Methods of minimizing free energies directly

• Published in: Journal of phase equilibria 1997-12, Vol.18 (6), p.544-545
• Main Authors: SUTTON, A. P, HAIRIE, A, HAIRIE, F, LEBOUVIER, B, NOUET, G, PAUMIER, E, RALANTOSON, N
• Format: Article
• Language: English
• Subjects: Applied sciences; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Heat capacities of solids; Metals. Metallurgy; Physics; Thermal properties of condensed matter; Thermal properties of crystalline solids; Thermodynamic properties
• ISSN: 1054-9714; 1544-1032
• DOI: 10.1007/BF02665808

Standard simulation techniques can be found in the literature to evaluate free energies of materials by thermodynamic integration. These technqieus, though straightforward, are demanding computationally as one has to evaluate an equilibrium internal energy at a succession of temperatures. However, if one is concerned with the free energy of a solid, or the excess free energy of a defect within the solid, at temperatures where atoms remain confined to potential wells, then a variety of simpler and much faster direct methods of minimizing free energies can be adopted. The direct methods are based on the quasi-harmonic approximation (QA) to the free energy. Here one recognizes that atoms vibrate about particular mean positions. Rather than working with fixed average atomic positions, which do not vary with temperature, one regards these mean positions as variational parameters with which the free energy of the system can be minimized. In this way, the QA captures some of the anharmonicity in the exact free energy that is altogether absent in the harmonic approximation. It has been shown that the QA is a remarkably successful technique for evaluating structures and excess free energies of defects in crystalline solids at elevated temperatures.