### Development of a dynamic Monte Carlo code for atomic diffusion calculations

Diffusion processes in solids are relevant for the kinetics of many microstructural changes that occur during preparation, processing, and heat treatment of materials. Typical examples are nucleation of new phases, diffusive phase transformations, precipitation of a second phase, recrystallisation, high-temperature creep, and thermal oxidation. To reach a deep understanding of diffusion in solids, one needs information on the position of atoms and how they move in solids. The atomic mechanisms of diffusion in crystalline solids are closely connected with defects. Point defects such as vacancies or interstitials are the simplest defects and often mediate diffusion in crystals. Ab initio methods as DFT (Density Functional Theory) can provide fundamental information, such as the stable positions of atoms in a crystal lattice and their jumping rates between two neighour sites. However, it is not trivial to obtain diffusion coefficients from these fundamental properties because, in complex solid crystals, there are usually various point defects (vacancy and interstitial positions) and hence several diffusion paths are possible for the diffusing atom. Analytical solutions of multi-state diffusion problems are generally complex. A good alternative is to resource to Kinetic Monte Carlo (KMC), which is a particular Monte Carlo method used for processes with known rates such as atom migration. It consists of mapping N possible events that can occur from a given state. Each event is defined by jump frequency, displacement and cumulative function of the jump frequency: all these input quantites can be obtained from the DFT calculations.

The main aim of this project is to develop a Kinetic Monte Carlo code for studying diffusion of atoms in crystals. The code will receive as input data the results of DFT calculations, which will be performed with the VASP code. The first applications will address the diffusion of interstitial atoms (B, O, N, C) in Ti-Al alloys. The code will be validated by comparison with the analytical solution of the simplest crystal lattices (as the tetragonal TiAl) and then it will be applied for the study of diffusion in more complex geometries (as the hexagonal Ti3Al).