From experimental results it is known that the unit cell of the nanomesh on rhodium consists of 13x13 h-BN or 12x12 Rh atoms. Schematically it means that 13 boron (B) or nitrogen (N) have to "sit" on 12 Rh, as it is shown on the left. This means that the position of the B or N atoms is not always the same compared to the Rh atoms of the substrate.

The figure on the right describes the force acting on N (blue curve) or B (red curve) atoms of the nanomesh in function of the distance between the Rh surface and the nanomesh. The results show that N is always repelled from the surface (positive force), in contrast to B, which is always attracted (negative force). Nevertheless they are repelled or attracted with different intensities, so that formation of the nanomesh is possible. The N repulsion is balanced by the B attraction when the distance between the nanomesh and the Rh surface is about 2.2 Å. No nanomesh can exists much closer to the substrate since the N repulsion becomes too high. When the distance between the nanomesh and the Rh surface increases, the nanomesh is still bound to the surface since the B attraction dominates.

The differences in the B and N forces is due to different occupation degrees of the bonding and antibonding states of the respective electronic structures at different energies.

The maps on the left show the forces acting on N (left) and on B (right) when these atoms are located at 2.17 Å (uper maps) and 2.57 Å (lower maps) above the Rh surface. The different colors correspond to the force with which the B or N atoms are attracted/repelled from the Rh surface. The red color corresponds to stronger repulsion, and blue corresponds to stronger attraction. From these maps (also see below) we see that the N repulsion is the weakest in the pores (top site) and strongest on the wires (near fcc), while for B the opposite happens.

Remember that B and N atoms have to occupy different positions compared to the Rh surface atoms due to the fact that 13 boron nitride atoms have to take place on 12 Rh atoms (lattice mismatch). In addition, N atoms repel themselves due to a polarization effect mediated by different deformations of the boron nitride bonds. Since this NN repulsion decreases the force acting on N, the curvature of the nanomesh monolayer is enhanced. The force constant acting only on N is 6.8 eV/Ų.

Finally it has to be emphasized that the B-N bond is rather stiff with a force constant of 48.6 eV/Ų, so that almost no modification of the bond length happens.

All these information allowed to simulate the full nanomesh, which is presented on the right. The upper right figure shows a map of the high of the N atoms with respect to the Rh surface. The blue "circles" correspond to the pores, where the nanomesh lies at the nearest of the Rh surface at a distance of about 2.2 Å. The wires around the pores have two different regions. The red one is 2.7Å above the surface, and the yellow one sits 2.5 Å above the Rh. An atomic distribution model of these three main regions is also given.

This model reproduces perfectly STM measurements of the nanomesh (image just above this text) taken at 77K. In STM measurements of the nanomesh, only N atoms are visible. The comparison with the map on the right is therefore possible. At such cold temperatures the atomic movements are reduced, allowing to get images with very high resolution. Each "ball" corresponds to an N atom. This image shows that the nanomesh forms a continuous layer with visible pores.

The lower right figure shows the arrangement of the B, N and Rh atoms over one unit cell (delimited by black lines in the upper map). This model shows clearly that N (yellow) sits exactly on top of a Rh atom only in the middle of a pore, while B (light blue) sits exactly in-between Rh atoms. The position of the boron nitride atoms relative to the Rh ones is always more shifted when you go from a pore to a wire. At the highest region of the wire, neither N (red) nor B (dark blue) sit on top of a Rh atom, but they form an hexagonal ring around it. In the lower part of the wires, colored in yellow in the map, the B sit on top of the Rh atom.

Simulations predict that the pores occupy around 70% of the nanomesh, whereas the other 30% correspond to the wires. The transition between the pores and the wires is relatively abrupt and the high difference between these two regions has been calculated to be 0.55 Å, which is close to STM measurements.

The last experimental measurements (figure on the left) confirm that the two sigma pics detected by UPS correspond to two different species of the nanomesh. STM measurements performed at sample bias voltages corresponding to the energy position of these pics enhance the wires (top) or the pores (bottom), which appear bright, respectively.


In conclusion, the boron nitride nanomesh on Rh(111) surfaces consists of a single h-BN layer, which is highly corrugated. The 2- nm-sized pores are formed by regions where the layer binds strongly to the underlying metal, while the regular hexagonal network of mesh wires represents regions where the layer is not bonded to the rhodium surface but only through strong cohesive forces within the film itself.