Surface coverage dependent mechanisms for the absorption and desorption of hydrogen from the W(110) and W(100) surfaces: a DFT investigation.

Herein, we investigate the saturation limits of hydrogen on the (110) and (100) surfaces of tungsten via Density Functional Theory (DFT) and complement our findings with experimental measurements. We present a detailed study of the various stable configurations that hydrogen can adopt upon the surfaces at coverage ratios starting below 1.0, up to the point of their experimental coverage ratios, and beyond. Our findings allow us to estimate that the saturation limit on each surface exists with one monolayer of hydrogen atoms adsorbed. In the case of (110) this corresponds to a coverage ratio of one hydrogen atom per tungsten atom, while in the case of (100) a full monolayer is present at a coverage ratio of 2.0. Preliminary Low Energy Ion Scattering (LEIS) and Direct Recoil Spectroscopy (DRS)measurements complement these results and tend to confirm the findings obtained by DFT. In particular, the preferred adsorption sites on both surfaces at any coverage, the reconstruction of the (100) surface and the saturation limits agree well. We show that depending on the coverage, hydrogen surface binding energies can be of the same magnitude as binding energies to defects like vacancies. As a consequence, surface effects should be included in models aiming to simulate retention and desorption of hydrogen from the bulk.

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 co-existence 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.

In this work, a kinetic model is presented to describe hydrogen absorption and desorption from tungsten at different surface coverages. Activation energies for hydrogen absorption into the bulk and desorption from the surface of tungsten are modelled by functions that depend explicitly and continuously on the hydrogen surface coverage. A steady-state model is developed to derive these activation energies from experimental data. The newly developed coverage dependent activation energies are then implemented in the non steady-state rate-equation code MHIMS. Published experimental results on D uptake and retention of self-damaged tungsten exposed to 0.28 eV deuterium atoms at different temperatures ranging from 450 K to 1000 K can be successfully described with this approach. Finally, the steady-state model is applied to determine surface concentration, bulk concentration and migration depths of hydrogen isotopes in tungsten exposed to various atomic fluxes and temperatures ranging from milder conditions in laboratory experiments to divertor strike point conditions in tokamaks.