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

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 (√3 × √3 )R30° phase a continuous phase transition to a striped superheavy domain-wall phase (α phase) occurs at temperatures below 7.3 K and densities between 1.05 and 1.16 (densities ρ are given in units of the complete C √3 phase). With increasing density the system undergoes a first-order phase transition to the γ phase. This phase (1.19≤ρ≤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 γ phase locks into higher-order commensurate phases, a (5 √3 ×5 √3 ) phase (δ phase) and a (4×4) phase (ε phase). A detailed description of domain-wall lattice models is presented. At densities beyond ρ=1.33 a uniformly compressed IC phase was found. At temperatures above ≊7 K a reentrant fluid phase (β 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≤ρ≤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.