Two-dimensional vacancy platelets as precursors for basal dislocation loops in hexagonal zirconium

Zirconium alloys are widely used structural materials of choice in the nuclear industry due to their exceptional radiation and corrosion resistance. However long-time exposure to irradiation eventually results in undesirable shape changes, irradiation growth, that limit the service life of the component. Crystal defects called  loops, routinely seen no smaller than 13 nm in diameter, are the source of the problem. How they form remains a matter of debate. Here, using transmission electron microscopy, we reveal the existence of a novel defect, nanoscale triangle-shaped vacancy plates. Energy considerations suggest that the collapse of the atomically thick triangle-shaped vacancy platelets can directly produce  dislocation loops. This mechanism agrees with experiment and implies a characteristic incubation period for the formation of  dislocation loops in zirconium alloys.


Calculation of the energy of TVPs, one to six atomic layers thick
Plate-like voids along the basal plane are observed in Mg and Zr with the electron beam directed along the [21 ̅ 1 ̅ 0] direction [1][2][3]. High-resolution TEM images have provided evidence that a growing void has a thickness varying from 3 to 6 atomic layers [3]. Since the experimentally observed platelet vacancy cluster, or triangle vacancy plate (TVP), is found stable with only a few atomic layers, we calculated the energy of a TVP, considering thicknesses varying from 1 to 6 atomic layers. It is conjectured that the collapse of the TVP can produce a <c> dislocation loop of radius R once it attains a critical size, above which the energy of the loop becomes lower and is favored.
The energy of a TVP as a function of , the number of atomic layers, can be expressed as: where is the area of basal plane, is the lateral area per atomic layer of a thin vacancy TVP.
The energies and are the surface energy of basal and lateral planes. For = , Eqn.
(1 ) becomes Considering the effect of hydrogen on the surface energy of basal plane [4,5], we adopt = ≈ 0.80 J/m 2 to calculate the formation energy of TVP. The relationship between L and R is There are several reports that indicate that the trace elements or alloying elements play a critical role in the nucleation of irradiation defects. In general, voids are more easily formed in alloys than in pure FCC metals [6]. For HCP metals, like Zr, less is known, but from the relatively few studies, the void formation under neutrons irradiation seems difficult without the assistance of impurity gases or other alloy elements [7,8]. Several studies have attributed the formation of platelet or faceted voids in Zr after electron irradiation, to trace amounts of Fe [1,2]. Vacancy <c> loops are also mostly found in samples with impurity contents [8][9][10], another indication of their significant effect on vacancy effects. Atomistic calculations have shown that even 1ppm of solute Fe can decrease the formation energy of vacancy in Zr [10,11]. Hydrogen can also reduce the surface energy of basal plane in Zr and promote the aggregation of vacancies as well [4,5]. Other alloying elements, such as Sn, have been found to reduce the stacking fault energy for about 50% [12]. Impurities like oxygen also decrease the surface energy of voids in Ni and but cannot stabilize vacancy on basal plane in Zr [13,14]. The current energy-based estimate does not account for the kinetics and non-equilibrium conditions created by continuous ion bombardment. The formation of one to three layered TVPs is likely even in an ideally pure metal without the assistance of trace elements. Table S1.

Figure S5
Fig. S5. The inside/outside contrast of tiny <a> dislocation loops with sizes smaller than 5 nm formed after He irradiation at 350C. The red and yellow arrows mark the interstitial or vacancy loops, respectively.