Internal Relations between Crystal Structures and Intrinsic Properties

Mar 29, 2018 - covalency (bond strength (S) and the covalence (fc)) of the Mo−. O bonds in ..... *E-mail: [email protected] (F. Shi), Tel & Fax.:...
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Internal Relations between Crystal Structures and Intrinsic Properties of Nonstoichiometric Ba1+xMoO4 Ceramics Chao Xing,†,# Jianzhu Li,†,# Jing Wang,†,# Huiling Chen,† Hengyang Qiao,† Xunqian Yin,† Qing Wang,† Ze-ming Qi,‡ and Feng Shi*,† †

School of Material Science & Engineering, Shandong University of Science and Technology, Qingdao, 266590, P.R. China National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, 230029, P. R. China

‡

ABSTRACT: Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics were fabricated by a conventional two-step sintering technique. X-ray diffraction patterns show that there appeared new diffraction peaks when x > 0, which were identified as Ba2MoO5. The Rietveld refinement results indicate that the unit cell volume is the largest at x = −0.02, because it has the lowest packing fraction and covalency. The far-infrared reflectivity (IR) spectra were fitted and analyzed for calculating the intrinsic properties, which comply well with the data obtained from microscopic polarizabilities and damping coefficient angle. The proportion of each mode in the dielectric response demonstrates that the Ba−O8 polyhedra have a decisive role on the dielectric properties. And based on the Raman modes, the internal relations of the structural-properties were revealed with the changes of Ba2+ content.

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INTRODUCTION In recent years, microwave dielectric ceramics (MWDCs) have played a decisive role in the modern communication system as components such as dielectric resonators and filters, which have three important property parameters, that is, large dielectric constant (εr) for reducing the size of the communication equipment, high quality factor (Q × f) for improving the selectivity of the frequency, and near-zero temperature coefficients (τf) for keeping the high-temperature resistance of electronic devices.1−4 Up to date, many kinds of MWDCs have been developed: (1) SrLa(R0.5Ti0.5)O4 (R = Mg, Zn), (2) A(B′1/2B″1/2)O3-system (A = Ba2+, Sr2+, Ln2+; B′ = Mg2+, Zn2+, Co2+, Ni2+, Mn2+; B′′ = Sn2+, W2+), (3) AMoO4 (A = Ca, Sr, Ba), (4) (Mg1−xLnx)2Al4Si5O18+x (Ln = La, Sm), etc.5−12 Among the above MWDCs, AMoO4-type (A = Ca, Sr, Ba) ceramics are promising as εr ≤ 20 with a scheelite structure, space group of I41/a, and the divalent A2+ as well as the hexavalent Mo6+ cations have eight and four O2− ligands, respectively.13,14 BaMoO4 ceramic is regarded as a potential material for microwave application due to its high Q × f value, and much attention has been paid to this system by many researchers. For example, Choi et al.11 have found that the BaMoO4 system exhibited excellent properties with εr = 9.3, Q × f = 37200 GHz, and τf = −79.24 ppm/°C. (1−x)BaMoO4·xTO2 ceramics were also studied by Guo et al.,15 and τf was regulated to positive direction with the increase in the TiO2 content, the excellent properties of εr = 14, Q × f = 48360 GHz, τf = +13.9 ppm/°C were obtained when x = 0.338. However, as shown from previous literature,16 a limited but detectable change in composition has a crucial influence on the crystal structures and the dielectric properties, especially, nonstoichiometry.17 Up to date, the lattice characteristics, dielectric properties, and vibrations attributes of © XXXX American Chemical Society

the nonstoichiometric BaMoO4 ceramics were not studied and unknown, which inhibits their further development in basic theory and engineering application. In this work, the nonstoichiometric Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics were fabricated by a conventional two-step sintering technique. The crystal structures and morphologies were characterized by X-ray diffraction (XRD) and SEM. Raman and Fourier transform far-infrared reflection (FTIR) spectra were employed to analyze the lattice vibrational modes of the nonstoichiometric Ba1+xMoO4 ceramics. The full width at halfmaximum (fwhm) values of Raman modes obtained with the Lorentzian model were used to study the phonon characteristics and to explore the information about the crystal structures of the samples. The intrinsic properties (permittivity and dielectric loss) were calculated using the four-parameter semiquantum (FPSQ) model as well as the Clausius−Mossotti (C-M) and damping equations from the perspective of micropolarization. The real and imaginary parts of the permittivities were presented to check the vibrator parameters. The internal correlations between the crystal structures and the intrinsic properties were established, which help the further development in basic theory and engineering application for the nonstoichiometric ceramics.

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EXPERIMENTAL SECTION

Nonstoichiometric Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics were fabricated by a conventional two-step sintering technique. The BaCO3 and MoO3 powders with the purity of 99.0% were used as raw materials. These materials were mixed evenly with zirconia balls in polyethylene jars for 6 h, dried, and calcined at 850 °C for 4 h. Milled and dried again, Received: March 29, 2018

A

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry the powders were pressed into chips of 15 mm × 1 mm in size and then sintered at 1100 °C for 4 h. Before testing X-ray diffraction, scanning electron microscope, Raman, and FTIR, the micron-scale Al2O3 powders were used to polish the surfaces of the samples, which were rubbed off about 20 μm. A Rigaku D/max-2000 X-ray diffractometer was used to characterize the synthesized phases. The patterns of XRD were collected from 10° to 80° using step-and-scan mode (0.02°, 2θ step size, and 1s per step) with Cu Kα incident source. The microstructure images of the samples were collected though SEM (model as Nova Nano SEM45). Raman spectra were gathered at room temperature through a Nexus 670 spectrometer equipped with a liquid-N2-cooled CCD detector and an Olympus BXL microscope (100× and 20× objectives). The FTIR spectra from 50 to 1000 cm−1 were obtained at room temperature in a vacuum through a Bruker IFS 66v FTIR spectrometer with DTGS detector and He−Ne laser source. The mid-infrared spectra (500−1000 cm−1) were measured with Ge-coated KBr beamsplitter and far-infrared spectra (50−700 cm−1) were collected with Mylar beamsplitter.

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RESULTS AND DISCUSSION Figure 1 shows the XRD patterns of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics sintered at 1100 °C for 4 h. All the XRD patterns Figure 2. Unit cell representation of BaMoO4 ceramic.

Table 1. Wyckoff Positions of Atoms in the Unit Cell of BaMoO4 element Ba1 Mo1 O1 O2

x

site 4b 4a 16f 16f

0.00000 0.00000 0.14300 0.23400

y 0.75000 0.25000 0.14300 0.23400

z 0.37500 0.12500 0.21900 0.05100

atom 2+

Ba Mo6+ O2− O2−

occupancy 1 1 0.5 0.5

an example, which shows a high coincidence between the diffraction patterns of observed and calculated, as confirmed by the gray line (difference line) in Figure 3, indicating the valid structural model and the reliable refinement result. Figure 4 presents the lattice parameters of samples, which shows the largest unit cell volume appears at x = −0.02. Additionally, the packing fraction of the samples and the covalency (bond strength (S) and the covalence ( fc)) of the Mo− O bonds in the [MoO4]2− tetrahedra were calculated by the given equations:19

Figure 1. X-ray diffraction patterns of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics sintered at 1100 °C for 4 h.

were identified as a phase of BaMoO4 with the tetragonal scheelite structure (JCPDS#29-0193). No second phase is detected at x ≤ 0; however, an extra peak appears at around 30° (marked as * in Figure 1) when x > 0, i.e., the second phase (Ba2MoO5, JCPDS#25-0011), whose content increases with the increasing Ba2+ content. The shift tendency of the (200) peak in the inset figure shows that the peak shifts to a lower angle, as compared to a pure phase sample, and the larger the absolute value of x, the greater the shift. The unit cell and atom sites of BaMoO4 were presented in Figure 2 and Table 1, respectively, which is composed of Ba2+ cations and [MoO4]2− tetrahedra. And the polyhedron centered on Mo6+ ions is a slightly deformed tetrahedron with O−Mo−O angles of 108.3° and 111.8°, respectively.18 To further study the crystal structures of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03), XRD data were refined by the Rietveld method, and the results were listed in Table 2. The representative refinement pattern and morphology of Ba0.99MoO4 was given in Figure 3 as

S = (R /R1)−N

(1)

fc = αS M

(2)

Atomic packing fraction =

2 × VA + 2 × VB + 8 × VO a 2 × (c /2) (3)

For eqs 1 and 2, where R is the Mo−O bond length in the [MoO4]2− tetrahedron, which was calculated and listed in Table 3, R1 and N are 1.882 and 6.0, respectively, i.e., empirical parameters related to specific cation sites and anion−cation pair, presented by Brown et al.20 Moreover, the empirical constants α and M of Mo element were given in ref 21, i.e., 0.49 and 1.57, respectively, which depend on the number of electrons in the core. For eq 3,22 where VA, VB, and VO are the volumes of cation and oxygen ions at positions A/B and O, a and c are the lattice parameters of the a and c axes in the tetragonal system, respectively. B

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 2. Crystallographic Data of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) Ceramics Derived from the Rietveld Refinement of XRD Data Ba1+x MoO4 crystal structure space group a (Å) c (Å) cell Volume (Å3) density (g/cm3) units per cell (Z) software range in degree Rwp Rp R-Bragg GOF packing fraction (%)

x = −0.03

x = −0.02

x = −0.01

5.5832 12.8228 399.7112 4.940

5.6043 12.8373 403.1964 4.940

5.5824 12.8225 399.5901 4.941

11.73 7.45 1.553 1.30 56.874

11.98 10.43 4.190 1.35 56.485

12.26 10.47 2.715 1.57 57.098

x=0 scheelite I41/aZ 5.5787 12.8225 399.0657 4.948 4 Topas3 10° ≤ 2θ ≤ 80° 11.95 9.00 1.471 1.21 57.277

x = 0.01

x = 0.02

x = 0.03

5.5818 12.8185 399.3750 4.944

5.5823 12.8143 399.3193 4.945

5.5827 12.8169 399.4556 4.943

11.34 8.56 0.837 1.61 57.334

10.11 8.49 1.236 1.97 57.446

12.04 8.73 0.583 1.49 57.530

Figure 3. Collected (blue circles) and refined (red line) XRD data, as well as difference profile (gray line below the pattern), for the Rietveld refined result of the Ba0.99MoO4 ceramics. The inset figure is the SEM image under magnification of 10,000 times.

The calculated results of bond strength (S) and the covalence fc were plotted in Figure 5, which show these two values increase with the increasing of x value, except for the sample at x = −0.02, whose packing fraction and covalency have the lowest values. The decrease of the covalency leads to an increase in the volume of the tetrahedron and a decrease in the packing fraction, which results in a substantial increase of the unit cell volume. Raman spectroscopy is generally considered as a reliable instrument for the determination of phase discrimination, and it can also be related to the vibrational characteristics of the ceramics.23 As for the molybdate, the [MoO4]2− molecular group is a unit with strong covalent bond of Mo−O inside, which couples with the Ba2+ cations through the weak electrical attraction. Therefore, two parts: external and internal bands, are included in the lattice vibrational modes. 24According to the group theory, 26 different vibrations exist in the BaMoO4 system, which can be presented by the following formula:16 Γ = 3Ag + 5A u + 5Bg + 3Bu + 5Eg + 5Eu

Figure 4. Lattice parameters of Ba1+xMoO4.

(4)

where all g vibrations (3Ag, 5Bg, and 5Eg) are Raman active, 4Au and 4Eu are IR active (3Bu are silent modes), and one Eu and Au C

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 3. Bond Length of Ba−O, Mo−O Bond in Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) Ceramics bond length (Å)

x = −0.03

x = −0.02

x = −0.01

x=0

x = 0.01

x = 0.02

x = 0.03

Ba−O(1)×4 Ba−O(2)×4 dave‑(Ba−O) Mo−O(1)×4 Mo−O(2)×4 Mo−O(3)×4 dave‑(Mo−O)

2.7031 3.0746 2.8889 1.5643 1.6172 2.8864 2.0226

2.7083 3.0828 2.8956 1.5678 1.6218 2.8936 2.0277

2.8936 3.0743 2.9840 1.5642 1.6170 2.8861 2.0224

2.7024 3.0732 2.8878 1.5638 1.6163 2.8851 2.0219

2.7023 3.0738 2.8881 1.5639 1.6167 2.8855 2.0220

2.7023 3.0738 2.8873 1.5639 1.6167 2.8855 2.0220

2.7022 3.0739 2.8881 1.5639 1.6168 2.8856 2.0221

wavenumbers of collected Raman and the relative vibrational modes of Ba0.99MoO4 are listed in Table 4. As shown in Figure 6, Table 4. Observed Raman Wave Numbers and Relative Vibrational Modes of Ba0.99MoO4 Ceramics vibration modes Bg Eg Ag Eg Ag Bg Eg Eg Bg Ag

frequency (cm−1) 76.220 108.627 141.914 190.599 325.381 345.428 360.373 791.816 838.141 890.774

assignment 2−

[MoO4] and Ba2+ motions vext − external modes vf.r. − free rotation mode v2 − the Mo−O bending v4 − the Mo−O bending v3 − the Mo−O stretching v1 − the Mo−O stretching

Figure 5. Packing fraction and covalence of Ba1+xMoO4.

10 Raman peaks were observed and marked, among which the modes above 325 cm−1 (mode-5 to mode-10) are the internal modes, and the modes below 325 cm−1 (mode-1 to mode-4) are assigned as the external modes. The internal modes are assigned as (a) the Mo−O stretching vibrations: ν1 and ν3, (b) the Mo−O bending modes: ν2 and ν4. Moreover, there are also four external models, namely (1) three translational modes (mode-1 to mode3)18,26 and (2) one free rotational mode (mode-4).24 Figure 7 shows the IR reflectivity spectra of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics within the range of 50 cm−1 to 1000 cm−1; all seven IR active vibrational bands were observed, which keep in line with the vibrational analysis by other

are defined to zero frequency from acoustic bands. According to previous literature,25 on a similar structure, the internal modes with cubic point symmetry Td24 belong to the vibrations within the [MoO4]2− molecular unit with fixed center of mass (>300 cm−1). The external mode is a lattice vibration related to the movements of the Ba2+ cation and the [MoO4]2− molecular unit.25 This classification helps to distinguish the internal vibrations and vibration patterns outside the space group. Figure 6 presents the Raman spectra of the Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics in the frequency range 10−1000 cm−1; the

Figure 7. Collected (red circles) and fitted (blue lines) IR spectra for the Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics.

Figure 6. Raman spectra of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics. D

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry researchers.16,27 Two external modes can be detected, namely mode-1 and mode-2, and mode-1 is assigned to the translational mode of Ba−O. Five internal modes, named as mode-3 to mode7, are shown in Figure 7. With the variation of Ba content, mode7 changed a little in shape; the mode became smoother at x < 0 and became more sharp at x > 0, which indicates that the ordering of [MoO4]2− tetrahedral at x = 0 is better than other samples. When x > 0, the [MoO4]2− tetrahedra of the samples are distorted, which possibly affect the intensities of the internal modes. Based on the equation of Fresnel, the complex dielectric ε* has a significant relationship with the IR reflectivity (R), and thus, using the Focus program, the complex dielectric properties of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics can be deduced from the FPSQ model based on fitting of the IR spectra, whose equations are presented as follows:28 n

ε*(ω) = ε′(ω) − iε″(ω) = ε∞ ∏ j=1

ceramics mainly depend on the external modes, and the calculated properties from the FPSQ model are listed in Table 6. Table 6. Dielectric Constant and Loss Values Calculated by FPSQ (I) and by C-M and Damping Equations (II) of the Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) Ceramics x

εI

tan δI (×10−4)

εII

tan δII (×10−4)

−0.03 −0.02 −0.01 0 0.01 0.02 0.03

9.89 9.99 10.09 10.13 10.27 10.39 10.72

4.79 5.55 5.03 5.13 5.70 5.97 7.82

8.86 9.12 9.39 9.63 9.96 10.27 10.60

3.81 3.97 4.01 4.45 4.92 5.16 5.70

The real permittivity ε′ and imaginary permittivity ε″ of Ba0.99MoO4 (x = −0.01) ceramics obtained from the fitting process based on the FPSQ model were shown in Figure 8, which

Ω2jLO − ω 2 + iωγjLO Ω2jTO − ω 2 + iωγjTO (5)

R(ω) =

ε* − 1 ε* + 1

2

(6)

where ε∞ is the optical permittivity, which is caused by electron polarization; n denotes the number of phonon modes; and ΩjTO, γjTO, ΩjLO, and γjLO are defined as the frequency and damping coefficient of the jth transverse and longitude bands of the lattice vibration, respectively.29 The results are listed in Table 5 at x = −0.01 as an example. Table 5. Fitting Parameters of Infrared Reflectivity Spectrum of Ba0.99MoO4 Ceramic (x = −0.01)a modes

ΩjTO (cm−1)

γjTO (cm−1)

ΩjLO (cm−1)

γjLO (cm−1)

Δεj

tan δj/ω (×10−4)

1 2 3 4 5 6 7

97.39 136.95 294.52 323.75 374.56 805.70 886.99

11.455 6.39 14.26 11.30 6.47 33.56 109.14

114.04 167.79 299.12 332.09 376.79 824.67 896.48

7.46 19.13 9.64 5.85 6.42 87.10 20.00

3.7055 1.5589 0.1564 0.1799 0.0391 0.2147 0.0674

4.4300 0.5261 0.0255 0.0192 0.0179 0.0110 0.0093

a

Figure 8. Real part (a) and imaginary part (b) of the complex dielectric properties of Ba0.99MoO4 ceramic calculated by the FPSQ model.

implies that the dielectric constants of Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics in the microwave frequency band are only contributed by ion displacement polarization and electronic polarization, and no other low frequency polarization makes contribution to the dielectric constant, i.e., dipole polarization, which belongs to the intrinsic permittivity. Figure 9 plotted the dielectric constants (a) and the dielectric losses (b) of the external modes’ contribution with the change of x value. As presented in Figure 9 and based on Table 5, we can know that mode-1 and mode-2 occupy higher proportion in the total dielectric constant and loss as compared with other modes. Mode-1 has the largest contribution, which is attributed to the translational motion of Ba−O. Mode-2 depends on the rotation of the Ba2+ ions, similar to the report in ref 25. The Ba2+ content may have greater impact on mode-1 by affecting the behavior of Ba2+ ions in Ba−O8 polyhedrons, which in turn improve the influence of mode-1 on the dielectric constants and losses. In common sense, the dielectric loss in the microwave frequency band consists of two parts: the intrinsic loss and the extrinsic loss.30 The intrinsic loss depends on the lattice vibration, while extrinsic loss is affected by defects such as pores and impurities. Therefore, there is a close relationship between the dielectric loss and the atomic packing fraction, as

ε∞ = 4.17.

Since the vibrational modes of the infrared-region are important to the Ba1+xMoO4 ceramics, it is essential to calculate the contribution of each mode to the dielectric response. The permittivity εj and dielectric losses tan δj/ω were determined in the infrared-region based on the following equations:2 εj =

ε∞

2 ∏k (ΩkLO − Ω2jTO)

2 Ω2jTO ∏k ≠ j (ΩkTO − Ω2jTO)

tan δj/ω =

(7)

εjγjTO/Ω2jTO ε∞ + ∑j εj

(8)

where the εj and tan δj/ω are the phonon contributions to the permittivities and dielectric losses. As shown from Table 5, the contributions of the external modes to the permittivities and the dielectric losses are much higher than those of the internal ones. Therefore, the permittivities and the dielectric losses of the E

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

loss have a negative correlation. While at x ≥ 0, with the increase in the Ba2+ content, a positive correlation between the packing fraction and dielectric loss is observed, which is different from the common sense stated above and may be related to the second phase. The relative permittivity εr originates from the molecular polarization in the microscopic scale, based on the Clausius− Mossotti equation (short for C-M equation), which correlates the microscopic polarizability and macroscopic dielectric properties. The molecular polarizability can be obtained by eq 9, referring the results of Shannon,31 and accordingly, the intrinsic permittivity can be obtained by the C-M eq 10. αe(AMoO4) = α(A2 +) + α(Mo6 +) + 4α(O2 −) εr =

(9)

3Vm + 8παe 3Vm − 4παe

(10)

where Vm is the molar volume and αe is the micropolarizability. The calculated dielectric constants are listed in Table 6. The frequency and damping can affect the fwhm of Raman spectra according to the classical radiation theory. The damping coefficient (γ) and the dielectric loss (tan δ) can be obtained by eqs 11 and 12, respectively:32 FWHM = γ γ 2 + 4ω02 /2ω0

(11)

⎛ γ ⎞ tan δ ≈ ⎜ 2 ⎟ω0 ⎝ ϖT ⎠

(12) −1

where ω0 is the center frequency of the Bg (Ba) (76 cm ) mode and ϖT is the angular frequency of the lattice vibration transverse optical mode. The calculated dielectric losses by damping equation are also listed in Table 6, which implies that the values calculated from C-M and damping equations agree well with the data of the FPSQ model. The relationships among the dielectric constants, the dielectric losses, and fwhm values of Bg (Ba) are shown in Figure 11, which

Figure 9. Contributions of external modes to permittivities (a) and dielectric losses (b).

shown in Table 2, and the internal relations of those are presented in Figure 10. As shown in Figure 10, with the decrease in the Ba2+ content (at x ≤ 0), the packing fraction and dielectric

Figure 11. Relationship among fwhm values of Bg (Mode 1) phonon modes, permittivity, and the dielectric loss calculated by damping equation as a function of x values.

indicates a positive correlation exists among them. The increase in the fwhm values of the Bg (Ba) mode is related to the increase in distortion in Ba−O8 polyhedra, which enhances the molecular polarizability of the samples, and thus, the permittivities increase accordingly. The damping coefficient of the lattice vibration is an important parameter affecting the dielectric loss of the ceramics. In general, the larger the damping coefficient, the larger the

Figure 10. Relationship of packing fraction, dielectric loss (calculated by FPSQ), cell volume as a function of x value. F

DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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intrinsic loss. That is, as the fwhm value of the Bg (Ba) mode increases, the damping coefficient of the lattice vibration increases, which causes the intrinsic loss to increase.

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CONCLUSION In summary, the Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics were fabricated by a conventional two-step sintering technique. XRD patterns show that the second phase (Ba2MoO5) appears when x > 0, and its content increases with the increase of Ba element. The Rietveld refinement results indicate that the unit cell volume is the largest at x = −0.02, for the possessing of the lowest packing fraction and covalency. There are positive correlations between the dielectric properties and the fwhm values of the Bg (Ba) modes because these values are related to the distortion in the Ba−O8 polyhedron and damping factors. The IR spectra analyzed by the FPSQ model were extrapolated to the microwave region, and the calculated dielectric properties from the fitting results are similar to those values calculated by Clausius− Mossotti and damping equations, which indicated that the dielectric constants of the Ba1+xMoO4 (−0.03 ≤ x ≤ 0.03) ceramics in the microwave frequency band are contributed by ion polarization and electronic polarization, and no other low frequency polarization contribution exists. The proportion of each mode in the dielectric response demonstrates that the external modes belonging to the Ba−O8 polyhedra have a decisive role on the dielectric properties of the samples.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (F. Shi), Tel & Fax.: +86 532 80691718. ORCID

Feng Shi: 0000-0003-1043-2838 Author Contributions #

C.X., J.L., and J.W. contributed equally to this work and should be considered co-first authors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Taishan Scholarship Project of Shandong Province, China (No. tshw20130956), Natural Science Foundation of Shandong Province, China (Grant No.ZR2016EMM21), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (Grant No. 2016RCJJ002), and the Opening Project of State Key Laboratory of High Performance Ceramics and Superfine Microstructure (Grant No. SKL201503SIC).

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DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b00841 Inorg. Chem. XXXX, XXX, XXX−XXX