Bipolarons in boron-rich icosahedra: Effects of carbon substitution

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.