*3.2. Cascade Simulations*

Typical time evolutions of defects in U-Mo alloy under different Mo contents are given in Figure 4. Similar curves were observed in all cases, in which the counts of defects increase rapidly to a peak value and decrease in a gradually reducing speed. Overall, the addition of Mo increases residual defect populations and Figure 5 shows that with the Mo content, increasing high percentages of residual defects were distributed in large clusters. It could then be inferred that Mo plays a negative role in the recrystallization process of the cascade damage, which in the case of pure U lattice only produces dispersed residual defects in a low population. Considering the inherent impurity of Mo, the recrystallization of bcc lattice with high symmetry might have been interfered with by the local stress and distortion provided by solute Mo atoms.

**Figure 4.** Time evolutions of the defect count in U-Mo systems with different Mo contents.

**Figure 5.** Size distributions of residual defect clusters versus Mo contents.

However, as shown in Figure 6a, a remarkable fall in residual defect populations was found when Mo contents exceeded 5 wt.%, suggesting that the decrease of Mo content from that in fuel alloys (>7 wt.%) brings about more irradiation damage with a potential acceleration of defect evolution. Meanwhile, the onset of IIR was suggested to be highly correlated with the accumulation of defect structures near GBs [31]. It could be further inferred that the local depletion of Mo in U-Mo potentially has an important influence on IIR and even accelerates swelling behavior from the primary stage. Actually, in U-Mo alloys with a relatively low Mo content (U-7 wt.% Mo), an increased swelling has already been observed [32].

**Figure 6.** Statistical results of (**a**) residual defect population and (**b**) peak values of defect population during cascade simulations with different Mo contents.

## **4. Discussion**

To investigate the underlying mechanism of the reduction of residual defect population, further attention was first paid to the spatial distribution of residual defects. Figure 7a shows the average distances between residual defects and the initial position of PKA as a function of Mo content and it could clearly be seen that the increase of Mo content restricts the spatial distribution of residual defects. Meanwhile, it could also be noted based on Figure 6b that the peak values of defect population decrease as Mo contents increase, suggesting that cascade processes are considerably limited in smaller volumes with a higher mass fraction of Mo. In general, a lattice with a lower local distortion favors a long-range transfer of kinetic energy by atomic interactions, in which case the cascade process produces more chains of interstitials squeezed in special crystal orientations, that is, crowdions. Through snapshots of defect spatial evolutions during the cascade processes, the present study also revealed that the majority of crowdions in the form of long chains vanished at the end of the simulation, which might have resulted from the reverse of displacement of those interstitial atoms. The transient formation of the crowdions could partially account the remarkable spikes in defect counts in Figure 4, especially with a lower mass fraction of Mo.

Moreover, the present study also examined the average atomic fractions of Mo among atoms with a displacement of more than 1 Å under different Mo contents, as shown in Figure 7b. Ignoring the case of pure U, Mo fractions in displaced atoms have always been observed to be lower than that in the total simulation bulk, which could also serve as a corroboration of the negative role of Mo in kinetic energy transfer. It could then be inferred that the introduction of Mo hinders the swelling of the displacement spike and thus restricts the spatial distribution of defects, which results in a higher probability of defect annihilation and a partial decrease of the residual defect population.

**Figure 7.** (**a**) Average distances between residual defects and the initial position of PKA as a function of Mo content and (**b**) Average atomic fractions of Mo among atoms with displacement more than 1 Å as a function of Mo content. The corresponding Mo atomic fractions in the total simulation bulk are also shown for comparison.

#### **5. Conclusions**

In the present research, an ADP was developed to capture atomic behaviors in U-Mo systems. Macroscopic properties including lattice constants, cohesive energies, and elastic constants were reproduced moderately well. Meanwhile, reasonable corrections were also implemented in the intermediate range of the potential, with a good agreement with DFT results. Moreover, the newly constructed potential was applied to simulations of primary radiation damage in U-Mo alloys and an uplift of residual defect population was observed when Mo content decreases to 5 wt.%. This indicates an increase of defect evolution and serves as a corroboration of the critical role of Mo depletion near GBs in the onset of IIR, and of accelerated swelling behavior in nuclear fuels.

**Author Contributions:** Conceptualization, W.L., J.L. (Jiahao Li), J.L. (Jianbo Liu), B.L. and W.O.; methodology, W.L. and J.L. (Jiahao Li); software, W.O.; validation, W.O.; formal analysis, W.O.; investigation, W.O.; resources, B.L.; writing—original draft preparation, W.O.; writing—review and editing, J.L. (Jianbo Liu). All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China, grant number No. 2017YFB0702401, and the National Natural Science Foundation of China, grant number No. 51631005.

**Acknowledgments:** The authors acknowledge Yi Wang and Jingcheng Chen for providing inspiration for dealing with technical problems.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

