Bipolarons in boron-rich icosahedra: Effects of carbon substitution.

Abstract

Analysis of electronic-transport and magnetic measurements on boron carbides has indicated that charge transport occurs via bipolaron hopping between the twelve-atom icosahedral structural units of these solids. Two types of isoelectronic icosahedral units are neutral icosahedral boron clusters (${\mathrm{B}}_{12}$ icosahedra) and positively charged clusters of eleven boron atoms and a carbon atom [(${\mathrm{B}}_{11}$C${)}^{+}$ icosahedra]. In particular, the transport analysis assumes that it is energetically favorable for an electron pair to occupy a (${\mathrm{B}}_{11}$C${)}^{+}$ icosahedron rather than a ${\mathrm{B}}_{12}$ icosahedron. Here, we study the energy changes and atomic displacements associated with adding two electrons to a (${\mathrm{B}}_{11}$C${)}^{+}$ icosahedron in neutral surroundings and compare our results with our previous study of two electrons added to an analogous ${\mathrm{B}}_{12}$ icosahedron. We find that the addition of the two electrons reduces the (${\mathrm{B}}_{11}$C${)}^{+}$ system's energy by about 18 eV.Most of this energy reduction, \ensuremath{\simeq}16--17 eV, is associated with the two electrons filling bonding orbitals associated with all of the atoms of the positively charged icosahedron. The remainder of the energy reduction is associated with the polaronic displacements, the contraction of the icosahedron induced by the placing of the two electrons in icosahedral bonding orbitals. Indeed, the energy reduction associated with adding two electrons to form a (${\mathrm{B}}_{11}$C${)}^{\mathrm{\ensuremath{-}}}$ icosahedron is greater than that associated with adding two electrons to form a ${\mathrm{B}}_{12}$${\mathrm{}}^{2\mathrm{\ensuremath{-}}}$ icosahedron by about 14 eV. This is because the increased Coulombic attraction of the two electrons arising from the extra positive charge provided by the carbon nucleus exceeds the increases in electronic kinetic energy and electron-electron repulsion energy associated with the icosahedron's reduced symmetry. Thus, it is energetically preferable for an electron pair to occupy a (${\mathrm{B}}_{11}$C${)}^{+}$ icosahedron rather than a ${\mathrm{B}}_{12}$ icosahedron. This supports the notion, arising from analysis of electronic transport experiments, that bipolaron hopping occurs between ${\mathrm{B}}_{11}$C icosahedra.