Three-phase borate solid solution with low sintering temperature, high quality factor, and low dielectric constant: Experimental and DFT study

The sintering and microwave dielectric properties of a ceramic material based on Mg 2+ substituted Zn 3 B 2 O 6 have been widely studied using first principles calculations and experimental solid-state reactions. Characterization methods include the Network Analyzer, X-ray, Raman diffraction, scanning electron microscopy, energy-dispersive spectroscopy, and differential-thermal & thermo-mechanical analyzer. The increasing amount of Mg 2+ results in the appearance of Mg 2 B 2 O 5 and ZnO, and the mutual substitution (Mg 2+ and Zn 2+ ) phenomenon has emerged in Zn 3 B 2 O 6 and Mg 2 B 2 O 5 . The mechanisms have been explained with the help of DFT calculations. The bond parameters and electron distributions of the ZnO 4 tetrahedron and the MgO 6 octahedron have been modified due to substitution. The sintering, substitution, and phase formation properties have been analyzed quantitatively through the energy parameters. The best dielectric properties were obtained for x=0.20 sintered at 950℃, ε r =6.47, Q × f =89,600GHz (15.2GHz), τ f =-48.6ppm/℃, relative density=96.7%. The substitution of Mg 2+ to Zn 2+ is a feasible method to improve the microwave dielectric properties of the Zn 3 B 2 O 6 ceramic.


Introduction
Low temperature co-fired ceramics (LTCC) technology has attracted significant research interest recently due to its ability of large scale three-dimensional integration with passive devices. For the inner electrode, the maximum processing temperature of LTCC is the melting point of Ag (961℃). [1] The materials used in the field of microwave communication require both low dielectric constant (εr) and high quality factor (Q×f). [2] Hence, considering both the electrical characteristics of the material and the processing temperature, the ceramic with low εr, high Q×f, and low densification temperature has great potential application value in the field of LTCC. [3,4] Ceramic material based on Zn3B2O6 (ZBO) has recently been studied in the context of batteries and luminescence, but studies on the sintering and microwave dielectric properties of ZBO are less common. [5,6] Wu et al. reported that the ZBO ceramic demonstrated good dielectric properties when sintered at 925℃, i.e., εr=6.7, Q×f=58, 500GHz, τf =-58ppm/℃, and relative density=96%. [7] While the dielectric constant and the sintering temperature of ZBO ceramic are acceptable, the Q×f value can be improved. Dosler et al. have found that the dielectric properties of the Mg3B2O6 (MBO) ceramic are εr=7, Q×f=108,000GHz, τf =-69ppm/℃, and relative density=97% sintered at 1350℃. [8] Considering that the Q×f value of MBO is larger than that of ZBO, and the densification temperature of ZBO is smaller than that of MBO, we speculate that the addition of MBO into ZBO is a possible way to synthesize a composite ceramic with both low densification temperature and high Q×f value without the increasing the εr.
The composite ceramic, (1-x)ZBO+xMBO (x=0.00-0.40), was synthesized through the solid-state reaction method. The analysis of microstructure, sintering property, and microwave dielectric properties is included in the discussion. Additionally, the first principle calculation based on the density functional theory (DFT) was used to provide theoretical interpretations.

Experimental procedures
The raw materials, ZnO, MgO, and B2O3, of analytical purity, were from Chron Chemicals Co.
Ltd., Chengdu, China. According to the stoichiometric ratio (10 mol% excess of B2O3 for the compensation), these powders were pre-milled for 12h, pre-sintered at 850℃ for 4h and milled again for 12h. The medium of milling was distilled water and agate balls. The resulting powders were mixed with the polyvinyl alcohol binder (5wt%), pressed into disks (6mm in thickness and 12mm in diameter), and sintered at 900-1000℃.
The Cambridge Serial Total Energy Package (CASTEP) was used to perform the first principles calculation, and the Vanderbilt ultrasoft pseudopotential was adopted to approximate the interaction of ions and electrons. The exchange-correlation interaction was approximated through the Perdew-Burke-Ernzerhoff function. The linear response method was used to calculate the vibration of atoms. The configuration of the valence electrons was taken as 3d 10 4s 2 for Zn, 2p 6 3s 2 for Mg, 2s 2 2p 4 for O, and 2s 2 2p 1 for B. After testing, the parameter of the energy cutoff and the k-point mesh were set as 375eV and 4×4×3, respectively. Other parameters include 0.01eV/Å (maximum force), 0.02GPa (maximum stress), 5.0×10 −6 eV/atom (total energy), 5.0×10 −6 eV/atom (energy), and 0.005Å (maximum displacement). The optimization of geometry was obtained using the Broyden-Fletcher-Goldfarb-Shanno algorithm. The substituted system was constructed based on a relaxed super cell (1×2×2, 176 atoms), and the formation energy was obtained using Eq. 1, [9] Do where EDo and EUnDo are the total energy of the doped cell and un-doped cell, pi represents the chemical potentials of the substituted atom, and ki represent the unite coefficient.
X-ray diffraction (XRD: DX-2700, Haoyuan Co.) with Cu Kα radiation was used to measure the crystal data of samples, which were processed using the Rietveld profile refinement method. The (f0), [11]   6 0 The Archimedes method was used to measure the bulk density. [12] The theoretical τf, εr, and Q values were calculated with the mixing rule, [13][14][15] where va(b) is the volume fraction of phase a(b); τfa(b), εra(b) and Qa(b) are the dielectric properties of phase a(b). The activation energies (Ea) were calculated using the Arrhenius expression, [16] 1 ln ln a E k z RT       (6) where R (8.3145J/K/mol) is the gas constant, k is the heating rate (5, 10, and 15K/min), T is the temperature (Kelvin), and z is Arrhenius constant. temperatures. The relative density value shows a trend of (i) first increasing and then decreasing for samples sintered at 900℃, (ii) monotonous decreasing for samples sintered at 925℃, and (iii) wavy for the one sintered at 950 and 975℃. The peak density value was 96.7% for the sample with x=0.20 sintered at 950℃. The variation trend that the Q×f value presents is in accordance with that of the relative density, and it peaked at x=0.20, 89,600GHz at 15.2GHz, which can be attributed to the strong interdependence between these two parameters. As x increases, the εr value shows a monotonously decreasing trend, except for the sample sintered at 900℃, which shows a parabolic trend, and εr=6.47 as x=0.20 sintered at 950℃. The relative density variation could be one reason for the variation of the εr value since the sample with a high level of densification shows a relatively high εr value and samples with low density show low εr values. The τf value shows an overall increasing trend with τf=-48.6ppm/℃ for x=0.20 sintered at 950℃. Therefore, a moderate addition of Mg 2+ improved the densification level, Q×f value, and thermal stability while decreasing the εr value of the ZBO ceramic. As shown in increasing Mg 2+ -ions. Considering that the ionic radius of Zn 2+ (0.60Å) was larger than that of Mg 2+ (0.57Å) and that the Mg 2+ concentration increased with increase in the x value, the ion substitution level of Mg 2+ to Zn 2+ (ZBO ceramic) could have strengthened, and that of Zn 2+ to Mg 2+ (Mg2B2O5 ceramic) could have weakened, thus, explaining the variation in volume. [34] The detailed lattice parameters obtained from refinement are provided in Fig. 2e, Table I Mg 2+ to Zn 2+ for ZBO ceramic and Zn 2+ to Mg 2+ for Mg2B2O5 ceramic, and the formation of ZnO ceramic can explain this discrepancy. The fraction of Mg2B2O5 and ZnO ceramic increased with the addition of Mg 2+ when x≥0.10. Since the densification temperature of ZBO is 925℃, the increasing density for the sample with x=0.05 sintered at 900℃ should be attributed to the decreasing densification temperature due to lattice distortion, and the decreasing density value for the same sample sintered at 925-975℃ can be ascribed to the over-sintering. The decreasing density of samples sintered at 900, and 925℃ is a result of the formation of Mg2B2O5, which has a densification temperature of about 1280℃. [19] The increment of density for samples sintered at 950 and 975℃ can be attributed to the reduction in the extent of over-sintering, and any subsequent decrease is the same as that of the sample sintered at a lower temperature. Since the Mg2B2O5 ceramic has a relatively lower εr (6.2) and

Results and discussion
higher τf (-18ppm/℃) compared to that of the ZBO ceramic, the formation of a heterophase can explain the difference between the measured and calculated εr/τf value except for the density level variation. [19] However, the Q×f value of the composite ceramic with x=0.20 sintered at 950℃ is larger than that of both ZBO and Mg2B2O5 (32,100GHz at 12.6GHz) ceramic. [19] These phenomena can be explained by the modification of the crystal structure led by mutual substitution, the formation of a solid solution with three phases, and the improved density level. Furthermore, the existence of the ZnO phase also has an impact on the sintering and dielectric properties of the composite ceramics.
The Raman spectra of all samples were obtained to further study phase formation, as shown in where R corresponds to the Raman mode, and IR corresponds to the Infrared mode. Considering the testing error due to the peak overlap, sample shape, and temperature of the test environment, the peaks   The microstructure of the samples sintered at 950℃ is shown in the SEM images in Fig. 4. The trapped pores (pink circles) and melting grain boundaries (blue circles) are observed in Fig. 4(a-c), and abnormal grain growth is observed in Fig. 4(d) which is scattered with large grains (green circles). A compact microstructure is obtained in the sample with x=0.20, and any further addition of Mg 2+ leads to the reduction of grain size (yellow circles) and the emergence of pores (pink circles) at the same sintering temperature. The behavior observed from the SEM images fits well with the relative density trends observed. Fig. 4(i-m)  In order to analyze the sintering property of the (1-x)ZBO+xMBO (x=0.00-0.40) ceramics, TG, DSC and TMA were conducted ( Fig. 6(a-c)). The temperature increase from 100℃ to 300℃ led to a weight loss of about 11%. The first stage of weight loss can be ascribed to the removal of hydration water, and the decomposition of H3BO3 (formed from the reaction of B2O3 and distilled water). The further decomposition of H3BO3 could be responsible for the second stage of gradual weight loss (slight) from 300℃ to 600℃. After that, the dynamic atom equilibrium was achieved, and the negligible weight loss was observed for temperatures higher than 600℃. The DSC curves show an endothermic peak at around 200℃, corresponding to the first stage of weight loss. The exothermic peak near 610℃ can be ascribed to the crystallization of the ZBO ceramic and the further decomposition of H3BO3. The exothermic peak at a relatively higher temperature (blue dotted box) could be attributed to the formation of Mg2B2O5, which corresponds to further weight loss near 680℃ (blue dotted box). It should be noted that the increasing Mg 2+ content shifts the weight loss and endothermic peak near 200℃ to a lower temperature, and also shifts the exothermic peak for the formation of ZBO ceramic to a relatively higher temperature. The TMA patterns show that the onset point of shrinkage move to a higher temperature, which matches the observations from the TG and DSC. Hence, the addition of Mg 2+ led to a slightly higher temperature window of densification of the ZBO ceramic, and the heterophase was formed with a relatively high x value. The activation energy was calculated at the temperature where 3%, 6%, and 9% shrinkage was observed to further investigate the sintering properties. The lnk versus 1/T plots are shown in Fig. 6(d-k). [36] Calculations ( Fig. 6(l)) show that the Ea value tends to decrease and then increase. The initial decrease of Ea demonstrates that the lattice distortion (led by 5% Mg 2+ substitution) could lower the densification temperature of ZBO ceramic as discussed in context to the relative density. The followed increase in Ea verifies that the heterophase could indeed increase the densification temperature of the composite ceramic at x≥0.10.
Specifically, the sample with the addition of 5% Mg 2+ had the lowest Ea (407183kJ/mol), and the Ea value for x=0.20 sample was 598221kJ/mol. properties. The crystal structure and schematic diagram of the ion substitution can be observed in Fig. 7. There are three types of ZnO4 tetrahedrons in ZBO and two types of MgO6 octahedrons in Mg2B2O5, as illustrated in Fig. 7(b, e). Each zinc/magnesium atom has been substituted by magnesium/zinc atom one by one, and the microstructural properties (electron density, bond length and population) of the atomic groups have been modified after optimization of geometry ( Fig. 7(c, f), Fig. 8, Table Ⅱ). The modification of the position of the ion happened for each ZnO4 tetrahedron and MgO6 octahedron.
According to the value shown in Table Ⅱ Fig. 9. The formation energy of all doped crystals for the ZBO ceramic is negative, and for the Mg2B2O5 ceramic it is positive. The minimum value of formation energy for the doped ZBO system is -4.5116eV (Zn2 site), and the formation energy value of the Mg1 and Mg2 sites is the same. Hence, the ZBO system with the Zn2 site substitution is more stable, and Zn2 site is preferable and more likely to be occupied. The possibility of the Mg1 and Mg2 site to be occupied is equal, and the doping process of Mg 2+ to the ZBO ceramic is more thermodynamically spontaneous than that of Zn 2+ to the Mg2B2O5 ceramic. The designed and measured total energy/mol for the (1-x)ZBO+xMBO (x=0.00-0.40) composite ceramics were obtained (the formation energy was not considered), as shown in Fig. 9(b).
Both the designed and measured total energy/mol show an increasing trend. The former is larger than that of the latter for x=0.05-0.40, and the system with relatively low energy is more stable and spontaneous to form. Hence, for the system with x>0.00, the component fraction discrepancy between the designed and measured sample results from both the larger concentration of Zn 2+ and lower total energy. These discussions further confirm the XRD refinements.

Conclusion
The sintering and microwave dielectric properties of the Zn3B2O6 ceramic, with a large number of