**1. Introduction**

Tungsten (W), owing to its high melting temperature, good thermal conductivity, and low sputtering yield, is believed to be the most promising candidate for plasma-facing materials (PFMs) in fusion reactors [1–4]. During the operation of the reactors, high-energy neutrons escaped from the plasma will bombard on PFMs, creating plenty of self-interstitial atoms (SIAs) and vacancies in them [5]. These point defects further aggregate into small vacancy clusters including voids and dislocation loops [6–10]. Experimental observations showed voids and dislocation loops are major defect clusters in pure W at the low dpa level (less than 1.54) in the temperature range from 300 to 900 ◦C [11]. The dislocation loop can be either the vacancy dislocation loop or the interstitial dislocation loop with different properties [10–13]. The existence of various irradiated defects makes the system difficult to be understood. The interactions between them further complex the system, which is believed to play an important role in the microstructural evolution of PFMs. For examples, the dislocation loop can grow or shrink by absorbing SIAs and vacancies, respectively [14,15]. Two dislocation loops attract or repel each other when they are in different relative positions [16]. The dislocation loops and voids act as an obstacle to the dislocation glide [17–23]. For the interaction between the dislocation loop and the dislocation, it closely depends on the character and nature of the loop, and their relative

**Citation:** Li, L.; Wang, H.; Xu, K.; Li, B.; Jin, S.; Li, X.-C.; Shu, X.; Liang, L.; Lu, G.-H. Atomic Simulations of the Interaction between a Dislocation Loop and Vacancy-Type Defects in Tungsten. *Metals* **2022**, *12*, 368. https://doi.org/10.3390/ met12030368

Academic Editor: Alain Pasturel

Received: 25 January 2022 Accepted: 17 February 2022 Published: 22 February 2022

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positions and temperature [16,18–20]. For the interaction between voids and dislocations, the presence of an edge dislocation in the vicinity of the void can generate a stress field that impacts on the motion of the dislocation [23]. Therefore, understanding the interaction between these defects is very important to explore their microscopic mechanism and thus correlate them to the macroscopic mechanical properties [10,16,20,21,23].

Several previous studies focused on the interaction behaviors between vacancy-type defects and dislocation loops in iron [23–26]. Dislocation loops act as biased sinks that attract SIAs and vacancies. For the interaction between a vacancy and SIA clusters (9-127SIAs), the vacancy can be annihilated only when it is placed along the edge of the dislocation loop and parallel to the Burgers vector. When the vacancy is in a site next to the center of the cluster, it does not annihilate with SIAs but affects the motion of the cluster, reducing or even preventing its migration [24]. Furthermore, their interactions are temperature and cluster size dependent. Thus, the vacancy has an influence on the movement and evolution of the dislocation loop. When the vacancies aggregate into vacancy clusters, they can further interact with the dislocation loop in a large distance. The vacancy clusters can attract the dislocation loop due to the elastic interaction between them [27]. Molecular dynamics (MD) simulations showed that when the vacancy cluster is placed within the interaction distance to a 1/2[111] dislocation loop in W, it directly diffuses towards the vacancy cluster. The diffusion speed of the dislocation loop is related to the shape, size, and position of the vacancy clusters. The vacancy clusters can be annihilated eventually if the dislocation loop is large enough [27]. However, although several studies of the interaction between vacancy-defects and dislocation loops have been done for iron, there is still a lack of relevant investigations on W, in which the stable structure of the interstitial crowdion and the diffusion mechanism of the dislocation loop are different from that of ion [28,29]. Therefore, the objective of this work is to systematically investigate the interaction between a dislocation loop and a vacancy-type defect in W.

In this work, we study the interaction behaviors of the dislocation loop and a vacancy, di-vacancy, and vacancy clusters by using the molecular statics (MS) and MD simulations. We first calculate the binding energies of two types of 1/2[111] dislocation loops to a monovacancy. To validate the simulation results, the widely-used elasticity theory (ET) is performed to calculate their binding energies [24–26]. Then we calculate the binding energies of the 1/2[111] interstitial dislocation loop to a divacancy and a vacancy cluster using MS simulations. The effect of the vacancy cluster on the mobility of the 1/2[111] dislocation loop at different temperatures is also investigated using MD simulations. We hope our results can provide useful datasets for large-scale simulations such as kinetic Monte Carlo, cluster dynamics, and dislocation dynamics and help to study the long-term and large-scale microstructure evolution in W under irradiation.
