Elasticity and piezoelectricity of zinc oxide crystals, single layers, and possible single-walled nanotubes

The elasticity and piezoelectricity of zinc oxide $\left(\mathrm{ZnO}\right)$ crystals and single layers are investigated from the first-principles calculations. It is found that a $\mathrm{ZnO}$ thin film less than three $\mathrm{Zn}\text{−}\mathrm{O}$ layers prefers a planar graphitelike structure to the wurtzite structure. $\mathrm{ZnO}$ single layers are much more flexible than graphite single layers in the elasticity and stronger than boron nitride single layers in the piezoelectricity. Single-walled $\mathrm{ZnO}$ nanotubes (SWZONTs) can exist in principle because of their negative binding energy. The piezoelectricity of SWZONTs depends on their chirality. For most $\mathrm{ZnO}$ nanotubes except the zigzag type, twists around the tube axis will induce axial polarizations. A possible scheme is proposed to achieve the SWZONTs from the solid-vapor phase process with carbon nanotubes as templates.

Figure 1

(Color online) $\mathrm{ZnO}$ single layers. The left side is a single layer taken from the wurtzite $\mathrm{ZnO}$ crystal while the right one is the optimized structure which is a planar hexagonal lattice. The small and large balls represent zinc and oxygen atoms, respectively.

Figure 2

(Color online) Unrolled honeycomb lattice of an SWZONT. By rolling up the sheet such that the atoms in the two ends of the vector ${\mathbf{C}}_h$ coincide, a nanotube is formed. The vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are unit vectors of the hexagonal lattice. The translational vector $\mathbf{T}$ is perpendicular to ${\mathbf{C}}_h$ and runs in the direction of the tube axis.

Figure 3

Binding energy $\left(E_b\right)$ and radius $\left(R\right)$ of different SWZONTs.

Figure 4

(Color online) Schematic diagram of the vapor-solid phase process to synthesize SWZONTs with carbon nanotube (CNT) array as templates.