A low-firing melilite ceramic Ba2CuGe2O7 and compositional modulation on microwave dielectric properties through Mg substitution

A melilite Ba2CuGe2O7 ceramic was characterized by low sintering temperature and moderate microwave dielectric properties. Sintered at 960 °C, the Ba2CuGe2O7 ceramic had a high relative density 97%, a low relative permittivity (εr) 9.43, a quality factor (Q×f) of 20,000 GHz, and a temperature coefficient of resonance frequency (τf) −76 ppm/°C. To get a deep understanding of the relationship between composition, structure, and dielectric performances, magnesium substitution for copper in Ba2CuGe2O7 was conducted. Influences of magnesium doping on the sintering behavior, crystal structure, and microwave dielectric properties were studied. Mg doping in Ba2CuGe2O7 caused negligible changes in the macroscopic crystal structure, grain morphology, and size distribution, while induced visible variation in the local structure as revealed by Raman analysis. Microwave dielectric properties exhibit a remarkable dependence on composition. On increasing the magnesium content, the relative permittivity featured a continuous decrease, while both the quality factor and the temperature coefficient of resonance frequency increased monotonously. Such variations in dielectric performances were clarified in terms of the polarizability, packing fraction, and band valence theory.


Introduction 
The development of wireless communication and broadband network technology has dramatically increased the demand for microwave dielectric materials, † Changzhi Yin and Zezong Yu contributed equally to this work. as potential candidates for microwave communication. Besides, given the identical valence and effective ionic radius for Mg 2+ and Cu 2+ in a tetra-coordinated group, the substituted magnesium in Ba 2 CuGe 2 O 7 is expected to induce certain structural variation on an either macroscopic or microscopic scale, which in turn engenders property evolutions. Doping effects on the sintering behavior, crystal structure, and microwave dielectric properties were studied.

1 Material synthesis
A simple solid-state route was employed to fabricate Ba 2 Cu 1x Mg x Ge 2 O 7 ceramics (x = 0, 0.2, 0.4, 0.6, and 0.8) using high-purity BaCO 3 , CuO, GeO 2 , and MgO (99.9%, Shanghai Aladdin, China) as raw materials, which were weighted according to the stoichiometry. Powder mixing via ball milling was conducted at a speed of 200 r/min for 4 h. After calcined at 900 ℃ for 4 h, the powders were secondly milled for particle uniformity, after which an appropriate amount of polyvinyl alcohol binder (5 wt%) was added. Then green pellets were pressed into cylinders with a diameter of 12 mm and 6 mm of thickness under a uniaxial pressure of 100 MPa. All green pellets firstly sintered at 550 ℃ with a heating rate 1.5 ℃/min for 6 h to remove the organic binder. And then, sintering behavior was performed in a temperature range from 900 to 1140 ℃ to achieve the best density, which was measured based on the Archimedes method.

2 Characterizations
The phase formation and purity were determined by X-ray diffraction using a Bruker Corporation diffractometer (D8 ADVANCE03030502, Karlsruhe, Germany). The Rietveld parameters of the scale factor, zero shift, unit cell parameters, background polynomial, profile parameters, atomic positional coordinates, and isothermal factors were refined step-by-step to improve the value of reliability factors. The microstructures were performed on the polished and thermal etched surfaces of the Ba 2 CuGe 2 O 7 (BCG) ceramics and measured by a scanning electron microscope (JSM-6701 F, Akishima City, Japan). Before SEM measurements, gold sputtering was done using a sputter coater (Ted Pella, USA). Micro Raman Spectroscopy System (Witec, Ulm, Germany) is used for obtaining the Raman spectra with an argon ion laser (λ = 514.5 nm) as the excitation light. Raman shifts were measured with a precision of ~0.3 cm -1 . The spectral resolution is of the 1 cm -1 order and the range of it is 150-1200 cm -1 . Microwave dielectric properties were measured by a Vector Network Analyzer (Rohde & Schwarz, Munich, Germany). According to the Hakki-Coleman method, the relative permittivity (ε r ) and quality factor (Q×f) were measured in the frequency range 10-16 GHz with a TE011 resonant mode. The temperature coefficient of resonance frequency (τ f ) was determined by recording the frequency drift over a temperature range from 25 to 85 ℃ in a temperature cavity and calculated based on the equation: To explore the sintering behavior of Ba 2 CuGe 2 O 7 ceramics, the microstructure evolution and density variation as a function of sintering temperature was recorded and shown in Fig. 2. Evident grain growth was detected accompanied by a decrease in porosity as the sintering temperature increased, both signatures for densification. Consequently, a dense microstructure with grains about 5-7 m was obtained after sintered at 960 ℃ ( Fig. 2(d)). Correspondingly, the density ( Fig.  2(f)) experienced an obvious increase from 4.65 g/cm 3 (~92% theoretical density) at 900 ℃ to 4.93 g/cm 3 (~97%) at 960 ℃. The slight decrease in density www.springer.com/journal/40145 (4.89 g/cm 3 ) when sintered at 980 ℃ might be related to the large grains that give rise to re-entrant pores, as shown in Fig. 2(e). Figure 3 shows the variations in the dielectric properties ( r , Qf, and  f ) of the Ba 2 CuGe 2 O 7 ceramics sintered at a temperature range from 900 to 980 ℃. As the sintering temperature increased both  r and Qf revealed a similar change trend resembling the density ( Fig. 2(f)). A saturated value of  r  9.43 and Qf  20,000 GHz was obtained in the sample sintered at 960 ℃. It is well known that synergetic contributions from the extrinsic and intrinsic factors engender the overall variation in dielectric performances [20][21][22]. Herein, the strong correlation of the relative permittivity and quality factor on the density reveals a predominant role of density on the dielectric properties of Ba 2 CuGe 2 O 7 . By contrast, the  f was weakly dependent on the sintering temperature and fluctuated around -76 ppm/℃. In summary, a composition sintered at 960 ℃ possessed the optimal microwave dielectric properties with  r = 9.43, Qf = 20,000 GHz, and  f = -76 ppm/℃. The lower densification temperature of Ba 2 CuGe 2 O 7 ceramic than the melting point of the Ag electrode suggests that it has a promising application prospect in LTCC technology. Figure 4 shows XRD patterns, backscattering micrograph (BSEM), and EDS profile of the cofired Ba 2 CuGe 2 O 7 ceramic with the silver electrode at 960 ℃. By elaborate comparison with the  standard JCPDF cards, the diffraction peaks of silver are separated from those of the melilite. Two kinds of grains with different morphologies and element contrasts (bright grains and dark grains) can be detected. Combined with the EDS analysis, the bright grains are confirmed to be the Ag electrode.
By comparison with Ba 2 MgGe 2 O 7 ( r = 7.76, Qf = 20,700 GHz, and  f = 55 ppm/℃), the present Cubased compound has a higher relative permittivity, while its quality factor and the thermal stability of resonance frequency are inferior to those of Ba 2 MgGe 2 O 7 [14]. Thus, Mg substitution for Cu in Ba 2 CuGe 2 O 7 was conducted with an attempt to tune the dielectric performances of Ba 2 CuGe 2 O 7 and to correlate such dielectric evolutions to the composition and crystal structure.

2 Effects of magnesium substitution on crystal structure and microstructure
The equivalent substitution of Mg for Cu caused no change in the macroscopic crystal structure of melilite Ba 2 CuGe 2 O 7 but indeed induced continuous variation in lattice parameters. Figure 5 is observed for all compositions and by indexing with ICDD # 89-5260 for Ba 2 CuGe 2 O 7 , all peaks can be assigned and no additional peak is detected. The compositional-induced shift of (211) peak to the higher angle provides evidence of magnesium solution, despite the shift is not sizeable. The lattice parameters refined by the least-square method are obtained from Rietveld refinements. As presented in Fig. 5(b), an evident decrease in a is accompanied by a continuous increase in c, giving rise to a slight and monotonous decline in the unit cell by 0.18%. Otherwise, the linear variation in lattice parameters validates the Vegard's law for a solid solution. These results indicate the scheduled magnesium could completely dissolve into the lattice of melilite to form an infinite solid solution. Rietveld refinements, shown in Fig. 6, further verifying the phase purity and structural stability, are characterized by the good match between the calculated and experimental profiles and the reliable residual factors. It should be noted that the structural model was established based on the parent Ba 2 CuGe 2 O 7 and the sequences for refinements were set as scale factor, zero shift, background, lattice parameters, peak function parameters, and atomic positions, etc. Importantly, the atomic position for magnesium was fixed in the Cu positions and their distribution was set as random.
Figures 7(a) and 7(b) illustrate the variation in bulk density as a function of sintering temperature and composition. All compositions exhibit an analogous dependence on sintering temperature of the density. An initial substantial increase in bulk density explains the crucial role of sintering temperature in promoting densification. A maximum bulk density ( m ) was achieved at a characteristic temperature (recognized as the optimized temperature, T m ) depending on composition. The compositional dependence of the  m and T m values is shown in Fig. 7(b), from which we can see that all compositions have a high relative density (> 96%), suggesting they are applicable for subsequent dielectric characterizations. The much higher melting point of MgO (2852 ℃) than that of CuO (1026 ℃) accounts for the increase in sintering behavior.  and thermal etched surfaces of Mg-doped BCG along with their respective grain size distribution. Dense microstructures with few pores were developed for each compound, coincident with their high relative density. The similar grain morphology validated no structural transformation by Mg doping, which coincides with the XRD observation. Besides, the grain size distribution (in the inset of Fig. 8) for all compounds is alike, giving rise to their close average grain size, as shown in Fig. 8(f).   Raman scattering is known to be highly sensitive to the local structure variations, especially those induced by composition [12,23]. For a tetragonal P-42 1 m unit cell in Ba 2 CuGe 2 O 7 , theoretically, the Raman active vibration modes are predicted based on the factor group theory and listed in Table 1 along with the Wyckoff sites. A total number of 45 ( = 10A 1 + 7B 1 +10B 2 +18E) Raman active modes are estimated. Figure 9(a) shows the room-temperature Raman spectra of the Ba 2 Cu 1-x Mg x Ge 2 O 7 samples. Due to the low density and overlapping of some modes, only a limited number of Raman modes (11)(12)(13)(14)(15)(16) are observed via the Gauss-Lorenzian deconvolution ( Fig. 9(b)), among which the three strongest peaks appear around 775 cm -1 , 500 cm -1 , and 258 cm -1 , respectively. As well known, the Raman spectroscopy includes the internal vibrations of the framed polyhedron (either tetrahedron or octahedron for oxides) and the external ones from translational and liberational moves [23]. Generally, the binding energy in the polyhedral is larger than the intergroup or crystal energy, and thus the internal Raman modes usually appear at highfrequency bands. Thus, the strongest peak around 775 cm -1 is assigned as the symmetric stretching vibration of [GeO 4 ], and the Raman mode around 500 cm -1 and 258 cm -1 corresponds to the asymmetric and symmetric bending of [GeO 4 ], respectively. Nevertheless, the Raman modes related to the translation of Cu 2+ /Mg 2+ locate around 200-225 cm -1 and 280-300 cm -1 , as previously reported [12]. It should be noted that in the structure of melilite More importantly, an extra mode in the parent Ba 2 CuGe 2 O 7 phase arises at 804 cm -1 and its intensity becomes weaker on the increasing magnesium content. This mode is assigned as the asymmetric stretching vibration of [GeO 4 ]. By comparing the Raman modes for Ba 2 MgGe 2 O 7 and Ba 2 ZnGe 2 O 7 , a pretty evident difference lies in the absence or presence of this 804 cm -1 mode. In consideration of their same structure and atomic distribution, this distinction in Raman spectroscopy is believed to be related to the local structure distortion by Zn replacement for Mg. Similar phenomenon observed in this work validates the influences of magnesium substitution on the local structure.
In summary, magnesium substitution in Ba 2 CuGe 2 O 7 does not cause macroscopic phase transformation, or induce the second phase, or change the grain morphology and grain size distribution, but the evolutions in XRD peaks and Raman modes reveal that such doping indeed arouses local structural distortion, which could exert significant influences on dielectric properties.

3 Effects of magnesium substitution on dielectric properties
Figures 10(a) and 10(b) represent the change of relative permittivity (ε r ) and quality factor (Q×f) as a function of sintering temperature. For each composition, both ε r and Q×f value increased as the sintering temperature increased and then decreased slightly. Importantly, the variation tendency of ε r and Q×f versus sintering temperature is similar to that of density, being an indicator for the crucial role of density on dielectric performances. Generally, the highest ε r and Q×f values for each position are achieved in the densest sample. Figures 10(c) and 10(d) summarize the optimum ε r and Q×f values for various compositions. Strong dependence on composition is visible for both quantities. Relative permittivity features a noticeable decrement with increasing Mg content from 9.05 at x = 0 to 7.92 at x = 0.8. Conversely, the quality factor exhibits a continuous rise from 20,000 to 31,370 GHz as the amount of Mg increased from 0 to 0.8. As well known, the relative permittivity and losses at microwave frequency bands not only depend on the intrinsic factors, but also the extrinsic ones from density (or pore), grain size, phase constitution, and phase transition, etc. [20,[24][25][26]. Evidenced from the crystal structure and microstructure, magnesium substitution did not cause phase transformation, or induce the second phase, or change the grain morphology and grain size distribution. Thus, effects from these extrinsic factors (density, grain size, phase transition, second phase) on the dielectric properties can be ruled out. Hence, it is rational to conclude that the compositional variation in relative permittivity and quality factor is mainly controlled by the intrinsic influences.
Theoretically, the relative permittivity is inherently affected by the molecular polarizability ( T D  ) and unit volume ( m V ) based on the Clausius-Mossotti equation a V with composition, being characterized by a linear decrease. This result accounts for the underlying decrease of relative permittivity by magnesium substitution. Nevertheless, the calculated permittivities according to the Clausius-Mossotti equation are much smaller than the measured ones and the separation between them is about 7.1%-18.0%, decreasing with an increase of composition x, as shown in Fig. 10(c). Shannon ascribed such discrepancy as ionic or electronic conductivity, and/or structural distortion like rattling or compressed cations [27]. This large deviation, especially in Ba 2 CuGe 2 O 7 , is an indicator of the local structural distortion and Mg doping released such distortion, which would inevitably influence the physical properties, e.g., dielectric properties. Such local distortion on relative permittivity can be reflected by the bond characteristics estimated by the electronegativity difference (Δe). According to Pauling' rule [28], the electronegativity difference for Ba 2 Cu 1-x Mg x Ge 2 O 7 is calculated as in Mg content. The intrinsic influence on quality factor can be reflected by the packing fraction, as empirically summarized by Kim et al. [29,30]. For a certain material system, the higher of the packing fraction, the smaller space for the thermal motion of cations or anions, thus leading to lower dielectric losses [31]. The packing fraction is defined as the total volume of packed ions over the volume of the unit cell and the calculated values are shown in Fig. 10(d). A consistent increase in packing fraction with the quality factor is seen because magnesium substitution in BCG heightened the packing fraction, leading to more close packing of ions, which in turn results in low dielectric losses. On the other hand, the release of local structural distortion with Mg doping partly accounts for the diminished dielectric loss.
A linear increase in the temperature coefficient of resonance frequency (τ f ) is illustrated in Fig. 11 as the amount of Mg substitution increases from 0 to 0.8. It is well known that the  f value is correlated with the temperature coefficient of the relative permittivity ( ε ) by the relation τ f = -( ε /2+α L ) (α L represents the linear thermal expansion coefficient, which is usually a constant about 10 ppm/℃). Thereby, the composition dependence of τ f can be analyzed by studying the respective variation in  ε value. Derived from the definition for  ε , Bosman and Havinga divided the formula as follows [32]: where ε and α m represent the relative permittivity and polarizability, respectively. A is the direct dependence of the polarizability on temperature, being generally negative; B (generally positive) denotes the variation in polarizability concerning to the thermal change of volume; and C, in general negative, directly represents the volume change on temperature. The magnitudes of the variables B and C are similar and in opposing signs. Hence, the relative magnitude between A and (B+C) determines the signs and magnitude of  ε values. Particularly, both B and C terms involve in the volume variation, which would be reflected through the bond valence of ions. According to the previous reports on the calculation of bond valence [33][34][35][36], the Mg substitution effect on the bond valence of Cu-O in BCG is evaluated and shown in Fig. 11. In contrast to the variation tendency in the τ f value, a steady decrease occurs in the bond valence. The decreasing bond valence reveals the reduced structural distortion caused by magnesium doping. The thermal energy is preferential to recover the structural distortion, giving rise to a larger (B+C) than A term, and thus a negative τ f value. Therefore, the present rising τ f value can be explained by the decrease in the structural distortion, as indicated by the decreased bond valence. Table 2 compares the sintering temperature and microwave dielectric properties of some melilite structured ceramics. As expected, either Si-based or Ge-based melilite compounds possess low permittivities (ε r < 10), moderate Q×f values, and negative τ f values. Table 2 Sintering temperature and microwave dielectric properties of some melilite structure ceramics

Conclusions
In summary, we fabricated a series of magnesium substituted Ba 2 CuGe 2 O 7 ceramics and detailed the effects of magnesium on the sintering behavior, structure (both macroscopic and microscopic), and microwave dielectric properties. XRD and SEM results revealed that magnesium doping induced limited variations in the macroscopic structure and microstructure features. On the contrary, the densification temperature was remarkably raised from 960 to 1120 ℃; meanwhile, Raman spectra provided an indicator of considerable change in the local structure, as characterized by the alteration in the Raman shift and width. Moreover, on increasing the magnesium content, the dielectric properties decreased from 9.43 to 7.92 which are attributed to the lower ionic polarizability of magnesium and the released local structural distortion, while the quality factory (Q×f) increased from 19,560 to 31,370 GHz because of the increasing packing fraction. A monotonous increase in τ f was induced by magnesium substitution, which was explained by the decreased bond valence of Cu/Mg-O. This work provides a potential method to tune the thermal stability of Ba 2 CuGeO 7 realized by increasing the bond strength through substituting larger cations, e.g., Ni 2+ for Cu 2+ or Si 4+ for Ge 4+ .