JAEA-Conf 2011-002 - 日本原子力研究開発機構

High energy
particle
Vacancy
JAEA-Conf 2011-002
Figure 8. Multiscale modeling of irradiation effects by high energy particles.
To estimate the PKA energy spectrum under high energy proton irradiation, the PHITS code was used. The
code was the first general-purpose heavy ion transport Monte Carlo code covering the incident energies from
several MeV/nucleon to several GeV/nucleon. It was developed for general purpose calculations based on the
NMTC/JAM code [9], which is widely used for hadron transport calculations. In the PHITS code, the HIC code
[10], which is used in the HETC-CYRIC code [11], was revised into the JQMD code [12] for heavy ion nuclear
reaction simulation. This is because the JQMD code is based on a more modern nucleus-nucleus reaction model
than QMD, while the HIC is based on a traditional intranuclear-cascade-evaporation model. The PKA energy
spectrum of 3 mm thick Ni irradiated by 3GeV protons was calculated. The PKA energy dependence of damage
energy deposition indicated that the highest energy deposition was caused by 65 keV PKAs.
As mentioned in 2.1, a high energy PKA produces a large cascade, which can be divided into subcascades.
The subcascade formation energy of Ni was estimated to 10 keV [8]. Therefore we assumed the formation of
several 10 keV subcascades for the initial damage structure instead of large cascades. The number of 10 keV
subcascades during irradiation was obtained from the PKA energy spectrum calculated by the PHITS and by
PKA energy spectrum analysis [1, 2].
Molecular dynamics (MD) was employed to calculate the defect clusters and freely migrating defects from
subcascades of 10 keV. The size of the model lattice was 35×35×35 lattice constants. An EAM potential with
the parameters proposed by Daw and Baskes [13] was used. A periodic boundary condition in three directions
and an NVE ensemble (i.e., fixed number of atoms, cell volume and energy) were used for the simulation.
Three MD runs were performed and the results indicated that, on average, seventeen vacancies and seventeen
interstitials were formed in each 10 keV subcascade. Using the point defect distribution determined by MD, the
kinetic Monte-Carlo simulation was performed and a cluster of three point defects was formed on average.
These values were then used in a defect structural evolution.
The damage structural evolution was estimated using reaction kinetic analysis [14]. The following
assumptions were used in the calculation. (1) Mobile defects: interstitials, di-interstitials, tri-interstitials,
vacancies and di-vacancies. (2) Point defect clusters of four point defects or more were assumed to be stable
clusters. (3) The time dependence of ten variables: concentration of interstitials, di-interstitials, tri-interstitials,
interstitial clusters (interstitial type dislocation loops), vacancies, di-vacancies, tri-vacancies, vacancy clusters
(voids), the total interstitials in interstitial clusters, and the total vacancies in vacancy clusters. (4) Interstitial
clusters (three interstitials) and vacancy clusters (three vacancies) were also formed directly in cascades. The
formation rates were obtained by MD simulation. (5) The material temperature was 423 K during irradiation.
The result of 10 dpa irradiation was as follows: the void concentration was 5.93x10 -4 /atoms, the void size was
four vacancies and the dislocation density was 1.1x10 9 cm/cm 3 .
Changes in mechanical property were calculated by three dimensional DDD [15]. In the usual DDD
simulation [16], a curved dislocation line was treated as a connection of short straight segments to simplify the