*3.1. Thermodynamic Prediction*

The polythermal section displayed in Figure 1a shows the solidification behavior of the experimental alloys. As can be seen, La had no significant influence on the equilibrium phase composition and transformation temperatures. In this respect, despite the high melting point of the element, alloying with La did not aggravate industrial compatibility of the base alloy since the liquidus temperature, the key factor for energy consumption in melting, was relatively low (635–637 ◦C), thus starting the solidification from the α-Al phase. Moreover, as can be seen from the magnified section (Figure 1b), the liquidus line goes down slightly along with the area related to the formation of the α-Al phase, likely due to nearness to the eutectic point (4.5 wt.% La, 625 ◦C) adjoining to the area for LaSi2 primary phase appearance. The liquidus projection shown in Figure 1c reveals that the region for undesirable primary intermetallic crystallization was highly beyond the experimental concentrations of La and Si.

The equilibrium solidus decreased with an increase in La concentration but remained relatively high (578–583 ◦C). It should be noted that the TCAl4 database does not consider solubility of Al in the LaSi2 phase, i.e., the existence of the ternary Al2LaSi2 found in the study [25], though a wide composition range of this phase was reported previously and showed a wide homogeneity in Al content [26]. Since this work does not aim to discover new intermetallics, possible La- and Si-rich phases will be referred to as AlLaSi phase. This may bring some limitations for reliable predicting, but some important conclusions can be deduced due to the depletion of the aluminum melt with Si ultimately being considered. The experimental alloys complete their solidification in the three-phase region α-Al + LaSi2 + Mg2Si. However, the calculation shows that further transformations may proceed in the solid-state with the consistent formation of Al11La3 phase instead of the LaSi2 phase and Al3Mg2 phase. Solid-state di ffusion of La in α-Al is negligible, and this transformation can

probably be suppressed, which will lead to the formation of as-cast structure α-Al + LaSi2 + Mg2Si (near-equilibrium solidus region).

**Figure 1.** (**a**) Polythermal section of the Al-Mg-Si-La system at 4 wt.% Mg and 0.5 wt.% Si; (**b**) magnified polythermal section showing the change in liquidus and solidus temperatures; (**c**) liquidus projection of the Al-Mg-Si-La system at 4 wt.% Mg.

The equilibrium phase mass fractions in the L1 (0.1 wt.% La) and L5 (1 wt.% La) alloys are plotted in Figure 2a. Generally, in the temperature range 0 to 485 ◦C, La does not influence the amount of Mg2Si and Al3Mg2 phases (1.36 and 7.6 wt.% respectively) but sufficiently changes the amount of the Al11La3 phase (from 0.17 wt.% to 1.71 wt.%, respectively). It can be assumed that the fractions of phases in the as-cast state may correspond to the three-phase region α-Al + LaSi2 + Mg2Si due to low solubility of La in α-Al during the suppressed transformation of α-Al + LaSi2 + Mg2Si into α-Al + Al11La3 + Mg2Si. It is profoundly visible from Figure 2b that in comparison to the plot at 20 ◦C, at 560 ◦C (corresponded to α-Al + LaSi2 + Mg2Si region near-equilibrium solidus) the higher La content leads to the higher fraction of the LaSi2 phase and the lower fraction of the Mg2Si phase. This relationship achieves equality (0.5 wt.%) at about 0.48 wt.% La after which the ternary phase is the dominating phase (e.g., 1.2 wt.% LaSi2 vs. 0.1 wt.% Mg2Si in L5 alloy).

The considered equilibrium solidification analysis is very helpful for predicting of phase composition of the alloys. However, the actual solidification always occurs in non-equilibrium conditions, implying suppressed diffusion and termination after precipitation of the lowest melt-point phase. The non-equilibrium solidification path was plotted according to the Scheil–Gulliver model (*D*Liquid = <sup>∞</sup>, *D*Solid = 0, where *D* is a diffusion coefficient). The non-equilibrium solidification terminates in a phase region α-Al + Al11La3 + Mg2Si + Al3Mg2, where the breakup of the LaSi2 phase is also considered (Figure 3). It has already been stated that La slightly decreases liquidus temperature, but it was also observed to have a quite significant influence on the non-equilibrium solidus as well. In comparison to the equilibrium solidification range, the non-equilibrium one for all alloys was approximately fourfold higher. Since the formation of the LaSi2 phase in alloys L1–L5 promotes a reduction in Mg2Si and increase in free Mg, it bonds with Al into Al3Mg2 phase, which solidifies at a relatively low temperature (450 ◦C for the base L0 alloy vs. 424 ◦C for other ones, see in Table 2). Accordingly, this may aggravate casting properties due to the wider solidification range. Moreover, the curves show a reduction in a region for primary α-Al formation as a result of La addition (down to halvation at 1 wt.% La), as well as strong domination of La-containing phases. On the one hand, this result seems to be promising due to the increase in eutectic fraction, possibly providing better

casting properties and possible heterogeneous nucleation of α-Al on the eutectic particles' surfaces. Nevertheless, on the other hand, this may cause inadequate growth of the excessive brittle intermetallics, especially the LaSi2 phase nucleating before other ones, adversing ductility, and fracture toughness. To gain further insight into the La effect on the structure formation, the as-cast state samples will be studied in the next sections.

**Figure 2.** Calculated phase fractions for L1 and L5 alloys as a function of temperature (**a**); calculated phase fractions in Al—4 wt.% Mg—0.5 wt.% Si alloy for 20 ◦C and 560 ◦C as a function of La content (**b**)**.**

**Figure 3.** Calculated non-equilibrium solidification curves of the L0 and L5 alloys according to Scheil–Gulliver simulation.


**Table 2.** Calculated critical solidification temperatures of the experimental alloys.
