The effect of multi-occupancy traps on the diffusion and retention of multiple hydrogen isotopes in irradiated tungsten and vanadium

TL;DR

This work develops a tractable, first-principles–driven framework for diffusion and retention of hydrogen isotopes in irradiated tungsten and vanadium by incorporating multi-occupancy traps and multiple isotopes. It introduces a dynamic steady-state formulation that generalizes the Oriani approach, derives closed-form expressions for the effective diffusivity under equilibration, and extends the theory to multi-isotope systems with zero-point energy corrections. Using DFT-calculated energies for W and V monovacancies and a parameter-free comparison to isotope-exchange experiments in self-irradiated tungsten, the study demonstrates that multi-occupancy traps significantly alter diffusion and retention relative to single-occupancy models, with material-specific trends (monotonic in W vs non-monotonic in V). The methodology, implemented in a MOOSE-based PALIOXIS framework, provides a viable route to predictive hydrogen inventory assessments in fusion-relevant materials, and highlights the importance of trap occupancy, ZPE effects, and defect distributions in determining long-term retention.

Abstract

We propose a computational scheme for the diffusion and retention of multiple hydrogen isotopes (HI) with multi-occupancy traps parameterized by first principles calculations. We show that it is often acceptable to reduce the complexity of the coupled differential equations for gas evolution by taking the dynamic steady state, a generalisation of the Oriani equilibrium for multiple isotopes and multi-occupancy traps. The effective gas diffusivity varies most with mobile fraction when the total gas concentration approximates the trap density. We show HI binding to a monovacancy in vanadium produces a non-monotonic dependence between diffusivity and gas concentration, unlike the tungsten system. We demonstrate the difference between multiple single occupancy traps and multi-occupancy traps in long-term diffusion dynamics. The applicability of the multi-occupancy, multi-isotope model in steady state is assessed by comparison to an isotope exchange experiment between hydrogen and deuterium in self-ion irradiated tungsten. The vacancy distribution is estimated with molecular dynamics, and the retention across sample depth shows good agreement with experiment using no fitting parameters.

Figures (10)

• Figure 1: A schematic illustration of a three-level trap. Mobile gas interstitial sites are separated by distance $a$ and migration activation barrier $E_m$. All H atoms in a trapped occupancy state have the same detrapping energy. In this work the detrapping energy from a trap in occupancy state $s$ is the sum of the binding and migration energies. A D atom has a different zero point energy to H, so its migration barrier and binding energy are different.
• Figure 2: The ${\bf G}$ matrix spectral gap (Hz), the rate of convergence to steady state, at various mobile H concentrations and temperatures for W and V monovacancies.
• Figure 3: The trapped concentration of H and T in V monovacancies at 300K and density $\rho=10^{-3}$ at. fr. as a function of the loading gas concentration for H $\rightarrow$ T as well as T $\rightarrow$ H. Note the $y$-axis is reflected over $y=0.5 \times 10^{-4}$ at. fr.
• Figure 4: The effective diffusivity of H in W and V, with equilibrated monovacancies at trap density $10^{-3}$ at. fr., as a function of inverse temperature across several total gas concentrations $c$. The black line denotes perfect lattice diffusivity.
• Figure 5: Normalised effective diffusivity for H in W and V, with one six-occupancy equilibrated trap with incremental binding energies $\{E^b\}$; six single occupancy equilibrated traps labelled by index $i=1,...,n$ where the $i^{th}$ trap has binding energy $E^b_i$; and one single occupancy trap with $E^b_1$. The trap density is $10^{-3}$ at. fr. for all cases.