Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations

Abstract

Abstract Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ( $$N_\text {V}$$ N V ), He atoms ( $$N_\text {He}$$ N He ), and temperature (T). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of $$N_\text {V}$$ N V vacancies and $$N_\text {He}$$ N He helium atoms, the $$N_\text {He}/N_\text {V}$$ N He / N V ratio that causes the event, the resulting increase in $$N_\text {V}$$ N V , and the associated shift of the bubble depth are formulated as a function of $$N_\text {V}$$ N V and T. In the bursting model, a bubble must simultaneously reach a certain depth and $$N_\text {He}/N_\text {V}$$ N He / N V ratio in order to burst. The burst depth and $$N_\text {He}/N_\text {V}$$ N He / N V are also modeled as a function of $$N_\text {V}$$ N V and T. The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.