Analysis of lattice locations of deuterium in tungsten and its application for predicting deuterium trapping conditions

Retention of hydrogen isotopes (protium, deuterium, and tritium) in tungsten is one of the most severe issues in the design of fusion power plants, since significant trapping of tritium may cause exceeding radioactivity safety limits in future reactors. Hydrogen isotopes in tungsten can be detected using the nuclear reaction analysis method in the channeling mode (NRA/C). However, the information hidden within the experimental spectra is subject to interpretation. In this work, we propose the methodology to interpret the response of the experimental NRA/C spectra to the specific lattice locations of deuterium by simulations of the NRA/C spectra from atomic structures as obtained from the first-principles calculations. We show that trapping conditions, i.e., states of local crystal structures retaining deuterium, affect the lattice locations of deuterium and the change of lattice locations can be detected by the ion channeling method. By analyzing the experimental data, we are able to determine specific information on the deuterium trapping conditions, including the number of deuterium atoms trapped by one vacancy as well as the presence of impurity atoms along with deuterium in vacancies.

Figure 1

Information about the model targets for NRA/C simulations. (a) Depth distributions of deuterium concentration (blue) and damage profile in dpa (black) in tungsten irradiated with 30 keV deuterium as calculated by SRIM, depth distributions of vacancy concentration (orange) obtained from the dpa profile and deuterium concentration in simulation targets (green). (The arrow indicates the axis of the damage profile in dpa.) (b) Illustration for the projection of a deuterium atom (orange) in a tungsten (blue) unit cell onto three different {001} planes. (The deuterium atom is located at a TIS.)

Figure 2

Example spectra obtained using 750 keV ${}^3\mathrm{He}$ ions on simulated targets along the [001] direction at different polar angles and at random configurations: (a) NRA/C spectra generated from targets with deuterium located at TIS and (b) RBS spectra. The region of interest (ROI) for the angular scan calculations is represented by the colored region. The inset in (a) shows the locations of TIS (blue hexagon), OIS (orange square) and tungsten atoms (blue circle) viewed along the [001] direction.

Figure 3

Locations of hydrogen (a) in perfect tungsten, (b) bonding to a $\langle 11\xi \rangle$ self-interstitial atom, (c) bonding to a carbon atom and (d) bonding to an oxygen atom as determined by DFT calculations. The tungsten, hydrogen, carbon and oxygen atoms are represented by the blue, orange, green and red circles, respectively. Projections of hydrogen atoms (gray) to three {001} planes are displayed on the blue planes, in which the intersection points of gray lines indicate the TIS. The $\langle 11\xi \rangle$ dumbbell is connected by the orange line.

Figure 4

Comparison of experimental (dots) and simulated (lines) RBS/C and NRA/C angular scans through the [001] axis of tungsten, in which deuterium atoms are retained at different conditions: (a) retained in perfect tungsten, (b) bonding to a $\langle 11\xi \rangle$ self-interstitial atom, (c) bonding to a carbon atom, (d) bonding to an oxygen atom, [(e)–(h)] bonding to a vacancy with the number of deuterium atoms ranging from 1 to 12, [(i) and (j)] bonding to a vacancy containing a carbon atom (1 to 6 deuterium atoms), [(k) and (l)] bonding to a vacancy containing an oxygen atom (1 to 6 deuterium atoms), [(m) and (n)] bonding to a vacancy containing a helium atom (1 to 6 deuterium atoms), [(o) and (p)] bonding to a vacancy containing 2 helium atoms (1 to 6 deuterium atoms). The red, orange and green markers on the top left corner indicate a low possibility of corresponding condition (due to low solubility or low binding energy), significant difference between simulation and experiments for the corresponding condition and the most promising condition, respectively. (Experimental values are extracted from the P-V experiments [17].)

Figure 5

Positions of hydrogen atoms (orange) in a vacancy: from (a) to (l) the number of hydrogen atoms is increased from 1 to 12. Other notations are same to those in Fig. 3. For simplicity, the projections to the (100) and (010) planes are not shown for cases with more than two hydrogen atoms.

Figure 6

Positions of hydrogen atoms, relative to the OIS and TIS, as a function of the number of hydrogen atoms in a vacancy or vacancy complex. The hydrogen atoms are bonding to (a) a vacancy (orange) and a vacancy complex containing (b) a carbon (green), (c) an oxygen (red), (d) a helium atom (purple), and (e) two helium atoms (brown), respectively. (Note that some symbols are overlapping).

Figure 7

Binding energies of a hydrogen atom to vacancy complexes: (a) a vacancy with $(i-1)$ hydrogen atoms, (b) a vacancy containing a carbon (green) or oxygen (red) atom and $(i-1)$ hydrogen atoms, and (c) a vacancy containing multiple helium and $(i-1)$ hydrogen atoms. The binding energies without and with the ZPE correction are represented by hollow and solid markers, respectively. The black dashed line represents an estimated threshold energy for the detrapping of hydrogen at room temperature.

Figure 8

Positions of hydrogen atoms (orange) in a vacancy containing a carbon atom [(a)–(f)] and containing an oxygen atom [(g)–(l)]. The carbon and oxygen atoms are represented by the green and red circles, respectively. Other notations are the same to those in Fig. 3. (The projections to the (100) and (010) planes are not shown for vacancies with more than 2 hydrogen atoms for the sake of simplicity.)

Figure 9

Positions of hydrogen atoms (orange) in a vacancy containing one helium atom [(a)–(f)] and containing two helium atoms [(g)–(l)]. The helium atoms are represented by the purple circles. Other notations are the same to those in Fig. 3. (The projections to the (100) and (010) planes are not shown for vacancies with more than 2 hydrogen atoms for the sake of simplicity.)

Figure 10

Average positions of hydrogen atoms (relative to the OIS and TIS) bonding to different types of vacancy complex.

Figure 11

Probability density distributions of hydrogen atoms bonding to a vacancy at 300 K viewed along the [001] direction obtained from ab initio MD simulations for: (a) one hydrogen atom bonding to a vacancy and (b) 12 hydrogen atoms bonding to a vacancy. The probability of hydrogen at one position increases with a warmer background color. The locations of TIS (blue hexagon), OIS (orange square) and tungsten atoms in a perfect unit cell (blue circle) are indicated.

Figure 12

Concentrations of ${\mathrm{V}}_1{\mathrm{D}}_i$ under the P-V experimental conditions obtained from the rate equation modeling using binding energies (a) without the ZPE correction and (b) with the ZPE correction. (The arrows indicate an increase of filling level.)

Figure 13

Analysis of positions of deuterium in different irradiation conditions: Experimental (dots) and simulated (lines) NRA/C and RBS/C angular scans for (a) 30 keV deuterium implanted to tungsten (the P-V experiments) and (b) 15 keV deuterium implanted to tungsten under low and high radiation damage induced by 750 keV ${}^3\mathrm{He}$ ions, (c) simulated NRA/C angular scans for 15 keV deuterium implanted to tungsten with lattice distortion ranging from 5% to 20% (dashed lines) and (d) illustration of deuterium positions that are used to fit NRA/C results with high damage shown in (b). The angular scans are through the [001] axis. (Experimental values in (a) and (b) are extracted from Refs. [17] and [18], respectively.)