“…We have carried out phonon calculations for a number of systems including pure As [115] and B, [116] borides, [117] boron carbide, [112] ternary Al, [118] and Mg systems. [119] The predicted thermodynamic properties as a function of temperature compare well with experimental data when available.…”
Section: Thermodynamics At Finite Temperaturesmentioning
confidence: 99%
“…The decision made for the enthalpy of formation of Ca 2 Sn is also of the utmost importance for calculations in multicomponent Ca-Sn-Mg alloy systems, such as the extension of the Ca 2 Sn liquidus surface and other equilibria involving this dominating phase. [121] In the ternary Al-Ni-Y system, ten ternary compounds were investigated [118] using the quasi-harmonic approximation to obtain both enthalpy and entropy of formation. They are used in the prediction of the Al-rich region of the Al-CoNi-Y system, resulting in good agreement between phase fractions from the Scheil simulation when compared with experimentally determined data for three Al-rich quaternary alloys.…”
Section: Thermodynamics At Finite Temperaturesmentioning
Thermodynamics is the key component of materials science and engineering. The manifestation of thermodynamics is typically represented by phase diagrams, traditionally for binary and ternary systems. Consequently, the applications of thermodynamics have been rather limited in multicomponent engineering materials. Computational thermodynamics, based on the CALPHAD approach developed in the last few decades, has released the power of thermodynamics and enabled scientists and engineers to make phase stability calculations routinely for technologically important engineering materials. Within the similar time frame, first-principles quantum mechanics technique based on density functional theory has progressed significantly and demonstrated in many cases the accuracy of predicted thermodynamic properties comparable with experimental uncertainties. In this paper, the basics of the CALPHAD modeling and first-principles calculations are presented emphasizing current multiscale and multicomponent capability. Our research results on integrating first-principles calculations and the CALPHAD modeling are discussed with examples on enthalpy of formation at 0 K, thermodynamics at finite temperatures, enthalpy of mixing in binary and ternary substitutional solutions, defect structure and lattice preference, and structure of liquid, super-cooled liquid, and glass.
“…We have carried out phonon calculations for a number of systems including pure As [115] and B, [116] borides, [117] boron carbide, [112] ternary Al, [118] and Mg systems. [119] The predicted thermodynamic properties as a function of temperature compare well with experimental data when available.…”
Section: Thermodynamics At Finite Temperaturesmentioning
confidence: 99%
“…The decision made for the enthalpy of formation of Ca 2 Sn is also of the utmost importance for calculations in multicomponent Ca-Sn-Mg alloy systems, such as the extension of the Ca 2 Sn liquidus surface and other equilibria involving this dominating phase. [121] In the ternary Al-Ni-Y system, ten ternary compounds were investigated [118] using the quasi-harmonic approximation to obtain both enthalpy and entropy of formation. They are used in the prediction of the Al-rich region of the Al-CoNi-Y system, resulting in good agreement between phase fractions from the Scheil simulation when compared with experimentally determined data for three Al-rich quaternary alloys.…”
Section: Thermodynamics At Finite Temperaturesmentioning
Thermodynamics is the key component of materials science and engineering. The manifestation of thermodynamics is typically represented by phase diagrams, traditionally for binary and ternary systems. Consequently, the applications of thermodynamics have been rather limited in multicomponent engineering materials. Computational thermodynamics, based on the CALPHAD approach developed in the last few decades, has released the power of thermodynamics and enabled scientists and engineers to make phase stability calculations routinely for technologically important engineering materials. Within the similar time frame, first-principles quantum mechanics technique based on density functional theory has progressed significantly and demonstrated in many cases the accuracy of predicted thermodynamic properties comparable with experimental uncertainties. In this paper, the basics of the CALPHAD modeling and first-principles calculations are presented emphasizing current multiscale and multicomponent capability. Our research results on integrating first-principles calculations and the CALPHAD modeling are discussed with examples on enthalpy of formation at 0 K, thermodynamics at finite temperatures, enthalpy of mixing in binary and ternary substitutional solutions, defect structure and lattice preference, and structure of liquid, super-cooled liquid, and glass.
“…(11)-(13) [28,29]. (13) where n(ε) is the electronic DOS at each energy level ε, f is the Fermi distribution function, ε F is the energy at the Fermi level.…”
Section: Theorymentioning
confidence: 99%
“…With the quasiharmonic approach, the Gibbs free energy which is approximated by the Helmholtz free energy for condensed phases can be expressed [27][28][29] as,…”
Section: Theorymentioning
confidence: 99%
“…It should be noted that the Helmholtz free energy is a function of both volume and temperature. Within the harmonic approximation at fixed volume, the vibrational free energy of a structure F ph can be calculated from its phonon density of state (DOS) [28][29][30],…”
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