## 2 Materials and Method
### Data reduction, Quantification, and Visualization
#### 2.6.3 Factors Affecting Phase Quantification  
Phase quantification is influenced by four main factors that have to be taken into account when interpreting hyperspectral Raman images, namely (i) crystal orientation, (ii) grain size, (iii) temperature dependence of band position and linewidth, and (iv) the Raman scattering cross-sections of the mineral phases. For anisotropic crystals, the intensity of a Raman band depends on the angle of incidence of the laser beam in relation to crystal lattice orientation, bond polarizabilities, and the state of polarization of the incident laser beam and therefore relative band intensities of a mineral phase change with crystal orientation, whereas the band shape and position is independent of crystal orientation. Room-temperature, unpolarized Raman spectra of fibrous Kopparberg wollastonite collected with the crystal fiber axis parallel and vertical to the electric field vector of the incident light are very similar, i.e., only the weak Raman bands are strongly polarized [35]. In contrast, due to the symmetry of the crystal structure, Raman spectra of rutile oriented with the crystal c-axis parallel and perpendicular to the polarization of the laser beam vary strongly [36]. It is clear that any differences in relative Raman band intensities due to the orientation of the crystal affects the CLS fitting procedure. However, most of the mineral phases occurring during the experiments presented here exhibit limited orientation effects that do not significantly affect the fitting result. Nevertheless, for minerals with relative large orientation effects like gehlenite, reference spectra were recorded in a number of different orientations and implemented in the CLS fitting procedure. A positive side effect is that the orientation effect can be used to systematically study grain rotation during firing, which is particularly important for our understanding of the dynamics of crystal growth processes in ceramics with potential for certain device applications [37]. With Raman spectroscopy relative crystal orientations can be determined rapidly and accurately without the necessity of sample preparation [37]. Raman spectra of single crystals compared to those of powders reveal differences in linewidth and intensity of the fundamental Raman bands (Figure 7). In addition, the spectra of some mineral powders show additional bands which are likely due to surface scattering [27]. The former can be due to local heating and/or quantum confinement [38], whereby the latter becomes significant only in nanocrystalline materials and here mainly effects the lattice modes. The dependence of linewidth on grain size was already studied, for instance, by several authors for TiO\({}_{2}\) nanocrystals [39; 40; 41] and nanometer-sized diamonds [38; 42; 43]. [PERSON] et al. [44] studied the influence of the size of diamond particles, ranging in size from 0.25 to 10 \(\upmu\)m, and the beam power, varied between 8 to 100 mW, on  
Figure 6: The effect of image smoothing on a hyperspectral Raman image of a sintered ceramic (Kln\({}_{60}\)Qtz\({}_{15}\)Cal\({}_{25}\), T\({}_{\text{max}}\) = 1097 \({}^{\circ}\)C). (**a**) unsmoothed and (**b**) smoothed image. Note that in particular grain boundaries are better displayed in the smoothed image. the fundamental diamond Raman band near 1332 cm\({}^{-1}\). They explained an observed systematic downshift of the Raman band frequency as reflecting both the decrease of particle size and a local temperature increase of about 500 \({}^{\circ}\)C, which depends on the thermal conductivity path available in the specific configuration [44]. Therefore, the reference spectra used for the CLS fitting procedure were mainly obtained from pellets made from powdered samples with grain sizes between 5 and 30 \(\upmu\)m (E1B) rather than from single crystals.