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Both the intergranular and intragranular segregation of phosphorus may significantly contribute to irradiation embrittlement of reactor pressure vessel steels. The modeling of phosphorus radiation-induced segregation at cylindrical (dislocations), spherical (precipitates and voids) and flat (sample surfaces, grain boundaries) point defect sinks has been carried out in order to compare the kinetics and extent of segregation at various point defect sinks. Dilute Fe-P alloys relevant to model and VVER-440 pressure vessel steels were considered. It is shown that the time to reach steady state phosphorus concentration near dislocation or precipitate is much less than that near grain boundary. Although the steady state phosphorus concentration near dislocations or precipitates is much less than that near grain boundary, a “fast” phosphorus segregation at these sinks may lead to decreasing the free phosphorus content in the matrix and to reducing its subsequent accumulation on grain boundaries at high densities of internal sinks. A more significant effect on the kinetics of grain boundary phosphorus segregation could be caused by the contribution of precipitates to point defect sink strength.

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Kinetics of phosphorus accumulation on grain boundaries (GB) in iron-based alloys is treated theoretically, taking into account both the radiation-induced segregation (RIS) in the matrix and the Gibbsian adsorption (GA) at GB. For steady-state conditions analytical expressions are derived for component profiles near GB and component concentrations on GB. Modeling of phosphorus accumulation at GB in iron alloys is carried out using two different models: 1) the McLean's model generalized to take into account the radiation-enhanced phosphorus diffusion via vacancy and interstitial mechanisms as well as RIS near GB, 2) a model of RIS in a ternary Fe-P-Ni alloy accounting for the binding energy of phosphorus atoms with interstitials as well as a possibility of high phosphorus content near GB at high irradiation doses. Predictions of modeling are analyzed regarding the dependence on temperature, dose and Fe and P diffusion parameters available for iron alloys. It is shown that the GB phosphorus concentration calculated as a function of temperature reveals one or two maxima depending on dose and the choice of material parameters.

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