Atomistic informed phase-field modeling of edge dislocation evolution in Σ3, Σ9, and Σ19 silicon bi-crystals

Abstract

A phase-field method is utilized to investigate the progression of dislocations in silicon bi-crystals under shear stresses at different temperatures. The study main feature is that the primary parameters of the phase field model such as the Burgers vector, the slip system height, and the distance between the dislocation cores are derived from molecular dynamics simulations at different temperatures. These calculations exhibit close alignment with existing theoretical predictions and unlike previous models, lead to a more physical dislocation growth. Due to the generation of dislocation pileup at one grain and consequently, the high stress concentration at the grain boundary, two titled slip systems at $\pm {30}^o$ appear in the adjacent grain, along with the amorphization near the grain boundary. Here, the number of dislocations for each slip system is calculated using both the molecular dynamics and phase field methods for different temperatures and under different applied shear stresses and a good agreement between their results is found. As result, the number of dislocations enhances as the temperature or the applied shear increases but not proportionally for all the slip systems. This is evidenced by a reduction in attraction forces and changes in atomic arrangement. The transformation work fields resolved by the phase field method are also compared among three silicon structures. Additionally, a parallel set of slip systems was analyzed, where different dislocations slide over each other, resulting in highly dense pileups along the grain boundary. Out of the three structures that were examined, the ∑19 structure shows the most prominent changes in atomic structure, indicating a higher propensity for such changes in equivalent conditions. The survey also confirms that all the samples under study retain structural stability within the working temperature range of 100 K to 600 K. However, as the temperature exceeds 600 K, the system loses its stability. Also, increasing the applied shear stress shows a higher impact on the ∑19 structure. Consequently, both embedded external shear stress, and working temperature are identified as critical factors influencing the dislocation evolution in silicon bi-crystals.