# Solid Fraction Determination at the Rigidity Point by Advanced Thermal Analysis
## 4 Discussion  
We can observe that some of the alloying elements have a statistical significance for the FRP calculation. In general, an increase in the percentage of one alloying element promotes a decrease of FRP value, because there is a decrease of the solidification and related temperatures up to a minimum solidification temperature in the eutectic composition. Analyzing the results obtained, we can observe that Si, Cu, Mn, Ti, Zn, Pb and Sn promote a reduction in FRP values, postponing the moment when the stiffening phenomenon occurs and increasing the solidification time. In the case of the alloying elements Mg, Fe, Ni, Cr and Sr, the FRP values increase, obtaining a stiffened network in less time. As indicating by [PERSON] [40] some elements in low percentages such as Sn, Sc, Zr, Ti, Sr and Sb are added to improve the properties of aluminum alloys. In some cases, they can appear as traces or as impurities, but because of their effect on the final properties it is important to have a control of alloy composition before casting. For example, the addition level of only a 0.064% Ti resulted in a smaller grain size microstructure and only a 0.009% B promoted a change to a coarser-equiaxed structure [41]. We can compare in Figure 6 the microstructures of alloys 7 and 12, which have respectively the highest and lowest FRP values of the alloys studied. We can observe how the sample with the higher FRP values shows more intermetallic phases, with larger dimensions that promote a more difficult feeding in the interendritic space [42]. The intermetallic phases obtained in the sample with the lowest FRP value are smaller and less numerous, with some small shrinkage porosity. This is in agreement with a study showing that shrinkage porosity nucleates and grows in regions of a casting where the solid fraction is the lowest [43]. The studied alloy 7 is less eutectic than alloy 12, which is almost eutectic. A near-eutectic alloy has a very short freezing rate, so precipitates form almost immediately near the solidification point and do not have enough time to form coarse intermetallic particles. Additionally, in near-eutectic alloys, the shrinkage porosity is usually small compared with hypoeutectic alloys. The observed percentage of interendritic shrinkage porosity in sample 12 is small. The largest positive effect with statistical significance is obtained with Si. It is well known that as the Si content increases, the solidification time increases and a decrease in the liquidus temperature of up to 12% is also observed [44]. Si precipitates in different phases, but in the presence of Mg, Si reacts with Mg to form Mg\({}_{2}\)Si, which is the preferred \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Si** & **Mg** & **Fe** & **Cu** & **Ni** & **Cr** & **Mn** & **Ti** & **Zn** & **Pb** & **Sn** & **Sr** \\ \hline
2.95 & 0.19 & 1.03 & 0.77 & 0.12 & 0.10 & 3.19 & 0.41 & 0.7 & 0.2 & 0.81 & 2.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical Student “\(t\)” coefficients for FRP. Figure 6: Microstructures of the alloy 7 and 12.  
precipitation phase for Mg. However, almost all the Si in this alloy remains as pure Si in the eutectic area. We can see in Figure 7 how a Sr-modified alloy with a high level of alloying elements and Si has very fine polyhedral particles, with small precipitates and some isolated black particles. There are only a few acicular precipitates, but they do not block the liquid feed from the interdendritic space. Due to the low proportion of Mg in the alloy, no Mg\({}_{2}\)Si phases have been detected in the SEM+EDS analysis, with the Mg dissolved within the aluminum matrix. SEM+EDS determination of the different observed phases shows that the polyhedral and skeleton-like particles correspond to Fe-based precipitates with Cr and Mn. The acicular precipitates correspond to the thinner \(\beta\)-Al\({}_{5}\)FeSi phase and the thicker and shorter Al\({}_{3}\)Ni phase, as shown in Figure 8 by the electro image with the analysis of chemical composition in weight performed.