Bond ionicity, lattice energy, bond energy and the microwave dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x ceramics

Journal Pre-proof Bond ionicity, lattice energy, bond energy and the microwave dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x ceramics

Mi Xiao, Susu He, Jiao Meng, Ping Zhang PII:

S0254-0584(19)31227-1

DOI:

https://doi.org/10.1016/j.matchemphys.2019.122412

Reference:

MAC 122412

To appear in:

Materials Chemistry and Physics

Received Date:

26 July 2019

Accepted Date:

03 November 2019

Please cite this article as: Mi Xiao, Susu He, Jiao Meng, Ping Zhang, Bond ionicity, lattice energy, bond energy and the microwave dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x ceramics, Materials Chemistry and Physics (2019), https://doi.org/10.1016/j.matchemphys. 2019.122412

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Journal Pre-proof Bond ionicity, lattice energy, bond energy and the microwave dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x ceramics Mi Xiao1, Susu He, Jiao Meng, Ping Zhang2 School of Electrical and Information Engineering & Key Laboratory of Smart Grid of the Ministry of Education, Tianjin University, Tianjin 300072, P. R. China

Abstract: The intrinsic relationship between crystal structure, surface topography, P-V-L theory and dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) ceramics prepared by a normative solid-state reaction route were determined. X-ray diffraction patterns demonstrated that the appropriate addition of excess or insufficient niobium ions could not destroy the crystal phase, but change the lattice parameters and unit cell volume. Meanwhile, the formation of pure phase with monoclinic wolframite structure and P2/c space group was confirmed. The Rietveld refinement was used to obtain structure parameters and investigate the crystal structure of the specimens. SEM showed that insufficient niobium ions didn’t show any impact on the dense structure, and the excess niobium ions promoted the growth of grains, but caused the appearance of undesired rough surfaces. The microwave properties as a function of the niobium ions content were found to be closely related to bond ionicity, lattice energy and bond energy calculated according to the P-V-L theory. As a result, when x was taken as -0.04 for the MgZrNb2+xO8+2.5x ceramics sintered at 1320°C, the best dielectric properties, εr=25.62, Q×f=80828.1GHz, τf=-44.64ppm/°C, were successfully obtained. Keywords: Crystal structure; Rietveld refinement; Dielectric properties; P-V-L theory

1. Introduction New advances in the modern wireless communications industry, microelectronic equipment, intelligent systems and other core industries[1,2] require high flexibility, miniaturization, low-cost and high frequency microwave components, which further raises the standards for microwave dielectric ceramics[3,4,5,6]. The dielectric ceramics that can be used in practical applications must meet the following requirements: (1) large permittivity (εr) to facilitate the miniaturization of equipment; (2) high quality factor (Q×f) to increase frequency selectivity; (3) near-zero temperature coefficient of resonant frequency (τf) to guarantee the frequency stability[7,8.9].

1 2

Corresponding Author, [email protected] Corresponding Author, [email protected]

Journal Pre-proof It was reported that the Nb-based oxide ceramics with same monoclinic structure, such as AZrNb2O8[10] (A: Zn and Mg) and Zn3Nb2O8[11], showed superior dielectric properties. Among them, the MgZrNb2O8 ceramic, which presented the excellent properties, εr=9.6, Q×f=58500GHz, τf=31.5ppm/°C, attracted many researchers’ attentions, and many efforts had been made for the sake of further improve the quality factor. Depending on the approximate ionic radius and similar chemical properties, bivalent ions such as (Co2+ and Ni2+) [12,13]and pentavalent ions (Sb5+ and Ta5+) [14]

were used to substitute a small amount of equivalent ions (Mg2+ and Nb5+) in MgZrNb2O8

ceramic respectively, which were advantageous for improving dielectric properties further. On the other hand, adjusting the stoichiometry of an element in the system is another way to improve dielectric properties. Many researches had reported that a slight excess and deficiency of A or Bsite ions of some other ceramics had a significant effect on phase composition, compactness and dielectric properties. For example, Wang et al.[15] investigated the effect of Mg non-stoichiometry on microstructure and dielectric performance of Li3Mg2NbO6 system, and reported that Q×f value significantly increased from 90000GHz to 140000 GHz when the amount of Mg in molecular formula was increased from 2 to 2.04. Li et al. [16] found that V ionic deficiency contributed to an increase in quality factor of Ca5Mn4V6+xO24 ceramics. Nevertheless, the non-stoichiometry influence of MgZrNb2O8 ceramic had not explored and revealed yet. In this work, in addition to preparing MgZrNb2+xO8+2.5x ceramics by the standard solid phase method, we also explored the influence of intrinsic factors, such as the bond ionicity, lattice energy and bond energy calculated according to P-V-L theory, on the dielectric properties. It was found that insufficient or excessive Nb-ions could produce vacancies, causing changes in lattice parameters. Meanwhile, intrinsic factors were found to depend on lattice parameters, and the internal connection between intrinsic factors and dielectric properties of MgZrNb2+xO8+2.5x ceramics was systematically discussed.

2. Experimental procedure The MgZrNb2+xO8+2.5x (x =-0.08, -0.04; 0; 0.04; 0.08) specimens were synthesized through the normative solid-state reaction method using high-purity oxide powders (99.9%): MgO, ZrO2, and Nb2O5. The oxide powders were weighed according to the non-stoichiometric ratio and ball-milled with zirconium balls for 7h in distilled water. Subsequently, the mixtures were fully dried, and then calcined at 1050°C for 3 h in air, to form the MgZrNb2O8 phase. After that, the compounds were

Journal Pre-proof ball milled again under the same condition as above to obtain more uniform small-sized particles. After dried, the compounds were mixed with 8wt% paraffin as a binder and pressed into disk-type pellets with a diameter of 10 mm and a thickness of 5 mm under the pressure of 3MPa. The pellets were sintered at 1280°C-1340°C for 8h with a heating rate of 3°C/min. The microscopic morphology of the as-fired surfaces of MgZrNb2+xO8+2.5x specimens was observed by scanning electron microscopy (SEM, ZEISS MERLIN Compact). The phase composition and crystal structures of the sintered specimens were determined by Rigaku Ultima Lv over the 2θ scanning range of 20 - 80°. In addition, the microwave dielectric properties (εr and Q×f ) of the sintered pellets were measured using a network analyzer in the frequency range of 8-10GHz. τf was calculated through Eq. 1. f85 - f25

τf = f25(85 - 25) × 106

(1)

where f25 and f85 denote the resonant frequencies at 25°C and 85°C, respectively.

3. Data processing Fig. 1 exhibits the X-ray diffraction patterns of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) ceramics sintered at 1320°C. The XRD patterns of the specimens can be well matched with the standard PDF card (ICDD #48-0329) of MgZrNb2O8 phase and no secondary phase is detected, which indicates that the composition of the crystal phase is not changed by the excessive or insufficient niobium ions. In addition, it is clearly observed from the inset figure that the enlarged diffraction peak around 30° exhibits a tendency to shift to a low angle and then back to a high angle ith the increase of |x| value, which indicated that the increase of x can lead to the increase of the unit cell volume and then decrease.

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Fig. 1 the XRD patterns of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens sintered at 1320°C

The Rietveld refinement is performed by using the software of Full-Prof to obtain structural parameters, such as lattice parameters, bond length and unit cell volumes, of which the motivation is to lay the groundwork for the calculation of the theoretical densities[17] and the complex chemical bond[18]. Parameters such as scale factor, zero point, background, half-width, asymmetry parameters, unit-cell parameters, atomic positional coordinates, temperature factors are refined step-by-step to improve the value of reliability factors(Rp and Rwp). When they are less than 15%, the refined results are acceptable. And in this way the positions of each atoms in the lattice were finally confirmed. The Rietveld figure (Fig. 2) of the MgZrNb1.96O7.9 ceramic is taken as a representative, in which the black curve denotes the calculated data, red circles denote the observed data, and blue lines at the bottom reflect the differences between the observed and the calculated data. And obviously, the calculated data are consistent with the observed data, implying the reasonability and accuracy of the obtained refined data. With the increase of Nb5+ amount, atomic interaction in MgZrNb2+xO8+2.5x ceramics increases first and then decreases, resulting in the change of bond length and cell volume. The detailed structural parameters in the entire range of compositions are summarized in Table 1 and Table 2, from which we can see that the Rietveld reliability factors are less than 15%, implying the reliability of the simulation results. Besides, the Rietveld refinement result is in accordance with the XRD patterns shown in Fig. 1.

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Fig. 2 the Rietveld refinement pattern of MgZrNb1.96O7.9 specimens sintered at 1320°C Table 1 the lattice parameters of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens x

a(Å)

b(Å)

c(Å)

β

Vcell(Å3)

Rp(%)

Rwp(%)

-0.08

4.8169

5.6448

5.0934

91.5364

138.44

11.1

10.9

-0.04

4.8168

5.6476

5.0928

91.5211

138.49

12.8

11.3

0

4.8203

5.6516

5.0972

91.5387

138.81

11.7

11.2

0.04

4.8187

5.6500

5.0955

91.5280

138.68

11.8

11.5

0.08

4.8194

5.6490

5.0937

91.5271

139.62

12.7

12.1

Table 2 the bond lengths of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens x

dMg/Zr-O(1)(Å)

dMg/Zr-O(2)1(Å)

dMg/Zr-O(2)2(Å)

dNb-O(1)1(Å)

dNb-O(1)2(Å)

dNb-O(2) (Å)

-0.08

1.9721

2.1008

2.2158

2.0034

2.1675

1.9108

-0.04

1.9898

2.0945

2.2156

2.0099

2.1586

1.9100

0

1.9842

2.1030

2.2225

2.0228

2.1559

1.9016

0.04

1.9778

2.1031

2.2287

2.0143

2.1743

1.8992

0.08

1.9802

2.0984

2.2362

2.0224

2.1712

1.8927

Recently, the P-V-L theory generalized by Zhang and Zhao [19] made it possible to disassemble the multi-bond systems and is applied successfully to interpret the dielectric properties of complex crystals. The above related theory can be referred to ref.[12] and the related data to explain the dielectric properties are listed in Table 3. Table 3 fi μ, U (kJ mol−1) and E (kJ mol−1) of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens

Journal Pre-proof x

ftotal i

-1 Utotal cal (KJ mol )

-1 Etotal cal (KJ mol )

-0.08

6.8494

52189

4278.7

-0.04

6.8551

52271

4279.7

0

6.8547

52249

4276.0

0.04

6.8507

52224

4275.3

0.08

6.8483

52223

4273.9

where fi total represents the total bond ionicity and can be used to predict the change in dielectric constant, Utotal cal represents the total lattice energy and is composed of ionic part and covalent part. The effect of ionic part on lattice energy is mainly attributed to the repulsive interactions of ion pairs and electrostatic interactions, and the covalent part is due to the overlap of electron clouds. Etotal cal represents the total bond energy and can be obtained by the chemical bond and the electronegativity [20,21].

4. Results and discussions Fig. 3 shows the relative densities as a function of sintering temperatures for the MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens. The relative densities of the MgZrNb2+xO8+2.5x specimens sintered at 1280°C-1340°C are obtained from the ratio of the apparent densities calculated through the Archimedes method to the theoretical densities calculated by the crystal parameters obtained from Rietveld refinement. The relative densities of all the specimens increase firstly and then decrease along with the sintering temperature. This phenomenon is ascribed to the fact that suitable sintering temperature is beneficial to the densification of ceramics, while the too much higher sintering temperature results in the fast grain growth, and pores will be trapped and difficult to be eliminated, leading to the decrease in relative densities. At the same time, with the increase of x, it is found that the sintering temperature of the maximum of relative densities shift from 1320°C to 1300°C. That is to say, excessive Nb ions can promote the sintering process. Moreover, the relative densities of ceramics samples sintered at 1320°C are all above 96% and thus 1320°C can be considered as the most appropriate sintering temperature.

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Fig. 3 The relative densities of the MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens as a function of sintering temperature

The SEM images of MgZrNb2+xO8+2.5x specimens sintered at 1320°C are described in Fig. 4. When x≤0, the grain sizes of the specimens are similar. However, as the value x increases, the grains become bigger, and the surface of the specimens become rough. The reason for this phenomenon may be that the optimum sintering temperature is reduced from 1320 to 1300, and excessive sintering temperature may cause abnormal grain growth.

Fig. 4 The SEM images of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens sintered at 1320°C; (a) x=-0.08; (b) x=0.04; (c) x=0; (d) x=0.04; (e) x=0.08

Journal Pre-proof MgZrNb2O8 system belongs to the monoclinic wolframite structure with P2/c space group. Fig. 5 shows the coordination atoms schematic of MgZrNb2O8 system, in which there is only one MgZrNb2O8 molecule in the unit cell, containing two Nb5+ ions and two Mg2+/Zr4+ ions. All cations are surrounded by six O2+ ions, constituting AO6-octahedrons as the basic unit of the material, and these octahedrons are interconnected with each other via vertex, as shown in Fig. 5. The properties of the material will be determined by the interaction of the octahedrons. When x < 0, the lattice forms the Nb vacancies and O vacancies，i.e., MgO + ZrO2 + (1-x)Nb2O5 → MgZrNb2(1-x)(VNb)2xO3O5(1-x)(VO)5x

(2)

where VNb and VO are the vacancies existing at Nb2+ ions sites and O2+ ions sites, which will lead to the shrinkage of the AO6-octahedron and thereby give rise to the decrease of the cell volume (as proved in Table 1). Similarly, when x > 0, the excessive Nb5+ and O2+ ions are bound to lead to the formation of Mg/Zr vacancies, causing a similar situation, the shrinkage of the AO6-octahedron and the decrease of the cell volume (also proved in Table 1).

Fig. 5 The coordination atoms schematic of MgZrNb2+xO8+2.5x phase

It is reported that the dielectric constant εr of microwave dielectric with a single-phase can be influenced by internal factors of ionic polarizability as well as external factors, such as the relative densities of specimens

[22,23,24].

Nevertheless, the relative densities of MgZrNb2+xO8+2.5x (-

0.08≤x≤0.08) specimens sintered at 1320°C are greater than 95% and no second phase appeared in this study, so the influence of the ionic polarizability on the dielectric constant of the MgZrNb2+xO8+2.5x specimens will be the dominance. In addition, the ionic polarizability is confirmed to be positively correlated with the bond ionicity fi, which can be calculated according to ref. [12]. According to the calculation formula[12], the bond ionicity is determined by the unit cell volume and

Journal Pre-proof bond length. Fig. 6 gives the change of εr as well as the total bond ionicity with x, from which we can see that εr and the total bond ionicity show the similar trend: increased firstly along with the x, and then decreased when x≥-0.04. The relationship of εr and bond ionicity fi can be shown as Eqs.3. εr =

n2 - 1 1 - fi

+1

(3)

where n represents the refractive index. It is seen obviously from Eqs.3 that when x<0, the increase of total bond ionicity expectedly results in the larger dielectric constant. When x ≥0, the increase of x is accompanied by a decrease in the optimum sintering temperature, which means the grain growth was accelerated, and this will inevitably form more closed pores and results in a decrease in dielectric constant. Hence, the decrease of dielectric constant is the result of lower bond ionicity and closed pores.

Fig. 6 The εr and the total bond ionicity of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens sintered at 1320°C

For the ceramics with a relative density over 95%, the influences of extrinsic factors like grain size, relative density and secondary phase, on the quality factor Q×f can be neglected, and the Q×f is mainly affected by the intrinsic factors [25]. The dependence of Q×f on internal loss results from lattice vibration modes, which can be determined by total lattice energy [10]. The increase of lattice energy contributes to the reduction of dielectric loss and the improvement of the quality factor. Similar to ionic polarizability, lattice energy is also extremely dependent on unit cell volume and

Journal Pre-proof bond length. Fig. 7 shows the lattice energy and Q×f of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens as a function of value x. Both functions of MgZrNb2+xO8+2.5x specimens initially increase and then decrease with the increase of x. When x<0, the total lattice energy increases to the benefit of the increase of quality factor. While when x≥0, the abnormity of grain size and the total lattice energy together weaken the quality factor, leading to decrease in the quality factor.

Fig. 7 The Q×f and total lattice energy of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08) specimens sintered at 1320°C

For the ceramics with octahedral structure, the temperature coefficient of the resonant frequency τf is determined by the bond energy (E)[26]. Larger bond energy can predict smaller |τf| value. In the MgZrNb2O8 system, all cations form oxygen octahedrons with the nearby oxygen ions. The larger the bond energy, the larger the restoring force applied to oxygen octahedrons, suppressing the distortion of oxygen octahedrons caused by the external environment, which will be beneficial to formation of more stable system, leading to the smaller τf. As described in Fig. 8, with the increase of the Nb5+ content, the |τf| value became larger, reached the maximum when x=-0.04 and then decreased, depicting similar tendency as the total bond energy. The essence of the above phenomenon is that when x≥-0,04 the restoring force becomes smaller to reverse the octahedral distortion, resulting in the increase of system instability

Journal Pre-proof and the increase of the |τf| value.

Fig. 8 The τf and the total bond energy of MgZrNb2+xO8+2.5x (-0.08≤x≤0.08)specimens sintered at 1320°C

5. Conclusion In this experiment, the non-stoichiometric MgZrNb2+xO8+2.5x(-0.08≤x≤0.08) ceramics were prepared by a normative solid-state reaction route. The influences of excessive and insufficient niobium ions contents on the crystal structures, surface topography and microwave dielectric performance of MgZrNb2+xO8+2.5x specimens were systematically researched. A single phase with monoclinic wolframite structure and P2/c space group was detected by XRD, and XRD patterns indicated that the small change in content of niobium ions affected the lattice parameters and unit cell volume rather than the phase composition of specimen. SEM showed that pure phase MgZrNb2O8 was formed and the superfluous niobium ions could promote the growth of grains. On the base of Rietveld refinements, the P-V-L theory was used as a means to analyze dielectric properties for the entire component. The dielectric properties as a function of Nb-site content were found to be dependent on bond ionicity, lattice energy and bond energy. As a result, it was found that a little nonstoichiometric adjustment of the component may be beneficial to the improvement of microwave dielectric properties through minor distortion of the lattice, and when x=-0.04, the

Journal Pre-proof best dielectric properties of MgZrNb2+xO8+2.5x specimens sintered at 1320°C were achieved: εr=25.62, Q×f=80828.1GHz, τf=-44.64ppm/°C.

Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 51877146).

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Journal Pre-proof Dear Editor, We would like to submit the enclosed manuscript entitled “Bond ionicity, lattice energy, bond energy and the microwave dielectric properties of non-stoichiometric MgZrNb2+xO8+2.5x ceramics”, which we wish to be considered for publication on “Materials Chemistry and Physics”. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

Yours sincerely, Susu He Corresponding author: Name: Mi Xiao E-mail: [email protected]

Journal Pre-proof Highlights 1.

Microstructures and dielectric properties of sintered ceramics were studied.

2.

Relations between crystal structure and dielectric properties were investigated.

3.

Complex chemical bond theory was used to explore the structural characteristics.

4.

The obtained ceramics could be promising materials for further researching.