## 3 Applications
### Isothermal Mineral Reactions and Grain Growth  
Understanding the kinetics of sintering reactions is necessary to systematically control the manufacturing process of a ceramic, but also to understand metamorphic rock-forming processes in nature. Even if a mineral transformation is thermodynamically favored, it is not guaranteed that the transformation will occur at any measurable rate. The reaction rate strongly depends on the mechanisms involved in the reaction process and can change with time and temperature. Grain  
Figure 12: Raman images of a sample composed of quartz and calcite fired to the last temperature step of 1106 \({}^{\circ}\)C (**a**) and quenched to RT (**b**). At 1106 \({}^{\circ}\)C calcite is decomposed to CaO and CO\({}_{2}\) and quartz completely reacted to \(\upalpha\)’L-Ca\({}_{2}\)SiO\({}_{4}\) (a). After cooling with a cooling rate of 10\({}^{\circ}\)C/min to RT lime has reacted with atmospheric CO\({}_{2}\) to calcite (b). During cooling, \(\upalpha\)’L-Ca\({}_{2}\)SiO\({}_{4}\) has transformed into \(\beta\)-Ca\({}_{2}\)SiO\({}_{4}\) (tarnite). Note the slight offset and grain boundary shifts, which is due to differential shrinkage of the sample during cooling. boundaries move and rearrange so as to increase the average size and decrease the grain boundary area per unit volume [66]. Here, isothermal _in situ_ experiments were performed to study the effect of time on the formation of calcium silicates and grain growth during firing. One major advantage over conventional quench experiments is that the same sample position/material is continuously investigated without the need for quenching a new sample at each time step. For the experiment, a mixture of quartz and CaO (mass ratio 1:1) was fired with a heating rate of 10 \({}^{\circ}\)C to 848 \(\pm\) 5 \({}^{\circ}\)C and 12 hyperspectral Raman images (100 \(\times\) 100 \(\upmu\)m, 1 \(\upmu\)m step size, SWIFT 1.6 \(\upmu\)m/s) were recorded step by step within a dwell time of about 24 h. After the last hyperspectral Raman image had been taken, the sample was cooled to RT with a cooling rate of 10 \({}^{\circ}\)C/min. During the first 10 h, the sample has significantly shrunk, which is reflected by a shift of the imaged area (Figure 13). [PERSON] and co-authors also observed increased shrinkage within the first 10 h of isothermal sintering of CaSiO\({}_{3}\) at 1100 \(\pm\) 5 \({}^{\circ}\)C and explained this phenomenon by incomplete densification and increased porosity of the samples during the first few hours [67]. In order to semi-quantify the apparent mineral content and grain size distribution over time, an area of 80 \(\times\) 80 \(\upmu\)m\({}^{2}\) was selected, which is more or less present in each image (white dotted squares Figure 13). For quantification, the marked area was used. Note that due to the three-dimensional shrinking of the sample, a complete match cannot be achieved. During the recording of the first hyperspectral Raman image at 848 \(\pm\) 5 \({}^{\circ}\)C calcite was still decomposing to CaO and CO\({}_{2}\) (Figure 13). Note that in this case, the decomposition reaction was significantly faster than the image recording time (cf. Figure 2), reflected by the observation that calcite is still visible within the first rows of the image, but is not detected anymore afterwards. At the same time, \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) formed from a solid-state reaction between lime and quartz, which transformed to larnite during cooling (cf. RT image in Figure 13). The fraction of \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) increased linearly with time, while simultaneously the fractions of the CaO and quartz decreased also linearly (Figure 14). Figure 13: Hyperspectral Raman images of a green body composed of a mixture of quartz and CaO (mass ratio 1:1).