Charge transfer and negative curvature energy in magnesium boride nanotubes

Using first-principles calculations based on density functional theory, we study the energetics and charge transfer effects in ${\mathrm{MgB}}_x$ nanotubes and two-dimensional (2D) sheets. The behavior of adsorbed Mg on 2D boron sheets is found to depend on the amount of electron transfer between the two subsystems. The amount is determined by both the density of adsorbed Mg as well as the atomic-scale structure of the boron subsystem. The degree of transfer can lead to repulsive or attractive Mg-Mg interactions. In both cases, model ${\mathrm{MgB}}_x$ nanotubes built from 2D ${\mathrm{MgB}}_x$ sheets can display negative curvature energy: a relatively unusual situation in nanosystems where the energy cost to curve the parent 2D sheet into a small-diameter nanotube is negative. Namely, the small-diameter nanotube is energetically preferred over the corresponding flat sheet. We also discuss how these findings may manifest themselves in experimentally synthesized ${\mathrm{MgB}}_x$ nanotubes.

Figure 1

Left: Curvature energy per atom versus diameter for model ${\mathrm{MgB}}_8$ nanotubes made from the Mg-doped $\alpha$ sheet. The diameter refers to that of the underlying boron nanotube. Right: Structure of the ${\mathrm{MgB}}_8$ sheet used to form these nanotubes. Large blue balls are Mg, small gray balls are B.

Figure 2

Left: Curvature energy per atom versus diameter for model nanotubes made from the hexagonal ${\mathrm{MgB}}_2$ sheet. The diameter refers to that of the underlying boron nanotube. Right: Structure of the hexagonal ${\mathrm{MgB}}_2$ sheet used to form the nanotubes. Large blue balls are Mg, small gray balls are B.

Figure 3

Structures, adsorption energies, and Mg-Mg distances for six Mg-doped $\alpha$-sheet structures: (a) isolated Mg, (b) Mg dimer, (c) ${\mathrm{MgB}}_8$, (d) ${\mathrm{Mg}}_2{\mathrm{B}}_8$, (e) ${\mathrm{Mg}}_3{\mathrm{B}}_8$, and (f) ${\mathrm{Mg}}_{25}{\mathrm{B}}_{72}$. Large blue balls are Mg, small gray balls are B.

Figure 4

Fermi level of boron sheets with respect to vacuum from DFT-LDA calculations versus hexagonal hole density $\eta$. The red circles are the calculated data, and the blue solid curve is a fit to guide the eye.

Figure 5

Electron transfer in e/Mg from absorbed Mg to boron sheets calculated using maximally localized Wannier functions (blue circles) and Löwdin orbitals (red squares) for a variety of boron sheets as a function of the hexagonal hole density $\eta$ of the sheets.