A thermodynamic analysis of the Fe-Nb-P ternary system has been carried out using the CALPHAD method. Among the three binary systems present in this ternary phase diagram, the phase equilibria in the Nb-P binary system, on which very few studies have been reported, were thermodynamically analysed. The thermodynamic properties of various phosphides and of a bcc solid solution obtained from first-principles calculations were utilized in this analysis to compensate for the lack of available experimental data. By applying these procedures, a highly plausible Nb-P binary phase diagram was established over the entire composition range. The thermodynamic descriptions of the Fe-Nb and Fe-P binary systems were taken from previous studies. The thermodynamic parameters of the Fe-Nb-P ternary system were evaluated based on experimental data for the phase boundaries and estimated thermodynamic properties of the ternary phosphides obtained using first-principles calculations. The calculated phase equilibria were in good agreement with the available experimental data. From the calculated results, we confirmed that the ternary phosphide, FeNbP, took part in equilibria with most of the binary phosphides.KEY WORDS: phase diagram; thermodynamic analysis; CALPHAD; first-principles calculations. 947© 2009 ISIJ appearing in the Nb-P binary system and the ternary phosphides was evaluated using the WIEN2k software package, 10) based on the Full Potential Linearized Augmented Plane Wave (FLAPW) method with a Generalized Gradient Approximation (GGA).11) We assumed Muffin radii of 2.0 au (0.106 nm) for Fe and Nb and 1.9 au (0.1005 nm) for P, and the plane wave basis set up to the cut-off energy of 20 Ry (270 eV) was utilized in our computations.2.1.2. Free Energy of the bcc Solid Solution in the Nb-P Binary System In addition to the formation energy of the various phosphides, the Gibbs energy of formation of the bcc solid solution (a) of the Nb-P binary system was evaluated using first-principles calculations. The procedure for obtaining the Gibbs free energy of formation is explained in this section.First, 36 types of bcc-based ordered superstructures, such as D0 3 , B2, and B32, were constructed by changing the stack of pure element planes along a given direction in the parent bcc structure lattice, [12][13][14] and the total energies of those structures were calculated using the WIEN2k software package.10) Then, the energy of formation of the bccbased ordered f phase, DE f form , was obtained from the total energy by subtracting the concentration-weighted averages from the total energy of the pure elements:.......... (1) where c i is the concentration of element i. The term E f total denotes the total energy of the f superstructure, whereas the terms E total bcc-Nb and E total bcc-P refer to the total energy of bcc Nb and hypothetical bcc P, respectively. The energy of formation, DE f form , can be also expressed as the sum of effective interaction energies for clusters, such as a point, nearest and second nearest neighbor pairs, a tri...
A thermodynamic analysis of the Fe-Mn-P ternary system has been carried out using the CALPHAD method. Among the three binary systems relevant to this ternary phase diagram, the thermodynamic parameters of the Mn-P binary system were evaluated in this study. The enthalpy of formation of the binary phosphides obtained from our first-principles calculations was utilized in the present analysis to compensate for the lack of available experimental data. The thermodynamic descriptions of the Fe-Mn and Fe-P binary systems were taken from previous studies. The phase equilibria in the Fe-Mn-P ternary system were analysed based on the experimental data on the phase boundaries. The calculated phase diagrams are in agreement with the experimental results.
A thermodynamic analysis of the Fe−M−P (M = Nb, Ti) ternary system has been performed by combining first-principles calculations with the CALPHAD approach. Because of the lack of experimental information available, thermodynamic properties of orthorhombic anti-PbCl2-type FeMP were evaluated using the Full Potential Linearized Augmented Plane Wave method, and the estimated values were introduced into a CALPHAD-type thermodynamic analysis. Applying this procedure, the phase diagrams of the Fe−M−P ternary phase diagrams whose contents are uncertain so far were calculated with a high degree of probability. Phase diagrams for high-purity ferritic stainless steels obtained following the same procedure are also presented.
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