Incommensurate grain-boundary atomic structure

Abstract

Grain-boundary atomic structures of crystalline materials have long been believed to be commensurate with the crystal periodicity of the adjacent crystals. In the present study, we experimentally observed a Σ9 grain-boundary atomic structure of a bcc crystal (Fe-3%Si). It is found that the Σ9 grain-boundary structure is largely reconstructed and forms a dense packing of icosahedral clusters in its core. Combining with the detailed theoretical calculations, the Σ9 grain-boundary atomic structure is discovered to be incommensurate with the adjacent crystal structures. The present findings shed new light on the study of stable grain-boundary atomic structures in crystalline materials.

Fig. 1. ADF STEM image of Σ9 {221} symmetric tilt GB of the Fe-3mass%Si bicrystal.

The inset is the averaged image of the GB structure units. The scale bar represents 1 nm.

Fig. 2. Energetically stable Σ9 {221} GB structures predicted by theoretical calculations.

a, b The most stable GB structures derived from DFT calculations based on the γ-surface method and from MD calculations based on the simulated annealing method, respectively. c, d The experimental ADF STEM images of the GB structure units superimposed with the predicted structures shown in a and b, respectively. e Calculated GB energies versus simulation cell sizes along the [110] viewing direction using simulated annealing. The most stable GB energies in each simulation cell size are connected by the dashed line.

Fig. 3. Orthogonal views of the stable GB core structures described by their building units.

a–c Orthogonal views of the stable GB core structures derived by simulated annealing and their polyhedral model for the 1 × 3, 1 × 5, and 1 × 8 cell sizes, respectively. Building units of the stable GB core structures: d icosahedral cluster, e double icosahedral cluster, and f double pentagonal antiprism. The stable GB core structures for 1 × 2, 1 × 4, 1 × 7 cells are shown in Supplementary Fig. 11.

Fig. 4. Snapshots of the GB core structures simulated by MD with the 1 × 8 cell under a constant temperature of 300 K.

a–c Orthogonal views of the snapshots. The position category of the center atoms: ‘i’ or ‘p’ (see text), is shown beside the structure models. The elapsed times corresponding to b and c are 500 and 1000 fsec with a as the reference. d–f Polyhedral models of the snapshots. The name of the building units: ‘I’, ‘D’, or ‘P’ (see text), are shown beside the polyhedral models.