Parameter-free quantitative simulation of high-dose microstructure and hydrogen retention in ion-irradiated tungsten

Hydrogen isotopes are retained in plasma-facing fusion materials, triggering hydrogen embrittlement and changing tritium inventory as a function of exposure to neutron irradiation. But modeling highly damaged materials—exposed to over 0.1 displacements per atom (dpa)—where saturation of damage is often observed, is difficult because a microstructure containing high density of defects evolves nonlinearly as a function of dose. In this study we show how to determine the defect and hydrogen isotope content in tungsten exposed to high irradiation dose, using no adjustable or fitting parameters. First, we generate converged high dose ($>1$ dpa) microstructures, using a combination of the creation-relaxation algorithm and collision cascade simulations. Then we make robust estimates of vacancy and void regions using a modified Wigner-Seitz decomposition. The resulting estimates of the void surface area enable predicting the deuterium retention capacity of tungsten as a function of radiation exposure. The predictions are compared to ${}^3\mathrm{He}$ nuclear reaction analysis measurements of tungsten samples, self-irradiated at 290 K to different damage doses and exposed to low-energy deuterium plasma at 370 K. The theory gives an excellent match to the experimental data, with both model and experiment showing that 1.5–2.0 at.% deuterium is retained in irradiated tungsten in the limit of high dose.

Figure 1

Vacancy concentration as a function of MD cascade count. The canonical dpa rate is the gradient of vacancy concentration as a function of $N_{\mathrm{casc}}$ at $N_{\mathrm{casc}}=0$, indicated by the solid line.

Figure 2

A comparison of three vacancy detection methods: alpha hull (AH), Wigner-Seitz (W-S), and the isosurface method developed here. (a) Performance of defect detection algorithms with homogeneously distributed vacancies. (b) Performance with single spherical void. Solid line indicates perfect vacancy counting. Note the W-S algorithm performs perfectly in these cases.

Figure 3

Small vacancy clusters identified using Wigner-Seitz occupation (left), Delauney triangulation (AH method) (center), and Wigner-Seitz isosurfaces, described here (right).

Figure 4

A comparison of the Wigner-Seitz (W-S) algorithm to the isosurface method developed here when applied to vacancy loops. (a) Performance of void detection algorithm with prismatic vacancy loops in bcc tungsten. Two Burgers vectors ($\mathbf{b}=1/2\langle 111\rangle ...$ and $\mathbf{b}=\langle 001\rangle$) are considered. Note that the W-S algorithm returns the number of vacant lattice sites exactly, whereas the isosurface method usually returns zero void space. (b) Slice through a [001] vacancy loop viewed in the [001] orientation containing 25 vacant lattice sites, atoms colored by depth. Isosurface showing the position of four voids overlaid.

Figure 5

A simulation cell generated with CRA simulations to 1 cdpa, then relaxed with MD cascades. The periodic replicas show (top) void detection using isosurfaces; (center) Wigner-Seitz point defect detection shows vacancies (red) and interstitials (blue); (bottom) local strain calculation showing the ${\epsilon }_{xz}$ component colored from blue (compressive $-5\%$) through white (no strain) to red (tensile $+5$%), where $z$ is the long axis direction (here shown horizontally). A dxa analysis [73] is overlaid to show the dislocation loops and network. Green lines have Burgers vector $1/2\langle 111\rangle$ and pink lines $\langle 100\rangle$. Visualisation performed with Ovito [74].

Figure 6

CRA simulations annealed with MD cascades. Solid symbols: CRA simulation only. Open symbols: CRA simulations with MD annealing. Solid line: MD cascades only, i.e., perfect lattice starting point. Inset: Same data plotted on a linear scale shows a match between MD cascade only and CRA $+$ MD simulation techniques.

Figure 7

A count of point defects for high dose microstructure simulations. Interstitials counted using W-S method. Vacancies in clusters counted using isosurface method, and vacancies in loops taken as difference between total vacant lattice sites (W-S) and vacancies in clusters. Open symbols are the result of using CRA simulations alone. Solid symbols are the result of using MD and CRA $+$ MD relaxed simulations. The lines are to guide the eye between sets of points.

Figure 8

Deuterium (D) concentration assuming 5 D atoms per monovacancy equivalent. Note the displacement damage scale $x$-axis is split into logarithmic and linear halves to emphasize the saturation level in the high dose limit.