D. A. Mirzaev

Tetragonality and the distribution of carbon atoms in the Fe–C martensite: Molecular-dynamics simulation

In the statistical theory of the ordering of carbon atoms in the z sublattice of martensite, the most important role is played by the parameter of the strain interaction of carbon atoms λ0, which determines the critical temperature of the bcc–bct transition. The values of this parameter (6–11 eV/atom) obtained in recent years by the methods of computer simulation differ significantly from the value λ0 = 2.73 eV/atom obtained by A. G. Khachaturyan. In this article, we calculated the value of λ0 by two methods based on the molecular-dynamics simulation of the ordering of carbon atoms in the lattice of martensite at temperatures of 500, 750, 900, and 1000 K in a wide range of carbon concentrations, which includes ccrit. No tails of ordering below ccrit have been revealed. It has been shown analytically that there is an inaccuracy in the Khachaturyan theory of ordering for the crystal in an elastic environment. After eliminating this inaccuracy, no tails of the order parameter appear; the tetragonality changes jumpwise from η = 0 to ηcrit = 0.75 at ccrit = 2.9kT/λ0 instead of ηcrit = 0.5 and ccrit= 2.77kT/λ0 for an isolated crystal. Upon the simulation, clustering of carbon atoms was revealed in the form of platelike pileups along {102} planes separated by flat regions where no carbon atoms were present. The influence of short-range order in the arrangement of neighboring carbon atoms on the thermodynamics of ordering is discussed.

Role of stresses and temperature in the Z ordering of carbon atoms in the martensite lattice

A numerical solution is given to the equation of the statistical Zener theory of the predominant ordering of carbon atoms in the z sublattice of octahedral interstices of martensite in carbon steels depending on the stress and temperature. It has been found that the external compressive stress applied along the axis of martensite tetragonality decreases the order parameter and that there is a critical value of the stress above which the degree of tetragonality of the lattice falls off jumpwise to zero. Based on the numerical analysis, a discussion of the dependences of the degree of ordering of carbon atoms and the critical stress on the temperature and carbon concentration has been performed.

Features of Isothermal Formation of Carbide-Free Bainite in High-Carbon Manganese-Silicon Steel

Change in the stability of overcooled austenite of high-carbon manganese-silicon steel relative to decomposition via the intermediate stage upon isothermal holding and martensitic γ → α transformation upon subsequent cooling has been studied using dilatometry and X-ray diffraction. The kinetics of low-temperature bainite transformation has been studied. The tetragonality of the crystal lattice of bainite α-phase caused by the superequilibrium content of carbon was found.

The Formation of Carbide-Free Bainite in High-Carbon High-Silicon Steel under Isothermal Conditions

It is shown that a carbide-free bainite structure can be formed in high-carbon steel of the Fe–Si–Mn–Cr–V system using a traditional furnace facility. The structural aspects of bainitic transformation developing under isothermal conditions at 300°C have been studied by the methods of X-ray diffraction and transmission electron microscopy. Orientation relationships between crystalline lattices of γ and α phases have been established. A superequilibrium carbon concentration in the bainite α phase has been determined.

Origin of abnormal formation of pearlite in medium-carbon steel under nonequilibrium conditions of heating

The structure and kinetics of the formation of austenite in medium-carbon steel during shortterm heating above the temperature Ac1 followed by accelerated cooling are analyzed. It has been shown that the abnormal formation of pearlite in steel results from the concentrational and structural inhomogeneity of austenite, as well as the presence of carbide particles in ferrite areas.

Molecular-Dynamics Simulation of the Influence of Silicon on the Ordering of Carbon in the Martensite Lattice

The results of computer simulation of the influence of silicon impurities on the degree of tetragonality and on the interaction of carbon atoms in the body-centered cubic (BCC) lattice of iron by the molecular-dynamics method are reported. The influence of silicon on the martensite-lattice parameters has been established, as well as the dependence of the deformation interaction parameter λ0 determining the critical temperature of the BCC–BCT (body-centered tetragonal) transition on the silicon concentration, is calculated on the basis of the Zener–Khachaturyan theory of ordering. It is found that the λ0 parameter decreases by 18% from 5.2 to 4.2 eV/atom upon an increase in the silicon content up to 10 at %.

Interaction between Carbon Atoms and Carbon Activity in fcc Iron: Thermodynamic Theories and Computer Simulation

The literature data on the interactions between carbon atoms and the methods of calculating its activity in the γ-iron lattice have been analyzed. Both statistical thermodynamic results and the data obtained by methods of computer simulation have been considered. To compare the available results, the simulation of the carbon activity in austenite using the Monte Carlo method has been carried out. It has been shown that the experimental curve of the concentration dependence of the carbon activity can be reproduced using a large number of strongly differing energies of interactions between carbon atoms in the first two coordination shells. Thus, the problem of determining the parameters of the С–С interaction in fcc iron according to the data on the activity is mathematically ill posed and first-principles calculations are necessary. It has been shown that, at carbon concentrations of up to 7 at %, the approximate statistical theories lead to accurate results. An analysis of the results of an ab initio simulation showed that the inclusion of the interaction between carbon atoms in the third and fourth coordination shells hardly affect the carbon activity.

Ab initio Computer Simulation of Carbon–Carbon Interactions for Various Spacings in BCC and BCT Lattices of Ferrite and Martensite

The ab initio computer simulation of lattice parameters and local structure distortions caused by interstitial carbon atoms in the iron-carbon system has been carried out using WIEN2k software. For the calculations, the full-potential method of linearized augmented plane waves (LAPWs) taking into account the generalized gradient approximation of PBE–GGA was used in a supercell of 54 iron atoms with periodic boundary conditions. The carbon dissolution energy has been found to be 0.85 eV for bcc iron, and 0.79 eV for bct iron. The carbon–carbon interaction energies in the ferromagnetic bct iron have been calculated. It has been found that accounting for tetragonal distortions considerably changes the interaction energy of carbon atoms in comparison with that of the bcc iron. Both the maximum degree of tetragonality of iron and the maximum attraction of carbon atoms have been observed for the case of carbon atoms placed in octahedral pores of the same type. If carbon atoms are in different types of octahedral pores, the tetragonal distortion of the lattice is weak. The obtained results are in good agreement with the Zener–Khachaturyan hypothesis and experimental data of Kurdyumov.

Possibility of Abnormal Formation of Pearlite in Medium-Carbon Steel After Short-Term Heating to a Temperature Above Ac 1

The kinetics of phase recrystallization and formation of structure in medium-carbon steels under short-term heating at a temperature exceeding Ac1 and accelerated cooling is studied. The conditions of implementation of two mechanisms of abnormal formation of pearlite differing in the lengths of the diffusion paths of carbon are determined, and the morphology of the pearlite is described.

Interaction of Hydrogen Atoms with Vacancies and Divacancies in bcc Iron

The paper presents the results of both ab initio and thermodynamic analysis of vacancy and divacancy formation and hydrogen interaction with them in alpha (bcc) iron. Ab initio calculations were performed by DFT method using LAPW in WIEN2k package. Monovacancy formation energy was found to be 2.15 eV and divacancy binding energy 0.22 ± 0.01 eV. Equlibrium fraction of vacancies bound into divacancies is of the order of 10–5 even at the highest temperatures close to bcc → fcc transformation point. Hydrogen has a strong interaction with monovacancies (vacancy-hydrogen binding energy decreasing from 0.60 to 0.31 eV for the first–fifth H atom inside a single vacancy) but has only a small effect on divacancy formation energy that is equal to 0.28, 0.19 and 0.17 for the case of joining of VH + V, VH + VH and VH2 + VH2, respectively. This means that the presence of hydrogen cannot significantly increase the equilibrium concentration of divacancies.