The binary phase diagrams of the YCl3–ACl (A=Li, Na, K, Rb, Cs) systems were studied using the CALPHAD technique and nonlinear mathematical method. The new modified quasi-chemical model in the pair-approximation for short-range ordering was applied to describe the Gibbs energies of the liquid phase in these systems. And the paper created the Artificial Neural Networks (ANN) model to study the interaction coefficients of two ending compounds composing the binary systems which are important for thermodynamic study of multi-elements system. Based on measured phase equilibrium data, a set of thermodynamic functions has been optimized and calculated. The effects of ionic radius, electronegativity and mole fraction of YCl3 on interaction coefficients were investigated in more detail. Highlights ▸ The binary phase diagrams of the YCl3–ACl (A=Li, Na, K, Rb, Cs) systems were studied using the CALPHAD technique. ▸ The new modified quasi-chemical model in the pair-approximation for short-range ordering was applied to describe the Gibbs energies of the liquid phase in these systems. ▸ The paper created, for the first time, the way of using Artificial Neural Networks—a powerful nonlinear science tool to study the interaction coefficients of two ending compounds composing the binary systems which are important for thermodynamic study of multi-elements system. ▸ Based on measured phase equilibrium data, a set of thermodynamic functions has been optimized and calculated. ▸ The effects of ionic radius, electronegativity and mole fraction of YCl3 on interaction coefficients were investigated in detail and some laws were described.

The standard magnetic model in the current CALPHAD modeling is based on the Inden–Hillert–Jarl model and an empirical constraint due to Weiss and Tauer that can be used to connect ferromagnetism and antiferromagnetism. In this work, we demonstrate that many artifacts can be produced by using the current approach when modeling systems with elements of different forms of magnetism. We then propose several simple measures to improve the standard magnetic model so that a physically and numerically correct and more accurate description for the Gibbs energy of magnetic ordering can be obtained in normal situations. Especially, we have assumed that each magnetic phase always possesses both ferromagnetic and antiferromagnetic states, with one of them stable and the other non-stable. The concept of ‘effective magnetic moment’ has also been introduced as a measure of the maximum magnetic entropy. A case study on the Al–Cr–Fe system has been performed at 0 K showing the importance of reasonable description of the magnetic phase diagrams. It has been stressed that the extended magnetic model in this work can be further employed for bridging atomistic and phenomenological modeling for multi-scale simulation. Graphical abstract Download : Download full-size image Highlights ▸ The standard magnetic model in the state-of-the-art CALPHAD approach is improved. ▸ The concept of effective magnetic moment is introduced as a measure of maximum magnetic entropy. ▸ The low temperature CALPHAD method calls for meticulous investigation of magnetic phase diagrams. ▸ A case study on the Al–Cr–Fe system demonstrates the importance of magnetic phase diagrams.

First-principles calculations are performed in order to calculate the energies of formation of different point defects in the ordered B2 phase of the Ti–Al system. The dominant point defects in the sublattice of the B2-TiAl structure are determined to be either substitutional vacancies or anti-site defects. Based on the results of first-principles calculations, substitutional vacancies are considered in the sublattice for the CALPHAD assessment ( Al , Ti , Va ) 0.5 : ( Al , Ti , Va ) 0.5 . A self-consistent set of thermodynamic parameters is obtained. Phase equilibria in the Ti–Al binary system are reproduced using these thermodynamic parameters. Highlights ▸ We have studied the formation of point defects in the ordered B2 phase in the Ti–Al system. ▸ Enthalpy of formation of vacancies and anti-site atoms was calculated using DFT. ▸ Concentrations of point defects at finite temperatures were calculated using first-principles. ▸ The Gibbs energy model of the B2 and A2 phases was revised to include vacancies. ▸ Ti anti-sites in the Al sublattice and vacancies in the Ti sublattice are the dominant point defects.

The phase equilibria of the binary Gd–Zr system have been investigated by combining electrostatic levitation of the melt with in situ high energy synchrotron X-ray diffraction. The liquidus line was experimentally assessed between 1500 and 1800 K from the diffraction data. At T=1495±10 K the eutectic reaction L↔bcc-Gd+bcc-Zr is evident. The eutectic composition x=18±2 at% Zr is determined from the in situ diffraction data and confirmed by the analysis of the microstructure of cast alloys. The so far unknown coexistence of bcc-Gd and bcc-Zr is observed for the temperature range 1450 K

DOI: https://doi.org/10.1016/j.calphad.2012.08.001 Cited: 0 Download: 0

The ground states and the solid state part of the phase diagram of V–Ta alloys are examined by combining the Density Functional Theory based total energy calculations with the cluster expansion and the Monte Carlo techniques. In agreement with experiments, our cluster expansion of V–Ta alloy, based on the bcc lattice, does not find any compound ground state. Cluster expansion of V–Ta, based on C15 Laves lattice, on the other hand, clearly establishes that V2Ta is the ground state composition. Phase equilibrium computed by Monte Carlo simulations, using these cluster expansion Hamiltonians, produces phase boundaries in good agreement with CALPHAD and experimental literature.

A complete thermodynamic description of the Bi–Mg–Sn ternary system was obtained by means of the CALPHAD (CALculation of PHAse Diagram) technique. The solution phases, Rhomb, Bct_A5 and Hcp_A3, are modeled with Redlich–Kister equation. The associate model has been used to describe the liquid phase with the constituents of the species Bi, Bi2Mg3, Mg, Mg2Sn and Sn. The non-stoichiometric compounds Mg2Sn and α-Bi2Mg3 as well as its high temperature variant β-Bi2Mg3 were described by the sublattice models (Bi,Mg)2(Bi,Sn)1, (Bi,Sn,Va)2Mg3 and (Bi,Sn)1(Bi,Sn,Va)3Mg6, respectively. The Bi–Mg–Sn ternary system has been modeled thermodynamically for the first time and the calculated phase equilibrium relations and thermochemical properties are consistent with the experimental results available in literatures.

The thermodynamic properties of lead have been evaluated up to 2400 K. By discarding discrepant specific heat measurements included in previous reviews it has been possible to determine the specific heat curve of the solid phase to an accuracy exceeding 0.1% above 210 K. Selected values include an enthalpy of sublimation of 195.2±0.4 kJ/mol for the monatomic gas phase at 298.15 K, a dissociation enthalpy D0 of 82.1±1.0 kJ/mol for the diatomic gas species at absolute zero and a derived equilibrium boiling point of 2020 K at one atmosphere pressure.

In the present work, an attempt to provide thermodynamic descriptions for the Cr–Nb–C and Mn–Nb–C systems was made. Various descriptions for most of the binary systems had been already available, so a selection between parameters sets was made. An additional partial reassessment was needed for the Cr–C system for the better correspondence with recent experimental data for the liquidus. To describe solubility of Nb in manganese and chromium carbides enthalpies of formation for hypothetical end members were calculated using ab initio methods. The thermodynamic descriptions of ternary systems were extrapolated from corresponding binary systems and optimized taking into account existing experimental data for the ternary systems. Highlights ▸ Enthalpies of formation for hypothetical Nb carbides were studied by ab intio methods. ▸ Parameters for the liquid phase in the Cr–C binary system were reoptimized. ▸ Assessments for Cr–Nb–C and Mn–Nb–C systems were made for the first time.

In the present work the thermodynamic parameters of the Fe–Mn–Nb–C system are assessed with CALPHAD technique using computerized optimization procedure (PARROT). Descriptions for most of the binary and ternary systems are already available so a selection between sets of parameters was made. An additional reassessment was needed for the Fe–Nb system for the better description of experimental data on the solubility of NbC in fcc Fe in the Fe–Nb–C system. The description of the Fe–Mn–Nb–C system was made as an extrapolation from ternary systems. The obtained set of parameters was tested against existing experimental data on NbC solubilities. Highlights ▸ The Fe–Nb system was reassessed. ▸ The Fe–Mn–Nb–C system was assessed. ▸ The solubility of NbC in austenite was calculated and compared with experimental data.