Abstract
Nano-structured superlattices may have novel physical properties and irradiation is a powerful mean to drive their self-organization. However, the formation mechanism of superlattice under irradiation is still open for debate. Here we use atomic kinetic Monte Carlo simulations in conjunction with a theoretical analysis to understand and predict the self-organization of nano-void superlattices under irradiation, which have been observed in various types of materials for more than 40 years but yet to be well understood. The superlattice is found to be a result of spontaneous precipitation of voids from the matrix, a process similar to phase separation in regular solid solution, with the symmetry dictated by anisotropic materials properties such as one-dimensional interstitial atom diffusion. This discovery challenges the widely accepted empirical rule of the coherency between the superlattice and host matrix crystal lattice. The atomic scale perspective has enabled a new theoretical analysis to successfully predict the superlattice parameters, which are in good agreement with independent experiments. The theory developed in this work can provide guidelines for designing target experiments to tailor desired microstructure under irradiation. It may also be generalized for situations beyond irradiation, such as spontaneous phase separation with reaction.
Highlights
Nanoscale self-organization has led to the formation of a variety of two-dimensional (2D) and three-dimensional (3D) patterned structures such as nanoparticle superlattice[1,2], surface quantum dots and ripples[3,4], nanodroplets[5], and void and gas bubble superlattices[6], in pure metals, alloys, ceramics and semiconductors
The pattern selection by dynamic instability is very sensitive to the dynamic parameters especially near post-bifurcation regime, implying that distinctively different patterns may form in the same material system, which is inconsistent with experimental observations that the superlattice structure is unique in a given material
For all 2D and 3D simulations, void superlattices have been obtained with proper choices of irradiation conditions
Summary
Nanoscale self-organization has led to the formation of a variety of two-dimensional (2D) and three-dimensional (3D) patterned structures such as nanoparticle superlattice[1,2], surface quantum dots and ripples[3,4], nanodroplets[5], and void and gas bubble superlattices[6], in pure metals, alloys, ceramics and semiconductors. The dynamic instability analysis in reaction-diffusion systems involves defect production, annihiliation and reactions, which captures the dynamic nature of defects, including SIAs, vacancies, their clusters and loops It overlooks the thermodynamic origin of the void formation. Recent 2D phase field simulations demonstrate that bubble superlattice can form in an elastically anisotropic matrix[19] It has difficulties in explaining the long-range ordering at the early, nucleation stage[9]. In addition to anisotropic elasticity, another mechanism proposed to understand the superlattice symmetry is anisotropic defect diffusion, such as 1D20–22 and 2D23 diffusion of self-interstitial atoms (SIAs) and/ or SIA clusters/loops These mechanisms, especially the 1D SIA and SIA cluster diffusion, seem consistent with many experimental observations, with support from recent 2D phase field[24,25] and 3D objective kinetic Monte Carlo (KMC) simulations[26,27]. The theory is capable to guide new experiments in various materials and under different irradiation conditions
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