We performed ab initio density functional theory simulations of $\frac{1}{2}⟨111⟩$ interstitial dislocation loops, closed and open vacancy loops, $⟨100⟩$ interstitial loops and voids in tungsten, using simulation cells involving from 2000 to 2700 atoms. The size of the loops transcends the microscopic scale and reaches the mesoscopic scale where asymptotic elasticity treatment applies. Comparing the formation energies of dislocation vacancy loops and voids, we conclude that a void remains the most energetically favorable vacancy defect over the entire range of sizes investigated here. A closed $\frac{1}{2}⟨111⟩$ vacancy loop is more stable than an open loop if the number of vacancies in the loop is greater than $$45, corresponding to the diameter of the loop of approximately 1.8 nm. We have also computed elastic dipole tensors and relaxation volumes of loops and voids, representing the source terms in continuum models for radiation induced stresses and strains in the material. A detailed analysis of metastable configurations of closed and open vacancy loops performed using molecular statics simulations shows that vacancy loop configurations are not unique, and significant fluctuations of defect structures may occur in the course of microstructural evolution under irradiation.

中文翻译：

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钨中位错环和空隙的多尺度分析

我们进行了从头算密度函数理论模拟 $\frac{\mathrm{1个}}{2}⟨111⟩$ 间隙错位循环，封闭和开放的空位循环， $⟨100⟩$使用涉及2000到2700个原子的模拟单元，钨中的填隙环和空隙。环的大小超过微观尺度，并达到应用渐近弹性处理的介观尺度。比较位错空位环和空位的形成能，我们得出结论，在这里研究的整个尺寸范围内，空位仍然是最有利于能量的空位缺陷。一个封闭的$\frac{\mathrm{1个}}{2}⟨111⟩$如果回路中的空位数量大于$ 45（对应于约1.8 nm的回路直径），则空位回路比开环更稳定。我们还计算了弹性偶极张量以及环和空隙的弛豫体积，它们代表了连续模型中辐射引起的材料中应力和应变的源项。使用分子静态模拟对闭合和开放空位环的亚稳态构型进行的详细分析表明，空位环构型不是唯一的，并且在辐照下的微观结构演变过程中，缺陷结构可能会发生明显的波动。