FWF - Kontinuumsmod. der Keimb. - From atomistic to continuums modelling of nucleation

The goal of the project is in pursuing a combined theoretical and experimental effort for the understanding of the nucleation process of small precipitates for materials of technological interest. Continuum theory is very successful in modelling materials properties for complex multi-component materials with a large number of particles. A corresponding numerical model has been developed recently. However, continuum mechanical approaches reach their limitation when the size of particles becomes smaller than about 10nm, since precipitates of this size contain only a small number of atoms and continuum mechanics is inappropriate in this case. For small precipitate dimensions, clearly an atomistic description is needed which on one side is able to provide accurate results for bonding energies and related quantities, purely based on the basic laws of quantum physics without the need of any empirical parameters. Within the framework of density functional theory such calculations can be done with high quality for ordered compounds with up to 100 atoms in a unit cell. On the other hand, a procedure must be designed to go far beyond the limitations of such rather small number of atoms but still maintaining the quantum accuracy. This can be achieved with the cluster expansion method, by which a lattice is decomposed into small basic building elements bound together by interaction energies, which can be found from fitting the cluster expansion to a suitably selected set of density functional calculations. Such a strategy proved very fruitful for binary compounds even allowing to derive shape and sizes of precipitates by making use of Monte Carlo techniques. In our project, studying Cu precipitates and Al-Ni precipitates in Fe, the cluster expansion and MonteCarlo techniques have to be extended to ternary systems. This is a very challenging part of the project but we believe that due to the strong national and international cooperation with leading experts we will succeed. The results of the atomistic modelling and the results from a comprehensive experimental program (EF-TEM, HRTEM, APFIM, SANS) will be used to develop a model, which bridges the continuum mechanical world to the world of single atoms. The accompanying experiments on well-defined samples of the above mentioned materials will provide a reliable basis on which the theoretical results can be tested. This combination -from Schrödinger's equation via continuum modelling to applied materials science is a unique effort in Austria and will hopefully stimulate more and stronger links between basic research and technology.