Eshelby Twist and Magic Helical Zinc Oxide Nanowires and Nanotubes

Twisted zinc oxide nanowires and nanotubes were recently synthesized by screw-dislocation growth. We show theoretically that once their diameter increases above a critical size of the order of a few atomic spacings, the existence of these structures can be rationalized in terms of the energetics of surfaces and veritable Eshelby’s twist linear elasticity mechanics supplemented by a nonlinear core term. For Burgers vector larger than the minimum allowed one, a twisted nanotube with well-defined thickness, rather than a nanowire, is the most stable nanostructure. Results are assistive for designing ultrathin nanostructures made out of nonlayered materials.

Figure 1

Atomistic representations of the relaxed configurations (left) and plots of the formation energy versus the twist angle (right) for (a) $\{5,1{\}}_{3b}$ and (b) $\{5,2{\}}_{3b}$ ZnO NTs. The Eshelby twist angles of 6.3° and 6.0°, respectively, are indicated by down arrows. The outer radius is $R=14.7\AA$. The purple (gray) plane is the cut made to create the dislocation. Note the intrinsic twist.

Figure 2

(a) Snapshots from PBC MD simulations of a $\{3,0{\}}_b$ ZnO NW. The hatched area depicts the dislocation core region. Instantaneous temperature from MD simulations (b) under PBC and (c) objective boundary conditions. The graphs of the shifted strain energy $E_{\xi }$ for twisted and untwisted ZnO NWs (d) and rescaled twist rate (e) versus the dislocation line position. Microscopic data and continuum predictions are shown with symbols and lines, respectively.

Figure 3

Comparison for the electronic band structure of (a) $\{3,0{\}}_b$ and (b) $\{3,0\}$ ZnO NWs.

Figure 4

(a) Formation energy and (b) intrinsic twist rate for ZnO NTs with different Burgers vector magnitudes, $0b$ (pristine structures), $1b$, and $3b$, versus the ration $r/R$. NTs with equal outer radii $R$ are shown in the same color. Lines correspond to Eqs. (4, 5) and symbols are the microscopic data. Arrows indicate the “magic” twisted NT structures.