A. A. Mirzoev

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.

Thermodynamic analysis of the formation of tetragonal bainite in steels

In the articles of Bkhadeshia, a new class of high-strength steels based on the structure of carbidefree bainite with an enhanced carbon content has been developed. According to Bkhadeshia, the main factor responsible for the high solubility of carbon is the occurrence of a tetragonality of the bainite lattice. To check this effect, in this article, the theory of tetragonality of martensite of iron alloys developed by Zener and Khachaturyan was applied to bainite under the assumption that the precipitation of carbides is prohibited. Equations for the chemical potentials of carbon and iron in austenite and in tetragonal ferrite have been derived. The equilibrium of these phases has been considered, and the calculations of the boundary concentrations of carbon and iron at different temperatures (300–1000 K) and at different parameters of the deformation interaction λ0 have been performed. The rigorous calculations confirmed Bkhadeshia’s hypothesis that the suppression of the carbide formation during the formation of bainite leads to an increase in the carbon solubility in the bcc phase.

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.

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 %.

Structure and Stability of Intermediate (Fe, Cr)7C3 Carbides

The paper presents a systematic approach to calculate the structure and stability of intermediate (Cr, Fe)7C3 carbides in hexagonal and orthorhombic phases within the framework of density functional theory. It was shown, that the formation energy of the system changes non-monotonically with chromium concentration; the fact is consistent with thermodynamics. It was found, that some intermetallic carbides in the system are more stable than binary counterparts.

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.

Hydrogen interaction with ferrite/cementite interface: ab initio calculations and thermodynamics

ABSTRACT The paper presents the results of ab initio modelling of the interaction of hydrogen atoms with ferrite/cementite interfaces in steels and thermodynamic assessment of the ability of interfaces to trap hydrogen atoms. Modelling was performed using the density functional theory with generalised gradient approximation (GGA’96), as implemented in WIEN2k package. An Isaichev-type orientation relationship between the two phases was accepted, with a habit plane (101)c ∥ (112)α. The supercell contained 64 atoms (56 Fe and 8 C). The calculated formation energies of ferrite/cementite interface were 0.594 J/m2. The calculated trapping energy at cementite interstitial was 0.18 eV, and at the ferrite/cementite interface – 0.30 eV. Considering calculated zero-point energy, the trapping energies at cementite interstitial and ferrite/cementite interface become 0.26 eV and 0.39 eV, respectively. The values are close to other researchers’ data. These results were used to construct a thermodynamic description of ferrite/cementite interface-hydrogen interaction. Absorption calculations using the obtained trapping energy values showed that even thin lamellar ferrite/cementite mixture with an interlamellar spacing smaller than 0.1 μm has noticeable hydrogen trapping ability at a temperature below 400 K.

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.

On the Theory of Tetragonality of Martensite Crystals Surrounded with Elastic Matrix

The paper is dedicated to the study of thermodynamic stability of tetragonal and cubic states of dilute Fe–C interstitial solid solutions. The combination of the thermodynamic theory and atomistic simulations results was used. This approach allowed us to analyze a widespread theory of carbon ordering in martensite crystal lattice enclosed in an elastic matrix developed by A.G. Khachaturyan. The key parameter of the theory is λ0, the strain interaction parameter. The value of λ0 calculated by A.G. Khachaturyan for a free martensite crystal (2.73 eV/atom ) yields the critical concentration of carbon ccrit=0,55 wt. % for room temperature. In fact, according to the experimental works this concentrations is close to 0.25 wt. %. A.G. Khachaturyan offered an improved theory of carbon ordering based on the assumption that decreasing the sizes of crystals along z axis will cause elastic resistance from surrounding crystals. The stresses arising when the martensite crystal is enclosed in an elastic matrix causes the appearance of a “tail” of order parameter at concentrations below the ccr for free crystal, which explained the discrepancy between Khachaturian’s theory and the experimental data. However our analysis shows the absence of this “tail” that means incorrect calculation of λ0 parameter. Over the last ten years the calculations of the strain interaction parameter λ0 have been made. The values of the parameter λ0 range from 5 to 10 eV/atom, in contrast to 2.73 eV/atom as defined by A.G. Khachaturyan. This fact has a great effect on the estimates of the critical carbon concentration at room temperature. This concentration becomes close to 0.2 wt. %, the value previously indicated by G.V. Kurdjumov. The reasons of abnormal tetragonality observed in the 0.2–0.6 wt. %C range are also considered.