Thermodynamic Analysis of the Fe-Al-C Ternary System by Incorporating ab initio Energetic Calculations into the CALPHAD Approach

Abstract

A thermodynamic analysis of the Fe-C-Al ternary system has been carried out covering a wide range of temperatures and composition. Special care was taken to the expression of the free energy for the ternary Perovskite carbide phase, Fe 3 AlC (k), by considering the crystallographic similarity between the k phase and the L1 2 structure. The free energy was calculated using the (Fe,Al) 3 (Fe,Al) 1 (C,Va) 1 sublattice model, and the k and L1 2 structures were treated as a continuous solution. Because of the lack of experimental information available, the thermodynamic properties of the E2 1 structure were evaluated using the Full Potential Linearized Augmented Plane Wave (FLAPW) method.The ab initio energetic calculations show that the stable E2 1 structure of the k phase is highly preferred compared with the metastable Fe 3 Al-L1 2 structure. Contour plots of the charge density for the k phase indicate that the bonding between the Fe and C atoms forms in the Fe 3 AlC-E2 1 structure, and that this interaction between the atoms enhances the energetic stability of the k phase.According to our phase diagram calculations, the k phase is in equilibrium with the fcc Fe, B2-type intermetallic compound, as well as the graphite phase. This finding is in good agreement with previous experimental results.KEY WORDS: phase diagram; thermodynamic analysis; ab initio energetic calculations; ternary carbide. alloy from the formation of a coherent fine microstructure consisting of an fcc solid solution and the k phase is attracting great attention. 4) Regardless of such a promising potential for this new material, little information on the thermodynamic properties of this carbide phase is known. Thus, we have attempted to calculate the formation energy of Fe 3 AlC using a first principle band energetic calculation method. The objective of the present study was to introduce estimated values into a CALPHAD-type thermodynamic analysis, and to clarify the full phase equilibria of the Fe-Al-C ternary system. Computational ProceduresThe formation energy of the phase was calculated using the FLAPW method. A brief outline of the computational method and a description of the Gibbs free energy for each phase adopted in the thermodynamic analysis will be presented. Ab initio Energetic CalculationsThe FLAPW method, as embodied in the WIEN2k 5) software package, is one of the most accurate schemes for electronic calculations and allows for very precise calculations of the total energies in a solid, and was employed in our energetic calculations. The FLAPW method uses a scheme for solving many-electron problems based on the local spin density approximation (LSDA) technique. In this framework, a unit cell is divided into two regions: non-overlapping atomic spheres and an interstitial region. Inside the atomic spheres, the wave functions of the valence states are expanded using a linear combination of radial functions and spherical harmonics, while a plane wave expansion is used in the interstitial region. The LSDA technique includes an approximat...

Ab Initio calculations of phase stabilities in the Fe−Al−C system and CALPHAD-Type assessment of the iron-rich corner

“…The only published value to which this is comparable was calculated recently by Ohtani. [9] The authors used the FLAPW method in the GGA approximation with the WIEN2k package. They report À27.9 kJ/mol.…”

“…The perovskite k-Fe 3 AlC carbide, in particular, is hardly known. Partial information has been published: Palm and Inden have investigated experimentally specific Gibbs isotherms of the Fe-Al-C system, [8] and recently, Ohtani et al [9] published a Fe-Al-Ni-C phase diagram based on ab initio calculations.…”

A phase-field method coupled with CALPHAD for the simulation of ordered κ-carbide precipitates in both disordered γ and Rahnama1, Dashwood2, Sridhar3 2017Computational Materials Science18190View full textAdd to dashboardCite

“…Experimental studies on phase equilibria have been, thus, carried 45 out for the Fe-Al-C [33] and Fe-Mn-Al-C [34] systems. Furthermore, CALPHAD type thermodynamic calculations have been extensively performed in materials science to critically assess the phase relations under arbitrary thermodynamic conditions, for instance investigation of the Fe-Al-C system has been done by Ohtani et al [35] and Connetable et al [48] where the ordered κ-carbide in the Fe-Al-C ternary sys-50 tem was calculated by applying formalisms that allow intermixing between Fe and Al, and non-stoichiometry in the carbon content. However, a narrow range of Al content were calculated in both studies.…”

Forming of cast Fe – 45 at.% Al alloy with high content of carbon

“…The phase composition of this alloy as given in the phase diagram [7] (see Fig. 2) is iron aluminide FeAl plus aluminium carbide Al 4 C 3 , which was identified by X-ray diffraction.…”

“…These authors identified two-phase material α-FeAl + C (graphite). By contrast, Ohtani et al [7] found using CALPHAD a mixture of α-FeAl + Al 4 C 3 under the same conditions. Recently also the Fe 3 Al-type aluminides were used to be hardened by carbon (~ 4-5 at.…”