Energy of mixing and magnetic state of components of Fe-Mn alloys: A first-principles calculation for the ground state

Methods of first-principles computer simulation have been used to calculate the magnetic moments at the component atoms and the energies of mixing in substitutional fcc and bcc solid solutions of manganese in iron. It has been established that the energies of mixing in α and γ solid solutions have not only different magnitudes but even different signs. It is shown that in α solid solutions there is a thermodynamic anomaly at a manganese concentration of approximately 1.5 at. %, namely, a change in the concentration dependence of the energy of mixing caused by a reorientation of magnetic moments at manganese atoms. With increasing Mn content in dilute solutions, there occurs a continuous variation of the orientation of magnetic moments of manganese atoms from strictly antiparallel with respect to the ferromagnetic iron matrix to predominantly parallel one.     

Theoretical study of phase stability in Ni-Al and Ni-Ti alloys

The thermodynamic stability of the bcc and fcc based ordered phases in Ni-Ti and Ni-AI has been studied with a highly accurate first-principles electronic structure method. The occurrence of a martensitic transformation in Ni-AlB2 ordered intermetallic alloys is discussed with relation to the existence of intermediate structures between bcc and fcc based phases. It is shown that closely related ordered structures can exist on fcc and bcc lattices in the composition range where the transformation occurs. The Ni-rich side of the Ni-Al phase diagram has been computed, and a comparison with a recent assessment is made. In addition, the rather unusual appearance of the NiTi B2 ordered structure in the phase diagram is discussed. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October 21–23,1991, in Cincinnati, Ohio. This symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

Theoretical study of phase stability in Ni-Al and Ni-Ti alloys

The thermodynamic stability of the bcc and fcc based ordered phases in Ni-Ti and Ni-AI has been studied with a highly accurate first-principles electronic structure method. The occurrence of a martensitic transformation in Ni-AlB2 ordered intermetallic alloys is discussed with relation to the existence of intermediate structures between bcc and fcc based phases. It is shown that closely related ordered structures can exist on fcc and bcc lattices in the composition range where the transformation occurs. The Ni-rich side of the Ni-Al phase diagram has been computed, and a comparison with a recent assessment is made. In addition, the rather unusual appearance of the NiTi B2 ordered structure in the phase diagram is discussed. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October 21–23,1991, in Cincinnati, Ohio. This symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

Thermodynamic modeling of the Ba–Ni–Ti system

The binary Ba–Ni and Ba–Ti systems are modeled by computational thermodynamics using the CALculation of PHAse Diagram (CALPHAD) method, wherein the thermodynamic parameters of disordered bcc, fcc and hcp phases are evaluated in terms of the first-principles calculations using the special quasirandom structures (SQSs). In combination with the Ni–Ti system modeling in the literature, the phase equilibria of the Ba–Ni–Ti system are predicted. Isothermal section of the ternary system is presented.     

Thermodynamic Assessment of the Fe-Y System

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First-principles calculations of the structural and thermodynamic properties of bcc,fcc and hcp solid solutions in the Al–TM (TM = Ti,Zr and Hf) systems: A comparison of cluster expansion and supercell methods

The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al–TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (Δ_mE) calculated by CE and dilute supercells agree very well. In the concentrated region, the Δ_mE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of Δ_mE for hcp Al–Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al–TM-based alloys.     

Structural energies and phase stability in Ni-Cr alloys

The structural energy difference between stable bcc and metastable fcc structures of Cr are investigated via a detailed first-principles and phenomenological study of the thermodynamic properties of Ni-Cr alloys. Our work focuses on the large discrepancies between the first-principles calculations of structural energies and those obtained from phase diagram studies. For the Ni-Cr system, we find that the existing phase diagram and thermochemical data are insufficient to assess accurately the structural energies of Cr. Electronic structure calculations based on a tight-binding (TB) approximation for the alloy Hamiltonian are used, together with available thermochemical data, to obtain more reliable estimates of structural energies. This research was funded by the National Science Foundation under grant No. DMR 85-10594.     

Thermodynamic database of the phase diagrams in Cu-Fe base ternary systems

A thermodynamic database of the Cu-Fe-X [X: aluminum (Al), cobalt (Co), chromium (Cr), manganese (Mn), molybdenum (Mo), niobium (Nb), nickel (Ni), vanadium (V)] systems was developed by the CALPHAD (Calculation of Phase Diagrams) method, where the Gibbs energies of solution phases such as the liquid, face-centered-cubic (fcc), body-centered-cubic (bcc), and hexagonal-close-packed (hcp) phases are described by the subregular solution model, while the those of the bcc phase in the Cu-Fe-Al system and of all compounds are described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, much information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Cu-Fe base alloys.     

On the mechanism of nucleation of copper precipitates upon aging of Fe-Cu alloys

Structure of the Fe-5.5% Cu alloy has been studied after aging at 500°C to show that the lattice of copper precipitates changes with increasing time of holding at a temperature from bcc to 9R to fcc. The free energy of the solid solutions and the phase-separation diagrams of the bcc and fcc phases of copper have been calculated. Barriers for the nucleation of copper particles with the bcc and fcc lattices have been evaluated. Factors that favor the appearance of intermediate structural forms of copper, which precede the formation of the stable fcc phase, are discussed.     

Thermodynamic assessment of the Ho-Tb, Ho-Dy, Ho-Er, Er-Tb, and Er-Dy systems

The Ho-Dy, Ho-Tb, Ho-Er, Er-Dy, and Er-Tb phase diagrams are assessed and a thermodynamic database is now available for these systems. The calculated diagrams confirm the hypothesis that solutions of two rare-earth metals not more than two apart in atomic number can be approximated as ideal solutions, while if the difference is more than two, weak interaction parameters are needed. The bcc lattice stabilities for Ho and Er are estimated from intra-rare-earth phase diagram data and extrapolations from existing data for Gd, Dy, and Tb. An attempt to estimate the fcc lattice stability from high-pressure and temperature data was quite difficult but was done for Nd, Pr, and Gd. Moreover, estimates of lattice stabilities for the bcc and close-packed structure sequence of the rare-earth metals are available.     

A modified embedded-atom method interatomic potential for the Fe–H system

A modified embedded-atom method (MEAM) interatomic potential for the Fe–H binary system has been developed using previously developed MEAM potentials of Fe and H. The potential parameters were determined by fitting to experimental data on the dilute heat of solution of hydrogen in body-centered cubic (bcc) and face-centered cubic (fcc) Fe, the vacancy–hydrogen binding energy in bcc Fe, and to a first-principles calculation for the lattice parameter and bulk modulus of a hypothetical NaCl-type FeH. The potential accurately reproduces the known physical properties of hydrogen as an interstitial solute element in bcc and fcc Fe. The applicability of the potential to atomistic approaches for investigating interactions between hydrogen atoms and other defects such as vacancies, dislocations and grain boundaries, and also for investigating the effects of hydrogen on various deformation and mechanical behaviors of iron is demonstrated.     

Thermodynamic assessment of the Ho-Tb, Ho-Dy, Ho-Er, Er-Tb, and Er-Dy systems

The Ho-Dy, Ho-Tb, Ho-Er, Er-Dy, and Er-Tb phase diagrams are assessed and a thermodynamic database is now available for these systems. The calculated diagrams confirm the hypothesis that solutions of two rare-earth metals not more than two apart in atomic number can be approximated as ideal solutions, while if the difference is more than two, weak interaction parameters are needed. The bcc lattice stabilities for Ho and Er are estimated from intra-rare-earth phase diagram data and extrapolations from existing data for Gd, Dy, and Tb. An attempt to estimate the fcc lattice stability from high-pressure and temperature data was quite difficult but was done for Nd, Pr, and Gd. Moreover, estimates of lattice stabilities for the bcc and close-packed structure sequence of the rare-earth metals are available.     

Cu-Ni-Sn三元系相平衡的热力学计算

基于Cu-Ni-Sn三元系的相平衡和热力学的实验信息,采用亚正规溶体模型描述液相和fcc相的Gibbs自由能,为了预测该体系中bcc相的A2-B2有序-无序转变,bcc相的Gibbs自由能采用双亚点阵模型进行描述.利用CALPHAD(相图计算)方法评估了Cu-Ni-Sn三元系各相的热力学参数,计算的富Cu侧相图和热力学性质与实验数据比较一致.并对该三元系中bcc相的A2-B2有序-无序转变及fcc相的溶解度间隙进行了计算.这些计算结果对利用析出强化以及Spinodal分解开发高强度和高导电性的新型Cu基合金的组织设计具有一定的指导意义.     

Direct evidence of magnetically induced phase separation in the fcc phase and thermodynamic calculations of phase equilibria of the Co–Cr system

Two-phase equilibria between the ferromagnetic fcc and the paramagnetic fcc phase from 800 to 900 °C in the Co-rich region was determined using the diffusion couple technique. It was confirmed that a magnetically-induced miscibility gap of the fcc phase is formed along the Curie temperature.Thermodynamic calculation of the phase equilibria of the Co–Cr system was performed by optimizing the present results and the thermodynamic data in the literature. A set of thermodynamic values for describing the Gibbs energy of liquid, fcc hcp, bcc and sigma phases yielded good agreement between the calculated phase diagram and the experimental data. Moreover, the magnetically-induced miscibility gap between the ferromagnetic and paramagnetic hcp phases was also predicted. This kind of thermodynamic calculation of Co–Cr base alloys is quite useful for the alloy design of the magnetic recording media.     

First-principles study on the lattice stability of elemental Co,Rh,and Ir in the ⅧB group

Lattice constants, total energies, and densities of state of transition metals Co, Rh, and Ir in the VIIIB group with different crystalline structures were calculated via generalized gradient approximation (GGA) of the total energy plane wave pseudopotentiai method in first-principles. The lattice stabilities of Rh and Ir are △Gbcc-hcp △Gfcc-hcp 0, agreeing well with those of the projector augmented wave method in first-principles and the CALPHAD method in spite of elemental Co. Analyses of the electronic smlctures to lattice stability show that crystalline Rh and Ir with fcc structures have the obvious characteristic of a stable phase, agreeing with the results of total energy calculations. Analyses of atomic populations show that the transition rate of electrons from the s state to the p or d state for hop, fcc, and bcc crystals of Co and Rh increases with the elemental period number to form a stronger cohesion, a higher cohesive energy, or a more stable lattice between atoms in heavier metals.     

Thermodynamic assessment of the phase diagrams of the Cu-Sb and Sb-Zn systems

Thermodynamic assessments have been made for the Cu-Sb and Sb-Zn binary systems by means of the CALPHAD technique. The Gibbs energies of the liquid, bcc, and fcc phases are described by a substitution solution model and a Redlich-Kister formalism. All of the compounds were treated as stoichiometric compounds. Moreover, the liquidus temperatures of the Zn-rich portion in the Sb-Zn system were measured to check the unusual shape reported by previous work. It was confirmed that the liquidus line is not peculiar but smooth. A consistent set of the thermodynamic parameters was optimized to obtain a better fit between calculated results and experimental data including phase diagram and thermodynamic quantities.     

Thermodynamic assessment of the phase diagrams of the Cu-Sb and Sb-Zn systems

Thermodynamic assessments have been made for the Cu-Sb and Sb-Zn binary systems by means of the CALPHAD technique. The Gibbs energies of the liquid, bcc, and fcc phases are described by a substitution solution model and a Redlich-Kister formalism. All of the compounds were treated as stoichiometric compounds. Moreover, the liquidus temperatures of the Zn-rich portion in the Sb-Zn system were measured to check the unusual shape reported by previous work. It was confirmed that the liquidus line is not peculiar but smooth. A consistent set of the thermodynamic parameters was optimized to obtain a better fit between calculated results and experimental data including phase diagram and thermodynamic quantities.