THE TWO-DIMENSIONAL LIQUID-VAPOR COEXISTENCE LINE OF METHANE ADSORBED ON GRAPHITE

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Dynamics of one-dimensional and two-dimensional helium adsorbed on carbon nanotubes

We present inelastic neutron scattering measurements of the dynamics of helium adsorbed on carbon nanotube bundles. The goal is to determine the vibrational properties of the 1D and 2D quantum solids that are stabilized on the nanotube bundle surfaces at different fillings of 4He. The mean square vibrational amplitude in the 1D solid is large with a Lindemann ratio of $\gamma _{1D}=(\langle u^{2}\rangle )^{1/2}/a_{1}=0.25$ comparable to bulk solid 4He. The $\gamma _{2D}$ is significantly smaller. The frequency density of states of the 2D solid, $g(\omega)$, has a gap at $\omega \simeq$ 0.75 meV consistent with a commensurate lattice. The 1D solid has no gap or a gap smeared by disorder. The 1D and 2D $g(\omega)$ are well described by dispersion curves having no gap and a gap, respectively, with some vibration along additional dimensions indicated