## 2 Materials and Method
### Data reduction, Quantification, and Visualization
#### 2.6.3 Factors Affecting Phase Quantification
The temperature-dependent mode behavior of most of the relevant phases in silicate ceramics has already been studied by Raman spectroscopy, such as albite [22], wollastonite [35], gehlenite [15], diopside [45], pseudowollastonite [15; 45], and quartz [46]. However, the high-temperature Raman spectra reported in these studies were recorded with different instruments and under different analytical and experimental conditions (e.g., larger temperature steps) and are also not precise enough. We, therefore, collected in-house, high-precision, high-temperature reference Raman spectra of the relevant ceramic phases. These were used for the estimation of relative Raman cross sections that are needed (i) to determine the relative phase proportions from a mixed Raman spectrum, and (ii) to identify individual high-temperature phases in convoluted spectra. The transverse Raman scattering cross-section depends on many factors like pressure [47], temperature [48], and the crystal orientation with respect to the polarization direction of the incoming laser light [49]. The correct calculation of Raman intensities in the context of the polarization theory is difficult and involves an enormous calculation effort. Therefore, theoretical calculations of Raman intensities were less commonly performed than calculations of infrared or nuclear magnetic resonance spectra [50]. It is common practice to normalize Raman spectra to the maximum intensity [18; 51; 52; 53] or to divide the intensity of the Raman spectra by the power of the laser and the acquisition time [52; 54] to compare different Raman spectra. Therefore, in our first attempt [24], we normalized the reference spectra between 0 and 1 before using them for CLS fitting (Figure 8a). However, this procedure neglects the Raman cross sections of the mineral phases. In the present work, we, therefore, recorded the reference spectra at the same measurement conditions (i.e., laser wavelength and power, acquisition time, internal Ne lines, etc.) and used the processed reference spectra without normalizing the intensity for the CLS fitting procedure (Figure 8b). However, this approach does not consider all factors that affect the Raman intensities. The main source of errors, aside of instrument calibration errors, is related to the unpredictable loss of light at uneven surfaces by surface scattering. However, due to the equal procedure during data treatment, it is still possible to semi-quantify changes of mineral fractions and  
Figure 7: Comparison of Raman spectra from single crystals (E1A) and powders (E1B) of (**a**) calcite and (**b**) wollastonite. Numbers give the full width at half maximum (FWHM) of the respective band. Note that the Raman bands measured on powders are characterized by larger FWHM values. to monitor grain boundary movements during the experiment. From multiple Raman images of the same area of a fired CaO-SiO\({}_{2}\)-Al\({}_{2}\)O\({}_{3}\) ceramic (T\({}_{\text{max}}\) = 1097 \({}^{\circ}\)C), recorded using the same analytical parameters as for the _in situ_ experiments, we obtained empirical errors in order of \(\pm\)20 and \(\pm\)1% at a volume fraction of 0.3 and 75.00%, respectively, that scale with the square root of the average mineral fraction within the analyzed area (volume), as expected for errors relating to the Poisson statistics of counting rates.