A Comparison of the Relative Importance of Helium and Vacancy Accumulation in Void Nucleation

Mechanism map for nucleation and growth of helium bubbles in metals

“…(8) and (10) represent equilibrium conditions between a helium bubble and a matrix point defect, while Eqs. (9) and (11) show equilibrium condition among matrix point defects.…”

“…In the case of the equilibrium, Eqs. (9) and (11) are used to obtain C k (1), while in the case of irradiation condition where matrix point defects are not equilibrated with each other, C k (1) is usually provided by solving the simultaneous rate theory equations describing all defect interactions occurred in materials, such as the production, annihilation, recombination and clustering of point defects.…”

“…Although the details of the actual trajectory of helium bubbles in the map must be obtained by solving the simultaneous rate theory equations as has done by Mansur et al [5][6][7] and Stoller et al [8,9], it is considered that helium absorption is a rate controlling reaction for helium bubble growth, when helium inflow rate is not enough and therefore helium bubbles go along near the J grow = J shrink line. Such a rate controlling reaction may determine the incubation time of helium bubble growth.…”

“…Russell et al [1][2][3][4] derived equations describing the absorption and emission rates of vacancies and helium atoms to and from a helium bubble, respectively, and they suggested the nucleation path of the helium bubble. Mansur et al [5][6][7] and Stoller et al [8,9] derived an equation to evaluate void growth rate using the rates of vacancy absorption, vacancy emission and self-interstitial atom (SIA) absorption, and they applied it to simultaneous rate theory equations for evaluation of helium-assisted void growth and accumulation. All these theoretical treatments are well established, available for relatively lower concentrations of helium in metals, and can be applied enough to modeling the behaviors of fusion structural materials under irradiation, where helium is produced by (n, a) nuclear reactions.…”

A phase-field modeling of void swelling in the Austenitic stainless steel

“…The parameters for the Austenitic stainless steel is chosen as follows (at 873 K) (12)(13)(14)(15)(16): c eq v = 3.13 × 10 −8 , c eq i = 3.13 × 10 −8 , D v = 5.45 × 10 −9 cm 2 /s, D i = 1.17 × 10 −5 cm 2 /s. We obtained the values correspond to the equilibrium defect concentration is a 1 = 1.320160, a 2 = 4274538.0, a 3 = −8549080.0, a 4 = 4274540.0 (eV).…”