Observation of Transient and Asymptotic Driven Structural States of Tungsten Exposed to Radiation

Combining spatially resolved x-ray Laue diffraction with atomic-scale simulations, we observe how ion-irradiated tungsten undergoes a series of nonlinear structural transformations with increasing radiation exposure. Nanoscale defect-induced deformations accumulating above 0.02 displacements per atom (dpa) lead to highly fluctuating strains at $\sim 0.1\mathrm{dpa}$, collapsing into a driven quasisteady structural state above $\sim 1\mathrm{dpa}$. The driven asymptotic state is characterized by finely dispersed vacancy defects coexisting with an extended dislocation network and exhibits positive volumetric swelling, due to the creation of new crystallographic planes through self-interstitial coalescence, but negative lattice strain.

Figure 1

(a) Injected tungsten ion concentration and displacement damage calculated using srim for the 1 dpa sample. The blue solid line shows the nominal dpa predicted using a threshold displacement energy of 68 eV. The shaded region shows upper and lower dpa bounds corresponding to threshold displacement energies of 55 and 90 eV, respectively. (b) Diffracted x-ray intensity integrated in the tangential reciprocal space directions for the (008) Bragg peak of the 1 dpa tungsten sample. Intensity is shown as a function of the scattering vector magnitude $|\mathbf{q}|$ and sample depth. The superimposed red dotted line shows the fitted peak centers $q_{\text{fit}}(d)$. (c) Depth-averaged strain measured in ion implantation experiments. Horizontal error bars indicate the dpa uncertainty associated with the variation of assumed threshold displacement energies.

Figure 2

Representative Frenkel pair insertion simulations at 0.05 (top) and 0.3 (bottom) dpa using the CRA algorithm. The box size is $20.2\times 20.2\times 63.2{\mathrm{nm}}^3$, and the unconstrained cell dimension $\widehat{z}$ is horizontal. Vacancy (blue) and interstitial (red) clusters with $>3$ point defects are shown. Note the apparent formation of vacancy loops. A superimposed dislocation extraction algorithm analysis [62] shows both $1/2⟨111⟩$ (green) and $⟨100⟩$ (pink) dislocation lines. In the $y=0$ plane, the strain tensor component ${\epsilon }_{zz}$ is shown, with color scale blue, white, red representing $-5\%$, 0, $+5\%$ strain, respectively.

Figure 3

(a) Lattice strain and volumetric strain (dashed) derived from simulations. Shaded region denotes 1 standard deviation. The experimental strain data are scaled by a factor of 10 to compare trends as well as absolute values. Volumetric strain due to the injected self-ions is small. (b) Number of excess planes recorded in the simulation. (c) Defect dipole tensor density (see text) computed from simulation cell stress. Note the horizontal scale is the same for all three plots.

Figure 4

Left: a 199-interstitial (4 nm diameter) glissile loop with $\mathbf{b}=1/2⟨111⟩$ relaxed under a small uniaxial strain (viewed along the strain axis) exhibits a spontaneous rotation of the habit plane with no change in $\mathbf{b}$. (a) corresponds to zero applied strain, whilst (b) and (c) correspond to applied strains of $+1\%$ and $-1\%$, respectively. The effect is more pronounced for larger loops as the dipole tensor of a loop is proportional to the loop vector area [72, 73]. In projection onto the Burgers vector direction, the change of orientation of the loop is undetectable. This stems from the conservation of the relaxation volume of the loop $(\mathbf{b}·\mathbf{A})$ [73], where $\mathbf{A}$ is the vector area of the loop. Right: root-mean-square orientation of habit plane normal as a function of the dose. Shaded region is 1 standard deviation of the population. Standard error is order symbol size.