# Crystallization Kinetics of Sr-Modified Precipitation Hardening Al-Si-Cu Alloys
## 3 Discussion of the Research Results  
### Thermal-Derivative Analysis  
On the cooling curve occurs some characteristic inflection points coming from exothermic or endothermic reactions of the crystallizing phase transformations. It is difficult to determine unequivocally the crystallization temperature of the phases. The determination is possible using the first derivative curve of the cooling line in a function of time that mines using the DTA (Differential Thermal Analysis) curve, also called the derivative curve [22,23]. When crystallization heat is emitted, which means when crystallization proceeds, the momentary heat effect is described by the following interdependence:  
\[\frac{dQ}{dt}=c_{p}(t)m\bigg{[}\frac{dT}{dt}-\bigg{(}\frac{dT}{dt}\bigg{)}_{b} \bigg{]} \tag{1}\]  
Calculating the crystallization heat effect at time \(t\), it is necessary to also take into account the heat capacity, which depends on the ratio of the crystallized material and the remaining liquid metal. Heat capacity as a function of t is characterized by the following equation:  
\[c_{p}=c_{p_{Sol}}\int_{t_{L}}^{t}f_{S}(t)dt+c_{p_{Liq}}(1-\int_{t_{L}}^{t}f_{S} (t)dt) \tag{2}\]  
Total crystallization heat can be calculated using an integral of the following Equation (2):  
\[Q=c_{p}m\int_{t_{L}}^{t_{Sat}}\bigg{[}\frac{dT}{dt}-\bigg{(}\frac{dT}{dt} \bigg{)}_{b}\bigg{]}dt \tag{3}\]  
Description of equation factors: \(Q\)--crystallization heat, \(c_{p}\)--heat capacity and \(m\)--mass of the crystallized metal. In the time without any phase transformations, which means that no other heat sources are not present, the differential curve covers the base curve. Derivative calculations were performed after recording the temperature change over time until the point where a change in temperature induced no further changes over time, and a base curve was constructed using a Newtonian third degree polynomial [24]. Sr is a rather reactive element that can easily form oxides or intermetallic compounds with the alloying elements of the alloy. In fact, in the presence of Sr, some parts of the oxide layer on the surface of the melt and the entrained oxide films inside the molten alloy gradually transform into Sr-containing oxides. Due to the formation of Sr-containing compounds, with time, the modifying effect on the eutectic Si is lost [20]. The crystallization of AlSi6 Cu4 and AlSi6 Cu4 Sr0.2 alloys begins at point I (Figures 2 and 3) and indicates the nucleation of \(\alpha\) dendrites, while, in the case of the AlSi6 Cu4 Sr1 alloy, the liquidus temperature is determined by point I\({}_{\text{A}}\) (Figure 4), where the nucleation of the phases first occurs for Al\({}_{2}\)Si\({}_{2}\)Sr [25]. Strontium raised the nucleation temperature of the \(\alpha\)-phase by less than 2 \({}^{\circ}\)C during crystallization of the AlSi6 Cu4 Sr0.2 alloy, and, in the alloy with 1% Sr, this temperature is higher by more than 8 \({}^{\circ}\)C (Table 2), which may indicate an accelerated heterogeneous nucleation. At point II, where the crystallization curve assumes a zero value, \(\alpha\)-phase crystallization begins, and point III indicates the continued growth of \(\alpha\)-phase dendrites. The temperature corresponding to point IV on the crystallization curve reaches the highest values as a result of the crystallization of aluminum dendrites [8; 26; 27]. Nucleation of the phases Al\({}_{15}\)(Fe,Mn)\({}_{3}\)Si\({}_{2}\) begins at point V [17; 28]. Point VI determines the start of nucleation of the silicon eutectic. Strontium caused a decrease in the nucleation temperature of the eutectic by 9.8 \({}^{\circ}\)C and 12.6 \({}^{\circ}\)C for AlSi6 Cu4 Sr0.2 and AlSi6 Cu4 Sr1 alloys, respectively, while the undercooling occurring during the crystallization of the \(\alpha+\beta\) eutectic defined by points VII and VIII increased.