Computational modeling of radiation-induced segregation in concentrated binary alloys
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Computational modeling of radiation-induced segregation in concentrated binary alloys Santosh Dubey and Anter El-Azab School of Nuclear Engineering, Purdue University, West Lafayette, IN, USA ABSTRACT A sharp-interface model to study radiation-induced segregation in binary alloy has been developed. This model is based on a set of reaction-diffusion equations for the point defect and atomic species concentrations, with a stochastic, spatially-resolved, discrete defect generation terms representing the cascade damage. An important feature of this model, which is significantly different from the way radiation-induced segregation has been studied in the past, is that the role of the boundaries as defect sinks has been ensured by defining defect-boundary interactions via a set of reaction boundary conditions. Defining defect-boundary interactions in this way makes it possible to capture the process of segregation as a consequence of boundary motion. The model is tested in 2D for Cu-Au solid solution with the material surface being free to move. The Gear method has been used to solve the reaction-diffusion equations. Enrichment of Cu and depletion of Au have been observed near to the boundaries. INTRODUCTION In alloys under irradiation, the flux of point defects toward defect sinks brings about changes in the alloy composition near the defect sinks by a process called radiation-induced segregation (RIS). RIS is a non-equilibrium phenomenon and has been found to affect the diffusional and clustering behavior of the defects, thereby influencing almost all the basic kinetic processes and material properties. For instance, in austenitic stainless steels (Fe-Cr-Ni alloys), RIS leads to depletion of chromium at the grain boundaries, which is considered to be a reason behind the susceptibility of the material to inter-granular cracking in pressurized water reactor core by a process called irradiation-assisted stress corrosion cracking [1]. In concentrated alloys, RIS has been explained by invoking the concept of inverse Kirkendall effect (IKE) [2]. Since RIS plays a role in important surface and bulk phenomena like corrosion, sputtering, void swelling, etc, which are related to operational safety of nuclear reactors in the long run, it is instructive to perform a thorough and systematic study to understand the fundamental processes behind RIS with an objective to provide useful input for the development of radiation resistant materials for reactor applications. Several models have been proposed to study RIS in concentrated alloys employing the IKE formulation. Based on the way diffusion is treated, these models may be broadly classified into two classes. The first class of models uses a continuum model of diffusion using the framework of random alloy model of Manning [3]. Models by Wiedersich et al. [4], Marwick [2], Lam and Wiedersich [5], and Perks and Murphy [6] belong to this class. In Manning’s model, diffusion is based on vacancy mechanism; its extension to systems under irradiation [2-6], in which vacancies and interstiti
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