Thermodynamic analysis of the Fe–Ti–P ternary system by incorporating first-principles calculations into the CALPHAD approach

Ohtani, Hiroshi; Hanaya, N.; Hasebe, Mitsuhiro; Teraoka, Shin ichi; Abe, Masayuki

doi:10.1016/j.calphad.2005.09.006

Cited by 51 publications

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“…The calculated formation energies for these structures, including the hypothetical anti-PbCl 2 -type NbP 2 with the space group Pnma, correspond to the thermodynamic parameters required for formulating the Gibbs energy of the FeNbP phase, and the values are listed in Table 1. Figure 2 shows the total DOS of the anti-PbCl 2 -type Fe 2 P, 8) and the distribution of this DOS is similar to that of FeNbP shown in Fig. 1(a).…”

Section: The Electronic Structure and Phase Stability Ofmentioning

confidence: 62%

“…Each listed value is referred to as bcc Fe, bcc Nb, and black P. In the SGTE (Scientific Group Thermodata Europe) data file, 27) white P was adopted as the stable element reference for P, and thus black P is not the most stable state for P. However, in this study, the total energy of pure P was calculated using the crystallographic data of black P (space group Cmca) 26) because of the lack of information on the internal atomic positions for both white and red P, and we assumed that the phase stability of black P did not differ much from that of white P, following a previous study. 8) Thus, in our thermodynamic analysis, we regarded the calculated values listed in Table 1 as the formation enthalpy relative to bcc Fe, bcc Nb, and white P. Unfortunately, although there is no experimental information on the thermodynamic properties of Nb-P binary phosphides and ternary phosphides to be compared with the calculated values, the enthalpy of formation obtained from first-principles calculations seems to be reasonable after considering that agreement between calculated values and experimental results for the Fe-P binary phosphides was almost satisfactory.…”

Section: Calculation Of Enthalpy Of Formation Of Phosphidesmentioning

confidence: 99%

“…Unfortunately, because of the high volatility of P, the thermodynamic properties as well as phase equilibria in the Fe-M-P (where M indicates an alloying element) ternary system have been limited to the Ferich region, and there is not enough experimental information for the determination of reliable thermodynamic parameters of the systems concerned. To overcome the above difficulty, our group carried out thermodynamic analyses of the Fe-Ti-P 8) and Fe-Mn-P 9) ternary systems by incorporating thermodynamic properties of various phosphides obtained from first-principles calculations into the CALPHAD approach, and has clarified phase equilibria in these systems over the entire composition range.…”

Section: Introductionmentioning

confidence: 99%

“…The calculations also showed a significant hybridization between the 3d states of Fe and Nb and the 3p ϩ y y L In the orthorhombic anti-PbCl 2 -type structure of FeNbP with the space group Pnma, the Fe, Nb, and P atoms occupy three of the 4c internal positions of the Wyckoff-letter multiplicity. In our previous study, 8) we performed the electronic band energy calculations for the hypothetical antiPbCl 2 -type Fe 2 P (space group Pnma) by replacing the unlike atoms at the 4c sites by the same type of atoms. The calculated formation energies for these structures, including the hypothetical anti-PbCl 2 -type NbP 2 with the space group Pnma, correspond to the thermodynamic parameters required for formulating the Gibbs energy of the FeNbP phase, and the values are listed in Table 1.…”

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Thermodynamic Analysis of Phase Equilibria in the Fe–Nb–P Ternary System

et al. 2009

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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...

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Section: The Electronic Structure and Phase Stability Ofmentioning

confidence: 62%

Section: Calculation Of Enthalpy Of Formation Of Phosphidesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermodynamic Analysis of Phase Equilibria in the Fe–Nb–P Ternary System

et al. 2009

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“…FeTi is a thermodynamically stable [10][11][12] nonmagnetic [13] intermetallic compound with a bcc-based B2 structure and a melting point of approximately 1600 K. FeTi is of interest for its hydrogen absorption capabilities [14][15][16] and for its mechanical properties [17,18]. It has been the subject of a large number of experimental and theoretical studies including inelastic neutron scattering [19,20] and first-principles calculations [21][22][23].…”

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Thermally Driven Electronic Topological Transition in FeTi

et al. 2016

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Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M − 5 phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M − 5 phonon mode and an adiabatic electronphonon interaction with an unusual temperature dependence. DOI: 10.1103/PhysRevLett.117.076402 An electronic topological transition (ETT), first identified by Lifshitz [1], occurs when changes to a metal cause new features to appear in the topology of the Fermi surface [2]. Structural, mechanical, and electronic properties are usually altered by an ETT, which can be induced by alloying [3][4][5] or pressure [6][7][8]. Recently a novel temperature-induced ETT has been reported to alter magnetoresistivity [9]. In this Letter, we show through first-principles calculations and ancillary experiments how a thermally driven ETT drives anomalous changes in phonon dynamics.FeTi is a thermodynamically stable [10-12] nonmagnetic [13] intermetallic compound with a bcc-based B2 structure and a melting point of approximately 1600 K. FeTi is of interest for its hydrogen absorption capabilities [14][15][16] and for its mechanical properties [17,18]. It has been the subject of a large number of experimental and theoretical studies including inelastic neutron scattering [19,20] Forces and atomic configurations in the AIMD simulations were used to compute phonon energies at different temperatures with the temperature-dependent effective potential (TDEP) method [47,48], in which a model HamiltonianĤis used to sample the potential energy surface at the most probable atom positions, where p i and u i are the momentum and displacement of atom i, respectively, andΦ ij is a second-order force constant matrix. The force constants from Eq. (1) were used to obtain phonon dispersions and phonon DOS curves at temperatures from 300 to 1500 K (Fig. 1). Thermal expansion causes phonons to soften with temperature, and this was accounted for by the quasiharmonic calculations presented in the Supplemental Material [33]. The AIMD calculations were performed without thermal expansion, so Fig. 1 shows the thermal effects from pure anharmonicity and from the adiabatic EPI. These are significantly larger than the thermal softenings from quasiharmonicity reported in the Supplemental Material [33]. The nonadiabatic electron-phonon interaction (EPI) is well known from conventional superconductivity, where electrons are paired by phonons with wave vectors that span the Fermi surface [49,50]. With increasing temperature the PRL 117, 076402 (2016) P H Y S I C A L

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Representation Reaction Abilities of Structural Units and Related Thermodynamic Properties in Fe–P Binary Melts Based on the Atom–Molecule Coexistence Theory

Yang

et al. 2013

steel research int.

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A thermodynamic model for calculating the mass action concentrations of structural units in FeÀP binary melts based on the atomÀmolecule coexistence theory, i.e., AMCTÀN i model, has been developed and verified through comparing with the reported activities of both P and Fe in FeÀP binary melts with mole fraction x P of P <0.33 in a temperature from 1406 K to 1973 K. The calculated mass action concentration N P of P or N Fe of Fe has a very good 1:1 corresponding relationship with the reported activity a R,P of P or a R,Fe of Fe relative to pure liquid P(l) or Fe(l) as standard state, and can be applied to substitute the measured activity a R,P of P or a R,Fe of Fe in FeÀP binary melts. The Raoultian activity coefficient g 0 P of P and g 0 Fe of Fe in the infinitely dilute solution of FeÀP binary melts in a temperature from 1406 K to 1973 K have been determined from the calculated mass action concentrations N i of structural units in FeÀP binary melts. The activity a R,i , a %,i , and a H,i of P or Fe relative to three standard states have been obtained. The values of the first-order activity interaction coefficient e i i or e i i or h i i of P and Fe related with activity coefficients g i or f %,i or f H,i of P and Fe in FeÀP binary melts are also determined.

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Thermodynamic analysis of the Fe–Ti–P ternary system by incorporating first-principles calculations into the CALPHAD approach

Cited by 51 publications

References 12 publications

Thermodynamic Analysis of Phase Equilibria in the Fe–Nb–P Ternary System

Thermodynamic Analysis of Phase Equilibria in the Fe–Nb–P Ternary System

Thermally Driven Electronic Topological Transition in FeTi

Representation Reaction Abilities of Structural Units and Related Thermodynamic Properties in Fe–P Binary Melts Based on the Atom–Molecule Coexistence Theory

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