Energetics and thermodynamics of α-iron from first-principles and machine-learning potentials

Iron is a material of fundamental importance in the industrial and economic processes of our society as it is the major constituent of steels. With advances in computational science, much progress has been made in the understanding of the microscopic mechanisms that determine the macroscopic properties of such material at ordinary or extreme conditions. Ab initio quantum mechanical calculations based on density-functional theory (DFT), in particular, proved to be a unique tool for this purpose. Nevertheless, in order to study large enough systems up to length- and time-scales comparable with those accessible in experiments, interatomic potentials are needed. These are typically based on functional forms driven by physical intuition and fitted on experimental data at zero/low temperature and/or on available first-principles data. Despite their vast success, however, their low flexibility limits their systematic improvement upon database extension. Moreover, their accuracy at intermediate and high temperature remains questionable. In this thesis, we first survey a selection of embedded atom method (EAM) potentials to understand their strengths and limitations in reproducing experimental thermodynamic, vibrational and elastic properties of bcc iron at finite temperature. Our calculations show that, on average, all the potentials rapidly deviate from experiments as temperature is increased. At the same time, they suggest that, despite an anomalous rapid softening of its $C_{44}$ shear constant, the Mendelev03 parameterization is the most accurate among those considered in this work. As a second step, we compute the same finite-temperature properties from DFT. We verify our plane-wave spin-polarized pseudopotential implementation against selected zero temperature all-electron calculations, thus highlighting the difficulties of the semi-local generalized gradient approximation exchange and correlation functional in describing the electronic properties of iron. On the other hand, we demonstrate that after accounting for the vibrational degrees of freedom, DFT provides a good description of the thermal behavior of thermodynamic and elastic properties of $\alpha$-iron up to a good fraction of the Curie temperature without the explicit inclusion of magnetic transverse degrees of freedom. Electronic entropy effects are also analyzed and shown to be of secondary importance. Finally, we attempt at generating a set of highly flexible Gaussian approximation potentials (GAP) for bcc iron that retain ab initio accuracy both at zero and finite temperature. To this end, we use a non-linear, non-parametric Gaussian-process regression, and construct a training database of total energies, stresses and forces taken from first-principles molecular dynamics simulations. We cover approximately $10^5$ local atomic environments including pristine and defected bulk systems, and surfaces with different crystallographic orientations. We then validate the different GAP models against DFT data not directly included in the dataset, focusing on the prediction of thermodynamic, vibrational, and elastic properties and of the energetics of bulk defects.