Irradiation-Driven Compositional Changes in Alloys
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Irradiation-Driven Compositional Changes in Alloys Santosh Dubey1, Anter El Azab1 and Dieter Wolf2 1 2
Department of Scientific Computing, Florida State University, Tallahassee, FL, USA Argonne National Laboratory, Argonne, IL, USA
ABSTRACT A model to study the formation of compositional patterns in concentrated binary alloys under irradiation is presented. In this model, six atomic and defect species are considered: regular lattice atoms (A and B), dumbbell interstitials (AA, BB and AB) and vacancies. In addition to long range diffusion of these species, local defect-defect (vacancy-interstitial recombination) and defect-atom (dumbbell-atom) reactions have also been considered. The model tracks simultaneous evolution of all the species in reaction-diffusion formalism. Irradiation events are modeled as a stochastic point process which changes the concentration of all the species instantaneously in a random fashion. In each irradiation event, a spatial distribution of point defects (core-shell distribution: core dominated by vacancies and shell by interstitials) has been introduced in the system which drives the kinetics of diffusion and reaction. The model has been non-dimensionalized with respect to intrinsic length and time scales of the material system and solved numerically using finite difference technique. Applying this model to CuAu solid solution, we have shown that the alloy exhibits spinodal-like decomposition with specific steady state wavelengths that depend on the irradiation conditions. INTRODUCTION A material under sustained irradiation stays far away from equilibrium. It may decay to a lower energy metastable state by various dissipative processes, but not to an equilibrium state. One of the possible ways by which this may happen is by self-organization via selection of a specific spatial pattern, which is typical in driven materials [1]. Garner and coworkers [2] observed spinodal-like compositional self- organization in Fe-Ni and Fe-Cr-Ni invar alloys under irradiation, characterized by micro-oscillations in nickel composition of wave length tens of nanometer to micron over a range of 674-948K. This phenomenon was thought to be due to natural instability and radiation-induced segregation, cooperating to produce compositional selforganization in materials. Martin [3] was first to propose a reaction-diffusion model for immiscible binary systems to state the conditions under which solid solution may become unstable under irradiation. In this study, presence of interstitial-vacancy recombination was found to be the reason for instability of the solid solution. By using mean field type formulation, Martin [4] proposed another model to study solid solution instability as a result of competition between irradiation-induced atomic mixing (leading to disorder) and subsequent thermalization by diffusive jumps (leading to order). Enrique and Bellon [5] extended this model to emphasize the role of distance distribution of atomic relocations in formation of self-organized compositional patterns. These models i
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