Ab initio simulation of silicon influence on Fe$_3$C carbide formation in BCC-iron

Results of first-principles simulation of silicon influence of the energy of cementite formation and on partial enthalpy are presented in the article. Simulation was carried out in the frameworks of the Density Functional Theory (DFT) using the full-potential- linearized-augumented-plane-wave method (FP LAPW) taking into account the generalized gradient approximation (GGA’96) in WIEN2k software package. Various concentrations of silicon admixtures in cementite were studied, namely 1,6, 3,2 and 6 at. % for both the position of displacement of iron atom (positions S and G) and of carbon atom (position C). Volumetric optimization of all structures was carried out. Equilibrium parameters of the grid were determined both for cementite without admixtures (a = 4,510; b = 5,063; c = 6,747 Å), and for cementite with silicon, which excellently comply with experimental and theoretical data. Formation energy for concentration of 3,2 at. % in position C turned out to be $-$0,03 electron-volt, which can signify cementite’s stabilization. Though at that, partial enthalpy for all positions of silicon is positive which means that silicon remains in solid solution BCC-Fe, which is in a good compliance with results of other theoretical and experimental works. It was determined that the more is concentration of silicon, the lower is average magnetic moment on iron atoms. Moreover, it became possible to show that energy characteristics of the system significantly depend on the size of a super cell. This effect is connected with the use of periodic boundary conditions during calculations, and shows the presence of interactions between silicon atoms in neighboring super cells.