Fig. 4. Alignment of single-crystalline 2D islands with various symmetries on low-index fcc surfaces and hBN (0001) surface.

The 〈110〉 or 〈11$\overline{2}0$〉 crystallographic orientations of substrates are denoted by green lines. 2D islands are represented by purple polygons. The symmetry groups of the 2D material, substrate, and the system of the 2D island on the substrate are provided. The number of different symmetry operations of the substrate and the whole system are N_sub and N_2D@sub, respectively. The nitrogen and boron atoms are represented by blue and pink spheres, respectively. The relative anti-clockwise misorientation angles of grains with different orientations are given. Due to the C_3V symmetry of hBN, the edges of a 2D material, which are parallel to hBN 〈11$\overline{2}0$〉 directions, have different local environments and not equivalent, and thus are denoted by blue and green lines, respectively.