Reentrant melting of krypton adsorbed on graphite and the helical Potts-lattice-gas model.

Abstract

A model is constructed which explicitly includes the microscopic phenomena occurring in krypton adsorbed on basal graphite from submonolayer to dense-layer regimes. Second-layer adsorption is also included. The experimentally observed reentrant phase diagram, in the pressure and temperature variables, is reproduced. The problem requires different renormalization-group transformations at different length scales. Sublattice occupation and vacancy fluctuations are accounted for, starting from the length scale of the separation of adsorption sites. Dense domain-wall fluctuations, as well as their crossings and dislocations, are accounted for starting from the length scale of minimum wall separation. The physical mechanism for the reentrant phase boundary is clearly detected: At high temperatures, the first layer is disordered due to vacancies. As the system is cooled at constant pressure, condensation from the vapor permits epitaxial connectivity, and ordering takes place. Upon further cooling, further such condensation creates comparable quantities of heavy and superheavy domain walls connected by dislocations, which disrupt the long-range epitaxial (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 commensurate) order. Thus, the system disorders. Upon further cooling, further condensation creates predominantly the denser superheavy walls, which start crossing. Another phase transition occurs as the superheavy walls percolate into an infinite hexagonal network. The experimentally observed maximum temperature for commensurate order is accurately obtained, with the use of the known krypton potentials. The maximum pressure is obtained for a wall energy of 83 K per unit length. In the coverage and temperature variables, our calculated phase diagram agrees quantitatively with monolayer experimental data and suggests that second-layer phase separation rather than incommensurate melting has been detected by specific-heat measurements. Effective vacancies, namely adsorbed regions of short-range disorder, are also included in the theory and extend the range of first-order transitions. The movements of atoms away from lattice-gas positions are also accounted for.