Introduction of vacancy drag effect to first-principles-based rate theory model for irradiation-induced grain-boundary phosphorus segregation
Abstract
In order to examine the vacancy drag effect on phosphorus segregation at grain-boundaries, we estimated partial diffusion coefficients by kinetic Monte Carlo simulations considering atomic transitions for all the binding states of a phosphorus atom and a vacancy, and incorporated them into a rate theory model to simulate grain-boundary phosphorus coverage in neutron-irradiated reactor pressure vessel steels. As a result, it was confirmed that phosphorus atoms are transported to grain-boundaries by the vacancy drag effect. We found that the vacancy drag effect occurs even when only the first-nearest-neighbor binding states are considered, though it does not occur if the partial diffusion coefficients are obtained through the expression derived by theoretical analysis [Ebihara, et al., J. Nucl. Mater. 414 (2011) 328-335]. In addition, we found that grain-boundary phosphorus segregation is suppressed by the vacancy mechanism of phosphorus transport regardless of the vacancy drag effect.
From the early stage of dose to the stage of a certain dose, P transport to GB by the drag effect is efficient. It is confirmed from the fact that the term for the V mechanism in JP becomes negative as seen in Fig. 7c. In addition, since this term of the case including the 2nd-n.n.binding state is smaller than that of the other case, JP of the former case is smaller than that of the latter case (Fig. 7b). Thus, nP near GB in the case including the 2nd-n.n.binding state is larger than that in the other case as seen in Fig. 7a. After dose is beyond a certain value, np near GB becomes large in the both cases, so that ∇nP becomes a quite large negative value. Because of the large negative value of ∇nP, the term -DVPPnV∇nP becomes a large positive value. Thus, the term concerning the V mechanism in JP becomes positive (Fig. 7f). In addition, as shown in Table 2, the value of DVPP is larger in the case including the 2nd-n.n.binding state than in the other case. Thus, as seen in Fig. 7f, the term concerning the V mechanism in JP is larger in the former case than in the latter case. Owing to this difference in Fig. 7f, as seen in Fig. 7e, Jp of the case including the 2nd-n.n.binding state becomes larger than that of the other case, so that np of the former case becomes smaller than that of the other case (Fig. 7d). In short, after P atoms gather near GB, the gradient of P concentration becomes remarkable, so that the part of P atoms is transported from the vicinity of GB to the inside of grain by the gradient of P concentration. Since the value of DVPP in the 2nd-n.n.binding state is larger than that in the other case, the gradient of P concentration works more strongly, and the suppression of GB P segregation is more remarkable. Since DVPP does not become negative even if it is obtained from the theoretical analysis, the suppression of GB P segregation is considered to occur regardless of the V drag effect.- Publication:
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Journal of Nuclear Materials
- Pub Date:
- September 2013
- DOI:
- 10.1016/j.jnucmat.2013.05.066
- Bibcode:
- 2013JNuM..440..627E