Microstructure-Dependent Rate Theory Model of Radiation-Induced Segregation in Binary Alloys

Abstract

Conventional rate theory often uses the mean field concept to describe the effect of inhomogeneous microstructures on the evolution of radiation induced defect and solute/fission product segregation. However, the spatial and temporal evolution of defects and solutes determines the formation and spatial distribution of radiation-induced second phase such as precipitates and gas bubbles/voids, especially in materials with complicated microstructures and subject to high dose radiation. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed to investigate the effect of inhomogeneous thermodynamic and kinetics properties of defects on diffusion and accumulations of solute A in AB binary alloys. Four independent concentrations: atom A, interstitial A, interstitial B, and vacancy on [A, B] sublattice are used as field variables to describe temporal and spatial distribution and evolution of defects and solute A. The independent concentrations of interstitial A and interstitial B allow to describe their different generation rates, thermodynamic and kinetic properties, and release the assumptions of interstitial generation and sink strength used in the conventional rate theory. Microstructure and concentration dependent chemical potentials of defects are used to calculate the driving forces of defect diffusions. With the model, the effects of defect chemical potentials and mobilities on the RIS in polycrystalline AB model alloys have been simulated. The results demonstrated the model capability in predicting defect evolution in materials with inhomogeneous thermodynamic and kinetic properties of defects. The model can be extended to materials with complicated microstructures such as a wide range of grain size distribution, coating structure and multiphases as well as radiation-induced precipitation subject to severe radiation damage.

Microstructure-dependent rate theory model of defect segregation and phase stability in irradiated polycrystalline LiAlO2

“…Recently, we developed a microstructure-dependent rate theory model of RIS to take into account grain morphology and inhomogeneous thermodynamic and kinetic properties of defects in polycrystalline AB alloys [20]. A two sublattice model [A, B, V] I [A i , B i , V i ] II was used to describe the free energy of the system and defect evolution.…”

“…To clearly and concisely present the extension from the two sublattice model to three sublattice model, we first provide the brief derivation of defect evolution equation in two sublattice model [20], then describe how to deduce the equations in three sublattice model [Li, Al, II . Following to the rate theory, the evolution of chemical and defect concentrations in AB alloys with two sublattices is given by [8,20]:…”

“…ġd , ġS d and ġR d is the generation rate, sink rate, and recombination rate of defect d, respectively. The atom and lattice conservation requires the fluxes should satisfy the following equations [20,26]:…”

“…Inside the grains where f (η) = 0, the evolution equations ( 13)-( 16) become to the rate equations ( 6)- (20) of reference [8] with the assumption of…”

“…The phase field method is based on thermodynamic and kinetic properties of defects that can naturally describe inhomogeneous chemical potentials of defects associated with distributed structural defects, nonuniform chemistry, and long-range interactions. In our recent work [20] we developed a microstructuredependent rate theory of RIS model in a binary AB alloy by integrating rate theory and the concept of defect chemical potential used in phase-field models.…”