  In this work, we combine Density Functional Theory data with a Thermodynamic
and a kinetic model to determine the total concentration of hydrogen implanted
in the sub-surface of tungsten exposed to a hydrogen flux. The sub-surface
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 sub-surface of tungsten. Combining both these
models, two regimes are established in which hydrogen is preferentially trapped
at either 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, below is the vacancy regime in which super-saturated
layers form within tenths of 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.

Materials Science