Russian Physics Journal, Vol. 61, No. 2, June, 2018 (Russian Original No. 2, February, 2018)
COMPUTER SIMULATION OF ENERGY PARAMETERS AND
MAGNETIC EFFECTS IN Fe-Si-C TERNARY ALLOYS
Ya. M. Ridnyi, A. A. Mirzoev, D. A. Mirzaev UDC 6126.96.36.199:538.915
The paper presents ab initio simulation with the WIEN2k software package of the equilibrium structure and
properties of silicon and carbon atoms dissolved in iron with the body-centered cubic crystal system of the
lattice. Silicon and carbon atoms manifest a repulsive interaction in the first two nearest neighbors, in the
second neighbor the repulsion being stronger than in the first. In the third and next-nearest neighbors a very
weak repulsive interaction occurs and tends to zero with increasing distance between atoms. Silicon and
carbon dissolution reduces the magnetic moment of iron atoms.
Keywords: first-principle simulation, BCC iron, carbon impurity, silicon impurity, WIEN2k software package.
Iron-based alloys continue to be the main constructional materials despite the growth in production of plastic,
ceramics, and composites. This is because the relatively simple thermomechanical treatment can produce metastable
body-centered-cubic (BCC) or face-centered-cubic phases oversaturated with carbon (C) atoms. These phases possess
high strength and a range of other important physical properties including the electric and heat conduction, heat
resistance, magnetic permeability. These excellent properties are affected by a strong interaction of interstitial C atoms
with such alloying substitutional impurities as Al, Si, Ti, V, Cr, Mn, Co, Ni, Cu. However, an understanding of the
physical nature of this interaction is significantly below the developmental requirements for materials science. This is
largely due to the fact that the reciprocal influence of impurities is a problem of the atomic level which complicates its
macrographic examination. Therefore, this interaction is best investigated with ab initio atomistic simulation.
This work studies the interaction of C atoms with alloying impurities of silicon (Si) in BCC iron. In terms of
thermodynamics, the interaction between C and Si atoms is determined by the sign and the value of carbon activity
factor in Fe-Si-C ternary alloy, which is affected by silicon such that
is the carbon activity factor
obtained experimentally in Si-alloyed austenite or ferrite;
is the carbon activity factor for Fe–C binary alloy.
Mogutnov et al.  described the concentration dependence for the value of
ln 14.5f x
for α-phase solid
is the atomic fraction of silicon. In the simplest variant of statistical theory, the numerical factor of
is the averaged energy of Si and С atom pairs. Hence,
A positivity of
indicates that Si and C atoms repulse each other.
The way atoms interact with each other was also confirmed by Simonovic et al. , who used ab initio
calculations to measure the interaction energy of Si–C atom pairs positioned at subsequently increasing distances. It
turned out that Si and C atoms strongly repulse each other when the former locates in a zero lattice site, whereas the
National Research South Ural State University, Chelyabinsk, Russia, e-mail: firstname.lastname@example.org;
email@example.com; firstname.lastname@example.org. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2,
pp. 34–38, February, 2018. Original article submitted August 2, 2017; revision submitted November 20, 2017.
1064-8887/18/6102-0242 2018 Springer Science+Business Media, LLC