## 3 Applications
### Isothermal Mineral Reactions and Grain Growth
The sample 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 subsequently recorded within a dwell time of about 24 h to follow the isothermal reaction kinetics. Calcite still decomposed during recording the first Raman image. Simultaneously, \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) formed from CaO and quartz. With increasing sintering time, the content of \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) increased. During cooling, \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) transformed to larnite and remained metastably at RT. White rectangles mark the areas used for semi-quantitative determination of the phase composition (see text). The linear decrease of the reactant fractions with time suggests zero-order kinetics, which, however, is always a result or a kind of artifact of the conditions under which the reaction is carried out. For this reason, reactions that follow zero-order kinetics are often referred to as pseudo-zero-order reactions. A pseudo-zero-order behavior principally suggests that either only a small fraction of the reactants was able to react, which is continually replenished, or that the concentration of one reactant was much larger than those of the others. In our case, the latter explanation is more likely since the investigated area is dominated by lime that occurs with a volume fraction of about 60% in our experiment. Note that such a zero-order process cannot continue after one reactant has been exhausted or is protected against reactants by a solid reaction rim. If this point is reached, the reaction will change to another rate law such, for instance, the Avrami law [68], commonly used to describe the isothermal kinetics of phase and microstructure transformations, instead of falling directly to zero. In our experiments, this point was not reached within 24 h of sintering. In addition, Raman imaging also enables monitoring of single grain growth during ceramic firing. Understanding grain growth is important to nearly every engineered material as porosity and grain size affect the strength of polycrystalline ceramics in a similar manner [69]. The strength of ceramics decreases with an increase in porosity and grain size [67] and therefore a stable small grain size is desirable for materials that rely on strength, toughness, or formability [66]. For grain size analyses, an area was selected, where newly formed \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) is present. By using a color threshold, these image areas were converted into binary images with the aid of the graphics program ImageJ [70], which were then used to quantify the evolution of grain size of \(\alpha^{\prime}\)L Ca\({}_{2}\)SiO\({}_{4}\) as a function of time (data not shown here) by applying the \"Analyze Particles\" tool from ImageJ. With increasing sintering time, the grains of \(\alpha^{\prime}\)L-Ca\({}_{2}\)SiO\({}_{4}\) have grown and small grains have partly coalesced, whereby the average grain size (Figure 15, black squares) increased linearly over time, also indicating a pseudo-zero-order behavior. This supports the interpretation that the pseudo-zero-order behavior is due to the fact that the concentration of one reactant (CaO) was much greater than that of the others (quartz). In addition, the size of most single grains (e.g., grain 2, 3, 5, 6 in Figure 15) have increased linearly with time, whereas some grains (e.g., grains 1 and 4 in Figure 15) did not significantly grow at all. These grains must have been separated from a continuous flux of SiO\({}_{2}\) or CaO for some reasons and therefore could not grow further. The growth of grain 5, however, was not limited, since several small quartz grains were surrounded by a CaO matrix and thus the contact surfaces between CaO and SiO\({}_{2}\) were very large.