Atomic structures and mechanical properties of single-crystal GaN nanotubes

An approach is proposed to theoretically construct a realistic single-crystal GaN nanotube at atomic scale. The generated atomic structures of the single-crystal GaN nanotubes match the structural aspects from experiment very well. Our energetic calculations show that a single-crystal GaN nanotube with [100]-oriented lateral facets is more stable than that with [110]-oriented lateral facets, when they have around the same wall thickness. For a specified orientation of the lateral facets on the single-crystal GaN nanotubes, the energetic stabilities of the tubes obey a $P$ rule, in which $P$ is the ratio of the number of four-coordinated atoms to the number of three-coordinated atoms. Furthermore, the Young’s modulus of the considered GaN nanotubes decrease with increasing the ratio of the number of bulk atoms to the number of surface atoms in each type of tube. Our calculations and analysis demonstrate that the surface effect of a single-crystal nanotube enhances its Young’s modulus significantly.

Figure 1

The scheme of rolling a GaN slab up into a GaN nanotube. (a) a slab of GaN peeled from a wurtzite GaN, (b) a rolled GaN nanotube from (a), (c) the resulting structure of the GaN nanotube from MD simulation at $T=300\mathrm{K}$. (d) A steplike GaN slab. This defected slab is created through removing some atoms in related atomic layers in (a). (e) A rolled GaN nanotube containing topological defects. The apparent mismatch is circled in the figure. (f) The resulting structure of the defected GaN nanotube from our MD simulation at $T=300\mathrm{K}$.

Figure 2

Top view of GaN nanotubes with certain thickness of the wall. (a) The GaN nanotubes with [110]-oriented lateral facets (type-$\mathrm{A}$). (b) The GaN nanotubes with [100]-oriented lateral facets (type-$\mathrm{B}$). The axial directions of these GaN nanotubes are all along [001] direction.

Figure 3

The averaged energy per Ga-N diatom $\left(E_{\mathrm{Ga}\text{−}\mathrm{N}}\right)$ of each GaN nanotube as a function of the related ratio $P$. Here, $P$ is defined as the ratio of the number of four-coordinated atoms $\left(N_4\right)$ to the number of three-coordinated atoms $\left(N_3\right),P=N_4∕N_3$. The symbols stand for the calculated energies, and the lines are the results from fitting.

Figure 4

The obtained Young’s modulus as a function of $P$ for both type-$\mathrm{A}$ and type-$\mathrm{B}$ GaN nanotubes. The calculated Young’s modulus of 580 GPa for wurtzite GaN along [001] direction is also plotted as the dot line.