Influences of substituting of (Ni 1/3 Nb 2/3 ) 4+ for Ti 4+ on the phase compositions, microstructures, and dielectric properties of Li 2 Zn[Ti 1 − x (Ni 1/3 Nb 2/3 ) x ] 3 O 8 (0 ≤ x ≤ 0.3) microwave ceramics

: Complex ion substitution is gaining more attention as an appealing method of modifying the structure and performance of microwave ceramics. In this work, Li 2 Zn[Ti 1 − x (Ni 1/3 Nb 2/3 ) x ] 3 O 8 (LZTNN x , 0 ≤ x ≤ 0.3) ceramics were designed based on the complex ion substitution strategy, following the substitution rule of radius and valence to investigate the relationship among phase compositions (containing oxygen vacancies and Ti 3+ ions), microstructures, and microwave dielectric characteristics of the LZTNN x ceramics. The samples maintained a single Li 2 ZnTi 3 O 8 solid solution phase as x ≤ 0.2, whereas the sample of x = 0.3 produced a second phase with the LiNbO 3 structure. The appropriate amount of (Ni 1/3 Nb 2/3 ) 4+ substitution could slightly improve the densification of the LZTNN x ceramics due to the formation of the Li 2 ZnTi 3 O 8 solid solution accompanied by a decrease in the average grain size. The presence of a new A 1g Raman active band at about 848 cm − 1 indicated that local symmetry changed, affecting atomic interactions of the LZTNN x ceramics. The variation of the relative dielectric constant ( ε r ) was closely related to the molar volume ionic polarizability ( TD  ), and the temperature coefficient of the resonant frequency ( τ f ) was related to the bond valence ( V i ) of Ti. The increase in density, the absence of the Ti 3+ ions and oxygen vacancies, and the reduction in damping behavior were responsible for the decreased dielectric loss. The LZTNN0.2 ceramics sintered at 1120 ℃ exhibited favorable microwave dielectric properties: ε r = 22.13, quality factor ( Q × f ) = 97,350 GHz, and τ f = − 18.60 ppm/ ℃ , which might be a promising candidate for wireless communication applications in highly selective electronics. 


Introduction
The rapid growth of mobile communication systems, especially the prevalence of the fifth-generation wireless communication and the Internet of Things in recent years, has greatly stimulated the need for microwave devices such as dielectric resonators, oscillators, and antenna substrates.Therefore, microwave dielectric ceramics have become a major scholarly research topic as a key component for the fabrication of these electronics [1,2].In general, favorable performances of the microwave dielectric ceramics are the moderate relative dielectric constant (ε r ), highquality factor (Q×f), and near-zero temperature coefficient of resonant frequency (τ f ), which can ensure miniaturization of electronics, reduce insertion loss of the electronics at high frequencies, and maintain temperature stability of the electronics, respectively [3][4][5][6].To achieve this target, enormous efforts have been made to explore a variety of novel ceramic systems such as Li  [7][8][9][10][11][12][13][14].
Among these systems, cubic-spinel-structured Li 2 ZnTi 3 O 8 ceramics have attracted much interest due to their simple preparation process, promising dielectric properties (ε r = 25.6,Q×f = 72,000 GHz, and τ f = −11.2ppm/ ℃ ), and low material cost [14].Consequently, many researchers [15][16][17][18][19][20][21][22][23][24] have made great efforts to improve microwave dielectric properties by various methods including single-oxide doping, changing sintering techniques, heat treatment, and non-stoichiometric strategy.The single-oxide doping was once considered as an effective measure to improve the Q×f value with the substitutions of Mg 2+ , Co 2+ , Cu 2+ , and Ca 2+ by A-site Zn 2+ , and Sn 4+ and Al 3+ for B-site Ti 4+ [15][16][17][18][19].For example, Huang et al. [20] confirmed that the Q×f value of the Li 2 ZnTi 3 O 8 ceramics was significantly improved through the substitution of Mg 2+ and Co 2 for Zn 2+ , obtaining the Q×f values of 150,000 and 140,000 GHz for the compositions Li 2 (Zn 0.94 Mg 0.06 )Ti 3 O 8 and Li 2 (Zn 0.92 Co 0.08 )Ti 3 O 8 , respectively.However, this investigation was concentrated on the small amount of MgO and CoO (0.02 ≤ x ≤ 0.1) added to the Li 2 ZnTi 3 O 8 ceramics, and as such there are no more results for large amounts (x > 0.1).Moreover, the fundamental understanding of the relationship among compositions, microstructures, and microwave dielectric characteristics in this system was not well analyzed.Furthermore, scattered studies also indicate that this method may not always be effective in enhancing the Q×f value.Singh et al. [21] investigated the influence of the Ni 2+ substitution on the microwave dielectric properties of Li 2 ZnTi 3 O 8 , revealing that the Q×f value decreased with the increase in the Ni 2+ substitution content.In Ref. [25], the Q×f value of the Li 2 ZnTi 3 O 8 ceramics with 3 wt% Nb 2 O 5 was 66,304 GHz, showing a significant decrease in comparison to the undoped ones with Q×f = 72,000 GHz.These results lead us to a question.What will happen if we adopt a co-substitution method with equivalent ions in the Li 2 ZnTi 3 O 8 ceramics?So far, there have been only a few investigations on the performance regulation mechanism of the Li 2 ZnTi 3 O 8 ceramics.For example, how the oxygen vacancies and Ti 3+ ions, which are frequently generated in titanium-containing dielectric ceramics during the high-temperature sintering, affect Q×f is not well understood.Furthermore, Refs.[26][27][28][29][30][31][32][33][34][35] provide the evidence that the complex ion doping is a promising approach of improving the microwave dielectric properties of the titanium-containing ceramics such as Li  Consequently, the development of lead-free dielectric ceramics with good performances has become a hot topic in functional ceramic-related fields.We understand the relationship among the phase compositions (containing the oxygen vacancies and Ti 3+ ions), the microstructures, and the microwave dielectric characteristics by X-ray diffraction (XRD), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), and scanning electron microscopy (SEM) analysis together with energy dispersive spectroscopy (EDS) analysis in the present work.Our results prove that the (Ni 1/3 Nb 2/3 ) 4+ substitution is an effective way to obtain satisfactory Q×f in comparison with the unfavorable effect caused by mono-doped Ni or Nb in the Li 2 ZnTi 3 O 8 ceramics.On the other hand, our study will provide a theoretical guide for oxygen-vacancy control to improve the dielectric properties of the Li 2 ZnTi 3 O 8 ceramics by the complex ion substitution.

Experimental
The conventional solid-state method was conducted to synthesize the LZTNNx (x = 0-0.3)ceramics using analytical-grade ZnO, TiO 2 , NiO, Nb 2 O 5 , and Li 2 CO 3 (all with purity ≥ 99.9%) as starting materials.All starting materials were purchased from Shanghai Aladdin Biochemical Technology Co., Ltd., and they were used directly in the current experiment.Based on stoichiometric compositions, the required substances were weighed successively and were ball-milled in a nylon jar using absolute alcohol as a mixing medium for 12 h.The mixtures were dried, and then calcined at 900 for 4 h.Subsequently, the calcined powders ℃ were re-milled for 4 h in an absolute alcohol medium.After being dried, the re-milled powders were mixed with 8 wt% polyvinyl alcohol (PVA) solution as a binder, and then sieved with a 100-mesh standard sieve.The powders were pressed into disks of 10 mm in diameter and 5 mm in thickness under a pressure of 200 MPa.All disks were heated at 600 for 2 h to ℃ remove the organic binder and were sintered at 1060-1180 for 3 h.It is noted that all samples ℃ should be covered with sacrificial powders completely to impede the evaporation of a lithium element during the sintering process.
According to American Society for Testing Material (ASTM)-C20, bulk density of the sintered disks were measured by Archimedes method [35].Structural analysis of the sintered ceramics was performed via an X-ray diffractometer (D8 Advance, Bruker, Germany; Cu Kα, 1.5418 Å) operating at 30 mA and 45 kV.Normal analysis was carried out at 2θ = 10°-70° at a scan rate of 4 (°)/min.Quantitative phase analysis of the sintered ceramics was conducted by Rietveld refinement method using the General Structure Analysis System (GSAS) software (Los Alamos National Laboratory, USA).A field-emission scanning electron microscope (Nano 430, FEI, Japan) operating at 20 kV was employed to study the microstructures of fired pellets.Grain sizes of the fired pellets were determined by the linear intercept method using the Nano Measurer software (Laboratory of Surface Chemistry and Catalysis, Fudan University, China).To obtain the grain size distribution, at least 100 grains were measured for each pellet.Elemental distributions of the fired pellets were determined using an energy dispersive spectrometer (AZtecOne, Oxford Instruments, UK).Raman spectra were collected within the limits of 100-1000 cm −1 using a Raman spectrometer (Invia, Renishaw, UK).An X-ray photoelectron spectrometer (Escalab 250Xi, Thermo Fisher Scientific, USA) operating at 12 kV and 6 mA was utilized to analyze binding energy of cations by means of an Al Kα X-ray source.The Thermo Advantage software (Thermo Fisher Scientific, USA) was used to fit the as-obtained XPS spectra.The microwave dielectric properties of the sintered disks were measured using a network analyzer (N5230C, Agilent, USA).The ε r value was obtained by the TE 011 resonant mode using Hakki-Coleman method utilizing the quickwave electromagnetic design software (QWED, Switzerland) [22].The measured specimens were placed between two wellpolished conducting plates which are coated with silver.The unloaded Q×f value was determined by the transmission cavity method with the TE 01δ resonance mode [40].The measured samples were placed inside a cylindrical metallic cavity made of copper with finely polished inner surfaces, which are coated with silver.The metallic cavity was closed and fed with a microwave by loop coupling.The τ f value was measured by placing the sample into a temperature chamber (STH-120, GZ-ESPEC, Japan) according to Eq. (1) [41]: where f(80 ) and ℃ f(20 ) denote the resonant ℃ frequencies at 80 and 20 ℃ , respectively.℃  analogous diffraction patterns as x ≤ 0.2, indicating that Ni 2+ and Nb 5+ may enter the Li 2 ZnTi 3 O 8 lattice to form solid solution.Three additional peaks (designated by the symbol "+") are detectable when x = 0.3.By tentatively indexing with the file (PDF Card No. 86-1512), the cubic Li 2 ZnTi 3 O 8 spinel structure with the P4332 space group is distinguished, whereas the second phase that existed in the composition of x = 0.3 is determined as LiNbO 3 with a rhombohedral structure according to the file (PDF Card No. 82-0459).As shown in Fig. 1(b), the diffraction peak shifts to the low 2θ position with the increase of the x value, implying that the cell volume (V) increases with the (Ni 1/3 Nb 2/3 ) 4+ concentration increasing.This result can be explained by the substitution of relatively larger (Ni 1/3 Nb 2/3 ) 4+ ions for smaller Ti 4+ ions.

Results and discussion
In addition, compared with the standard card of LiNbO 3 , the diffraction peaks in the sample of x = 0.3 slightly shift to a low 2θ angle, indicating that the second phase might be the LiNbO 3 solid solution.In Ref. [42], Câmara indicated that an unknown phase formed when doping 20 mol% Ni into the Li 2 ZnTi 3 O 8 ceramics, whereas Lv [43] found that the substitution of Ti with Nb led to the formation of a LiZnNbO 4 phase when the substitution amount was up to 20 mol%.Our results accompanied by Refs.[42,43] reveal that there would be a solid solubility limit regardless of Ni-/Nb-doped or (Ni,Nb)-codoped Li 2 ZnTi 3 O 8 , which differs from the substitution of Zn in Li 2 ZnTi 3 O 8 with Co or Mg since Shannon's effective ionic radii are very similar (0.74 Å to Zn 2+ radius, 0.745 Å to Co 2+ radius, and 0.72 Å to Mg 2+ radius), and Zn 2+ , Co 2+ , and Mg 2+ are isovalent [19,44].The possible reaction for the formation of the LiNbO 3 phase is The Rietveld refinement method is known to be a useful tool for providing important crystal structure information such as lattice parameters, bond length (d ij ), and phase content.To precisely obtain this information, this method was employed using the GSAS software based on the XRD data obtained in the 2θ range of 10°-120° at a scan rate of 1 (°)/min and a step size of 0.02°.Figures 2(a)-2(d) present the patterns after the fitting of the LZTNNx ceramics.The calculated patterns of all samples are in good agreement with those observed.The refined crystallographic parameters are shown in Table 1.It can be found that all R p values are lower than 10%, further confirming the credibility of the refinement results.The variations in the crystal structure caused by the substitution of Ti 4+ with (Ni 1/3 Nb 2/3 ) 4+ can be found in Table 1.The lattice constants (a, b, and c) and the V increase with the increase of the (Ni 1/3 Nb 2/3 ) 4+ amount.In Table 1, it is also found that with the (Ni 1/3 Nb 2/3 ) 4+ ion substitution amount increasing, the mean d ij of a Li    Besides, the gradually increased apparent density with the increase of the (Ni 1/3 Nb 2/3 ) 4+ amount is due to the obviously increased unit cell mass, whereas V varies little.In Fig. 3(b), ρ r increases from 96.22% to 97.16%, and then decreases to 96.24% with the x value increasing.The increase in ρ r indicates the densification of materials, which can be also confirmed by the SEM results.Therefore, it can be inferred that the appropriate amount of (Ni 1/3 Nb 2/3 ) 4+ promotes the sintering process of ceramics.It was reported that as the dopant was added into the main crystalline phase to produce the solid solution, it could activate lattice and enhance sintering [46].Thus, the increase in ρ r may be related to the formation of the Li 2 ZnTi 3 O 8 solid solution.It is worth noting that high ρ r (> 96%) is obtained in the LZTNNx ceramics, which is especially advantageous for the promotion of the microwave dielectric properties.

2 Density and microscopic morphology analysis
Figures 4(a)-4(d) exhibit the SEM images of the LZTNNx ceramics with various x values sintered at the optimum temperatures, and their insets display the grain size distribution and mean grain size of each sample.It can be found that all samples show relatively dense microstructures, which is in accordance with the results of density measurements (Fig. 3).Moreover, when the x value increases from 0 to 0.3, the average grain size of the samples significantly decreases from 75.9 to 29.9 μm.It can be speculated that the (Ni 1/3 Nb 2/3 ) 4+ co-doping can effectively inhibit the grain growth.All samples present relatively uniform microstructures except the one with x = 0.3, in which small amounts of tetragonal grains are found.The LZTNN0.2 ceramics sintered at 1120 were analyzed ℃ by the EDS mapping to further investigate its elemental distributions, as indicated in Figs. 4

(e)-4(i).
The EDS elemental mapping analysis confirms the presence of Zn, Ti, Ni, Nb, and O elements.Furthermore, all elements are homogeneously distributed in the ceramics without obvious enrichment.To identify the elemental contents and distributions of the grains with different morphologies in the LZTNNx ceramics, the  This result agrees well with the XRD results (Fig. 1).

3 Raman spectroscopy analysis
The Raman spectroscopy is a useful tool to provide subtle changes in the crystal structure, chemical bond vibration, and short-range ordering, and thus can be used for further investigating the correlation between the dielectric properties and the crystal structure.that the observed number of the modes is significantly less than that predicted by the group theoretical method owing to the overlapped and broadened Raman vibration bands or the low resolution of the apparatus.In our current work, the Raman spectrum of Li 2 ZnTi 3 O 8 has similar Raman active bands to those reported in Refs.[23,25,45].The Raman active bands at about 115, 156, 232, and 264 cm −1 are assigned to the E g mode, the Raman active bands at 352, 447, and 524 cm −1 are designated to the F 2g mode, and the Raman active bands at about 403 and 718 cm −1 belong to the A 1g mode.Among them, the Raman bands at 403 and 447 cm  Moreover, cation ordering is an important factor affecting Q×f of the microwave ceramics, which will be discussed in the microwave dielectric property analysis.
To study the relationship between the vibration mode and the microwave dielectric properties, the XPS PEAK41 software was utilized to fit the Raman spectra of the LZTNNx ceramics.Gaussian-Lorentzian modes of all samples are displayed in Fig. 6.Table 2 lists the Raman shifts and FWHMs of the Raman active mode at about 718 cm −1 .A redshift is observed in the Raman spectra, which may be derived from larger polarizability of (Ni 1/3 Nb 2/3 ) 4+ (3.06 Å) than that of Ti 4+ (2.93 Å).Higher molecular polarizability would have lower scattered energy, and hence lead to a low wavenumber [49,50].In addition, the FWHM has a significant contribution towards the Q×f value since it reflects the short-range ordering degree of the structure.

4 XPS analysis
To determine a surface chemical state, the XPS analysis was carried out for the LZTNN0.2ceramics sintered at 1120 as a representative.The binding ℃ energy shown in the XPS patterns is closely related to the chemical states of the elements.[LiO 6 ] octahedron [51].Zn 2p core levels (Fig. 7(c)) can be split into 2p 3/2 and 2p 1/2 doublets because of spin-orbit coupling, whose binding energy is 1021.09and 1044.11eV, respectively.The binding energy difference between the two lines of 23.02 eV is lying well within the standard reference value of ZnO [52].These results indicate that Zn atoms in the ceramics are in the +2 oxidation state.Figure 7(d) shows the presence of Ni in the +2 oxidation state, which is evidenced by the binding energy of the 2p 3/2 level (854.95eV) and 2p 1/2 level (872.48 eV) and the presence of two shake-up satellite peaks at higher binding energy at 861.43 and 879.84 eV.As shown in Fig. 7(e), the XPS peaks of Nb 3d spectra can be deconvoluted into two doublet peaks, which are located at 206.82 and 209.58 eV, and 206.43 and 209.13 eV, corresponding to Nb 5+ and Nb 4+ , respectively.The spin-orbital peak separation between each doublet is about 2.75 eV, which is consistent with the report by Jiang et al. [53].The coexistence of Nb 5+ and Nb 4+ species indicates that Nb 5+ ions in the ceramics are reduced to Nb 4+ ions during the sintering process.The relative content is Nb 5+ : Nb 4+ = 63 : 39 based on the calculation from the XPS data.In Fig. 7(f), the binding energy of Ti 2p electrons is 458.20 and 463.88 eV for 2p 3/2 and 2p 1/2 , respectively.The binding energy difference between the two peaks of 5.68 eV is found to be within the earlier reported value.No additional 2p 3/2 low binding energy shoulder at about 457.8 eV is detected, showing that there is only Ti 4+ present in the ceramics.In Fig. 7(g), oxygen high-resolution XPS spectra can be deconvoluted into two peaks.The peak at 529.67 eV is attributed to the oxygen bonded to a octahedral site cation, while the peak at 531.51 eV is assigned to the oxygen bonded to a tetrahedral site cation [54].No oxygen vacancies or adsorbed H 2 O are clearly detected in the lattice.

Ti e Ti
When Nb 5+ is introduced to replace Ti 4+ , it grabs the electrons produced by the oxygen vacancies to form Nb 4+ (Reaction ( 5)) due to its larger electronegativity (1.25) than that of Ti 4+ (1.09) [57], thereby inhibiting the reduction of Ti 4+ .5 4

Nb e Nb
     (5) On the other hand, the oxygen vacancies generated by Reactions (3) and ( 6) (substitution of Ti 4+ with Ni 2+ ) can be exhausted by the unreacted Nb 5+ (Reaction ( 7)): Therefore, the introduction of Nb 5+ together with its reduction may be the possible reason for the absence of the Ti 3+ ions and oxygen vacancies.The presence of only Ti 4+ has also been identified in Ba 6 Ti 2 Nb 8 O 30 and Ni-doped CaCu 3 Ti 4 O 12 systems [53,58], which coincides with our current findings.


), and microwave dielectric properties of the LZTNNx ceramics.It is obviously seen that the experimental relative dielectric constant (ε r-exp ) value gradually decreases with the increase of the x value, whereas the Q×f value initially increases, and then decreases.Meanwhile, the τ f value becomes more negative.Based on the discussion in Section 3.2, the ρ r of the LZTNNx ceramics is slightly enhanced.The ρ r of above 96% indicates that the influence of porosity on the microwave dielectric properties can be ignored.
Figure 8(a) demonstrates the variation of ε r for the LZTNNx ceramics sintered at various temperatures.It can be found that ε r of the LZTNNx ceramics first increases to the maximum value, and then decreases with an increase in the sintering temperature.For example, ε r gradually increases from 20.66 at 1060 ℃ to 22.13 at 1120 , and then decreases to 21.68 at ℃ 1150 as ℃ x = 0.2.This tendency is consistent with that of ρ r , which indicates that ρ r plays an important role in affecting ε r .
In addition to ρ r , several factors such as the crystal structure, secondary phase, and T D  also have important influences on ε r .The T D  can be estimated by Eq. ( 8): where .97 Å, and α(O 2− ) = 2.01 Å [59].The ε r-the can be determined by Clausius-Mosotti equation (Eq.( 9)) [60]: where b (= 4π/3) is a constant, and V m is the molar volume obtained by the XRD refinement.
To eliminate negative impacts of the porosity on ε r-exp , ε r-corr is calculated by Eqs.(10) and (11) [61]: where Q is the porosity, and t  is the theoretical density.4. All ε r-corr values are slightly higher than the ε r-exp values due to the presence of residual pores in the samples.In general, the residual pores in the sintered ceramic body are regarded as the second phase with ε r ≈ 1, which is the small-porosity limit of the relation for a continuous dielectric including vacuum spherical pores [62].As a result, as the dielectric contains several pores, its ε r will greatly reduce.In Fig. 3(b), the LTZNNx ceramics exhibit such high density (ρ r > 96%) that their ε r-corr values are slightly higher than the ε r-exp values.Moreover, the ε r-corr , ε r-exp , and ε r-the values decrease with the increased substitution of (Ni 1/3 Nb 2/3 ) 4+ for Ti 4+ .These variations are in good accordance with the variation of T  leads to high ε r-exp .In particular, it should be noted that all ε r-the values are remarkably higher than the ε r-exp values, and  between ε r-exp and ε r-the calculated according to Eq. ( 12) is about 26.8%-31.4%.This large  should be an indicator of local structural distortion and can be elaborated by the presence of "compressed" effects and "rattling" effects, resulting in low and high polarizabilities existing in the structure.According to Eqs. ( 13) and ( 14), the bond valence (V i ) of Ti 4+ in the LTZNNx ceramics is calculated, and the corresponding V i values are 3.57, 3.33, 3.25, and 3.04 for x = 0, 0.1, 0.2, and 0.3, respectively.Evidently, V i of Ti 4+ decreases linearly with the x value increasing.The computed results indicate that Ti 4+ is elongated with a smaller V i than a normal oxidation state, inevitably causing the tilting of the TiO 6 octahedrons and the weakened internal electric field between titanium ions and oxygen ions [63].Finally, the coupling polarization is reduced, and hence ε r is decreased.
where R ij is the bond valence parameter.The value of c is 0.37. Figure 9(a) displays Q×f of the LZTNNx ceramics as a function of the sintering temperature.Among them, the Q×f value of the LZTNN0.2ceramics exhibits the maximum value of 97,350 GHz when sintered at 1120 ℃.The Q×f has an identical change trend with the density, revealing that the density also has a decisive role in affecting the dielectric loss of the ceramics.Meanwhile, Q×f exhibits a strong dependence on ceramic composition.As shown in Fig. 9(b), Q×f shows a prominent promotion by ~41.7% from 68,705 GHz at x = 0 to 97,350 GHz at x = 0.2.Further still, the Q×f value (73,235 GHz) of the sample of x = 0.3 is significantly lower than those of other co-substituted ceramics due to its second phase of LiNbO 3 .However, it is still slightly higher than that of the un-substituted ceramics.The primary factors influencing the dielectric loss of the ceramics can be divided into extrinsic (e.g., density, porosity, phase composition, composition, grain size, and oxygen vacancy) and intrinsic losses (such as lattice vibration and cation ordering).In the present work, we utilized the XRD, Raman spectroscopy, and XPS to investigate the effects of the intrinsic factors and extrinsic factors on Q×f of the LZTNNx ceramics.Xiao et al. [23] studied the influence of the cation ordering on the microwave dielectric properties of the Li 2 ZnTi 3 O 8 ceramics by Ti-nonstoichiometry strategy and revealed that a significant improvement in the Q×f value was obtained due to the enhanced degree of the cation ordering.Similar relationship between the cation ordering and the Q×f can be found in the current LZTNNx ceramics.Both the Q×f value and the integrated relative intensity of the (111) order of the LZTNNx ceramics divided by that of the (311) order (I (111) /I (311) ) exhibit the same dependence on the composition, as shown in Fig. 9(b).As the x value increases, the maximum value of 0.28 for the (111) reflection order is achieved at x = 0.2.This implies that the sample with x = 0.2 has the highest Q×f value of 97,350 GHz.On the other hand, it is generally accepted that in several Ti-based microwave ceramics [64][65][66][67], the oxygen vacancies generated in the high-temperature sintering are responsible for the deterioration of Q×f.From the above XPS analysis, the substitution of Ti 4+ with (Ni 1/3 Nb 2/3 ) 4+ leads to the absence of the Ti 3+ ions and oxygen vacancies.Therefore, the Q×f values of the LZTNNx ceramics are improved to some extent.
In addition, the previous investigations have indicated that the intrinsic loss is also induced by non-harmonic vibration.The correlation between the intrinsic loss and the non-harmonic vibration can be expressed by Eqs. ( 15) and ( 16): where tanδ is the dielectric loss, and ω T is the angular frequency of the transverse optical frequency of the lattice vibration.established that τ f is closely related to the linear thermal expansion coefficient (α L ) and the temperature coefficient of the dielectric permittivity (τ ε ), as denoted by Eq. ( 17): Generally, α L is regarded as a constant (about 10 ppm/ ), whereas ℃ τ ε is a relatively variable parameter, which can be described by Eqs. ( 18)-( 22): 1 ( 1 ) ( 2 ) ( ) 3 where A represents the direct dependence of the polarizability on temperature (this variable generally is negative), and B and C represent the change of the relative permittivity, relative to the total effect of volume expansion.T is the temperature, and P is the pressure.α m , ε, and ε 0 represent the dielectric polarizability, the dielectric constant, and the vacuum dielectric constant, respectively.It is well known that ε 0 is a constant of 8.8542×10 −12 F/m, and the variation of ε r is very small.As a consequence, ε can be considered as a fixed value.Both the terms B and C correlate with the volume variation, which would be reflected by V i of the ions.The (Ni 1/3 Nb 2/3 ) substitution effect on V i of Ti in the LZTNNx (x = 0-0.3)ceramics is also shown in Fig. 10.In comparison with the variation tendency in the τ f value, a steady decrease is found in V i of Ti, implying the reduced structural distortion caused by the (Ni 1/3 Nb 2/3 ) doping.Therefore, the current declining τ f value is mainly due to the decrease in the structural distortion, as implied by the decreased V i .Table 5 summarizes some related research results of the Li 2 ZnTi 3 O 8 -based ceramics obtained by different processes.As displayed in Table 5, the ion doping containing the complex ion substitution has no obvious effect on the τ f value.However, the (Ni 1/3 Nb 2/3 ) 4+ complex ion substitution leads to the reduction in the ε r value, decreasing from > 25 to 22. (Zn 1/3 Nb 2/3 ) 4+ , and (Li 1/4 Nb 3/4 ) 4+ , the ceramics co-substituted by (Ni 1/3 Nb 2/3 ) 4+ still exhibits the highest Q×f value.As shown by the XRD and field-emission scanning electron microscopy (FE-SEM), the contribution from the second phase, density, and porosity can be neglected due to phase purity and high ρ r (> 95%).In this work, the enhanced Q×f value of the Li 2 Zn[Ti 0.8 (Ni 1/3 Nb 2/3 ) 0.2 ] 3 O 8 ceramics might be related to the decrease in non-harmonic lattice vibration and the absence of the Ti 3+ ions and oxygen vacancies, as revealed by the Raman spectra and XPS.

Conclusions
LZTNNx (0 ≤ x ≤ 0.3) ceramics were achieved via the conventional solid-state ceramic method.The effects of the substitution of Ti 4+ with (Ni 1/3 Nb 2/3 ) 4+ on intrinsic dielectric behavior were deeply studied.The XRD refinement results showed that the cubic-spinelstructured Li 2 ZnTi 3 O 8 solid solution with the P4332 space group was formed for the co-substituted ceramics.The microstructures of the LZTNNx (0 ≤ x ≤ 0.3) ceramics demonstrated that the (Ni 1/3 Nb 2/3 ) 4+ ion doping promoted sintering but inhibited grain growth.The Raman spectra revealed that the new A 1g Raman active band at about 848 cm −1 emerged in the co-substituted ceramics.The absence of the Ti 3+ ions and oxygen vacancies was confirmed by the XPS spectra.The ε -corr , ε r-exp , and ε r-the values decreased with the increased substitution of (Ni 1/3 Nb 2/3 ) 4+ for Ti 4+ .However, the variation tendency of T D  with the x value is rarely opposite to those variations.The (Ni 1/3 Nb 2/3 ) 4+ ion doping leads to a steady decrease in V i of Ti, and hence a gradual decline in the τ f value due to the decreased structural distortion.Compared with that of the pure Li 2 ZnTi 3 O 8 prepared in this work, the Q×f value was increased by 41.7%.Furthermore, the composition with x = 0.2 exhibited the optimized microwave dielectric properties with ε r = 22.13, Q×f = 97,350 GHz, and τ f = −18.60ppm/ .℃

3. 1
Phase composition and structural analysis XRD patterns of the LZTNNx (x = 0, 0.1, 0.2, and 0.3) ceramics sintered at their optimum temperatures (those ceramics showing the maximum relative density (ρ r ) values) are displayed in Fig. 1(a).All specimens show

Fig. 2
Fig. 2 Rietveld refinement patterns of LZTNNx ceramics: (a) x = 0, (b) x = 0.1, (c) x = 0.2, and (d) x = 0.3 and (e) crystal structure of LZTNN0.2 ceramics wherein Y obs is the experimental value of the plot, Y cal is the calculated value of the plot, and Y dif is the difference of intensity.

Figure 3
Figure 3 demonstrates apparent density and relative density of the LZTNNx ceramics sintered at various temperatures.The density that characterizes the densification of materials is one of the most important parameters for directly evaluating microwave dielectric characteristics.As the sintering temperature increases, the apparent density of the LZTNNx ceramics increases and reaches the maximum value.The apparent density slightly declines with the further increase in the sintering temperature.The ρ r of the samples shows a similar tendency irrespective of the x value.The optimum sintering temperatures of Li 2 ZnTi 3 O 8 and LZTNNx (x = 0.1, 0.2, and 0.3) ceramics are 1150 and 1120 , respectively.It is clear ℃ that a reduction in the sintering temperature of 30 is obtained when ℃ (Ni 1/3 Nb 2/3 ) 4+ is co-doped into the Li 2 ZnTi 3 O 8 ceramics.Besides, the gradually increased apparent density with the increase of the (Ni 1/3 Nb 2/3 ) 4+ amount is due to the obviously increased unit cell mass, whereas V varies little.In Fig. 3(b), ρ r increases from 96.22% to 97.16%, and then decreases to 96.24% with the x value

Fig. 3
Fig. 3 (a) Apparent density and relative density of LZTNNx ceramics sintered at various temperatures and (b) relationship between relative density at optimized sintering temperature and x value.

Fig. 4
Fig. 4 SEM images of LZTNNx ceramics with various x values sintered at the optimized temperatures: (a) x = 0 at 1150 , ℃ (b) x = 0.1 at 1120 , (c) ℃ x = 0.2 at 1120 , and (d) ℃ x = 0.3 at 1120 .The insets display grain size distribution and mean grain ℃ size of each sample.(e-i) elemental distribution mappings of LZTNN0.2 ceramics sintered at 1120 , (j) EDS elemental point ℃ scanning results of spot A, and (k) EDS elemental point scanning results of spot B.

Figure 5 (
Fig. 5 (a) Raman spectra of LZTNNx (x = 0-0.3)ceramics with different x values, (b) partially enlarged views of bands at 300-500 cm −1 , (c) changing curves of mode at about 718 cm −1 of Raman spectra, and (d) changing curves of mode at about 854 cm −1 of Raman spectra.
−1 are attributed to the stretching vibration of the Zn-O bond in the [ZnO 4 ] tetrahedron and the Li-O bond in the [LiO 4 ] tetrahedron, respectively, whereas the Raman peak at 718 cm −1 is ascribed to the stretching vibration of the Ti-O bond in the [TiO 6 ] octahedron.In general, a strong interaction between the ions will result in sharp and intense Raman active modes.As a result, the strongest mode at 718 cm −1 indicates that a strong interaction exists in the [TiO 6 ] octahedron.The dielectric properties of the Li 2 ZnTi 3 O 8 ceramics are closely related to the A 1g mode at 718 cm −1 , which has already been confirmed by many researchers [23,25,45].The influence of the (Ni 1/3 Nb 2/3 ) 4+ substitution on the chemical bond vibration characteristics of the LZTNNx ceramics are shown in Figs.5(b)-5(d).It is observed from Fig. 5(b) that the vibration peak position of the [ZnO 4 ] tetrahedron has no obvious change.Also, a clear shift of the vibration peak position of the [TiO 6 ] octahedron is hardly to be found in Fig. 5(c).However, in comparison with that of the sample (Li 2 ZnTi 3 O 8 ) of x = 0, the vibration peak position of the [TiO 6 ] octahedron in the samples with x = 0.1-0.3actually shifts to the low wavenumber direction by fitting the obtained Raman spectra, as shown in Table 2.These findings indicate that the Zn 2+ cations of the [ZnO 4 ] tetrahedron are not substituted, and the (Ni 1/3 Nb 2/3 ) 4+ complex cations enter into the [TiO 6 ] octahedron to replace Ti 4+ cations.In addition, as shown in Fig. 5(d), when the (Ni 1/3 Nb 2/3 ) 4+ complex cations are doped into the Li 2 ZnTi 3 O 8 ceramics, a new Raman active band appears at about 848 cm −1 .Moreover, the intensity of the new band increases with the increase of the (Ni 1/3 Nb 2/3 ) 4+ substitution amount.It is well known that the activities of the vibration modes are affected by the local and long ranges symmetry of materials.According to Wang et al. [47], as the ceramics become more disordered due to the variation of the local Figure 7 depicts the survey spectrum and the Li 1s, Zn 2p, Ti 2p, Ni 2p, Nb 3d, and O 1s high-resolution XPS spectra of the LZTNN0.2ceramics, and the fitting results are shown in Table 3.All the XPS peaks in Fig. 7(a) confirm the existence of the Li, Zn, Ti, Ni, Nb, and O elements by calibration based on the contaminated carbon C 1s peak at 284.8 eV.In Fig. 7(b), the XPS peak of Li 1s can be deconvoluted into two peaks that locate at approximately 54.45 and 54.00 eV, indicating different coordination environment of Li in the ceramics.The higher one should be attributed to Li of the [LiO 4 ] tetrahedron, while the lower one belongs to Li of the

Figure 8 (
Figure 8(b) presents the variations of T D  , T D m / V  , ε r-exp , and ε r-the with the x value.The ε r-corr values are given in Table4.All ε r-corr values are slightly higher than the ε r-exp values due to the presence of residual pores

Fig. 8
Fig. 8 (a) Variations of ε r for LZTNNx ceramics sintered at various temperatures and (b) variations of T D  , T D m / V 

Fig. 9
Fig. 9 (a) Variations of Q×f for LZTNNx ceramics sintered at various temperatures and (b) relationship between Q×f value, I (111) /I (311) , and FWHM of A 1g modes at about 718 cm −1 .
13.The relatively low ε r value (~20) makes Li 2 Zn[Ti 0.8 (Ni 1/3 Nb 2/3 ) 0.2 ] 3 O 8 ceramics a promising candidate for millimetre wave applications.Moreover, the highest Q×f value is obtained in this work.A significant improvement in the Q×f value up to 97,350 GHz is demonstrated for the Li 2 Zn[Ti 0.8 (Ni 1/3 Nb 2/3 ) 0.2 ] 3 O 8 ceramics, with 35.2% and 26.3% increases compared with those of the nominal Li 2 ZnTi 3 O 8 prepared by the solid-state reaction (SSR) method and the reaction-sintering process (RSP), respectively.The Q×f value in our work is increased by 54.5% with respect to that of the stoichiometric Li 2 ZnTi 3 O 8 .Compared to those of the counterparts doped by Ni 2+ ions and Nb 5+ ions, the Q×f value of the Li 2 Zn[Ti 0.8 (Ni 1/3 Nb 2/3 ) 0.2 ] 3 O 8 ceramics is increased by 323% and 46.8%, respectively.Even in comparison to the counterparts like (Al 0.5 Nb 0.5 ) 4+ ,

and microwave dielectric properties of LZTNNx ceramics
-corr represents the corrected relative dielectric constant; b ε r-the represents the theoretical relative dielectric constant; c Δ represents the deviation.
a ε r

Table 5 Some related research results of Li 2 ZnTi 3 O 8 -based ceramics obtained by different processes
a AT represents the annealing treatment.