Band Structure of `BeB2'

The actual composition of `BeB₂' as reported is Be_29.5B₈₁. The space group of the unit cell is P-62m. In the unit cell, there are 12 inequivalent B sites and 7 inequivalent Be sites, one of the latter being only half occupied.

VRML of Be₃₁B₈₁ crystal. Two rhombohedral unit cells are shown. The extra occupied Be sites are in green, and in the Be₂₉B₈₁ these sites are empty. Boron are in blue (two shades), Be are red. c axis is in the plane of the page in the initial orientation.
Discussion and images of the crystal structure (5/11)

Here are preliminary energy bands, based on a very crude full potential LAPW calculation. The self consistent potential uses 100 k points in the Fermi surface integration. We calculated band structures for two compounds

Be₃₁B₈₁ where the extra Be site is fully occupied.
Be₃₁B₈₁ where the extra Be site is empty.

The bands for Be₃₁B₈₁from -17 eV to +8 eV.
The bands for Be₃₁B₈₁ from -1.5 eV to +1 eV.
Results for Be₃₁B₈₁.
- There is a clear 0.85 eV gap between the valence bands and the conduction bands. The fermi energy is close to the bottom of the conduction bands.
- The valence band maximum is at A and lies 0.85 eV or so below the lowest conduction band.
- From the expanded view, we see two apparent hole-like bands (as of 4/24 peaking at E_F?) and one electron band (min at E_f-0.1 eV), all centered at M.
- Note that the bands at the edges of the conduction and valence band are very flat.
Bands for Be₂₉B₈₁. Here the fermi level lies below the gap (4 fewer electrons donated by Be) and the gap is somewhat wider than in Be₃₁.

Improved Calculations

We have now finished better calculations using 21 kpts in the IBZ and adding local orbitals for the 3s, 3p states on each atom. The band structure of Be₂₉B₈₁ is qualitatively the same as before, but the band gap has nearly doubled.

First we present results for Be₂₉B₈₁. While the band structure is qualitatively the same as our first calculation, the band gap is large and the uppermost three bands that cross the Fermi level have split off a bit from the tangle of states below it.

Bands without atomic character.
Bands for B on site 1.
Bands for B on site 2.
Bands for B on site 3.
Bands for B on site 4.
Bands for B on site 5.
Bands for B on site 6.
Bands for B on site 7.
Bands for B on site 8.
Bands for B on site 9.
Bands for B on site 10.
Bands for B on site 11.
Bands for B on site 12.
Bands for Be on site 13.
Bands for Be on site 14.
Bands for Be on site 15.
Bands for Be on site 16.
Bands for Be on site 17.
Bands for Be on site 18.

Here are the results for Be₃₁B₈₁. There is not as much change here; the band gap remains at 0.8 eV. Compare the corresponding figures for each atom and you will see qualitative agreement with the atomic character.

Bands without atomic character.
Bands for B on site 1.
Bands for B on site 2.
Bands for B on site 3.
Bands for B on site 4.
Bands for B on site 5.
Bands for B on site 6.
Bands for B on site 7.
Bands for B on site 8.
Bands for B on site 9.
Bands for B on site 10.
Bands for B on site 11.
Bands for B on site 12.
Bands for Be on site 13.
Bands for Be on site 14.
Bands for Be on site 15.
Bands for Be on site 16.
Bands for Be on site 17.
Bands for Be on site 18.
Bands for Be on site 19.