# Solid Fraction Determination at the Rigidity Point by Advanced Thermal Analysis
## 3 Results  
The RPT values used for the calculation of the FRP were those previously discussed, obtained and explained in our previous works [22]. To compare the values obtained, a comparison graph was used. As it can be observed in Figure 2, employing the SF values obtained, a regression coefficient of 0.81 was determined. The results obtained were compared with the scarce literature data [18; 19; 28; 38; 39] and were found to be within the  
Figure 1: Determination of RPT and FRP at the crossing point of the second and third derivative of the curve dT/dt vs. T.  
range of solid fraction values previously described in the literature. We can observe how a variation of the composition of the alloy at the studied limits promotes a clear variation of the FRP values. If we check values of the error bars, we can observe how the variation of values obtained between samples is quite small all the studied alloys, showing that the method employed is quite repetitive.  
Using linear regression calculations, the Equation below is obtained. FRP values are estimated as a function of the exact alloy composition, with their corresponding linear regression coefficient (r\({}^{2}\)) and standard error (S\({}_{\rm ey}\)). A negative value of a coefficient in the formula promotes a decrease in the estimated property value and a positive value provides an increase in the estimated property value. The calculation formula obtained for the determination of the FRP as a function of major and minor alloying elements is shown below in Equation (1). The first value of the formula is a constant or intercept, as the expected mean value of FRP when all the alloying elements are zero. The rest of the regression coefficients indicate the effect of each one of the elements on FRP value.  
\[\begin{array}{c}\text{FRP (\%)}=82.09-2.67.\text{Si}+1.70.\text{Mg}+4.61. \text{Fe}-11.30.\text{Cu}+1.88.\text{Ni}+1.64.\text{Cr}-\\ 18.35.\text{Mn}-6.16.\text{Ti}-12.41.\text{Zn}-3.62.\text{Pb}-52.98.\text{Sn}+ 161.77.\text{Sr}.\\ \text{r2}=0.81;\text{Sey}=3.41\end{array} \tag{1}\]  
We can observe how the formula obtained has a quite high correlation coefficient value (0.81) and small standard deviation (3.41), showing a good correlation between the predicted and obtained FRP values. Therefore, Si, Cu, Mn, Ti, Zn, Pb and Sn promote a reduction of FRP values, postponing the moment when the stiffening phenomenon occurs. This negative effect of Si can be seen in Figure 3 in weight percentage ranges between 7.5 and 12.5%, and in Figure 4 in the case of manganese up to 1 wt.%. On the other hand, Mg, Fe, Ni, Cr and Sr have the opposite effect, promoting the stiffened network to form faster. In the case of Sr, its positive effect on FRP in ranges from 0% to 0.08% by weight can be seen in Figure 5. Statistical t-values (t) were evaluated to define whether there is a statistically significant influence of a certain alloying element on the studied property. When the t-value is over 2.17, the corresponding alloying element studied has a statistically significant influence. The values obtained are summarized as follows in Table 2.  
Figure 2: Variation of the FRP value in function of the composition of the alloys.  
Figure 4: Comparison of FRP (%) as a function of Mn wt.%.  
Figure 5: Comparison of FRP (%) as a function of Sr wt.%.  
Figure 3: Comparison of FRP (%) as a function of Si (wt.%).