Dynamics of Nucleation in Solids: A Self-Consistent Phase Field Approach.

We derive a phase field method for computing rigorously the nucleation rate and the incubation time from the sole knowledge of the free energy of the system in the metastable regime. Our theoretical results are assessed against experimental data relative to demixing of an iron-chromium alloy. Our work clarifies the notions of nucleation rate and incubation time extensively used in classical nucleation theory (CNT) processes in solids. Our work thus emerges as an alternative to CNT but of more general applicability, and enables us to model the nucleation process across the whole range of condition encountered in first order phase transitions, an aspect in which CNT fails.

Predicting Nonequilibrium Patterns beyond Thermodynamic Concepts: Application to Radiation-Induced Microstructures.

In this work, we derive an analytical model to predict the appearance of all possible radiation-induced steady states and their associated microstructures in immiscible A_{c[over ¯]}B_{1-c[over ¯]} alloys, an example of a nonequilibrium dynamical system. This model is assessed against numerical simulations and experimental results which show that different microstructures characterized by the patterning of A-rich precipitates can emerge under irradiation. We demonstrate that the steady-state microstructure is governed by irradiation conditions and also by the average initial concentration of the alloy c[over ¯]. Such a dependence offers new leverage for tailoring materials with specific microstructures overcoming limitations imposed by the equilibrium thermodynamic phase diagram.

Symmetry Breaking Resulting from Long-Range Interactions in Out of Equilibrium Systems: Elastic Properties of Irradiated AgCu.

This work presents a consistent formulation of the phase-field approach to model the behavior of nonmiscible alloys under irradiation which includes elastic strain fields, an example of a long-range interaction. Simulations show that the spatial isotropy that is characteristic of radiation-induced patterns breaks down as a result of the elastic strain energy. The consequence of this is the emergence of superlattice structures under irradiation liable to modify macroscopic material properties. This approach is assessed against the experimental study of a AgCu alloy under irradiation: we compare our simulation results to measured solubility limits and Young moduli.

A model of defect cluster creation in fragmented cascades in metals based on morphological analysis.

The impacts of ions and neutrons in metals cause cascades of atomic collisions that expand and shrink, leaving microstructure defect debris, i.e. interstitial or vacancy clusters or loops of different sizes. In De Backer et al (2016 Europhys. Lett. 115 26001), we described a method to detect the first morphological transition, i.e. the cascade fragmentation in subcascades, and a model of primary damage combining the binary collision approximation and molecular dynamics (MD). In this paper including W, Fe, Be, Zr and 20 other metals, we demonstrate that the fragmentation energy increases with the atomic number and decreases with the atomic density following a unique power law. Above the fragmentation energy, the cascade morphology can be characterized by the cross pair correlation functions of the multitype point pattern formed by the subcascades. We derive the numbers of pairs of subcascades and observed that they follow broken power laws. The energy where the power law breaks indicates the second morphological transition when cascades are formed by branches decorated by chaplets of small subcascades. The subcascade interaction is introduced in our model of primary damage by adding pairwise terms. Using statistics obtained on hundreds of MD cascades in Fe, we demonstrate that the interaction of subcascades increases the proportion of large clusters in the damage created by high energy cascades. Finally, we predict the primary damage of 500 keV Fe ion in Fe and obtain cluster size distributions when large statistics of MD cascades are not feasible.

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.

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

In order to model the evolution of concentration profiles induced by ion beam mixing in thick layers, Monte Carlo simulations were performed to study in detail the transition probability controlling the evolution of this profile within the binary collision approximation. We demonstrate that this transition probability can be factorized in two distinct functions. The first one can be understood as a scale factor. The second one controls the dynamics of ion beam mixing which can be analyzed as a Levy flight. The power law form of the tail of this function closely linked to the cross section of a collision event is responsible for long tails of concentration profiles. We demonstrate that the Levy flight nature of ion beam mixing induces an enhancement of the evolution of the initial concentration profile.

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.