**4. Conclusions**

Variations of Mg within 0.3 ÷ 0.5%; Si within 1 ÷ 1.3%; Sc within 0.0 ÷ 0.3%; Zr in the range of 0.0 ÷ 0.15% have a complex effect on the microstructure formed during casting of these alloys. The most significant effect on the size of the grain structure is exerted by micro-additives of Sc and Zr. In Al0.3Mg1Si alloys, the complex additive 0.3Sc0.15Zr is able to refine the grain size by seven times. The refinement of the grain structure is influenced by two main factors: supercooling at the boundaries of the nucleus and the liquid phase, and the formation of Al3Sc particles in the liquid. The latter takes place at a concentration of 0.15% zirconium and 0.24% scandium in Al0.3Mg1Si alloys and 0.15% zirconium and 0.28% scandium in Al0.5Mg1.3Si alloys. The refinement of the grain structure by supercooling is more efficient in the Al0.5Mg1.3Si alloys, and with the primary Al3Sc phase in the alloys of the Al0.3Mg1Si type, where the scandium concentration required for the formation of this phase is reached earlier.

These alloys have a complex phase composition. After casting, it can be represented by both equilibrium and non-equilibrium phases; in addition, iron impurities have a significant effect. With regards to maximum binding of scandium to other elements, the preferable alloys are Al0.5Mg1.3Si. However, the Al0.3Mg1Si alloy is better for the effective dissolution of the Mg2Si phase, which occurs already at 450 ◦C. In general, compositions with combined alloying by small additions of Sc and Zr and mono additions of Zr seem to be most promising. Alloying Sc compositions with such an excess of silicon is practically unpromising.

The cooling time after solidification of the ingot is sufficient for the precipitation of fine particles. These particles are practically not tracked using scanning electron microscope SEM even at high magnification. However, they are very clearly identified using TEM, as well as by an increase in microhardness. The main type of particles is (AlSi)3Sc or (AlSi)3ScZr, depending on the presence or absence of zirconium. These particles appear during discontinuous precipitates in form of the L12-structure with dimensions of 15–20 nm and are semi- and completely coherent or in needle shape form (observed only in alloys with zirconium). The formation of coherent and semi-coherent particles in these alloys opens the possibility for their further production during heat treatment. β" (Mg5Si6)- particles are formed only in the alloy Al0.5Mg1.3Si0.3Sc, where there is enough magnesium for their precipitation. The addition of zirconium changes the phase composition and promotes the precipitation of large Mg2Si-type particles.

**Author Contributions:** Conceptualization, E.A. and S.K.; methodology, E.A., S.K. and J.H.; software, E.A. and S.K.; validation, E.A., S.K. and J.H.; formal analysis, E.A. and A.D.; investigation, E.A., M.L., V.B. and D.Z.; resources, E.A., J.H. and S.K.; data curation, E.A., J.H., S.K. and A.D.; writing—original draft preparation, E.A., J.H. and S.K.; writing—review and editing, E.A., J.H. and S.K.; visualization, E.A. and J.H.; supervision, S.K.; project administration, E.A. and S.K.; funding acquisition, S.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study is funded by a gran<sup>t</sup> of the Russian Science Foundation, project 21-19-00548, https://rscf.ru/project/21-19-00548/.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
