Symmetries of migration‐related segments of all [001] coincidence site lattice tilt boundaries in (001) projection for all holohedral cubic materials

Abstract

Utilizing bicrystallography in two dimensions (2D), the symmetries of migration related segments of Coincidence Site Lattice (CSL) boundaries are predicted for projections along their [001] tilt axis in grain boundaries of crystalline materials that possess the holohedral point symmetry of the cubic system (i.e. m3m). These kinds of "edge-on" projections are typical for atomic resolution imaging of such tilt boundaries with Transmission Electron Microscopes (TEM). Such images from a recently published aberration-corrected Z-contrast scanning TEM investigation [H. Yang et al., Phil. Mag. 93 (2013) 1219 and other studies facilitate the direct visual confirmation of our frieze symmetry predictions with experimental results.

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

“…the same five macroscopic parameters) can feature different types of frieze symmetries in edge-on projections, which correspond to different low-energy structures around the interface at the atomic level [37]. In bi-crystallographic terms, different types of frieze symmetries result for the same grain boundary in edge-on projections from the sectioning of a 2D periodic dichromatic pattern or complex with the same CSL index [37,44]. The sectioning process is also known as the scanning of a dichromatic space group of any dimension for different types of subperiodic groups [31,44].…”

“…(The 3D atomic arrangement around an interface plane results, for example, from the sectioning of a dichromatic space group into a layer group [31]. When a 2D periodic dichromatic pattern or complex is sectioned [44], a 1D periodic frieze symmetry group arises [37]. )…”

“…Note that the orientation relationship and crystallographic interface plane, i.e. the five macroscopic parameters, of the grain boundaries in all of these related studies were highly precise because they were prepared with the high-temperature diffusion bonding technique [33,37,45]).…”

“…All general grain boundaries with plane interfaces can, thus, in principle be approximated to periodic high CSL index grain boundaries and bi-crystallography [31,[37][38][39][40][41] is applicable to all of them. The predictions of frieze symmetry types in atomic resolution TEM images by means of 2D bicrystallography [37] are in principle also valid for all high (and low) CSL index grain boundary approximants to general ("quasi-periodic" and "quasi-symmetric") grain boundaries with planar interfaces.…”

Towards Generalized Noise-level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

“…More or less 1D periodic 2D images of crystalline materials such as aberration-corrected STEM images of plane coincidence site lattice (CSL) grain boundaries in edge-on projections which are atomically resolved [32][33][34][35][36] are known to be underlain by both predictable [37] types of frieze symmetries and 3D atomic level bi-crystal structures [38][39][40][41]. There is at present, however, no objective way to extract the parameters of grain boundary structures at the atomic level from such images.…”