Do Helium Monolayer Films Melt by Unbinding of Dislocations?

Citation

Greif, Jeffrey Mark (1982) Do Helium Monolayer Films Melt by Unbinding of Dislocations? Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7cwm-xp02. https://resolver.caltech.edu/CaltechTHESIS:07122018-101312147

Abstract

The Kosterlitz-Thouless-Nelson-Halperin-Young theory of melting in two dimensions by unbinding of thermally excited dislocation pairs is tested against thermodynamic data on monolayer films of ³He and ⁴He on graphite. It is shown using a new analysis of the theory in the asymptotic region that a definitive test is not possible with these data because the theory is expected to be most accurate in a regime very close to the melting transition which is inaccessible to experiments that are not performed on extremely long time and length scales.

One of the two unknown parameters of the theory, that which measures the resistance to twist of the monolayer with respect to the periodic substrate, is calculated, along with the equilibrium angle, to moderate accuracy using the most recent information about the helium graphite potential from atomic scattering experiments. The other parameter, which characterizes the energy of a dislocation core, is provisionally determined by finding what values make the heat capacity of the film, computed from the theory and elastic data on the film, are consistent with experimental results.

These computations are carried out using the full renormalization group equations, crossing the transition from the solid into into the region where those equations break down, by cutting off the integration at a finite value characteristic of the size of a graphite platelet, which works until the mean distance between free dislocations decreases to approximately the size of the patch. The core parameter falls in a range considerably larger than previously estimated for classical Lennard-Jones solids and other materials. Only at large values can the dislocation heat capacity be suppressed enough not to be inconsistent with experiment.

Non-rigorous interpolation methods were developed to try to include some quantum effects in the heat capacity calculations, but these improved the agreement between the theory and the experiments only slightly.

Also appearing for the first time are extensive tables of the thermodynamic functions of ³He for coverages ranging from .001 to 1 layer and temperatures from 50mK to 10K.

Thesis Files