Multiscale modelling of the interaction of hydrogen with interstitial defects and dislocations in BCC tungsten

Abstract

In a fusion tokamak, the plasma of hydrogen isotopes is in contact with tungsten at the surface of a divertor. In the bulk of the material, the hydrogen concentration profile tends towards dynamic equilibrium between the flux of incident ions and their trapping and release from defects, either native or produced by ion and neutron irradiation. The dynamics of hydrogen exchange between the plasma and the material is controlled by pressure, temperature, and also by the energy barriers characterizing hydrogen diffusion in the material, trapping and de-trapping from defects. In this work, we extend the treatment of interaction of hydrogen with vacancy-type defects, and investigate how hydrogen is trapped by self-interstitial atom defects and dislocations. The accumulation of hydrogen on dislocation loops and dislocations is assessed using a combination of density functional theory (DFT), molecular dynamics with empirical potentials, and linear elasticity theory. The equilibrium configurations adopted by hydrogen atoms in the core of dislocations as well as in the elastic fields of defects, are modelled by DFT. The structure of the resulting configurations can be rationalised assuming that hydrogen atoms interact elastically with lattice distortions and that they interact between themselves through short-range repulsion. We formulate a two-shell model for hydrogen interaction with an interstitial defect of any size, which predicts how hydrogen accumulates at defects, dislocation loops and line dislocations at a finite temperature. We derive analytical formulae for the number of hydrogen atoms forming the Cottrell atmosphere of a mesoscopic dislocation loop or an edge dislocation. The solubility of hydrogen as a function of temperature, pressure and the density of dislocations exhibits three physically distinct regimes, dominated by the solubility of hydrogen in a perfect lattice, its retention at dislocation cores, and trapping by long-range elastic fields of dislocations.

Observation of hydrogen trapping at dislocations, grain boundaries, and precipitates

“…A reasonable speculation is that an affinity between carbon and hydrogen might lead to the hydrogen trapping. However, a theoretical study showed that the carbon atoms in lattice defects have only a weak influence on the hydrogen trapping (37), and other modeling has successfully predicted the presence of trapped hydrogen at dislocations in a body-centered cubic lattice (38). Therefore, we believe that the observed hydrogen is directly related to the presence of lattice defects, rather than the result of attraction by segregated carbon atoms.…”

Three mechanisms of hydrogen-induced dislocation pinning in tungsten

“…The trap density ( dislocation density × hydrogen atom trapped per unit length lattice number density of tungsten ) is therefore in the order of 1.0 × 10 −6 atomic fraction. The input dislocation detrapping energy lies in the range of atomistic simulations [26,62], 1.28-1.36 eV for an edge dislocation, and 0.92-0.96 eV for a screw dislocation. The vacancy detrapping energy agrees well with atomistic simulations [63][64][65], being 1.65-2 eV up to the second filling level.…”

“…The corresponding results are summarized in table 1 and are consistent with the literature. The dislocation density is inferred from [60,61], as measured by transmission electron microscopy (TEM), to be in the range (1.9 ± 1.4-5.1 ± 1.7) × 10 12 m m −3 for pure tungsten from the same manufacturer which was recrystallized at 2000 K for 0.5 h and at 1873 K for 1 h. At 325 K, the hydrogen atom trapped per unit length of dislocation is calculated to be 1~2 in [62]. The trap density ( dislocation density × hydrogen atom trapped per unit length lattice number density of tungsten ) is therefore in the order of 1.0 × 10 −6 atomic fraction.…”

Impact of interstitial impurities on the trapping of dislocation loops in tungsten

“…Another study 18 has shown that H and He atoms are strongly bound to an edge dislocation with the interaction energy of − 0.9 and − 3.0 eV, respectively. In the work by De Backer et al 19 , the interaction of H isotopes with SIA clusters and dislocation loops up to 37 SIAs was addressed, where an interaction energy in the range of − 0.3 to − 0.7 eV was derived. Thus, no information on the interaction of C, O, N and He with SIA clusters (dislocation loops) and of O and N to edge dislocations has been published so far.…”