Neutron-diffraction study of the commensurate-incommensurate phase transition of deuterium monolayers physisorbed on graphite.

Abstract

Neutron-diffraction measurements have been performed to investigate in detail the commensurate-incommensurate (C-IC) phase transition of deuterium monolayers physisorbed on the basal planes of graphite. Several novel features have been observed. Above completion of the commensurate (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} phase a continuous phase transition to a striped superheavy domain-wall phase (\ensuremath{\alpha} phase) occurs at temperatures below 7.3 K and densities between 1.05 and 1.16 (densities \ensuremath{\rho} are given in units of the complete C \ensuremath{\surd}3 phase). With increasing density the system undergoes a first-order phase transition to the \ensuremath{\gamma} phase. This phase (1.19\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}1.32) can be described as a strongly density modulated phase, which is equivalent to a hexagonal IC phase with heavy domain walls. Due to its special modulation and rotational epitaxy, the \ensuremath{\gamma} phase locks into higher-order commensurate phases, a (5 \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{}5 \ensuremath{\surd}3 ) phase (\ensuremath{\delta} phase) and a (4\ifmmode\times\else\texttimes\fi{}4) phase (\ensuremath{\epsilon} phase). A detailed description of domain-wall lattice models is presented. At densities beyond \ensuremath{\rho}=1.33 a uniformly compressed IC phase was found. At temperatures above \ensuremath{\approxeq}7 K a reentrant fluid phase (\ensuremath{\beta} phase) is squeezed in between the C and IC phases, which is interpreted to be a domain-wall fluid. It evolves continuously to an isotropic fluid at temperatures above 18 K. Due to this unique sequence of phases occurring in a relatively wide density range (1\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}1.33), ${\mathrm{D}}_{2}$ on graphite can be regarded as a model system for the study of the C-IC phase transition. A phase diagram is proposed based on neutron-diffraction and specific-heat measurements. The results are compared to those of ${\mathrm{H}}_{2}$/graphite and discussed in the light of current theories of the C-IC transition.