Concentration profile distortion under ion beam mixing: an example of Levy flight

Radiation-Induced Patterning at the Nanometric Scale: A Phase Field Approach

The phase field approach was developed in the last 20 years to handle radiation damage in materials. This approach bridges the gap between atomistic simulations extensively used to model first step of radiation damage at short time and continuum approach at large time. The main advantage of such an approach lies in its ability to compute not only the microstructure at the nanometric scale but also to calculate generalized susceptibilities such as elastic constants under irradiation. After a brief description of the rate theory, used to model the microstructure induced by irradiation, we briefly discuss the foundation of the phase field method, highlighting not only its advantages, but also its limitations in comparison with the rate theory. We conclude this presentation by proposing future orientations for computing the microstructure in irradiated materials.

Patterning in systems driven by nonlocal external forces

This work focuses on systems displaying domain patterns resulting from competing external and internal dynamics. To this end, we introduce a Lyapunov functional capable of describing the steady states of systems subject to external forces, by adding nonlocal terms to the Landau Ginzburg free energy of the system. Thereby, we extend the existing methodology treating long-range order interactions, to the case of external nonlocal forces. By studying the quadratic term of this Lyapunov functional, we compute the phase diagram in the temperature versus external field and we determine all possible modulated phases (domain patterns) as a function of the external forces and the temperature. Finally, we investigate patterning in chemical reactive mixtures and binary mixtures under irradiation, and we show that the last case opens the path toward micro-structural engineering of materials.

Statistical Nature of Atomic Disorder in Irradiated Crystals

Atomic disorder in irradiated materials is investigated by means of x-ray diffraction, using cubic SiC single crystals as a model material. It is shown that, besides the determination of depth-resolved strain and damage profiles, x-ray diffraction can be efficiently used to determine the probability density function (PDF) of the atomic displacements within the crystal. This task is achieved by analyzing the diffraction-order dependence of the damage profiles. We thereby demonstrate that atomic displacements undergo Lévy flights, with a displacement PDF exhibiting heavy tails [with a tail index in the γ=0.73-0.37 range, i.e., far from the commonly assumed Gaussian case (γ=2)]. It is further demonstrated that these heavy tails are crucial to account for the amorphization kinetics in SiC. From the retrieved displacement PDFs we introduce a dimensionless parameter f_{D}^{XRD} to quantify the disordering. f_{D}^{XRD} is found to be consistent with both independent measurements using ion channeling and with molecular dynamics calculations.

Disrupted coarsening in complex Cahn-Hilliard dynamics

Predicting the pattern formation in a system maintained far from equilibrium is a complex task. For a given dynamics governed by the evolution of a conservative order parameter, recent investigations have demonstrated that the knowledge of the long time expression of the order parameter is sufficient to predict the existence of disrupted coarsening, i.e., the pinning of the inhomogeneities wavelength to a well defined value. However, there exists some dynamics for which the asymptotic form of the order parameter remains unknown. The Cahn-Hilliard-like equation used to describe the stability of solids under irradiation belongs to this class of equations. In this paper, we present an alternative to predict the patterning induced by this equation. Based on a simple ansatz, we calculated the form factor and proved that a disrupted coarsening takes place in such dynamics. This disrupted coarsening results from the bifurcation of the implicit equation linking the characteristic length of the dynamics (k_{m}^{∞})^{-1} to a control parameter describing the irradiation. This analysis is supported by direct simulations. From this paper, it clearly appears that the bifurcation of k_{m}^{∞} is a criterion for disrupted coarsening.

Cascade fragmentation under ion beam irradiation: a fractal approach

Based on the fractal nature of collisions, the fragmentation of displacement cascades is investigated. Introducing the caliper diameter to take into account large displacements of atoms in a collision cascade, it is possible to describe this fragmentation in terms of a threshold energy Ec. From the knowledge of Ec, the number and the volume fraction of subcascades produced is then derived. This last information allows us to classify the efficiency of impinging particles to induce structural changes of solids.