**4. Discussion**

Firstly, for explaining the absence of thermodynamically predicted formation of the Al3Mg2 phase and uncompromised formation of the Mg2Si phase, the solidification behavior of ternary Al-Mg-Si alloys will be considered. According to the binary Al–Mg phase diagram, the solubility of Mg in solid aluminum is about 17%. According to [27], the binary alloys with less than 3.5 wt.%Mg exhibit a single-phase microstructure containing only α-Al. However, the presence of the Al8Mg5 phase (also known and notified in this study as Al3Mg2) may be inhibited at a Mg content of more than 5 wt.% as a result of an increase in cooling rate due to deceleration of Mg enrichment in the melt during the final solidification stage [28]. Furthermore, the addition of silicon greatly reduced the solid solubility of Mg in α-Al. Conversely, the solid solubility of Si is reduced under the appearance of Mg (e.g., 1.17 wt.% Mg and 0.68 wt.% Si at the quasibinary line in Al-Mg-Si diagram [29]). Under these conditions, they both segregate to the front of solid/liquid interface, concentrating together in the final solidification zone, thus promoting the formation of the Mg2Si phase without alternative.

Secondly, for considering La-containing alloys, it was substantiated that they complete solidification in the α-Al + AlLaSi + Mg2Si region that, in turn, contradicts with a thermodynamic calculation showing the formation of only binary phases. Whilst the inhibition of the Al3Mg2 phase seems to be clear, the formation of the AlLaSi phase is under discussion. However, the latter has received a lot of attention recently by the discovery of the new phases (AlSi2La, Al2Si2La, and (Al1-*x*Si*x*)2La (0.075 ≤ *x* ≤ 0.18) in Al-Si-La system [26], the results are still not implemented in describing the solidification of commercial Al-Mg-Si alloys modified with La. Actually, the TCAl4 database, implemented into Thermo-Calc software, likely uses thermodynamic data regarding Al-La, La-Si, and Mg-La due to the lack of thermodynamic optimization of the Al-Mg-Si-La quaternary diagram even for the novel advanced TCAl7 database [30]. The formation of aluminides was observed in this study. The interaction between Mg and La in La-modified Al-4%Mg-0.5%Si alloys may not be anticipated. Not only the binary LaMg phase but also the ternary (Al,Mg)3La was observed in Mg-Al-La alloys [31]. However, since we showed a substantial Mg-enrichment of α-Al out of solidification and the clear presence of Mg2Si phases at up to 1% La, the Mg content is negligible for providing the formation of Mg-La phases. Studies also supported this and revealed such phases only in Mg alloys or Al alloys with more than 30% Mg content [32]. Besides, the study [33] reported an influence of isomorphic La and Ce on Al-3%Mg alloy and found only Al11La3 and Al11Ce3 phases.

For an explanation of intermetallic formation, we discovered very extensive recent e fforts on Si-alternative eutectic-forming elements (Ce, Ni, Ca, La, etc.). Meanwhile, there are similar compounds, Al2CeSi2 [1–3] and Al2CaSi2 [34], observed in Al-Si alloys that show a needle-like shape similar to the AlLaSi phase in the present work. Based on this, it is most likely that the composition of the observed AlLaSi phase is the same as of Al2LaSi2, corresponding to the same space group P3m1 as the ternary Al2CeSi2 and Al2CaSi2 [26]. In regards to RE Ce, current investigations on phase equilibria are focused on Si-rich Al-Mg-Si alloys solidifying under quaternary eutectic reaction L →α-Al + (Si) + Al2LaSi2 + Mg2Si [35]. Either way, there is no appropriate research on the solidification of Mg-rich Al-Mg-Si with REM. In contrast, the e fforts [36] toward the quaternary Al-Ca-Mg-Si diagram show a very similar phase composition at room temperature (Al3Mg2 + Al4Ca + Mg2Si) but also consider a formation of hexagonal Al2CaSi2 phase. It was also reported that peritectic reaction L + Al2CaSi2→α-Al + Al4Ca + Mg2Si is suppressed. In this respect, RE La may act as an alternative to Si because it is a common eutectic-forming element. It promotes the reduction of both in equilibrium liquidus and solidus, whilst the non-equilibrium solidus remains constant under an increase in La content. Therefore, we assumed that equilibrium invariant peritectic reaction L + AlLaSi →α-Al + Al11La3 + Mg2Si likely exists supported by Al depletion of the melt due to its solubility in AlLaSi phase and negligible in fraction (see point 3 in Figure 3) transition area L →α-Al + LaSi2(or AlLaSi) + Mg2Si. This reaction is likely to be suppressed, leading to the formation of the AlLaSi in the as-cast structure along with phases α-Al and Mg2Si.

Finally, a substantial effect of La on the eutectic Mg2Si phase was shown, notwithstanding the adverse degradation of the La-rich intermetallics at more than 0.5 wt.% La. Generally, the modifying effect may be described by heterogeneous nucleation and surface absorption. A study [18] reported the modification of the primary Mg2Si phase, referring to small (3.72%) lattice misfit between the La and Mg2Si phase causing heterogeneous nucleation of the Mg2Si particles on the La clusters during the early stage of the solidification. However, in our study, the Mg2Si phase precipitates according to the eutectic reaction along with AlLaSi (or Al2LaSi2) phase. The difference between two phases Mg2Si and Al2LaSi2 in lattice parameters and lattice-type is enormous (cubic lattice, Fm3m space group, 12 atoms/cell, a = 6.35 Å for Mg2Si [36] and hexagonal lattice, P-3m1 space group, a = 4.23 Å for Al2LaSi2 [26]). The possibility of the AlLaSi compound being a nucleus is minor based on the before mentioned observation. On the other hand, as it is shown in the section related to microstructural observation, the Mg2Si phase precipitates in the vicinity of the AlLaSi phase, showing the latter increased around and may act as a surfactant for the Mg2Si eutectic phase. This means that after the formation of the α-Al phase, the AlLaSi compound is further segregated at the solid-liquid interface of the Mg2Si phase. A quite similar effect is shown by La in modifying eutectic Si particles, which, as shown in [37], have a grea<sup>t</sup> similarity with the Mg2Si phase in terms of properties and solidification behavior.

The presented results are promising steps toward the development of the currently static research area on modification of eutectic Mg2Si in cast 5xx aluminum alloys. While the behavior of the intermetallics formation has been comprehended, the detailed mechanism of the modification process of eutectic Mg2Si with La remains debatable and additional investigations to find out will be performed in further works.
