## 3 Applications
### In Situ Observations of the Migration of Solid-Solid Reaction Fronts  
Reaction rims and corona textures are common non-equilibrium features in many metamorphic rocks [71; 72] and ancient ceramics [63]. As the reactant and product phases have different compositions, interlayer growth requires chemical mass-transfer which, in the absence of melts and fluids, can occur by diffusion only. At the same time, localized reactions must proceed at the'reaction interfaces', which divide the growing layers on either side [72]. Both processes may be rate limiting and the coupling between the two processes determines the overall reaction kinetics [72]. Two approaches are possible to identify the rate-limiting step and to identify the direction of the migration front: (i) the rim growth approach and (ii) experiments with isotopically doped reactants [71; 73; 74]. To study the solid-state reaction between quartz and time at the grain scale at high-temperatures, a mixture of quartz and CaO (mass ratio 0.93:1) was fired with a heating rate of 10\({}^{\circ}\)C/min stepwise (50 \({}^{\circ}\)C steps) from 660 \(\pm\) 5 \({}^{\circ}\)C to 1106 \(\pm\) 5\({}^{\circ}\)C. At each temperature step two 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 four hours. Above 884 \(\pm\) 5\({}^{\circ}\)C, dicalcium silicate \(\alpha^{\prime}_{\textrm{L}}\)-Ca\({}_{2}\)SiO\({}_{4}\) crystallized by the solid-state reaction between CaO and quartz, which was already observed in experiments with calcite instead of lime (cf. Section 3.2). In both experiments, \(\alpha^{\prime}_{\textrm{L}}\)-Ca\({}_{2}\)SiO\({}_{4}\) did not only nucleate and grow at visible grain boundaries with quartz grains (Figure 13) but also as many small grains within the CaO matrix. Most likely SiO\({}_{2}\) needed for the formation of dicalcium silicate derived from small invisible quartz particles that are more reactive than the larger ones due to their larger surface area. Such a grains size effect was also reported for feldspar by [PERSON] and co-workers, who studying the effect of particle size distribution in Na-feldspar/kaolinite system [75] and is consistent with Oswald ripening that is described by the  
Figure 15: The growth of individual grains as a function of time. The average grain size (black squares) increases linearly with increasing sintering time which corresponds to a pseudo-zero-order behavior. In addition, the size of most single grains (colored hexahedron, grain 2, 3, 5, 6) increases linearly with time. The lines represent linear least-squares fits to the data. Image size in the inset is 100 \(\times\) 100 \(\upmu\)m\({}^{2}\). Ostwald-Freundlich equation [76] in which surface tension causes small particles to dissolve and larger ones to grow. With increasing time (Section 3.2) or temperature (Section 3.3) dicalcium silicate rims have grown around larger quartz grains (Figures 13 and 16). However, with further increasing temperature (and time) the reaction direction seems to turn over and the dicalcium silicate phase clearly migrated inwards into the quartz grain and partially replaced it (Figure 16). This turn over can only be explained by a change in the mechanism of formation. Up to 929 \(\pm\) 5\({}^{\circ}\)C, a tens of micrometer thick \(\alpha^{\prime}\)\({}_{\mathrm{L}}\)-Ca\({}_{2}\)SiO\({}_{4}\) was formed at the interface between lime and quartz. [PERSON] & [PERSON] observed by thermal analysis of a 2 CaCO\({}_{3}\) + SiO\({}_{2}\) (mol ratio) mixture that the maximum of the dicalcium silicate formation occurs around 970 \({}^{\circ}\)C at virgin surfaces. They claim that the reaction decelerated because the grains were covered with a protective rim of Ca\({}_{2}\)SiO\({}_{4}\) and therefore the reaction could continue only by diffusion through this rim [77]. This interpretation agrees with our observations. After the \(\alpha^{\prime}\)\({}_{\mathrm{L}}\)-Ca\({}_{2}\)SiO\({}_{4}\) barrier was formed the reaction mechanism changed.