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Defects in Bilayer Silica and Graphene: Common Trends in Diverse Hexagonal Two-Dimensional Systems

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Defects in Bilayer Silica and Graphene: Common Trends in Diverse Hexagonal Two-Dimensional Systems

Torbjörn Björkman et al. Sci Rep.

Abstract

By combining first-principles and classical force field calculations with aberration-corrected high-resolution transmission electron microscopy experiments, we study the morphology and energetics of point and extended defects in hexagonal bilayer silica and make comparison to graphene, another two-dimensional (2D) system with hexagonal symmetry. We show that the motifs of isolated point defects in these 2D structures with otherwise very different properties are similar, and include Stone-Wales-type defects formed by structural unit rotations, flower defects and reconstructed double vacancies. The morphology and energetics of extended defects, such as grain boundaries have much in common as well. As both sp(2)-hybridised carbon and bilayer silica can also form amorphous structures, our results indicate that the morphology of imperfect 2D honeycomb lattices is largely governed by the underlying symmetry of the lattice.

Figures

Figure 1
Figure 1. Atomic structure of the two 2D structures.
(a) Graphene, top-view. (b) Texagonal bilayer silica (HBS), top-view. (c) Graphene, side-view. (d) HBS, side-view. (e) Tetrahedral structural units of the HBS structure.
Figure 2
Figure 2. Stone-Wales transformation in hexagonal bilayer silica.
(a) The pristine lattice is transformed (b) by means of rotation of a pair of structural units into (c) the final Stone-Wales defect. Note that this is a schematic illustration to visualise the transition between the initial and final topologies and that (b) does not necessarily represent an actual intermediate state.
Figure 3
Figure 3. 80 kV AC-HRTEM images of isolated defects.
Atomic models (top row) and AC-HRTEM images of isolated defects in HBS and graphene (middle and bottom rows, respectively). Stone-Wales and flower defects shown in (a) and (b) are purely structural defects with an atomic density identical to the pristine lattice. In contrast, double vacancy (c) and defects containing additional atoms (d) show density deficiency and excess, respectively. The network on top corresponds to the atomic positions in graphene and/or the positions silicon atoms in HBS. Note that the AC-HRTEM images in (c), in addition to the reconstructed divacancy schematically shown on the top row, show two merged defects of the same type, both for graphene and HBS.
Figure 4
Figure 4. Total energy as a function of successive Stone-Wales transformations in HBS for crystalline structure to the flower defect.
Black circles denote CFF and red squares DFT calculations. The insets shows strain fields around the SW defect (1 rotation), an intermediate structure after 4 rotations and the flower defect (6 rotations). Blue colour denotes expansion and red contraction in the distances between the neighbouring structural units (only connecting lines between the units are displayed).
Figure 5
Figure 5. 80 kV AC-HRTEM images of Stone-Wales transformations in HBS.
(a) Overview image of a disordered area of HBS. (b) Higher magnification image of the area marked in panel (a) along with a series of subsequent images of the same area showing intermediate atomic configurations during annihilation of a SW. (c) Two examples of SW transformations in crystalline HBS. The upper row: original AC-HRTEM micrographs. Lower row: same images with maximum filtering applied for better visibility of the defect structures.
Figure 6
Figure 6. (a) 80 kV AC-HRTEM image of grain boundaries in crystalline HBS.
(b) Example of a (1,0) grain boundary in HBS. The dashed blue lines indicates the boundary of the periodically repeating cell. The Burgers' vector, (b) for the (1,0) dislocation is indicated in the figure along with a corresponding Burgers' circuit in green. Only connecting lines between the structural units are displayed with non-hexagonal rings highlighted in pink. (c) Formation energy of different grain boundaries in HBS. CFF calculations are shown as filled symbols and DFT calculations as open symbols.
Figure 7
Figure 7. Effect of strain on the formation energy of SW.
(a) The dependence of the SW defect formation energy on various types of strain. Filled and open symbols denote CFF and DFT calculations, respectively. (b) Two Haeckelite structures produced from crystalline HBS (leftmost panels) by single SW transformations in an orthorhombic cell (upper panels, orange) and an initially hexagonal cell (lower panels, blue), four times larger than the primitive cell. Rightmost panels depict the crystalline structure subjected to a strain similar to that resulting from the Haeckelite transformation. (c) Diagram showing the energy differences for the structures in panel b, illustrating the energy gain in formation of the Haeckelite structure at large strains.

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