Hydrogen supersaturated layers in H/D plasma-loaded tungsten: A global model based on thermodynamics, kinetics and density functional theory data

In this paper, we combine density functional theory data with a thermodynamic and a kinetic model to determine the total concentration of hydrogen implanted in the subsurface of tungsten exposed to a hydrogen flux. The subsurface hydrogen concentration is calculated given a flux of hydrogen, a temperature of implantation, and the energy of the incoming hydrogen ions as independent variables. This global model is built step by step; an equilibrium between atomic hydrogen within bulk tungsten and a molecular hydrogen gas phase is first considered, and the calculated solubility is compared with experimental results. Subsequently, a kinetic model is used to determine the chemical potential for hydrogen in the subsurface of tungsten. Combining both these models, two regimes are established in which hydrogen is preferentially trapped either at interstitial sites or in vacancies. We deduce from our model that the existence of these two regimes is driven by the temperature of the implanted tungsten sample; above a threshold or transition temperature is the interstitial regime, and below is the vacancy regime in which supersaturated layers form within tenths of an angstrom below the surface. A simple analytical expression is derived for the coexistence of the two regimes depending on the implantation temperature, the incident energy, and the flux of the hydrogen ions which we use to plot the corresponding phase diagram.