Damage-tolerant nanotwinned metals with nanovoids under radiation environments

Material performance in extreme radiation environments is central to the design of future nuclear reactors. Radiation induces significant damage in the form of dislocation loops and voids in irradiated materials, and continuous radiation often leads to void growth and subsequent void swelling in metals with low stacking fault energy. Here we show that by using in situ heavy ion irradiation in a transmission electron microscope, pre-introduced nanovoids in nanotwinned Cu efficiently absorb radiation-induced defects accompanied by gradual elimination of nanovoids, enhancing radiation tolerance of Cu. In situ studies and atomistic simulations reveal that such remarkable self-healing capability stems from high density of coherent and incoherent twin boundaries that rapidly capture and transport point defects and dislocation loops to nanovoids, which act as storage bins for interstitial loops. This study describes a counterintuitive yet significant concept: deliberate introduction of nanovoids in conjunction with nanotwins enables unprecedented damage tolerance in metallic materials.

to exemplify the calculation method. In general, the formation energy at ITB-CTB network (1~2eV) is lower than that in crystal (3eV). When an interstitial is created within the crystal, the difference in the formation energy drives the interstitial to the 1D fast diffusion pipes, either at ITBs or defective CTBs. 5 Supplementary Figure 5. (a1-a2) Radiation induced interstitial stays as a split <001> dumbbell configuration with the lowest formation energy configuration (3.06eV). The migration of the interstitial is coordinated by rotating the dumbbell configuration by 90° with a translation of the center of mass by one nearest-neighbor distance (b, c1-c2), overcoming a tiny kinetic energy barrier (0.11eV) (d).

Supplementary Note 1: Fast diffusion channels associated with ITB-CTB network in nt Cu
Nt Cu intrinsically contains an ITB-CTB network that can act as fast diffusion channels for point defects. A systematic calculation of formation and migration energies (E f , E m ) for 14 interstitials inside crystal and along various types of diffusion pipes (see Supplementary Figure 4) is performed using atomistic simulation to obtain a complete view of diffusion channels in nt Cu.
Inside the crystal, radiation induced interstitials stay as a split <001> dumbbell configuration with the lowest formation energy configuration (3.06eV) (Supplementary Figure 5).
The migration of the interstitial is coordinated by rotating the dumbbell configuration by 90° with a translation of the center of mass by one nearest-neighbor distance, with a kinetic energy barrier of 0.11eV, which indicates that interstitials inside Cu crystal can quickly migrate onto twin boundaries nearby. The migration mechanism in the bulk we characterized in this study is identical to what suggested by Sørensen et al.(4) and Zhao and Shimomura (5).
At defective CTBs, radiation introduces ITB steps consisting of two types of dislocations: Shockley and Frank partials, generated either by dislocation-twin boundary interactions or accumulation of interstitials at CTBs. The dislocation-CTB interactions have been intensively discussed and summarized in literature (6)(7)(8)(9). These interactions result in mobile Shockley partials or immobile Frank partials on the CTB. On the other hand, the difference in formation energy and low migration energy drive interstitials generated in the bulk to accumulate at defective CTBs. As <001> dumbbell configuration cannot form on (111) twinning planes, interstitials could stay at CTBs without significant migration. Therefore, accumulation of interstitials leads to the formation of dislocations/dislocation loops at CTBs, e.g. Frank loops. It is worth mentioning that Shockley partials at twinning planes can quickly migrate on CTBs and deliver interstitials together associated with their glide on CTBs while immobile Frank partials can provide fast diffusion channels (see Supplementary Figure 4).
ITB structure can be represented as an array of Shockley partial dislocations on each {111} plane (3,10), as illustrated in the schematic (Supplementary Figure 4), containing three repetitive partial dislocations (b 1 , b 2 and b 3 ). Two fast diffusion channels along <110> dislocation lines are marked as channel 1 and channel 2. For channel 1, an interstitial initially stays at dislocation core in {111} layer sandwiched by b 1 and b 2 . With the coordination of atoms around, the interstitial migrates downward to another low-energy site, same as initial low-energy site. For channel 2, an interstitial has a spreading core associated with the distributed free volume along <110> dislocation line, and migrates with a super low energy barrier (0.01eV) by crowdion-like behavior.
The amount of ITB-CTB junction lines becomes significant in nt structure with highdensity TBs. We demonstrate three different structures with various combinations of partial dislocation at ITB-CTB junctions (b 1 /b 1 , b 2 /b 2 and b 3 /b 3 ) and study the formation and migration energies of interstitials at and along these junctions. In general, all these three channels have low formation and migration energies for interstitials ( Supplementary Figure 4), among which the diffusion channel with the combination of b 3 /b 3 shows a crowdion-like diffusion with an ultralow kinetic energy barrier of 0.01eV.

Supplementary Note 2: Discussion of cyclic variation of mobile dislocation loop density
We quantitatively explain this cyclic variation phenomenon as follows. The time (dose) dependent reduction in density of mobile interstitial loops, anni ()  t , due to their annihilation at voids is given by where V is the reduction in volume of voids due to absorption of dislocation loops (or segment),