Boron nitride formation on magnesium studied by ab initio calculations

Motivated by the state of the art method for producing boron nitride nanotubes in which magnesium has been speculated to act as a catalyst, we study the elemental chemistry of boron and nitrogen on the Mg(0001) surface using ab initio methods. We do this by considering the energetics of individual boron and nitrogen atoms, and the smallest boron and nitrogen containing molecules. We observe that magnesium promotes boron-nitride (BN) molecule formation on the catalyst surface. Based on the analysis of the behavior of BN molecules on the catalyst surface, we propose a possible route for further development of hexagonal BN sheets mediated by the catalyst

Figure 1

(Color online) Magnesium Mg(0001) surface. The top layer and the layer below are marked with lighter and darker shades, respectively. The unit cell used in this study is marked with blue color. The unit cell side is $\approx 9.6\text{Å}$ long and it corresponds to a $3\times 3$ periodicity. One side of the triangle connecting nearest neighbors in the topmost layer is $3.19\text{Å}$. Some special adsorption sites in the Mg(0001) are marked as follows: top, hcp, bri (bridge), and fcc. The fourfold tetragonal site is marked with “4” and the sixfold octahedral site with “6.” The tetragonal and octahedral sites are also illustrated from side at the rightmost panels. Distance from the tetragonal and octahedral sites to the surrounding Mg atoms are $\approx 2.0$ and $2.3\text{Å}$, respectively.

Figure 2

(Color online) Interlayer relaxations in a $1\times 1$ Mg(0001) slab: distances of layers $\left(\Delta d\right)$ when compared to the bulk magnesium case. $\Delta d=1\mathrm{\%}$ corresponds to an expansion of $26\text{mÅ}$ between the layers. Distances between layers $j$ and $j+1$ are plotted ($j=1$ being the topmost layer). The total number of layers $\left(n\right)$ is indicated in the insets of the figures. Slabs consisting of 4 up to 11 Mg(0001) layers have been considered. Relaxation patterns, when the three topmost layers are allowed to move (left panel “three free layers”) and when there are no fixed layers (right panel “free slab”) have been plotted.

Figure 3

(Color online) Variation in adsorption energies $\left(\Delta E_{ads}\right)$ for adsorbate N-2 (see Fig. 4) as a function of the number of magnesium layers in a $2\times 2$ slab. Two different simulations setups are considered: either only atoms in three topmost layers are allowed to move (blue squares) or all atoms in the slab are free to move (red triangles). Lines connecting the energy values in order to guide the eye have been plotted: values corresponding to even-numbered layers are marked with a solid line while values corresponding to odd number of layers are marked with a dashed line.

Figure 4

(Color online) Some of the most stable geometries for ${\text{B}}_2$, BN, and ${\text{N}}_2$ molecules and the B and N atoms on the Mg(0001) surface. Different geometries are tagged with the same labels as in Table . In the case of BN, magenta (blue) corresponds to boron (nitrogen). Some coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label CA.

Figure 5

(Color online) Intensity plot for charge distribution $\rho$ (surface and molecule)-$\rho$ (surface)-$\rho$(molecule), where $\rho \left(x\right)$ denotes the self-consistent charge distribution of either the isolated system ($x=\text{surface}$ or $x=\text{molecule}$) or the composite system ($x=\text{surface}$ and molecule). The plotting plane encloses the molecule axis and Mg(0001) planes are indicated with white lines. Positive values indicate accumulation of electrons. The plot corresponds to the adsorption geometry BN-1 of Fig. 4.

Figure 6

(Color online) Density of states of adsorbed ${\text{N}}_2$ molecule and the Mg substrate, projected into atom-centered magnesium orbitals (thick red line) and into N atom centered $s$ and $p$ orbitals (blue line). The electronic states have been identified using the molecular orbital theory (see, for example, Ref. 8). Panels $\left({\text{N}}_2\text{−}1\right)$ and $\left({\text{N}}_2\text{−}2\right)$ refer to the surface geometries in Table and in Fig. 4. In the inset of panel $\left({\text{N}}_2\text{−}2\right)$, the projected density of states for a situation where ${\text{N}}_2$ molecule is far away from the surface has been plotted. $E=0\text{eV}$ corresponds to the Fermi level.

Figure 7

(Color online) Density of states of adsorbed ${\text{B}}_2$ molecule and the Mg substrate, projected into atom-centered magnesium orbitals (thick red line) and into B atom centered $s$ and $p$ orbitals (blue line). For more details, see caption of Fig. 6.

Figure 8

(Color online) Density of states of adsorbed BN molecule and the Mg substrate, projected into atom-centered magnesium orbitals (thick red line) and into B and N atom centered $s$ and $p$ orbitals (blue line). For more details, see caption of Fig. 6.

Figure 9

(Color online) (a) Barrier for N diffusion (using three image points) and (b) BN association/dissociation reactions (with five image points) on the Mg(0001) surface as calculated with NEB. Atomic geometries along the minimum energy path have been illustrated in the insets.

Figure 10

(Color online) (a) Barrier for B diffusion (using five image points) and (b) ${\text{B}}_2$ (seven image points) and (c) BN association/dissociation reaction (three image points) on the Mg(0001) surface as calculated with NEB. Atomic geometries along the minimum energy path have been illustrated in the insets.

Figure 11

(Color online) Relaxation of BN molecules placed on the magnesium surface in the BN-1 adsorption geometry.