Title

AB INITIO DETERMINATION OF THERMODYNAMIC PROPERTIES OF METALS AND ALLOYS AND THEIR USE IN PHASE DIAGRAM CALCULATIONS

AB INITIO DETERMINATION OF THERMODYNAMIC PROPERTIES OF METALS AND ALLOYS AND THEIR USE IN PHASE DIAGRAM CALCULATIONS

Authorship

VŘEŠŤÁL, JAN; HOUSEROVÁ, JANA; ŠOB, MOJMÍR; FRIÁK, MARTIN

VŘEŠŤÁL, JAN

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HOUSEROVÁ, JANA

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ŠOB, MOJMÍR

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FRIÁK, MARTIN

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DOI

10.5151/2594-5327-2461

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Abstract

Calculation of phase diagram by CALPHAD method requires an expression for the Gibbs energy, with respect to standard element reference (SER) states, as a function of temperature, pressure and composition that has to be known for any phase. The problem with dynamic instability appears at non-zero temperatures. In this case, the Gibbs energies have to be regarded as some effective values, when they are used in calculations of phase equilibria at different temperatures. Total energy differences between various structures constitute a part of Gibbs energy differences and can be reliably calculated from first-principles. The full potential methods provide high-precision solutions of Kohn-Sham equations as well as total energies for a solid and the corresponding codes are easily available (e.g. WIEN, VASP, FHI, FLEUR, FPLO). The total energy differences between complex structures, such as sigma-phase, Laves phase etc., and SER states of elemental constituents, called also lattice stability differences, may complement existing values extracted more or less reliably for simple structures from the experimental data. Recently, phase diagrams of systems containing the sigma-phase, such as Fe-Cr and Co-Cr, have been reliably determined using ab initio total energy differences. The Fe-Mo phase diagram is presented in this work as a further example. The values of the enthalpy of formation of sigma-phase found on the basis of the phase equilibria calculations at higher temperature are compared with the energy of formation calculated by means of the LMTO-ASA and FLAPW methods.

Calculation of phase diagram by CALPHAD method requires an expression for the Gibbs energy, with respect to standard element reference (SER) states, as a function of temperature, pressure and composition that has to be known for any phase. The problem with dynamic instability appears at non-zero temperatures. In this case, the Gibbs energies have to be regarded as some effective values, when they are used in calculations of phase equilibria at different temperatures. Total energy differences between various structures constitute a part of Gibbs energy differences and can be reliably calculated from first-principles. The full potential methods provide high-precision solutions of Kohn-Sham equations as well as total energies for a solid and the corresponding codes are easily available (e.g. WIEN, VASP, FHI, FLEUR, FPLO). The total energy differences between complex structures, such as sigma-phase, Laves phase etc., and SER states of elemental constituents, called also lattice stability differences, may complement existing values extracted more or less reliably for simple structures from the experimental data. Recently, phase diagrams of systems containing the sigma-phase, such as Fe-Cr and Co-Cr, have been reliably determined using ab initio total energy differences. The Fe-Mo phase diagram is presented in this work as a further example. The values of the enthalpy of formation of sigma-phase found on the basis of the phase equilibria calculations at higher temperature are compared with the energy of formation calculated by means of the LMTO-ASA and FLAPW methods.

Keywords

ab initio calculations, phase diagram

ab initio calculations, phase diagram