Diffusion and melting in two dimensions: A quasielastic neutron scattering study of alkali metals in graphite

Abstract

Using quasielastic neutron scattering, we have studied the self-diffusion of alkali-metal atoms in stage-1 and stage-2 graphite intercalation compounds. For stage-1 compounds the diffusion proceeds via jumps to potential wells provided by the graphite substrate potential. The activation energies for diffusion in ${\mathrm{LiC}}_{6}$ and ${\mathrm{KC}}_{8}$ are 1.0 and 0.18 eV, respectively, and agree very well with theoretical values derived by DiVincenzo and Mele [Phys. Rev. B 32, 2538 (1985)] for the saddle-point energy between C-C bonds. The diffusion of alkali-metal atoms in stage-2 compounds is qualitatively very different from that in stage-1 compounds. The characteristics of the diffusive motion appear to be intermediate between those of a free liquid and a lattice liquid. The activation energies are considerably lower and compare with those of hydrogen in metals: ${E}_{a}$=0.126, 0.063, and 0.077 eV for K, Rb, and Cs, respectively, in stage-2 compounds. Moreover, the stage-2 compounds exhibit a continuous melting transition, which extends over several hundred degrees centigrade. Over this temperature range, liquidlike diffusive motion and solidlike phonon excitations coexist. We argue that this behavior is characteristic of the melting of a two-dimensional structure on a periodic substrate.