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

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 R3¯c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R⩈erline 3 c$$\end{document}, was detected by using X-ray diffraction at the sintering temperatures ranging from 700 to 850 °C. 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 °C for 6 h (εr = 10.37, Q×f = 71,748 GHz, and τf = −13.6 ppm/°C, εr is the dielectric constant, Q×f is the quality factor, and τf is the temperature coefficient of resonant frequency).


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 (ε r ), and a near-zero temperature coefficient of resonant frequency (τ f ) 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][4][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][7][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][10][11][12][13]. Many microwave dielectric ceramic systems  9 ceramic was investigated [12]. In order to improve Q×f of Ce 2 Zr 3 (MoO 4 ) 9 ceramics, doping (Mg 1/3 Sb 2/3 ) 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.

Experimental
Highly pure powders of CeO 2 , ZrO 2 , MoO 3 , MgO, and Sb 2 O 5 were weighed accurately based on the stoichiometric composition of Ce 2 [Zr 1−x (Mg 1/3 Sb 2/3 ) x ] 3 (MoO 4 ) 9 (0.02 ≤ x ≤ 0.10). The mixed powders were continuously rotated for 24 h with ethanol media and ZrO 2 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 TE 01δ cavity method with a network analyzer (N5234A, Agilent Co., USA) and the Hakki-Coleman dielectric resonator method. The τ f value was acquired by Eq. (1): where f T and f 0 represent resonant frequencies at 85 and 25 ℃, respectively. Relative density (ρ relative ) was applied via the following equations: where Z is the number of molecules, N A refers to Avogadro constant, A represents the relative atomic weight, and V m represents the unit cell volume.

Results and discussion
As shown in Fig. 1 indicated that the Pr 2 Zr 3 (MoO 4 ) 9 -like crystal structure with a 3 R c space group was obtained. According to the result, the composition of the crystal phase is not changed by the content of (Mg 1/3 Sb 2/3 ) 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].   www.springer.com/journal/40145 all specimens are listed in Table 2. The R wp , R p , and χ 2 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.
With the amount of (Mg 1/3 Sb 2/3 ) 4+ increasing, the linear variation in lattice parameters (a, b, and c) and V m are presented in Fig. 3. The lattice parameter c is linearly increased, but a, b, and V m are linearly decreased correspondingly along with the augment of (Mg 1/3 Sb 2/3 ) 4+ because the ionic radius of Zr 4+ (0.72 Å) is longer than that of (Mg 1/3 Sb 2/3 ) 4+ (0.64 Å) [16,17]. The schematic illustration (Fig. 4) and the refined atomic positions (Table 3)    apparent density drops to 3.81 g/cm 3 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 (Mg 1/3 Sb 2/3 ) 4+ substitution. The apparent densities of the major sample were approximately 3.80 g/cm 3 and the ρ relative 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 9 ceramics as a function of the sintering temperature; the relative densities of each composition are shown in the inset. and 0.05%, respectively, which are in consistent with the chemical formula. The ε r of ceramics with different (Mg 1/3 Sb 2/3 ) 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 ε r 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 ε r of Ce 2 [Zr 1−x (Mg 1/3 Sb 2/3 ) x ] 3 (MoO 4 ) 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 ε r existed almost similar trend with the apparent density, which indicated that the main contribution of the ε r was the apparent density.
The Q×f of Ce 2 [Zr 1−x (Mg 1/3 Sb 2/3 ) x ] 3 (MoO 4 ) 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 GHz, and τ f = −13.6 ppm/℃) were obtained at 725 ℃ for 6 h. At the optimal sintering temperature, the quality factor of Ce 2 [Zr 0.94 (Mg 1/3 Sb 2/3 ) 0.06 ] 3 (MoO 4 ) 9 ceramics has been greatly improved compared to previous reports, owing to the partial replacement of Zr 4+ by (Mg 1/3 Sb 2/3 ) 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.
where d μ and b μ are the bond length and correction factor, respectively, (Z A μ ) * is the effective number of valence electrons on cation A, (Z B μ ) * is the effective number of valence electrons on anion B, n 0 represents the refractive index, r 0 μ is the average radius of A and B in angstroms, m and n are obtained from the binary crystal A m B n type compounds, g E  represents the average energy gap, h E  represents the homopolar part, i f  is the bond ionicity of an individual bond , µ C represents the heteropolar part, and is Thomas-Fermi screening factor [22].
The f i is explored quantitatively as shown in Table 4. In addition, ε r and an individual bond ionicity f i(Mo1-O(2)) as a function of the content of (Mg 1/3 Sb 2/3 ) 4+ substitution are shown in Fig. 8. The ε r values display a decreasing tendency from 10.47 to 10.03 along with the augment of (Mg 1/3 Sb 2/3 ) 4+ . The positive correlation between relative permittivity and f i is described in Eq. (5). As increasing of (Mg 1/3 Sb 2/3 ) 4+ content, f i(Mo1-O(2)) and ε r values show the same tendency, which indicate the ε r values are strongly dependent on f i(Mo1-O(2)) .
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].
where bi U  and bc U  represent ionic energy part and covalent energy part, respectively. C f  is the bond ionicity of an individual bond . A Z  and B Z  are the valence states of cation and anion, respectively, which constituted the  bond.
Zhang et al. [23,24] had reported a strong relationship between bond energy E and τ f , which a smaller |τ f | corresponds to a higher bond energy value. The E value of an individual bond μ could be calculated by Eqs. (14)- (18) [25][26][27]: cA cB where E μ is bond energy for the type μ bond, which was composed of nonpolar covalence energy E c μ and  The τ f is obtained by Eq. (19) and the α is described via Eqs. (20)-(23): 3.1685 0.8376 where γ mn is a parameter of the binary bonding formula, Δ A is the periodic constant of cation, k is the Boltzmann constant, CA N  represents the coordination number of cations, τ ε is the temperature coefficient of the ε r , and μ mn F represents the proportion of μ bond. Calculated thermal expansion coefficient α values are shown in Table 7 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 Δε j is contribution from each mode, γ j 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, ω pj is the plasma frequency, ε * (ω) is the complex dielectric function, ω oj 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 Ce 2 [Zr 0.94 (Mg 1/3 Sb 2/3 ) 0.06 ] 3 (MoO 4 ) 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