## 1 Introduction  
Today the latest trends in the automotive industry for the manufacture of aluminum castings are based on the use of the High Pressure Die Casting (HPDC) process, especially for structural parts that are manufactured through vacuum assisted HPDC. Apart from the most employed AlSi\({}_{9}\)Cu\({}_{3}\) alloy, which is employed for standard injected parts, AlSi\({}_{10}\)Mg is the most commonly selected alloy for producing aluminum structural parts. This aluminum alloy combines high ductility values with a good crash performance [1]. A good definition of solidification characteristics of a specific aluminum alloy is very important for the accuracy of casting simulation results. Solidification of an aluminum alloy starts when in the molten metal small crystal nuclei begin to form, producing an undercooling of the melt. The temperature of the metal at this point is called the liquidus temperature. After this point, the metal continues to decrease its temperature, promoting the precipitation of \(\alpha\)-Al phase dendrites. The growth of dendrites involves two main processes: first, dendrites grow forward generating primary dendrites and second, dendrites grow sideways generating secondary dendrite arms until a primary dendrite meets another primary dendrite, forming a primary dendritic network. This point is called the dendrite coherency point (DCP), with its correspondent temperature and solid fraction. A subsequent growth in the preferred crystallographic direction of secondary and even tertiary the branches follows the primary dendritic network formation, with a coarsening of the arms of the secondary dendrites when they touch each other but without being able to support any tension load. Continuing with the cooling of the alloys, there is a moment when the coalescence ends. The temperature at this point, is known as the rigidity point temperature (RPT). The rigidity point (RP) is also called the mechanical coherence point or maximum packing fraction point. At the RP, solid bridges start to form between the solid particles and the structure becomes sufficiently coalesced and rigid to sustain considerable tensile strains and stresses with solid particles moving past each other due to the lubricating effects of the liquid film between them [2]. Interdendritic flow is restricted and should be maintained by the metastatic pressure of the feeding system or by the negative pressure caused by volume deficit, which is known as shrinkage porosity, and by capillarity forces. Bust feeding of the casting occurs between the rigidity and solidus temperature, due to the effect of the application of an external pressure which punctures the skin of the casting exceeding the internal pressure of the casting, and finally when there is a solid feed due to surface sinking of the solidifying casting surface [3]. Adequate control of the total alloy composition is crucial in obtaining quality castings from AlSi alloys, as both major and minor alloying elements have important effects on the solidification process [4]. However, there is a lack of knowledge about how the different minor alloying elements can act over the RPT values in the AlSi\({}_{10}\)Mg alloy, when combined with different percentages of the major and minor alloying elements and the effect of the calculation method employed to determine them. The development of the strength in the castings and the defect formation during the casting process are related to RPT. So, the analysis of the solidification region between dendrite coherency and RP is crucial in determining the effect of the alloying elements on the formation of casting defects, such as shrinkage porosity, macro-segregation, and hot tearing, to improve simulation and casting processes [5]. Thermal analysis (TA) is a widely employed system for quality control in aluminum casting plants. The obtained information can be employed in the subsequent secondary processes of the obtained cast parts.