SOLUBILITY OF CARBON, MANGANESE AND SILICON IN α-IRON OF Fe-Mn-Si-C ALLOYS

Natalia Filonenkoa,b,*, Alexander Babachenkob, Ganna Kononenkob, Ekaterina Dominab aState Institution “Dnipropetrovsk Medical Academy of the Ministry of Health of Ukraine” 9, Vernadsky Str., Dnipro, 49044, Ukraine bZ.I. Nekrasov Iron and Steel Institute of National Academy of Sciences of Ukraine 1, Akademika Starodubova Square, Dnipro, 49107, Ukraine *Corresponding Author: natph2016@gmail.com Received August 18, 2020; revised October 12, 2020; accepted October 13, 2020

As is known, there is currently a special interest in steels that have high strength and ductility. To increase the complex of mechanical properties in an economical way using alloying of alloys based on iron with manganese and silicon [1].
In the al loys of the Fe-Mn-Si-C system during the crystallization of the melt, the primary phase may be δ -iron with a carbon content of up to 0.2% (wt.), manganese up to 2% (wt.) and silicon up to 1% (wt.). During the crystallization of alloys of the Fe-Mn-Si-C system, successive transformations of peritectic were observed: L→L+δ→δ+γ→γ [2][3][4][5]. It is known that doping alloys based on iron with manganese and silicon has almost no effect on the temperature of point A1 and shifts point S (eutectoid point on the equilibrium phase diagram of the Fe-C system) to a low carbon content, which leads to an increase in the volume fraction of perlite in the microstructure [6].
According to the results presented in [7][8][9][10], the solubility of carbon in ferrite is in the alloys of the Fe-C system -0.095% (at.), Mn-C -6% (at.), silicon Fe-Si - [10][11][12][13][14][15][16][17][18].5% (at.), Mn-Si -18.5-10% (at.) in dependence from temperature. In the ternary system Fe-Mn-C are the solubility of carbon and manganese in α-iron at temperatures 505-971 K [4]. In this paper it is noted that at a temperature of 505 K the content of carbon in α-iron was 4·10 -9 % (wt.), and manganese -0.5% (wt.). The authors of [7] note that in the alloys of the Fe-Mn-Si-C system is the consistent formation of solid solutions, the carbon content of which is more than 0.08% (wt.). Thermodynamic databases (ThermoCalc, FactSage, MTDat, PANDAT, JMatPro, IDS and CALPHAD) are currently widely used in steel and alloy research, development of new materials and production technologies in the metallurgical industry, but the reliability of forecasts made with these programs is limited by the accuracy of thermodynamic data. Some experimental data, which are important for multicomponent systems, are quite old and insufficiently tested by modern experimental methods [11]. As is known, to predict the phase composition of alloys and phase transformations plays an important role solubility limit of the alloying elements in alloys.
The aim of this work was to determine the solubility limits of carbon, silicon and manganese in α-iron alloys of the Fe-Mn-Si-C system.

MATERIALS AND METHODS
Research carried out on alloys containing carbon 0.37-0.57% (wt.), silicon 0.23-0.29% (wt.), manganese 0.7-0.86% (wt.), the rest -iron. The smelting of alloys of the Fe-Mn-Si-C system was performed in a furnace in alundum crucibles in an argon atmosphere. The cooling rate of the alloys after casting was 10 K/s. Metallographic sections of Fe-Mn-Si-C alloys were made according to standard methods using diamond pastes. Chemical and spectral analysis were used to determine the chemical composition of the alloy [11]. The phase composition of the alloys was determined using an optical microscope "Neofot-21". The main results of micro-X-ray spectral analysis were obtained using an electron microscope JSM-6490 with a scanning attachment ASID-4D and energy-dispersive X-ray microanalyzer "LinkSystems 860" with software. X-ray diffraction analysis was performed on a DRON-3 diffractometer in monochromatized Fe-Kα radiation. The results of X-ray analysis in this alloy were discovered only two phases -ferrite and carbide (Fig. 1b). Carbide, as a structural component of perlite, was presented in these alloys of the Fe-Mn-Si-C phase Fe 2.7 Mn 0,3 C. It should be noted that perlite has two colors after surface etching of the samples with sodium pirate -light and dark. In perlite light r color content of manganese -0.37% (wt.), silicon -0,38% (wt.). In perlite dark color high content of alloying elements: manganese -0.79% (wt.), silicon -0.41% (wt.). Thus, the results make it possible to assert that in alloys formed a reason region richest manganese and silicon.
On the diffraction pattern, the α-iron lines were shifted toward larger angles compared to pure α-iron. The obtained result can be explained by the fact that the ferrite is doped with manganese and silicon and the ferrite lattice parameter changes. According to the results of micro-X-ray spectral analysis in ferrite, the manganese content was 1.27% (wt.), silicon -0.27% (wt.).
As Table shows, the characteristics of strength and hardness for all the alloys are high, and for the alloy containing carbon -0.57% (wt.), silicon -0.28% (wt.) and manganese -0.86 % (wt.), plasticity and fracture toughness are higher as compared to those for the other alloys that are used in the manufacture of railway wheels. A quasi-chemical method was used to determine the solubility of carbon, silicon, and manganese in the δ-and αiron of Fe-Mn-Si-C alloys. The structure of ferrite has a volume-centered lattice and belongs to the spatial group 9 h O -Im3m with 8 atoms in the first coordination sphere [12]. Each atom of the BCC lattice has six tetrahedral and three octahedral pores. Of the six atoms surrounding the octahedral pore, two are closest to the others [14]. The arrangement of carbon atoms in the BCC lattice can be described as follows: the arrangement of carbon atoms in the octahedral pore, which have four nearest metal atoms at a distance of 2.02 Ǻ, and two at a distance of 1,43 Ǻ, each metal atom has 8 neighbors, which are located on distances of 2,48 Ǻ from each other.
To obtain the calculated results of the solubility limit of carbon atoms in the ferrite lattice, a quasi-chemical method was used, taking in ti account data on the position of carbon in a solid solution of α-iron [13].
The interaction of Fe-Fe, Fe-C, Fe-Si, Fe-Mn and Fe-V atoms, where V is a vacancy can become side red as follows: the interaction energies of atomic pairs νFeFe, ν FeSi , ν FeV, ν FeC, ν FeMn and ν MnC . The results presented in [14][15] were used for numerical values of the interaction energy of pairs of atoms.
The free energy of ferrite can be determined by the formula: F = E -kTlnW, where E is the internal energy of ferrite, W is the thermodynamic probability of the placement of atom is the nodes of the crystal lattice of ferrite, k = 1,38·10 -23 J / K -Boltzmann constant, T -absolute temperature. Thus, the free energy of ferrite is determined as follows: To calculate the solubility of carbon in α-iron, wended it find the solution of the system of equations: The resulting system of equations (2) is transcendental. Usually the solution of such equations can be obtained graphically or numerically. But in the framework of this problem it is expedient to consider an asymptotic solution of the equations. For this we present the logarithm included in each of the equations of the system (1) in the form of Taylor series (this is acceptable in case of its convergence): To obtain an asymptotic estimate of system (2) solution it is sufficient to consider the first two terms of expansion in the logarithm expanding.
There sults of solving the system of equations showed that up to 0.09% (wt.) of carbon, manganese up to 3.5% (wt.), silicon -0.25% (wt.) can be dissolved in δ-iron. The obtained result regarding the carbon content in δ-iron is consistent with the results of [16][17].
Thus, the maximum solubility of carbon, manganese and silicon in α-iron alloys of the Fe-Mn-Si-C system have lower numerical values compared it the insolubility in the corresponding binary systems. The obtained results can be explained by the fact that there placement of iron atoms by manganese and silicon atoms in the α-iron lattice ads it the deformation of the lattice, which affects the solubility of carbon [14].