For full reference please see: Phys. Rev. B 83, 024101, 2011 We examine the behaviour of hydrogen ions, atoms and molecules in α-boron using density functional calculations. Hydrogen behaves as a negative-U centre, with positive H ions preferring to sit off-center on inter-layer bonds and negative H ions sitting preferably at in-plane sites between three B12 icosahedra. Hydrogen atoms inside B12 icosahedral cages are unstable, drifting off-center and leaving the cage with only a 0.09 eV barrier. While H 0 is extremely mobile (diffusion barrier 0.25 eV), H + and H − have higher diffusion barriers of 0.9 eV. Once mobile these defects will combine, forming H2 in the interstitial void space, which will remain trapped in the lattice until high temperatures. Based on these results we discuss potential differences for hydrogen behaviour in β-boron, and compare with experimental muon-implantation data.PACS numbers: 61.72. Cc,71.15.Mb,88.85.mh,13.35.Bv Boron is a fascinating elemental material about which we are still making many new discoveries. Only recently a new form of Boron was found, showing unusual negative-U behaviour between B 12 and B 2 sub-units within the crystal 1 . Sitting somewhere between metals and insulators on the periodic table, the bonding in boron is strongly dependent on local environment and factors such as temperature, pressure and impurities. The simplest such impurity is hydrogen, yet to date no studies exist of the behaviour of hydrogen in bulk boron.To date 16 allotropes of elemental boron have been reported. The best known crystal phases are the α-rhombohedral structure (α-boron) and the β-rhombohedral structure (β-boron), as well as two tetragonal modifications which are probably stabilized by foreign atoms 2 . The α-boron structure as the simplest of them contains 12 atoms in a rhombohedral unit cell forming a slightly distorted icosahedron (B 12 , see Figure 2). More complex, but thermodynamically stable at high temperatures is the β-boron crystal with a unit cell containing 105 atoms 3 . Compared with the α-boron phase, β-boron bulk is less dense and softer4 . An even more stable modification of β-boron has been proposed with 106 atoms in the unit cell 5 . Boron based nanostructures have also been proposed 6 , and boron single and double wall nanotubes and boron nanoribbons have been reported 7-9 .Boron compounds have been proposed as promising candidates for hydrogen-storage 10 , for example alkali doped boron sheets as possible hydrogen acceptors 11 . Although such applied studies are already underway, there still remains much to understand concerning hydrogen behaviour in the crystalline boron phases, which forms the subject of the current article. Given that the B 12 -icosahedron is the basic element for both rhombohedral modifications, we have focused on the simpler α-boron phase. Based on these results comparable sites for the β-boron phase are discussed.
I. COMPUTATIONAL DETAILSWe perform density functional theory calculations under the local density approximation as implem...