A fully ab initio based integrated approach to determining the volume and temperature dependent free-energy surface of non-magnetic crystalline solids up to the melting point was proposed. The approach was based upon density-functional theory calculations with a controlled numerical accuracy of better than 1meV/atom. It accounts for all relevant excitation mechanisms entering the free energy including electronic, quasiharmonic, anharmonic, and structural excitations such as vacancies. To achieve the desired accuracy of <1meV/atom for the anharmonic free-energy contribution without losing the ability to perform these calculations on standard present-day computer platforms, a numerically highly efficient technique was developed: a hierarchical scheme, called up-sampled thermodynamic integration using Langevin dynamics, was proposed which allows for a significant reduction in the number of computationally expensive ab initio configurations as compared to a standard molecular dynamics scheme. As for the vacancy contribution, concentration-dependent pressure effects had to be included to achieve the desired accuracy. Applying the integrated approach gave direct access to the free-energy surface F(V,T) for aluminum and derived quantities such as the thermal expansion coefficient or the isobaric heat capacity and allows a direct comparison with experiment. A detailed analysis permitted the tackling of the long-standing debate over which excitation mechanism (anharmonicity or vacancies) was predominant close to the melting point.

Ab initio Up to the Melting Point - Anharmonicity and Vacancies in Aluminum. B.Grabowski, L.Ismer, T.Hickel, J.Neugebauer: Physical Review B, 2009, 79[13], 134106