MODELLING THE DIFFUSION OF POINT DEFECTS USING MACHINE LEARNING

Work package:
Modelling crystalline systems using atomistic simulations based on density functional theory (DFT) is now widely used in solid-state physics. On the one hand, it allows us to understand and interpret experimental observations; on the other hand, it has proven predictive power. However, in most theoretical studies based on DFT, simulations are performed at 0K. The results of these simulations - such as formation energies, migration energies, and others - are then used pragmatically in thermodynamic or thermokinetic models to predict the behaviour of the crystalline system at elevated temperatures. The implicit effects of temperature are thus neglected. It is nevertheless possible to incorporate some of these effects, either by explicitly taking into account configurational, vibrational, and electronic entropic effects (using quantities also calculated at 0 K), or by adopting the so-called “quasi-harmonic” approximation, which allows for a first-order energy correction. In recent years, these approaches have proven capable, in a great many cases, of significantly improving our understanding of experimental observations (diffusion coefficients, segregation energies, etc.). However, in some cases, these approaches still do not allow us to correctly understand and predict the properties of crystalline systems at high temperatures. For example, the vacancy formation energies of many metallic materials calculated by DFT at 0 K are underestimated compared to the values measured near the melting point. Only approaches that account for anharmonic effects in crystal temperature allow us to determine the various physical quantities of interest. Various approaches have been proposed to explicitly account for these anharmonic effects - and thus temperature effects. They are based on DFT molecular dynamics simulations. Due to computational cost, their use is limited. At the same time, classical atomistic simulation approaches based on interatomic potentials obtained through machine learning (MLIP) have been developed. These classical simulations, which are less computationally expensive, use MLIPs optimised on DFT databases. They are therefore as accurate as the optimisation dataset and allow for atomistic simulations that are much faster than DFT. Temperature effects also become accessible. The objective of this work will be to use the MLACS code to generate these MLIPs from data derived from DFT calculations (VASP or QE). Specifically, this will involve determining the formation energy of point defects through thermodynamic integration, as well as evaluating the energy barriers associated with crystalline defects in titanium at high temperatures, for its hexagonal close-packed and face-centred cubic phases.