared reflectivity spectrum was recorded by a Bruker IFS66v FTIR spectrometer at National Synchrotron Radiation Laboratory (NSRL, BL01B infrared beamline station, University of Science and Technology of China, China). In addition, dielectric behaviors were surveyed by employing the TE01δ cavity method with a network analyzer (N5234A, Agilent Co., USA) and the Hakki–Coleman dielectric resonator method. The τf value was acquired by Eq. (1): 

where fT and f0 represent resonant frequencies at 85 and 25 ℃, respectively. 

Relative density (ρrelative) was applied via the following equations: 

where Z is the number of molecules, NA refers to Avogadro constant, A represents the relative atomic weight, and Vm represents the unit cell volume.

3 Results and discussion

As shown in Fig. 1, the X-ray diffraction patterns of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics are sintered under different temperatures for 6 h. A single phase was detected in all samples. The peaks of sintered ceramics assigned to the standard data for Pr2Zr3(MoO4)9 (JCPDS No. 52-0688), which indicated that the Pr2Zr3(MoO4)9-like crystal structure with a R3c space group was obtained. According to the result, the composition of the crystal phase is not changed by the content of (Mg1/3Sb2/3)4+ ions substitution [14]. In order to meet the needs of calculating density and complex chemical bonds, the structure, lattice parameters, bond length, and unit cell volumes were further analyzed and obtained by Rietveld refinement [15]. Nd2Zr3(MoO4)9 was chosen as the original model via FULLPROF program. Refinement plot of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics are displayed in Fig. 2, in which the observed values are expressed by red points, the calculated values are expressed by the black line, and different values between the observed and the calculated data are expressed by the blue curve. Obviously, excellent agreement is shown between the fitted values and the measured values. In addition, the refined discrepancy factors (Rwp, Rp, and χ²), Vm, and lattice parameters of all specimens are listed in Table 2. The Rwp, Rp, and χ² values were obtained in the range of 9.6%–11.1%, 6.6%–8.6%, and 1.70–2.23, respectively, indicating all the refinement results are acceptable and accurate. 

Fig. 1 XRD patterns of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) ceramics sintered at the densification temperature for 6 h. 

Fig. 2 Refinement results of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics calcined under various conditions as indicated: (a) x = 0.02, (b) x = 0.04, (c) x = 0.06, (d) x = 0.08, and (e) x = 0.10.

Table 2 Refinement parameters of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics sintered at the optimized sintering temperature

With the amount of (Mg1/3Sb2/3)4+ increasing, the linear variation in lattice parameters (a, b, and c) and Vm are presented in Fig. 3. The lattice parameter c is linearly increased, but a, b, and Vm are linearly decreased correspondingly along with the augment of (Mg1/3Sb2/3)4+ because the ionic radius of Zr4+ (0.72 Å) is longer than that of (Mg1/3Sb2/3)4+ (0.64 Å) [16,17]. The schematic illustration (Fig. 4) and the refined atomic positions (Table 3) of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 samples are exhibited clearly. The crystal structure of ceramics is composed of CeO9, Zr/Mg/SbO6, and MoO4 polyhedra with common vertex angle. 

Fig. 3 a, b, c, and Vm of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics as a function of the substitution amount of (Mg1/3Sb2/3)4+

Fig. 4 Schematic illustration of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics. 

Table 3 Refined atomic positions of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 samples

The apparent densities of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics as a function of the sintering temperature are illustrated in Fig. 5. As the temperature increases, the apparent densities of each composition increase at first and then decrease slightly. For example, the apparent density of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics increases from 3.71 to 3.83 g/cm³, and then the apparent density drops to 3.81 g/cm³ at 800 ℃. In general, an appropriate sintering temperature plays a vital role in the densification of the sample. The higher sintering temperature will accelerate the growth of crystal grains, and the pores will not be discharged in time, resulting in a poor densification sample. The maximum relative density of each composition is embedded in Fig. 5 as a function of (Mg1/3Sb2/3)4+ substitution. The apparent densities of the major sample were approximately 3.80 g/cm³ and the ρrelative also has reached more than 95%. It is noticeable that the good degree of densification was in accord with the SEM results. Figures 6(a)–6(e) depict the SEM microphotographs of the specimens at their optimal temperatures. It is quite clear that the dense microstructure and unambiguous grain boundary of the specimens can be observed. As provided in Fig. 6(f), EDS of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics is gained at 725 ℃ for 6 h. Atom ratios of O, Mo, Zr, Ce, Sb, and Mg are 73.56%, 16.91%, 5.93%, 3.48%, 0.07%, and 0.05%, respectively, which are in consistent with the chemical formula.

Fig. 5 Apparent densities of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics as a function of the sintering temperature; the relative densities of each composition are shown in the inset. 

Fig. 6 SEM microphotographs of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics at the densification temperature for 6 h: (a) x = 0.02, (b) x = 0.04, (c) x = 0.06, (d) x = 0.08, and (e) x = 0.10; (f) EDS analysis of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics sintered at 725 ℃ for 6 h; the atom ratios of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramic is shown in the inset of Fig. 6(f). 

The εr of ceramics with different (Mg1/3Sb2/3)4+ contents (x = 0.02, 0.04, 0.06, 0.08, and 0.10) as a function of the sintering temperature is revealed in Fig. 7(a). The factors that affect the εr are mainly divided into external parameters and intrinsic factors. Intrinsic factors include lattice structure and ionic polarizabilities, whereas external parameters include impurities, density, and second phase [18]. No secondary phase is detected in Fig. 1 and the lattice structure has no change. Thus, the εr of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics was determined mainly by the apparent density. Figure 5 shows that the apparent densities of the sample increased and then decreased slightly as the temperature increased. It was easy to notice that the εr existed almost similar trend with the apparent density, which indicated that the main contribution of the εr was the apparent density. 

Fig. 7 (a) εr and (b) Q×f values of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics sintered at 700–800 ℃. 

The Q×f of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics sintered at 700–850 ℃ for 6 h is plotted in Fig. 7(b). The quality factor depends on the presence of intrinsic and extrinsic dielectric losses at microwave frequencies. The extrinsic losses are dominated by porosity, secondary phase, and lattice defects, whereas the intrinsic loss is mainly contributed by lattice vibrational modes [19]. It was obvious that the Q×f of each composition existed similar trend, which increased firstly and then decreased. The optimal points of Q×f were presented at 800, 800, 725, 725, 725, and 775 ℃, In this study, the excellent properties of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics (εr = 10.37, Q×f = 71,748 GHz, and τf = −13.6 ppm/℃) were obtained at 725 ℃ for 6 h. At the optimal sintering temperature, the quality factor of Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramics has been greatly improved compared to previous reports, owing to the partial replacement of Zr4+ by (Mg1/3Sb2/3)4+ ions. 

As we know, chemical bond theory of complex crystals was used to characterize the intrinsic relationships between chemical bond and crystal structure. Wu et al. [15] successfully generalized P–V–L theory, suggesting that the crystalline structure parameters could be calculated by chemical bond. Any complex crystal can be decomposed into multiple binary crystals. The bond equation of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (0.02 ≤ x ≤ 0.10) ceramics was shown in Eq. (4). In this work, the Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics are constituted of Ce–O, Zr(Mg/Sb)–O and Mo–O bonds. The effective valences of cations are PCe = 3, PZr(Mg/Sb)= 4, and PMo = 6, and the valence of the oxygen ion follows Eq. (4). The effective valences in the Ce–O bond, Zr(Mg/Sb)–O bond, and Mo–O bond are PO–Ce = −2/3, PO–Zr(Mg/Sb) = −4/3, and PO–Mo = −3, respectively. 

The bond ionicity (fi) usually could be evaluated by using Eqs. (5)–(9) [15,20,21]:

where dμ and bμ are the bond length and correction factor, respectively, (ZAμ)* is the effective number of valence electrons on cation A, (ZBμ)* is the effective number of valence electrons on anion B, n0 represents the refractive index, r0μ is the average radius of A and B in angstroms, m and n are obtained from the binary crystal AmBn type compounds, Egμ represents the average energy gap, Ehμ represents the homopolar part, fiμ is the bond ionicity of an individual bond µ, Cµ represents the heteropolar part, and  exp(- ksµ roµ) is Thomas‒Fermi screening factor [22]

The fi is explored quantitatively as shown in Table 4. In addition, εr and an individual bond ionicity fi(Mo1–O(2)) as a function of the content of (Mg1/3Sb2/3)4+substitution are shown in Fig. 8. The εr values display a decreasing tendency from 10.47 to 10.03 along with the augment of (Mg1/3Sb2/3)4+. The positive correlation between relative permittivity and fi is described in Eq. (5). As increasing of (Mg1/3Sb2/3)4+ content, fi(Mo1–O(2)) and εr values show the same tendency, which indicate the εr values are strongly dependent on fi(Mo1–O(2)).

Table 4 fi of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02–0.10) ceramics sintered at the densification temperature for 6 h 

Fig. 8 εr and the Mo1–O(2) bond ionicity of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics as a function of the content of (Mg1/3Sb2/3)4+ substitution. 

Lattice energy can be used to predict and explain many physical and chemical properties of ionic crystals, so the larger the lattice energy, the more stable the structure. The lattice energy (U, Table 5) of specimen could be evaluated according to Eqs. (10)–(13) [15,20,21]. Figure 9 presents U(Zr(Mg/Sb)1–O(4)) values and the quality factor Q×f as a variation of (Mg1/3Sb2/3)4+ substitution. The Q×f values increased from 49,033 to 64,012 GHz, and then decreased to 48,690 GHz. They all show the same trend of increasing first and then decreasing, indicating that Q×f is mainly affected by U(Zr(Mg/Sb)1–O(4)).

Table 5 U of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02–0.10) ceramics sintered at the densification temperature for 6 h

Fig. 9 Q×f and the Zr(Mg/Sb)1–O(4) lattice energy of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics as a function of the content of (Mg1/3Sb2/3)4+ substitution. 

where Ubiμ and Ubcμ represent ionic energy part and covalent energy part, respectively. fCμ is the bond ionicity of an individual bond μ. ZAμ and ZBμ are the valence states of cation and anion, respectively, which constituted the μ bond. 

Zhang et al. [23,24] had reported a strong relationship between bond energy E and τf, which a smaller |τf| corresponds to a higher bond energy value. The E value of an individual bond μ could be calculated by Eqs. (14)–(18) [25–27]:

where Eμ is bond energy for the type μ bond, which was composed of nonpolar covalence energy Ecμ and complete ionicity energy Eiμ parts, SA and SB represent the electronegativity of ions, tc and ti are covalent and ionic blending coefficients, respectively, rcA and rcB are the covalent radii, and EA–A and EB–B are homonuclear 
bond energy [28]

The τf and an individual bond ionicity E(Mo1–O(1)) as a function of the content of (Mg1/3Sb2/3)4+ substitution are illustrated in Fig. 10. In addition, the calculated E values are shown in Table 6. The τf values of ceramics fluctuated slightly between −8.59 and −13.69 ppm/℃ with (Mg1/3Sb2/3)4+ increasing in our experiments. The E(Mo1–O(1)) and τf have the same trend, indicating that τf is mainly influenced by E(Mo1–O(1))

Fig. 10 τf and the Mo1–O(1) bond energy of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 ceramics as a function of the content of (Mg1/3Sb2/3)4+ substitution.

Table 6 E of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02–0.10) ceramics sintered at the densification temperature for 6 h

The τf is obtained by Eq. (19) and the α is described via Eqs. (20)–(23):

where γmn is a parameter of the binary bonding formula, ΔA is the periodic constant of cation, k is the Boltzmann constant, NCAμ represents the coordination number of cations, τε is the temperature coefficient of the εr, and Fmnμ represents the proportion of μ bond. Calculated thermal expansion coefficient α values are shown in Table 7. Obviously, the values of αZr(Mg/Sb)–O and αCe–O are positive. The values of αMo–O have a positive influence on τf because of αMo–O < 0. 

Table 7 α of Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02–0.10) ceramics sintered at the densification temperature for 6 h

As is known, it is difficult to detect the intrinsic loss and extrinsic loss of microwave dielectric ceramics by conventional testing methods. Far-infrared spectral analysis can reflect the intrinsic loss to a certain extent. These spectra were analyzed by using the classical harmonic oscillator model that was applied to study infrared spectroscopy. It relies on two equations: The standard Lorentzian formula (Eq. (24)) and the Fresnel formula (Eq. (25)) [29,30]. The dielectric loss tangent tanδ is evaluated by Eq. (26). 

where Δεj is contribution from each mode, γj is the damping factor, ω is frequency, ε' and ε'' are the real part and imaginary parts of the permittivity, respectively, ε is the relative permittivity caused by electronic polarization, ωpj is the plasma frequency, ε*(ω) is the complex dielectric function, ωoj is the transverse frequency, n is the number of transverse phonon modes, and R is the infrared reflectivity. 

As shown in Fig. 11(a), the fitted infrared spectrum of the Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 sample is depicted. The fitted infrared reflectivity spectrum is in good agreement with the measured part. In addition, real and imaginary parts of the permittivity are given in Fig. 11(b). Table 8 lists the fitted phonon parameters, indicating they are fitted with 16 modes. As compared with the measured permittivity, the calculated one was slightly large. The measured value (1.35×10−4) and calculated value (2.68×10−4) of the dielectric loss remained in the same order of magnitude. Both the fitted and measured values correspond well, which indicate that in the microwave frequencies, the dielectric polarization is mainly caused by absorption of phonons in the infrared region [31–33].

Fig. 11 (a) Measured (black line) and fitted (red line) infrared reflectivity spectra and (b) real and imaginary parts of the complex permittivity for Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramic sintered at 725 ℃ for 6 h. 

Table 8 Phonon parameters after fitting of the Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 sample sintered at 725 ℃ for 6 h

4 Conclusions  

Ce2[Zr1−x(Mg1/3Sb2/3)x]3(MoO4)9 (x = 0.02, 0.04, 0.06, 0.08, and 0.10) ceramics were fabricated well via the traditional solid-state method. The pure-phase with space group of R3c was detected for all specimens. The dense microstructure and clear grain boundary of specimens can be observed in SEM photos. The crystal structures were investigated deeply by the Rietveld refinement method. The εr, Q×f, and τf values of these samples were strongly dependent on chemical bonds such as fi(Mo1–O(2)), U(Zr(Mg/Sb)1–O(4)), and E(Mo1–O(1)), respectively. The infrared reflectivity spectra were in good agreement with the dielectric properties of samples. Meanwhile, Ce2[Zr0.94(Mg1/3Sb2/3)0.06]3(MoO4)9 ceramic with εr = 10.37, Q×f = 71,748 GHz, and τf = −13.6 ppm/℃ was obtained at 725 ℃ for 6 h. 

References: omitted

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