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Temperature-driven phase transitions from first principles including all relevant excitations: the fcc-to-bcc transition in Ca
The temperature-driven fcc-to-bcc phase transition in calcium is examined by a fully ab initio-based integrated technique including all relevant finite-temperature excitation mechanisms. The approach is based on density-functional-theory calculations with a controlled numerical stability of below 0.5 meV/atom for the electronic, quasiharmonic, and structural excitations and better than 1 meV/atom for the explicitly anharmonic contribution. The latter is achieved by successfully utilizing the recently developed hierarchical upsampled thermodynamic integration using Langevin dynamics method. This approach gives direct access to a numerically highly precise volume- and temperature-dependent free-energy surface and derived properties. It enables us to assign the remaining deviations from experiment to inherent errors of the presently available exchange-correlation functionals. Performing the full analysis with both of the conventional functionals, local density approximation and generalized gradient approximation, we demonstrate that-when considered on an absolute scale-thermodynamic properties are dictated by a strikingly similar free energy vs volume curve. Further, we show that, despite an error in the T = 0 K energy difference between the two phases (approximate to 6 meV in the present case), an excellent agreement of the temperature dependence of the Gibbs energy difference with experimentally derived data is feasible. This makes it possible, for instance, to unveil unreliable and possibly erroneous experimental input used in popular thermodynamic databases as we explicitly demonstrate for the isobaric heat capacity of calcium.