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The interaction and diffusion of lithium atoms in a (5,5) carbon nanotube is studied using density-functional theory. The Li-nanotube interaction perpendicular to the tube axis for a single Li inside and outside the tube is calculated and compared with the Li-graphene interaction obtained using the same technique. Both interactions are similar in the repulsive region but exhibit differences in their attractive part. Nevertheless, they can be described using a common parametrization. The Li-Li interaction is calculated as a function of their separation inside the tube. This interaction is similar to a screened repulsive Coulomb potential at small separations. However, at larger separations, the Li-Li interaction does not vanish and shows residual oscillations. This repulsive long-ranged interaction favors concerted diffusion of many Li atoms compared to the independent diffusion of individual Li inside the tube. The interaction and diffusion of lithium atoms in a ͑5,5͒ carbon nanotube is studied using density-functional theory. The Li-nanotube interaction perpendicular to the tube axis for a single Li inside and outside the tube is calculated and compared with the Li-graphene interaction obtained using the same technique. Both interactions are similar in the repulsive region but exhibit differences in their attractive part. Nevertheless, they can be described using a common parametrization. The Li-Li interaction is calculated as a function of their separation inside the tube. This interaction is similar to a screened repulsive Coulomb potential at small separations. However, at larger separations, the Li-Li interaction does not vanish and shows residual oscillations. This repulsive long-ranged interaction favors concerted diffusion of many Li atoms compared to the independent diffusion of individual Li inside the tube. Disciplines Engineering | Materials Science and Engineering Comments

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The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stability of a given grain boundary structure. For stable structures the continuum estimates of the effective moduli agree well with the exact effective moduli for the discrete model. Metastable and unstable structures are associated with a significant fraction of atoms (phases) for which the atomic-level moduli lose positive definiteness or even strong ellipticity. In those cases, the agreement between the effective moduli of the discrete and continuum systems breaks down.

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