Scientists of the Ural Federal University (UrFU, Yekaterinburg) have developed a universal mathematical equation for alloys at the solidification stage. The equation allows us to determine how the microstructure of any crystalline substances, including metals, depends on the flow of the liquid melt. In metallurgy, understanding such a process will allow you to control the physical properties of the final parts that are cast from molten metals.
"We can set the shape and properties of metal parts only at the very beginning - at the stage of casting from a liquid alloy. When the alloy is poured into a mold, it comes into contact with a medium having a temperature significantly lower than the melting point of the substance, during welding, the molten area is cooled by ambient air. In this case, the crystallization of the supercooled liquid begins," explains a senior researcher at the Laboratory of mathematical modeling of physico-chemical processes in multiphase media of UrFUEkaterina Titova. - Our boundary integral method allows us to determine the shape and size of small crystals in the microstructure of the alloy, which determine the mechanical strength of the material, its thermal and electrical conductivity, corrosion resistance. With the help of the equation, we can calculate the necessary flow of the alloy in shape to obtain the form of crystal growth that will provide the necessary properties of the metal part."
The boundary integral equation is developed for pure and two-component (binary) alloys. In such alloys, the impurity substance is dissolved in a small amount in a large volume of another metal. For example, aluminum alloys are often supplemented with copper, magnesium, manganese, silicon and zinc. Scientists also note that the alloy may consist of more substances, if we count all the dissolved substances as some average admixture. So, steel is made on the basis of a mixture of iron and carbon, adding various substances: chromium - for corrosion resistance of steel, manganese - to increase the hardenability of the material and other metals.
"The redistribution of alloying elements during solidification contributes to the appearance of local accumulations of sulfides, nitrides, oxides and carbides, which leads to heterogeneity of the properties of the finished metal product," notesEkaterina Titova. - Our calculations are applicable for any two-component or averaged alloys, where it is necessary to avoid the loss of the physical properties of the metal. But the model is not applicable in cases where it is important to know the distribution of all impurities separately."
With the help of calculations, it will be possible to give the final material the necessary physical properties. The results of the study are published in the Journal of Physics A: Mathematical and Theoretical. The development was supported by the Russian Scientific Foundation (project No. 21-71-00044, "Dynamics of the mobile boundary of the crystallization front in the convective melt flow").
