Development of a Systematic and Efficient Method for Searching for the Most Stable Grain Boundary Structures—A Method Based on Non-Identical Termination Combination

The rich diversity of grain boundaries (GBs) can affect macroscopic properties of entire material in various situations. Determining GB structures as systematically and as rapidly as possible is the first step toward understanding the properties of materials with GBs. Currently, a common method for determining the GB structure is a sequential grid search of rigid body translation (RBT), which is computationally expensive. Therefore, there is a need to develop a systematic and efficient method to search for the most stable GB structures.<br/>The GBs are generally considered to be complex and have random structures, but it is known that characteristic structures (structural unit) appear on some GBs [1][2]. In this study, we have found that the structural units of the most stable GBs are naturally reproduced in a comprehensive combination set of GB plane terminations without considering the variation in RBT. Since the number of GB plane terminations is limited systematically by the crystal geometry, it may be possible to reduce the number of candidates for searching the most stable GB structures by focusing only on non-identical GB plane terminations. Based on this assumption, here we propose a new method for searching the most stable GB structures based on the non-identical GB plane terminations.<br/><br/>We chose symmetric tilt GBs with three rotational axes of [100], [110], and [111] in fcc Cu and bcc Mo as our research targets. Based on coincident site lattice theory, 170 GBs with Σ less than 100 were selected. First, relaxation calculations have been performed based on conventional brute-force RBT grid searching method. Then, in the same way, the relaxation calculations have been performed only on structures with non-identical end-face (termination) combinations among them. The most stable GB’ s energies and computational cost obtained by these two methods were compared. In addition, we have taken one GB with Σ&gt; 100 (Σ157[001](-11 6 0)), which generally requires a large amount of computational cost to determine the most stable GB structure, as an example and evaluated utility of our new method. The relaxation calculations were performed with the LAMMPS code [3] and GB model were made by Interface Master [4].<br/><br/>For almost all of the 170 GBs, the most stable GB structures obtained from the structures screened by focusing on the combination of non-identical GB plane terminations have shown agreement with those obtained from the conventional brute-force calculations with high accuracy.<br/>We have also found that the number of the screened structures, with which is necessary to obtain the most stable GB, decreases down to several times value of Σ. For example, our method can find the most stable structure of Σ157[001](-11 6 0)ΣGB with only 1/120th the number of candidate structures of the conventional brute-force calculations. This result indicates that the selection of the candidate structures based on the GB plane termination is closely related to the conditions for the most stable GB structures and can be applied to the fast determination of GB structures. This result indicates that the generated structures by changing the GB plane termination are sufficient enough to determine the most stable GB structures.<br/><br/>These results suggest that the GB plane termination plays an important role in determining whether GB structures of single-element crystals become the most stable or not. To determine the most stable structure of GBs systematically and efficiently, it would be effective to focus on the combination of non-identical terminations. We are now applying this method to other GBs such as twist GBs and GBs in oxides.<br/><br/>[reference]<br/>[1] A. P. Sutton <i>et al</i>, Philos. Trans. R. Soc. Lond. A 309, 1–36 (1983).<br/>[2] K. Inoue <i>et al</i>, Mater. Trans. 56, 281–287 (2015).<br/>[3] A. P. Thompson <i>et al</i>. Comput. Phys. Commun. 271, 108171 (2022).<br/>[4] Y. S. Xie, K. Shibata, and T. Mizoguchi et al.., submitted.