The properties of materials, and thus their functionality, are determined by their structure: the crystal structure and defects such as dislocations at the atomistic scale, the grain/particle structure and arrangement of phases at the nano- to micrometric scale, and the eventual presence of surfaces. The structure, in turn, is essentially shaped during processing by self-organization and patterning processes that take place on a large range of length and time scales. A thorough understanding of these processes is therefore needed for a knowledge-based materials design.

Most of the current computational methods focus on specific scales ranging from particle based atomistic to continuum hydrodynamic levels. Such approaches usually encounter a common problem: how to bridge the complex material details with the much larger length and time scales of experimental relevance. A specific example would be the plastic deformations during the alloys processing. The understanding of such deformations requires detailed information of the microstructure resulting from instability occurring at the atomic scale during the solidification and the evolution of complex defects over a diffusive time scale.

Over the last two decades, the phase-field method has helped to achieve major breakthroughs in materials modeling at the mesoscopic scale. Its principle is to encode the geometry of grains, domains of phases, and surfaces in continuum fields that indicate the presence of a particular phase (‘phase fields’). The evolution equations are obtained from out-of-equilibrium thermodynamics and are coupled to relevant transport equations. More recently, the phase-field crystal model has been developed. In contrast to the classic phase-field models, in which atomistic details are averaged out, the structure of matter is represented by a local density field, so that the position of individual atoms as well as defects such as dislocations can be resolved. At the same time, diffusive time-scales are accessible, in contrast to molecular dynamics methods.

The main purposes of this reseach project is to apply the Phase Field method to:

• Connection between atomistic methods/experiments and the phase field approach.

A straight connection has been established between atomistic simulations (Molecular dynamics) and classical phase field approach via the Phase Field  Crystal method. Foundations of this approach in the term of dynamical classical functional theory was partly performed but open question as the calculation of the thermal noise form first principle or the clear definition of the average length scale associated with the coarse graining procedure extensively used in the PF need to be discussed. On the other hand, this continuum approximation remains mostly phenomenological and explicit connection with experimental methods assessing this approach need to be achieved.

• Application of these methods to discuss far from equilibrium materials

Many materials of interest are either manufactured or used in out of equilibrium conditions. At thermodynamic equilibrium, the notion of free energy or more generally of thermodynamic potentials is clearly demonstrated. Fart from equilibrium, no such potential exists and dynamical systems cannot be reduced to relaxation gradient flow and even in this case, a Lyapounov functional cannot always be computed. Extension of the PF methods to model these problem is still an open question.