Modeling of Thermodynamic Properties and Phase Equilibria for the Cu-Mg Binary System

Abstract

The phase equilibria associated with the binary Cu-Mg system are analyzed by applying results from firstprinciples calculations to a general solution thermodynamics treatment. Differing from previously reported models, we employ a four-species association model for the liquid, while the terminal and intermediate solid phases are modeled as substitutional solutions with one or two sublattices, respectively. The zero-Kelvin enthalpies of formation for the intermediate compounds, Cu 2 Mg-C15 (cF24) and CuMg 2 -C b (oF48) are computed using the Vienna Ab-initio Simulation Package (VASP). The Gibbs free energy functions for the individual phases are evaluated, and the resulting binary phase diagram is presented over the full composition range. While the phase diagram we propose exhibits only modest deviation from previously reported models of phase equilibria, our treatment provides better agreement with experimental reports of heat capacity and enthalpy of mixing, indicating a more self-consistent thermodynamic description of this binary system. The phase equilibria associated with the binary Cu-Mg system are analyzed by applying results from first-principles calculations to a general solution thermodynamics treatment. Differing from previously reported models, we employ a four-species association model for the liquid, while the terminal and intermediate solid phases are modeled as substitutional solutions with one or two sublattices, respectively. The zero-Kelvin enthalpies of formation for the intermediate compounds, Cu 2 Mg-C15 (cF24) and CuMg 2 -C b (oF48) are computed using the Vienna Ab-initio Simulation Package (VASP). The Gibbs free energy functions for the individual phases are evaluated, and the resulting binary phase diagram is presented over the full composition range. While the phase diagram we propose exhibits only modest deviation from previously reported models of phase equilibria, our treatment provides better agreement with experimental reports of heat capacity and enthalpy of mixing, indicating a more self-consistent thermodynamic description of this binary system. Keywords

Thermodynamic Treatment of Undercooled Cu-Mg Liquid and the Limits for Partitionless Crystallization

“…This is discussed in the remainder of the present section. The other relevant thermodynamic parameters are taken from our earlier work [3] as indicated in Table 3 and 4.…”

“…We adopt our previously reported approach [3] for the modeling of Gibbs free energies and associated phase equilibria for the Cu-Mg binary system, but we add a twostate treatment [31,32] of the undercooled elemental liquids. Thermodynamic functions for other pure element states are taken from the SGTE database, [30] as listed in Table 1.…”

“…To address the problem discussed earlier regarding the discontinuity in the heat capacity of the liquid phase, [3] we employ a two-state approach, [31,32] describing the liquid phase (L¢) as an ideal mixture of low-free energy ''solidlike'' particles and high-free energy ''liquid-like'' particles. Accordingly, for a single component, the molar Gibbs free energy of the mixture is written as…”

“…In a previous paper, [3] we modeled the thermodynamic properties and associated phase equilibria for the Cu-Mg binary system and compared the resulting phase diagram with the prior thermodynamic modeling reported by Coughanowr et al [4] and by Zou and Chang. [5] While those results are consistent with reported experimental data, we point out that the SGTE parameters [30] are not sufficient for describing the behavior of undercooled liquids.…”

“…2 for the Cu 14.4 Mg 85.5 composition. To address this problem here, we incorporate a two-state model [31,32] into our prior approach [3] to describe the thermodynamic properties of the undercooled liquids and to compute the relevant phase equilibria and limits for partitionless crystallization from the melt. We employ a CALPHAD [33,34] methodology, where the model parameters describing the Gibbs free energies associated with the formation of compounds or solution phases are determined through a systematic semi-empirical optimization, using available experimental data from calorimetry, x-ray diffraction, electron-probe microchemical analysis, and optical micrography.…”