Multi-scale modelling of point defects in body-centered cubic metals

The modelling of metals under extreme conditions requires a multi-scale approach. Indeed, for reasons of numerical complexity, it is not possible to use a unique formalism, accurate and transferable for all scales of simulation. In general, one or more methods have to be used for a given spatial and temporal scale. These methods are based on approximations - physical and/or numerical - which are more and more numerous when the simulated space and time scales increase. Multi-scale modelling can therefore be summarised as a - utopian - balance between simulated 'space-time' scales and representativeness of phenomena involved in the transformations of the system studied. Multi-scale methods applied to materials science must also take into account the effects of finite temperatures in order to simulate structures in their nominal conditions of industrial use. In recent years, temperature effects have been treated in the context of local approximations: harmonic and/or quasi-harmonic. Taking into account anharmonic effects remains difficult - but necessary to be representative of physical phenomena - and is a main research topic for the improvement of multi-scale models. The objectives of this thesis are (i) to develop new simulation tools to extend the applicability of multi-scale methods (ii) and to estimate finite temperature quantities. We rely on a set of methods, in full expansion in the field of materials science: Machine Learning. These methods allow to develop systematic statistical tools and to study correlations more easily. In a first step, we develop methods for fast estimation of quantities derived from the harmonic vibrational properties: the defect formation entropy and the attack frequencies. The formalism developed is accurate, transferable and allows to greatly reduce the numerical cost (traditionally evolving as O(N³) where N is the number of particles in the system) whose numerical complexity evolves as O(N). In a second step, we are interested in quantifying the influence of anharmonic effects for metallic systems. We develop a direct computational approach (coupling Machine Learning and free energy methods) to calculate the self-diffusion coefficient, with an accuracy of ab initio, in body-centered cubic metals. We directly confront our results with the experiment and we give a - general - explanation, for the cubic centered metals, of the anomalous behavior of the self-diffusion coefficient at high temperatures. (author)