Structural and Mechanical Properties of Boron Nanotubes
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Structural and Mechanical Properties of Boron Nanotubes
Matthew H. Evans , John D. Joannopoulos , and Sokrates T. Pantelides Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, U.S.A. Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A. ABSTRACT We report the results of first-principles calculations showing that boron can form a wide variety of metastable planar and tubular forms with unusual electronic and mechanical properties. The preferred planar structure is a buckled triangular lattice that breaks the threefold ground state degeneracy of the flat triangular plane. When the plane is rolled into a tube, the ground state degeneracy leads to a strong chirality dependence of the binding energy and elastic response, an unusual tubes derive their structure from property that is not found in carbon nanotubes. The achiral the flat triangular plane. The achiral boron nanotubes arise from the buckled plane, and have large cohesive energies and novel structures as a result. INTRODUCTION Boron, carbon’s first-row neighbor, has only three valence electrons. Its natural crystalline structure is a rhombohedral lattice with 12-atom icosahedral clusters at each lattice site [1]. Nevertheless, there are some intriguing similarities with carbon. Boron’s three electrons could in principle form hybrid orbitals that might lead to planar and tubular structures similar to those formed by carbon. Since carbon nanotubes and fullerenes [2] are metastable structures, formed only under kinetically constrained conditions [3], one might envision analogous boron structures. Indeed, initial results by Boustani et al. [4, 5] have demonstrated the possibility of such metastable structures with relatively low energy cost. There is an intriguing and potentially significant difference between carbon and boron, how ever. Boron has only three valence electrons, so that in -bonded planar or tubular boron struc tures the relative occupations of the - and the -bonded bands depends on the energetic positions and dispersions of the two bands, perhaps opening up a broader range of possibilities. In this paper, we examine in detail the electronic structure and relative stabilities of planar and tubular boron structures. We find that boron does form a stable -bonded hexagonal graphenelike sheet, but a planar triangular lattice has an even larger cohesive energy, though still smaller than that of the bulk -rhombohedral structure. The triangular planar structure has an unusual property. It is essentially a homogeneous electron gas system with a threefold-degenerate ground state. This degeneracy makes the flat triangular plane unstable with respect to buckling, which breaks the symmetry and introduces a preferred direction defined by strong bonds. When rolled into a tube, this preferred direction, which is not present in carbon nanotubes, defines the ch
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