(323e) Empirical Model of Helium Bubble Growth and Bursting Near W{100} Surfaces and Equation of State for Helium Bubbles in Tungsten

Fuzz formation in helium-implanted tungsten (W) is a complex, multi-physics phenomenon resulting from the combined effects of processes that include driven surface diffusion, subsurface helium (He) bubble dynamics, He bubble bursting, and loop punching, as well as anisotropies of material properties and substantial changes in material thermophysical properties in the damaged tungsten as a function of He content. Here, we study the subsurface bubble dynamics in order to develop predictive capabilities for He content by focusing on three important physical phenomena and physical dependences, namely, subsurface bubble growth, bubble bursting, and the effect of temperature on subsurface bubble dynamics.

We have performed molecular-dynamics (MD) simulations to study the growth of He bubbles under a W(100) surface until the bubbles burst. We study bubble 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 toward the surface. Subsequently, the MD data are used to derive empirical 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 respective parameters in the models. In the loop punching model, for bubbles consisting of N_V vacancies and N_He helium atoms, the N_He/N_V ratio that causes the event, the resulting increase in N_V, and the associated shift of the bubble depth are formulated as a function of N_V and temperature, T. In the bursting model, a bubble must reach a certain depth and N_He/N_V ratio, simultaneously, in order to burst. The burst depth and N_He/N_V ratio are also modeled as a function of N_V and T. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an equation of state (EOS) for He bubbles in tungsten. The EOS is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and bubble sizes up to about 3 nm in diameter. For completeness, a model is also derived to compute the bubble volume for a given N_V, N_He/N_V ratio, and T. 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. 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, we find that at a higher temperature, a bubble can burst from a deeper region.

In addition, a new EOS for a free helium gas is derived to improve an existing free-gas EOS that was fitted to experimental data over the range of 0.2−2 GPa and 75−300 K. The existing EOS agrees well with our MD data up to 500 K. However, it overpredicts the bubble pressure at temperatures higher than 933 K, and becomes increasingly inaccurate at higher temperatures and pressures higher than 2 GPa. The new free-gas EOS can accurately predict all the MD data included in the analysis (which span up to 54 GPa at 2500 K).