Crystalline, electronic, and magnetic structures of θ-Fe3C, χ-Fe5C2, and η-Fe2C from first principle calculation

Abstract

First principle calculations have been performed to study the crystalline, electronic, and magnetic structures of three iron-carbide systems: θ-Fe3C, χ-Fe5C2, and η-Fe2C. The Kohn-Sham equations were solved by applying the full-potential linearized augmented plane wave method. The generalized gradient approximation in the Perdew-Wang formalism was used to the exchange and correlation energy functional. The internal positions of atoms within the unit cell were optimized and the ground state properties such as lattice parameter and bulk modulus were calculated. The results are compared with experimental data when available. Comparison of the two metastable systems χ-Fe5C2 and η-Fe2C shows that the last one has lower formation energy; this is corroborated by the formation sequence observed during tempering. The electronic structures of the three carbides were then studied and the magnetic moments calculated by means of electronic spin-resolved density of state calculations at their equilibrium lattice constants and optimized internal parameters.

A first-principles study of cementite (Fe3C) and its alloyed counterparts: Elastic constants, elastic anisotropies, and isotropic elastic moduli

“…24,[62][63][64][65][66] Furthermore, our calculated lattice parameters of Fe3C agree to within ±1% of FP-LAPW values. 36,40 As discussed in a recent publication, 49 we have observed a good agreement between calculated and measured (when available) Wyckoff positions: agreement to within two significant figures is obtained for all non-symmetry-constrained Wyckoff positions between our calculations and reported experimental data.…”

“…49 Experimentally, the EOS parameters have been determined only for Fe 3 C using diamond-and-anvil apparatus 26,5,[59][60][61] and computationally using 36,39 employing FP-LAPW and CASTEP codes. In general, our B o is higher than experimental values that could be due to the fact that experiments were conducted at room temperature or higher.…”

“…7,[32][33][34][35][36][37][38][39][40][41][42] To the best of our knowledge, all first-principles calculations have been carried out only for Fe 3 C, and a very few attempts have been made to predict its stability and understand mechanical properties of multi-component cementite. Only recently, Jang et al 40 reported the effect of Si on the stability of Fe 3 C. The crystal structure of cementite, Fe 3 C, is well established.…”

First-Principles Calculations on Stabilization of Iron Carbides (Fe3C, Fe5C2, and η-Fe2C) in Steels by Common Alloying Elements

“…[6] Above 720 K (450°C), it has been observed that Fe 3 C forms exclusively. [1,2] Roughly, the carbides seem to precipitate in the order g-Fe 2 C; Fe 5 C 2 ; and Fe 3 C with increasing temperature [6,7] with the appearance of -Fe 2 C preceding g-Fe 2 C: Both kinetic and thermodynamic factors could be responsible for this observation. But the predominance of each of the carbide in a definite temperature range has been attributed to the lowering of its free energy (and hence stabilization) with temperature.…”

Control of iron nitride formation by a high magnetic field

“…[16][17][18] The temperature variations of magnetization of iron, Fe 4 N, and Fe 3 N can be calculated by the Weiss molecular field model. [19][20][21] The result shows that the magnetization of iron (M Fe ) is about 11.49 JT From Eq. (9), one may find that the critical nitrogen potential to form the Fe x N phase under a high magnetic field is higher than that in conventional nitriding and its value enhances with an increase in magnetic field intensity (H 0 ).…”