Crystal Structure, Infrared Reflection Spectrum, and Improved Microwave Dielectric Characteristics of Ba4Sm28/3Ti18O54 Ceramics via One-Step Reaction Sintering

High-k Ba4Sm28/3Ti18O54 ceramics with improved microwave dielectric characteristics were successfully fabricated using the one-step reaction sintering (RS) route. The sintering characteristics, microstructure, crystal structure, infrared reflection spectrum, and microwave dielectric characteristics of Ba4Sm28/3Ti18O54 ceramics prepared by the RS route were systematically investigated. Samples prepared by the RS route exhibited single-phase orthorhombic tungsten–bronze structure and dense microstructure at optimum sintering temperature. Compared with the conventional solid-state (CS) process, the Ba4Sm28/3Ti18O54 ceramics fabricated by the RS route presented a smaller temperature coefficient (TCF), a higher quality factor (Q × f), and a higher permittivity (εr). The improved microwave dielectric characteristics were highly dependent on the theoretical permittivity, atomic packing fraction, suppression of Ti3+, and Ti-site bond valence. Excellent combined microwave dielectric characteristics (TCF = −7.9 ppm/°C, Q × f = 9519 GHz, εr = 80.26) were achieved for Ba4Sm28/3Ti18O54 ceramics prepared by RS route sintered at 1400 °C, suggesting the RS route was a straightforward, economical and effective route to prepare high-performance Ba4Sm28/3Ti18O54 ceramics with promising application potential.


Introduction
Recently, the widespread application of 5G/6G wireless communication techniques has brought increasing requirements for high-performance microwave components (e.g., antennas, duplexers, filters, dielectric resonators, etc.) [1][2][3][4][5].Being a critical material for the fabrication microwave components, microwave dielectric ceramics have attracted continuing commercial and scientific attention because of their superior properties [6][7][8][9][10].Generally, high-performance microwave dielectric ceramics are desired to have a small temperature coefficient (τ f or TCF, here TCF is a measure of the "drift" with respect to the temperature of the resonant frequency) to meet thermal stability, a high quality factor (the quality factor (Q), which is a function of resonant frequency (f ), is sometimes expressed as Q × f ) to enable good frequency selectivity for microwave components, and a high permittivity (ε r ) in order to realize miniaturization [11][12][13][14][15].However, achieving the three dielectric characteristics mentioned above (high Q × f, small TCF, and high ε r ) simultaneously in high-k microwave dielectric ceramics for 5G applications is a significant challenge.
Recently, the one-step reaction sintering (RS) route without calcination and secondary ball-milling has been attracting considerable interest because of its high efficiency and process simplification.Du et al. [36] have successfully prepared AlON transparent ceramics with a transmittance of 73.2% at 1600 nm using one-step RS route and tape-casting technology.Liang et al. [37] reported the piezoelectric properties of Bi 4 Ti 3 O 12 ceramics could be significantly improved using the RS route and Ta/Mn co-doping.In addition, numerous microwave dielectric ceramics have been successfully fabricated using the RS route, such as BaTi  [38][39][40][41][42][43][44][45][46][47][48].Although there have been many studies on tungsten-bronze-structure BST microwave dielectric ceramics, the preparation of BST ceramics by the one-step RS route has not been reported until now.
One problem with using TiO 2 as a raw material is the reduction of Ti 4+ to Ti 3+ in high sintering temperature.This may result in the presence of oxygen vacancies (V •• O ), which are regarded as detrimental to microwave dielectric loss (tan δ = 1/Q).During the high-temperature sintering process in air, quasi-free electrons and oxygen vacancies (V •• O ) are simultaneously generated in the crystals owing to insufficient oxygen partial pressure [49,50].F-type color centers can be formed by oxygen vacancies (V •• O ) in combination with weakly bound electrons, which have three forms: O e ′ , oxygen vacancies with one trapped electron), and F (V •• O 2e ′ , oxygen vacancies with two trapped electrons) [51][52][53].The recent efforts to restrain the reduction of Ti 4+ and oxygen vacancies (V •• O ) have been a significant area of research.Doping is an effective method of reducing dielectric loss, thereby enabling the material to meet the requirements of commercial applications.The dielectric loss of TiO 2 -based microwave dielectric ceramics (TiO 2 , BaTi 4 O 9 , Na 0.5 Sm 0.5 TiO 3 , Ba 2 Ti 9 O 20, 0.73ZrTi 2 O 6 -0.27MgNb 2 O 6 , Ba 6−3x Sm 8+2x Ti 18 O 54 and Ba 6−3x Nd 8+2x Ti 18 O 54 ) will be significantly reduced by the introduction of a range of divalent or trivalent acceptor cations with ionic radii between 0.5 Å and 0.95 Å, such as Cr 3+ , Al 3+ , Ga 3+ , Zn 2+ , Mg 2+ , Mn 2+ , Cu 2+ and Co 2+ [21,49,50,[53][54][55][56][57][58].It is worth noting whether the dielectric loss of BST ceramics can be improved by RS route.
In this study, the BST ceramics with improved microwave dielectric characteristics prepared by the one-step RS route were first introduced.The effects of various sintering routes (CS and RS routes) on the crystal structure, microstructure, valence states of Ti ions, and microwave dielectric characteristics of the BST ceramics were studied.Based on the Rietveld analysis, the theoretical permittivity (ε the ), atomic packing fraction (P.F.%), and Ti-site bond valence (V Ti ) were analyzed to study the structural properties of BST ceramics.Furthermore, infrared reflection spectrum was employed to evaluate intrinsic dielectric characteristics of BST ceramics prepared by RS route.

Materials and Methods
Ba 4 Sm 28/3 Ti 18 O 54 ceramics were prepared via one-step RS and CS processes employing high-purity Sm 2 O 3 (99.99%,Aladdin, Shanghai, China), TiO 2 (99.84%,Zhongxing, Xiantao, China), and BaCO 3 (99.8%,Yuanda, Mianyang, China) powders.In particular, Sm 2 O 3 powder was calcined at 950 • C/4h for moisture removal.The oxide and carbonate powders were then weighted to achieve the desired stoichiometric ratio of Ba 4 Sm 28/3 Ti 18 O 54 (BST).For the RS process, the blended oxide and carbonate powders were milled in de-ionized water with ZrO 2 balls (diameter 2~8 mm) for 2 h.After oven drying at 120 • C/12 h, the drying oxide and carbonate powders were combined with the binder (10 wt% PVA).The ground and sieved powders were molded into cylindrical pellets (Φ8 × 5 mm, and Φ8 × 2 mm).For the CS process, the detailed experimental procedure was described in earlier work [5].All these pellets prepared by RS and CS route were subsequently sintered in an atmospheric environment at 1300 • C/4 h to 1450 • C/4 h. Figure 1 presents the detailed procedure for the preparation of BST ceramics by the RS route due to the absence of calcination and secondary ball-milling, the RS route is a simple and efficient preparation method compared to the CS route.
Ba4Sm28/3Ti18O54 ceramics were prepared via one-step RS and CS processes employing high-purity Sm2O3 (99.99%,Aladdin, Shanghai, China), TiO2 (99.84%,Zhongxing, Xiantao, China), and BaCO3 (99.8%,Yuanda, Mianyang, China) powders.In particular, Sm2O3 powder was calcined at 950 °C/4h for moisture removal.The oxide and carbonate powders were then weighted to achieve the desired stoichiometric ratio of Ba4Sm28/3Ti18O54 (BST).For the RS process, the blended oxide and carbonate powders were milled in de-ionized water with ZrO2 balls (diameter 2~8 mm) for 2 h.After oven drying at 120 °C/12 h, the drying oxide and carbonate powders were combined with the binder (10 wt% PVA).The ground and sieved powders were molded into cylindrical pellets (Φ8 × 5 mm, and Φ8 × 2 mm).For the CS process, the detailed experimental procedure was described in earlier work [5].All these pellets prepared by RS and CS route were subsequently sintered in an atmospheric environment at 1300 °C/4 h to 1450 °C/4 h. Figure 1 presents the detailed procedure for the preparation of BST ceramics by the RS route due to the absence of calcination and secondary ball-milling, the RS route is a simple and efficient preparation method compared to the CS route.

Results and Discussion
The XRD patterns of BST ceramics prepared using one-step RS and CS routes are displayed in Figure 2. As illustrated in Figure 2, all diffraction peaks of BST ceramics prepared by RS and CS routes corresponded to the tungsten-bronze phase (JCPDS No. 89-4356, Ba 3.99 Sm 9.34 Ti 18 O 54 ) with orthorhombic structure (Pbnm, No. 62) [28], and no diffraction peaks of impurity phases were detected over the entire sintering temperature range.Structural diagrams of tungsten-bronze-structure BST ceramics with VESTA3 projected along [001] and [100] are presented in Figure 3 [60].As shown in Figure 3a, the crystal structure of the tungsten-bronze-type BST ceramics consists of a three-dimensional framework of corner-sharing TiO 6 octahedron linked at the corners to form three types of cavities: diamond cavities (A1), large pentagonal cavities (A2), and small triangular cavities (C).Sm is expected to be located in A1 cavities and larger Ba in the A2 cavities.Small triangular cavities are empty [28].

Results and Discussion
The XRD patterns of BST ceramics prepared using one-step RS and CS routes are displayed in Figure 2. As illustrated in Figure 2, all diffraction peaks of BST ceramics prepared by RS and CS routes corresponded to the tungsten-bronze phase (JCPDS No. 89-4356, Ba3.99Sm9.34Ti18O54)with orthorhombic structure (Pbnm, No. 62) [28], and no diffraction peaks of impurity phases were detected over the entire sintering temperature range.Structural diagrams of tungsten-bronze-structure BST ceramics with VESTA3 projected along [ 001 ] and [100 ] are presented in Figure 3 [60].As shown in Figure 3a, the crystal structure of the tungsten-bronze-type BST ceramics consists of a three-dimensional framework of corner-sharing TiO6 octahedron linked at the corners to form three types of cavities: diamond cavities (A1), large pentagonal cavities (A2), and small triangular cavities (C).Sm is expected to be located in A1 cavities and larger Ba in the A2 cavities.Small triangular cavities are empty [28].

Results and Discussion
The XRD patterns of BST ceramics prepared using one-step RS and CS routes are displayed in Figure 2. As illustrated in Figure 2, all diffraction peaks of BST ceramics prepared by RS and CS routes corresponded to the tungsten-bronze phase (JCPDS No. 89-4356, Ba3.99Sm9.34Ti18O54)with orthorhombic structure (Pbnm, No. 62) [28], and no diffraction peaks of impurity phases were detected over the entire sintering temperature range.Structural diagrams of tungsten-bronze-structure BST ceramics with VESTA3 projected along [ 001 ] and [100 ] are presented in Figure 3 [60].As shown in Figure 3a, the crystal structure of the tungsten-bronze-type BST ceramics consists of a three-dimensional framework of corner-sharing TiO6 octahedron linked at the corners to form three types of cavities: diamond cavities (A1), large pentagonal cavities (A2), and small triangular cavities (C).Sm is expected to be located in A1 cavities and larger Ba in the A2 cavities.Small triangular cavities are empty [28].To further analyze the influence of various sintering routes and sintering temperatures on the lattice parameters and crystal structure of BST ceramics produced by the CS and RS routes, the Rietveld approach was applied using the GSAS application [61,62].The fitted (black solid line) and measured (orange dot) XRD profiles of BST samples fabricated using the CS and RS methods are represented in Figure 4, and the fitted XRD were in reasonable accordance with the measurements.Table 1 presents the calculation of structure parameters (a, b, c), cell volume (V), theoretical density (ρ th ), and reliability factors (R p , χ 2 , R wp ) of all BST ceramic samples.As illustrated in Table 1 and Figure 4, small reliability factors (R p , R wp ) of less than 10% were observed, indicating that the results of the refinement were acceptable.It should be noted that the cell volume of BST ceramics produced using the CS route (V = 2079.12Å 3  To further analyze the influence of various sintering routes and sintering temperatures on the lattice parameters and crystal structure of BST ceramics produced by the CS and RS routes, the Rietveld approach was applied using the GSAS application [61,62].The fitted (black solid line) and measured (orange dot) XRD profiles of BST samples fabricated using the CS and RS methods are represented in Figure 4, and the fitted XRD were in reasonable accordance with the measurements.Table 1 presents the calculation of structure parameters (a, b, c), cell volume (V), theoretical density (ρth), and reliability factors (Rp, χ 2 , Rwp) of all BST ceramic samples.As illustrated in Table 1 and Figure 4, small reliability factors (Rp, Rwp) of less than 10% were observed, indicating that the results of the refinement were acceptable.It should be noted that the cell volume of BST ceramics produced using the CS route (V = 2079.12Å 3     The as-fired SEM photographs of BST ceramics sintered at 1300 to 1450 • C produced by the RS and CS route are presented in Figure 5.As presented in Figure 5, it is clear that all BST samples prepared by the RS and CS routes have rod-shaped grains of tungsten-bronze structural ceramics [25].The number of rod-shaped grains increases when it is sintered at an increasing temperature from 1300 to 1450 • C. For the CS route, all ceramic samples sintered at different temperatures present a dense microstructure with well-defined grain boundaries, a gradually increasing grain size with increasing temperature is clearly observed, while for the RS route, the samples exhibit a porous and fine-grained microstructure when they are sintered at 1300 • C. For the samples sintered at 1400 • C and 1450 • C, the grain size increases with increasing sintering temperature, while the number of pores decreases significantly, and a relatively dense microstructure with well-defined grain boundaries is observed.Note that the grain size of the BST samples fabricated by the RS route is smaller than that of the CS route at the same temperature, which can be attributed to the absence of a calcination stage in the RS route.The as-fired SEM photographs of BST ceramics sintered at 1300 to1450 °C produced by the RS and CS route are presented in Figure 5.As presented in Figure 5, it is clear that all BST samples prepared by the RS and CS routes have rod-shaped grains of tungstenbronze structural ceramics [25].The number of rod-shaped grains increases when it is sintered at an increasing temperature from 1300 to 1450 °C.For the CS route, all ceramic samples sintered at different temperatures present a dense microstructure with well-defined grain boundaries, a gradually increasing grain size with increasing temperature is clearly observed, while for the RS route, the samples exhibit a porous and fine-grained microstructure when they are sintered at 1300 °C.For the samples sintered at 1400 °C and 1450 °C, the grain size increases with increasing sintering temperature, while the number of pores decreases significantly, and a relatively dense microstructure with well-defined grain boundaries is observed.Note that the grain size of the BST samples fabricated by the RS route is smaller than that of the CS route at the same temperature, which can be attributed to the absence of a calcination stage in the RS route.Figure 6a presents the relative densities of BST ceramics using RS and CS routes sintered at 1300 to 1450 °C.The relative densities (ρre) of BST samples can be evaluated by Equation (1) [47]: where ρre and ρbu are theoretical density (Table 1) and bulk density of BST ceramics, respectively.As a result of the increase in sintering temperature from 1300 to 1450 °C, the Figure 6a presents the relative densities of BST ceramics using RS and CS routes sintered at 1300 to 1450 • C. The relative densities (ρ re ) of BST samples can be evaluated by Equation (1) [47]: where ρ re and ρ bu are theoretical density (Table 1) and bulk density of BST ceramics, respectively.As a result of the increase in sintering temperature from 1300 to 1450 • C, the relative density (ρ re ) of the BST samples prepared by CS route exhibits a tendency to increase slowly and then decrease, a relative density of 96.88% was achieved for BST ceramic samples calcined at 1150 • C/4 h and sintered at 1400 • C/4 h.For the RS route, a greater increase in the ρre of BST ceramics was observed for the 1300 • C and 1400 • C temperature ranges, i.e., from a relative density (ρ re ) of 76.96% to 95.57%, indicating that rapid densification should take place at a temperature of over 1300 • C.This result is in accordance with that of SEM (Figure 5a).The improvement in relative density with increased temperature may be associated with porosity reduction.
that of SEM (Figure 5a).The improvement in relative density with increased temperature may be associated with porosity reduction.The permittivity and Q × f values of BST samples sintered at 1300 to 1450 °C using RS and CS routes are presented in Figure 6b and Figure 6c, respectively.The trends in permittivity and Q × f values of all BST ceramics produced by the CS and RS routes varying with sintering temperature is similar to the relative density (ρre).The increased permittivity (εr) is associated with a pore (εr = 1) reduction and an increase in relative density, and the improved Q × f values are related to the grain growth and reduction in grain boundaries.The TCF values of BST ceramics fabricated by RS and CS routes are shown in Figure 6d.This study shows that the sintering temperature is not directly related to TCF as a result of no other additional additives and the single-phase BST ceramic samples.Nearzero TCF values (around −10 ppm/°C) were obtained for all ceramic samples prepared by RS and CS routes.Interestingly, the BST ceramics produced by the RS route have improved microwave dielectric characteristics than those produced using the CS route at the optimum sintering temperature (1400 °C).The microwave dielectric characteristics of BST ceramics prepared by RS and CS routes sintered at 1400 °C are listed in Table 2. Compared to the CS route (εr = 79.38,Q × f = 8230 GHz, TCF = −12.1 ppm/°C), the BST ceramics fabricated by the RS route present a higher quality factor (Q × f = 9519 GHz), a lower dielectric loss (tanδ = 6.18 × 10 −4 ), a smaller temperature coefficient (TCF = −7.9ppm/°C), and a higher permittivity (εr = 80.26).The RS route is suggested to improve the microwave dielectric characteristics of BST ceramics.To investigate the effect of various preparation processes on the microwave dielectric characteristics of BST ceramics, atomic packing fraction, theoretical per- The permittivity and Q × f values of BST samples sintered at 1300 to 1450 • C using RS and CS routes are presented in Figures 6b and 6c, respectively.The trends in permittivity and Q × f values of all BST ceramics produced by the CS and RS routes varying with sintering temperature is similar to the relative density (ρ re ).The increased permittivity (ε r ) is associated with a pore (ε r = 1) reduction and an increase in relative density, and the improved Q × f values are related to the grain growth and reduction in grain boundaries.The TCF values of BST ceramics fabricated by RS and CS routes are shown in Figure 6d.This study shows that the sintering temperature is not directly related to TCF as a result of no other additional additives and the single-phase BST ceramic samples.Near-zero TCF values (around −10 ppm/ • C) were obtained for all ceramic samples prepared by RS and CS routes.
Interestingly, the BST ceramics produced by the RS route have improved microwave dielectric characteristics than those produced using the CS route at the optimum sintering temperature (1400 • C).The microwave dielectric characteristics of BST ceramics prepared by RS and CS routes sintered at 1400 • C are listed in Table 2. Compared to the CS route (ε r = 79.38,Q × f = 8230 GHz, TCF = −12.1 ppm/ • C), the BST ceramics fabricated by the RS route present a higher quality factor (Q × f = 9519 GHz), a lower dielectric loss (tanδ = 6.18 × 10 −4 ), a smaller temperature coefficient (TCF = −7.9ppm/ • C), and a higher permittivity (ε r = 80.26).The RS route is suggested to improve the microwave dielectric characteristics of BST ceramics.To investigate the effect of various preparation processes on the microwave dielectric characteristics of BST ceramics, atomic packing fraction, theoretical permittivity, bond valence, and vacancy defects were analyzed.The results of theoretical permittivity (ε the ), atomic packing fraction (P.F.%), and Ti-site bond valence (V Ti ) of BST ceramics produced by the CS and RS routes at optimal sintering temperature (1400 • C) are listed in Table 2. On the basis of previous literature [63,64], the theoretical permittivity (ε the ) can be evaluated using the Clausius-Mossotti (CM) formula (Equation ( 2)): where V m = V/Z denotes molar volume, and α the represents theoretical dielectric polarizability.The α the of Ba 4 Sm 28/3 Ti 18 O 54 ceramics can be calculated using Equation ( 3) [63]: where α(Ba 2+ ) = 6.4 Å 3 , α(O 2− ) = 2.01 Å 3 , α(Ti 4+ ) = 2.93 Å 3 , and α(Sm 3+ ) = 4.74 Å 3 .According to the CM formula, the theoretical permittivity (ε the ) is inversely proportional to the molar volume (V m ) when the theoretical dielectric polarizability of Ba 4 Sm 28/3 Ti 18 O 54 ceramics is constant.As listed in Table 1, due to cell volume (V = 2073.65Å 3 ) of BST ceramics fabricated by the RS route is smaller than that fabricated by the CS route (V = 2079.12Å 3 ), the theoretical permittivity calculated from CM formula of RS route (ε the = 43.27) is higher than the CS route (ε the = 41.65), and the tendency of measured permittivity (ε r ) is similar with the theoretical permittivity (ε the ).It is worth noting that the ε r is much higher than the ε the , which is attributed to the low symmetry structure of the BST ceramics.The same large deviations are found in other Ti-based microwave dielectric ceramics [30,[65][66][67].A higher Q × f value (9519 GHz) for the RS route prepared ceramic sample was achieved compared to a Q × f value (8230 GHz) for the CS route is shown in Table 2. Generally speaking, the total tanδ (1/Q) of functional ceramics is classified into the extrinsic and intrinsic loss.The extrinsic loss is primarily associated with pores, dopants, impure phases, lattice defects, grain boundaries, vacancy defects, etc., while intrinsic loss is primarily attributed to lattice vibration and structural characteristics.In this work, the effects of pores and impure phases on tanδ could be ignored as the BST ceramics produced by the CS and RS routes at optimum sintering temperature (1400 • C) with high densities (ρ re > 95%) and single-phase structure.
As reported by Kim et al. [68], dielectric loss (tanδ) is highly associated with structural characteristics of microwave ceramics.The structural characteristics of microwave ceramics could be assessed by the packing fraction, as this parameter is related to the cell volume (V) and effective ion size.On the basis of the results of Rietveld analysis, the packing fraction (P.F.%) of the BST ceramics prepared by the RS and CS routes is evaluated by means of Equation ( 4) [68]: where V refers to cell volume, r Sm , r Ba , r Ti , and r O are the effective ionic sizes of Sm (1.079 Å), Ba (1.52 Å), Ti (0.605 Å), and O (1.4 Å) [69], respectively.The packing fraction (P.F.%) of the BST ceramics is illustrated in Table 2.As presented in Table 2, a lower Q × f value (8230 GHz) corresponds to a smaller P.F.% (71.69%), and a higher Q × f value (9519 GHz) correlates with a higher P.F.% (71.88%).
In addition, the oxygen vacancy defect in Ti-based microwave dielectric ceramics is widely acknowledged and is believed to be balanced through the generation of Ti 3+ ions [49].The primary reason for the higher dielectric losses is thought to be the Ti 3+ ions in Ti-based ceramics.The mechanism could be represented by the following defect equation (Equations ( 5) and ( 6)) [50]: It is worth noting that the BST ceramics produced by the RS route at 1400 • C have a light yellow color, while those prepared by the CS route have a dark yellow color, as illustrated in Figure 6c.To explain this difference, valence states of Ti ions in BST ceramics prepared by the RS and CS routes were investigated by XPS analysis.In general, the two peaks of Ti 2p correspond to binding energies (B.E.) of approximately 458 (2p 3/2 ) and 464 (2p 1/2 ) eV [70].Figure 7 presents the XPS spectroscopy of Ti 2p for BST samples prepared by the RS and CS routes at 1400 • C. The 2p 3/2 and 2p 1/2 region of Ti 2p in BST ceramics was fitted well to the Gaussian/Lorentzian sub-peak by means of the XPS-PEAK41 software, and the results are given in Figure 7 and Table 3. Table 3 presents that the relative peak area ratio of Ti 3+ for the CS route (27.63%) is higher than the RS route (11.87%).This result suggests that the RS route is effective in suppressing the generation of trivalent titanium ions (Ti 3+ ), which improves the quality factor (tanδ) of the BST ceramic.The combination of packing fraction (P.F.%) and XPS analysis explains the higher quality factor (lower dielectric loss) of the BST ceramics prepared by the RS route.
In addition, the oxygen vacancy defect in Ti-based microwave dielectric ceramics is widely acknowledged and is believed to be balanced through the generation of Ti 3+ ions [49].The primary reason for the higher dielectric losses is thought to be the Ti 3+ ions in Tibased ceramics.The mechanism could be represented by the following defect equation (Equations ( 5) and ( 6)) [50]: 3

Ti e Ti
It is worth noting that the BST ceramics produced by the RS route at 1400 °C have a light yellow color, while those prepared by the CS route have a dark yellow color, as illustrated in Figure 6c.To explain this difference, valence states of Ti ions in BST ceramics prepared by the RS and CS routes were investigated by XPS analysis.In general, the two peaks of Ti 2p correspond to binding energies (B.E.) of approximately 458 (2p3/2) and 464 (2p1/2) eV [70].Figure 7 presents the XPS spectroscopy of Ti 2p for BST samples prepared by the RS and CS routes at 1400 °C.The 2p3/2 and 2p1/2 region of Ti 2p in BST ceramics was fitted well to the Gaussian/Lorentzian sub-peak by means of the XPS-PEAK41 software, and the results are given in Figure 7 and Table 3. Table 3 presents that the relative peak area ratio of Ti 3+ for the CS route (27.63%) is higher than the RS route (11.87%).This result suggests that the RS route is effective in suppressing the generation of trivalent titanium ions (Ti 3+ ), which improves the quality factor (tanδ) of the BST ceramic.The combination of packing fraction (P.F.%) and XPS analysis explains the higher quality factor (lower dielectric loss) of the BST ceramics prepared by the RS route.Table 2 shows that a smaller TCF value of −7.9 ppm/ • C (1400 • C) for the RS route prepared ceramic sample is obtained compared to the TCF value of −12.1 ppm/ • C (1400 • C) for the CS route.It was found that the TCF values of tungsten-bronze-structure Ba 6−3x R 8+2x Ti 18 O 54 (R = Eu, Sm, Nd, Pr, and La) were generally influenced by additives, composition, and structural characteristics [71].As all ceramic samples have no other extra additives and the unique composition Ba 4 Sm 28/3 Ti 18 O 54 , the key factor affecting their TCF may be the structural characteristics.Bond valence has been generally accepted as a useful tool for associating structural characteristics with TCF value.The bond valence (S jk ) of the BST ceramics prepared by the RS and CS routes is calculated by means of Equations ( 7) and (8) [68]: where d jk represents the bond length, and R jk denotes the bond valence parameter.The TCF values and the calculated Ti-site bond valence (V Ti ) of BST ceramics are presented in Table 2. Based on bond valence theory [47], the higher bond valence would lead to a higher restoring force of oxygen octahedrons, ultimately decreasing |TCF|.As shown in   Far-infrared (FIR) reflection spectrum is commonly applied to evaluate intrinsic dielectric characteristics of electronic ceramics by means of the classic oscillator theory (Equation ( 9)) [72]: where γ j , ω pj , ε ∞ , ω oj , and n are damping factor of the j-th mode, plasma frequency, optical frequency permittivity caused by electronic polarization, eigen frequency and sequence of phonon modes, individually.Equation ( 10) [72] illustrates the interrelation of complex permittivity (ε*(ω)) and reflectivity (R(ω)).
The room-temperature FIR spectrum of BST ceramics (50~1000 cm −1 ) sintered at 1400 • C using the RS route is illustrated in Figure 8a.The calculated FIR spectrum (red line) is consistent with the measured spectrum (black circle).Based on Kramers-Kronig (K-K) theory, the calculated FIR spectrum of BST ceramics prepared by the RS route is transformed into ε ′ (ω) and ε ′′ (ω), and this is presented in Table 5 and Figure 8b.Measured ε ′ (ω) (black triangle) and ε ′′ (ω) (blue triangle) are also shown Figure 8b.Compared to the theoretical permittivity value (43.27) calculated by the CM equation, the permittivity value (73.91) derived from the FIR spectrum is closer to the measured one (80.23),demonstrating that the dominant dielectric contribution of BST ceramics is phonon absorption.As can be seen in Table 5, the FIR spectrum of BST ceramics was fitted by the 24 individual modes.In particular, the eight infrared active modes (j = 1-8) below 220 cm −1 give the majority (84.07%) dielectric contribution to the permittivity.The ε ∞ value derived from Equation ( 10) is 4.69, only 6.3% of the total extrapolated permittivity (73.91), suggesting that ionic polarization plays an important role in the polarization that contributed to the ε r of BST ceramics.As can be seen in Table 5, the FIR spectrum of BST ceramics was fitted by the 24 individual modes.In particular, the eight infrared active modes (j = 1-8) below 220 cm −1 give the majority (84.07%) dielectric contribution to the permittivity.The ε∞ value derived from Equation ( 10) is 4.69, only 6.3% of the total extrapolated permittivity (73.91), suggesting that ionic polarization plays an important role in the polarization that contributed to the εr of BST ceramics.

Conclusions
For the first time, high-permittivity Ba 4 Sm 28/3 Ti 18 O 54 ceramics with improved microwave dielectric characteristics have been successfully fabricated by the one-step RS route.The effects of various sintering routes (CS and RS routes) on the crystal structure, microstructure, valence states of Ti ions, and dielectric characteristics of BST ceramics have been investigated.Single-phase orthorhombic tungsten-bronze-structure and densemicrostructure BST ceramics were achieved using RS and CS routes at the optimum sintering temperature (1400 • C).The FIR spectrum analysis presents that the modes below 220 cm −1 give the majority (84.07%) dielectric contribution to the permittivity of BST ceramics prepared by the RS route.Compared to other routes, the RS route without the calcination and secondary ball-milling processes is a straightforward, economical and effective method for preparing high-performance BST ceramics.

Figure 1 .
Figure 1.One-step reaction sintering process for BST ceramics.Figure 1. One-step reaction sintering process for BST ceramics.

Figure 1 .
Figure 1.One-step reaction sintering process for BST ceramics.Figure 1. One-step reaction sintering process for BST ceramics.

Figure 6 .
Figure 6.(a) Relative densities of BST ceramics; (b) εr of BST ceramics; (c) Q × f of BST ceramics (Inserted images show BST ceramics prepared by RS and CS routes sintered at 1400 °C); (d) TCF of BST ceramics using RS and CS routes.

Figure 6 .
Figure 6.(a) Relative densities of BST ceramics; (b) ε r of BST ceramics; (c) Q × f of BST ceramics (Inserted images show BST ceramics prepared by RS and CS routes sintered at 1400 • C); (d) TCF of BST ceramics using RS and CS routes.

Figure 7 .Table 3 .
Figure 7. XPS spectra of BST ceramics: (a) Ti 2p for RS route sintered at 1400 °C (b) Ti 2p for CS route sintered at 1400 °C.Table3.Binding energies and relative peak area ratio of Ti 2p spectra of BST ceramics using RS and CS routes.

Figure 7 .
Figure 7. XPS spectra of BST ceramics: (a) Ti 2p for RS route sintered at 1400 • C (b) Ti 2p for CS route sintered at 1400 • C.

Figure 8 .
Figure 8.(a) Calculated and measured infrared reflection spectrum.(b) Fitted complex dielectric response of BST ceramic using RS route.

Figure 8 .
Figure 8.(a) Calculated and measured infrared reflection spectrum.(b) Fitted complex dielectric response of BST ceramic using RS route.

Table 1 .
The refinement parameters of Ba 4 Sm 28/3 Ti 18 O 54 ceramics for RS and CS process.

Table 1 .
The refinement parameters of Ba4Sm28/3Ti18O54 ceramics for RS and CS process.

Table 2 .
The measured microwave dielectric characteristics (ε r , Q × f, tanδ and TCF), and calculated theoretical permittivity (ε the ), packing fraction (P.F.) and Ti-site bond valence of BST ceramics sintered at 1400 • C by RS and CS routes.

Table 3 .
Binding energies and relative peak area ratio of Ti 2p spectra of BST ceramics using RS and CS routes.

Table 2 ,
the V Ti of 4.136 v.u. for the RS route is higher than the 4.109 v.u. for the CS route, and the |TCF| of 7.9 ppm/ • C for the RS route is smaller than the 12.1 ppm/ • C for the CS route.As V Ti increases, the |TCF| value decreases.Microwave dielectric characteristics of high-k BST ceramics prepared by different routes are presented in Table4for comparison.Xu et al.

Table 4 .
Microwave dielectric characteristics of BST ceramics prepared by different method.

Table 5 .
Phonon parameters obtained from the fitting of the infrared reflection spectrum of BST.

Table 5 .
Phonon parameters obtained from the fitting of the infrared reflection spectrum of BST.