In this paper, large-scale molecular dynamic (MD) simulation is performed to investigate the concentration-dependent vacancy volume relaxation in Al, Cu, and Au, respectively. The vacancy volume relaxation factor is calculated and correlated to the microstructure change based on MD results. It is found that the vacancy volume relaxation factor is nearly a constant at low to mid-vacancy concentration level, i.e., from 10⁻⁶ to 10⁻³ of the lattice concentrations. However, the volume of vacancies will completely collapse at the high vacancy concentration, and the coalescence of vacancies will form massive dislocations. The simulation results are in good agreement with the existing data from both experiments and simulations in the literature. A uniform empirical equation is developed to obtain the vacancy volume relaxation factor as a function of vacancy concentration. Furthermore, the hydrostatic stress is also calculated based on MD simulations. This paper also discusses the relationship between the vacancy volume relaxation and the diffusion-induced strain, such as in the application of electromigration. For a constrained condition, the hydrostatic stresses obtained from MD-based vacancy volume relaxation and a commonly used stress-vacancy equation are compared. An insight on the critical vacancy concentration at which electromigration failure would occur is discussed in detail.

在本文中，进行大规模的分子动力学（MD）模拟，以研究Al，Cu和Au中浓度依赖的空位体积弛豫。根据MD结果计算空位体积松弛因子，并将其与微结构变化相关联。发现在低至中空位浓度水平时，空位体积松弛因子几乎恒定，即从10 ^-6至10 ^-3晶格浓度。但是，在高的空位浓度下，空位的数量将完全崩溃，并且空位的合并将形成大量的位错。仿真结果与文献中的实验和仿真现有数据吻合良好。建立一个统一的经验方程，以得到空位体积弛豫因子与空位浓度的函数关系。此外，还基于MD模拟来计算静水应力。本文还讨论了空位体积弛豫与扩散引起的应变之间的关系，例如在电迁移中的应用。对于约束条件，比较了基于MD的空位体积松弛和常用的应力-空位方程获得的静水应力。