# Mineralogical Transformations in Granitoids during Heating at Fire-Related Temperatures
## 4 Discussion
### Granitoid Theoretical Thermal Expansion  
Dilatometric measurements are the best method to determine the linear and volumetric thermal expansion of rocks. However, in some cases such as cultural heritage monuments, the sampling size required for this test cannot be achieved and an optional analysis is needed. The theoretical approach is envisaged when working with crystalline stones, in which porosity or other materials as salts are not considered as a variable [36, 50]. For this theoretical approach, the thermal expansion in the three main axes and of every mineral is considered together with the mineral proportion within the rock. Some authors [36] used a finite element model to estimate the micro stresses and thermal expansion of several granitoids up to 400 \({}^{\circ}\)C, and others [50] used the maximal and minimal linear expansion of each mineral for proposing a values' interval to fit with experimental data. These coefficients are multiplied by the percentage of each mineral in each rock. In both cases, mineral thermal expansion coefficients were extracted from literature [48, 50] and the rock thermal expansion calculated with a dilatometer with temperatures of approximately 100 \({}^{\circ}\)C. Following this pattern, it is assumed that minerals are pure, and with a determinate composition, and that their thermal expansions are always constant. However, the mineral expansion is not continuous due to the chemical changes that take place, such as the quartz alpha-beta transition noted above, the water loss, or the mica and clays decomposition at approximately 500-600 \({}^{\circ}\)C [23].  
The approach proposed in this research is to use the experimental thermal expansion coefficients obtained by XRD during heating up to 600-800 \({}^{\circ}\)C (depending on the XRD peaks definition) and to apply the model from [50] to obtain the rock thermal expansion up to high temperatures as are reached during a fire. The coefficients were calculated from 25-200 \({}^{\circ}\)C, 200-400 \({}^{\circ}\)C, and 400-600 \({}^{\circ}\)C from the statement of the non-homogeneous behaviour.  
From lattice measurements, the mineral thermal expansion was calculated for two of the granitoids, ER and G. The presence of muscovite and amphiboles in GS and NG made it difficult to present accurate data. As noted above, the minerals dimension varied with temperature in a non-linear pattern, and that was observed in the calculated linear thermal expansion of rocks, and in agreement with the behaviour of centimetric sample exposed to high temperatures (Figure 13). The maximal and minimal thermal expansion coefficients were used to calculate the rock thermal expansion evolution and compared with the experimental value obtained at 90 \({}^{\circ}\)C.  
ER showed a constant thermal expansion up to 400 \({}^{\circ}\)C for the maximal value. The random mineral orientation can be equilibrated for the crack formation over 130 \({}^{\circ}\)C and have as a result a comparable dilation coefficient. After this temperature, the mineral transformation revealed a mineral behaviour too separated and, in this case, the crack development by mineral expansion plays a more important role in the rock dilation than the minerals themselves. G has a progressive dilation up to 600\({}^{\circ}\) that indicates a lesser influence of mineral transformation at approximately 500-600 \({}^{\circ}\)C. As for ER, the maximal value for every mineral agrees with the values obtained for the whole rock.  
Figure 13 also shows the rock dilation if the data from references are considered for the model. ER highest values can be compared with the expansion calculated from the theoretical lower coefficients. G presented a good compromise with intermediate dilation of the results from this study and the results from the theoretical approach.