# Large Thermal Expansion LTCC System for Cofiring with Integrated Functional Ceramics Layers
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Heating Rate (K/min)** & **2** & **4** & **8** \\ \hline _xy_-shrinkage (\%) & 16.7(3) & 16.5(4) & 16.5(3) \\ \hline _z_-shrinkage (\%) & 19.5(5) & 19.3(6) & 20.7(8) \\ \hline density (g/cm\({}^{3}\)) & 2.82(2) & 2.82(1) & 2.82(2) \\ \hline porosity (\%) & 0.75 & 0.84 & 0.87 \\ \hline permittivity (1 kHz) & 6.5(5) & 6.4(5) & 6.6(5) \\ \hline permittivity (1 GHz) & 5.9(5) & 6.1(5) & 6.1(5) \\ \hline tan \(\delta\) (1 kHz) & 0.0004(8) & 0.0003(8) & 0.0003(8) \\ \hline tan \(\delta\) (1 GHz) & 0.0004(5) & 0.0004(5) & 0.0004(5) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Shrinkage, density, porosity, permittivity, and loss factor (@1 GHz) of CT708 samples, sintered at 900 \({}^{\circ}\)C, heated with heating rates. Figure 2: Dilatometer shrinkage and shrinkage rate curves of CT708 green tapes with heating rates of 2 K/min (**a**), 4 K/min (**b**), and 8 K/min (**c**). found. A dwell of 4 h upon sintering at 900 \({}^{\circ}\)C seems to overturn potential differences in density, which might be present directly at the end of the heating ramp. LTCC tapes of the CT700 series typically are based on BaO-Al\({}_{2}\)O\({}_{3}\)-B\({}_{2}\)O\({}_{3}\)-SiO\({}_{2}\) glasses with dispersed ceramic fillers. The phase composition of the CT708 green tape as obtained from X-ray diffraction (Figure 3a) consists of a glass phase with quartz as ceramic filler. In addition, small amounts of titania (anatase) and CoAl\({}_{2}\)O\({}_{4}\) spinel acting as blue pigment were found. Quantitative phase analysis of the initial CT708 composite powder was performed using Rietveld refinement. CT08 powder is composed of 60% of glass phase, 35% quartz as main ceramic filler, 4% anatase, 1% CoAl\({}_{2}\)O\({}_{4}\), and \(<\)1% of corundum (Al\({}_{2}\)O\({}_{3}\)). After firing at 900 \({}^{\circ}\)C (heating rate 2 K/min), a quite different phase composition is observed, as revealed from XRD (Figure 3b). Besides quartz and the residual glass phase, Celsian (BaAl\({}_{2}\)Si\({}_{2}\)O\({}_{8}\)) appeared as additional crystalline phase as result of glass crystallization. Quantitative phase analysis shows quartz and celsian to appear as main phases with concentrations of 35% each, respectively. Mixed (Ba/Sr)-celsian solid solutions Ba\({}_{1,\mathrm{y}}\)Sr\({}_{y}\)Al\({}_{2}\)Si\({}_{2}\)O\({}_{8}\) are known, and comparison of the XRD-pattern of celsian crystallizing from CT708 upon sintering with those of celsians with various Ba/Sr-ratios suggests, that the celsian phase in CT708 contains a significant concentration of Sr (about \(\gamma\cong\) 0.25). Fresnoite (Ba\({}_{2}\)TiSi\({}_{2}\)O\({}_{8}\)) was detected as third crystalline phase in sintered CT708 with a concentration of 11%. Fresnoite is known to be present in the BaTiO\({}_{3}\)-SiO\({}_{2}\) system [19]. Here in sintered CT708, as result of crystallization from the glass phase, it seems to consist of mixed (Ba/Sr) ions residing at the alkaline-earth positions. The amount of residual amorphous phase in sintered CT708 was determined to be 18%. These results indicate that the majority glass phase, which is present in the GCC-type initial CT708 composite powder, tends to crystallize, forming (Ba/Sr)-celsian and (Ba/Sr)-fresnoite upon firing. This is consistent with the observed dramatic decrease of the glass phase content. TiO\({}_{2}\), also present in the initial composite mix, is likely to act as nucleation agent and transforms into fresnoite. The observed crystallization behavior is also reflected in the DSC curve of the initial CT708 powder (Figure 1, inset). A sharp endothermic signal at about 570 \({}^{\circ}\)C signals the quartz phase transformation (q). The transformation temperature of the glass phase causes a significant shift of baseline observed at about 700 \({}^{\circ}\)C. Finally, a broad exothermic peak with its maximum at about 820 \({}^{\circ}\)C indicates the crystallization of the glass and celsian/fresnoite formation.