Melting transition of two-dimensional crystals

Abstract

The solíd-liquíd phase transítíon (PT) in two-dímensional crystals is studied under the assumption that it ís driven by the díssocíation of elastic dípoles. It ís shown that thís PT ís of tirst-order and corresponds to a díssocíatíon transítion of elastic dipoles. For systems where, via thermal nucleation metastable polycrystalline states are possible besides elastic-dipole formation, a more-complex phase díagram is postulated with !ines of tirst-and second-order PT. In the light of these concepts molecular-dynamics experiments with long-and short-range interactions in two and three dimensions are discussed. Solid-liquid PT observed in various experimental monolayer systems and showing tirst-and second-order PT are interpreted in terms of the theory developed.

Mobility measurements of two kinds of two-dimensional fluids. Methane adsorbed on graphite

“…Very recently, these views seem to have been confirmed experimentally for helium submonolayers [9]. However those predictions were questioned by other theorists [10][11][12] who claimed that melting is a first order transition, i.e. 2D isotropic liquid occurs suddenly at melting.…”

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting

“…(14) is given by disk of large enough radius R with two disks of small radii ε centered at x 1 and x 2 cut out. The integral (14) is evaluated by the limiting trick: we replace U(κ|x 1 − ξ|) by U(ρ|x 1 − ξ|) and drop the operator (D κ ) l out the integration symbol. We use Green's first identity [41] for thus arising integral over the multi-connected domain.…”

“…Dislocations are of importance also for two-dimensional melting [14][15][16][17] being an example of the defect-mediated phase transitions in the two-dimensional systems [18][19][20][21]. The textbooks [22,23] summarize a large body of original work on the gauge theory of the line-like defects and the phase transitions caused by their proliferation.…”

Shock waves in a transverse magnetic field

“…In a 2D system these dislocations are point defects which have a comparable entropy and energy to vacancies, and so are present in thermodynamic equilibrium. The presence of dislocation dipoles of this type has been postulated, and has been used to explore dislocation theories of (2D) melting (Cotterill et a1 1974, Holz and Medeiros 1978, Halperin and Nelson 1978. Such dislocation dipoles can exist in a monolayer, independent of the detailed structure of the substrate, but they are not necessarily the lowest-energy defect configuration.…”

“…The result arises from the lack of a dipole strain field of the K-dislocation configuration and the efficacy of the edge M-dislocations in accommodating misfit. This low energy means that the trigon is almost certainly the defect which should be considered in conjunction with 2D melting theories (Holz andMedeiros 1978, Halperin andNelson 1978), although this defect in itself may be insufficient to account in detail for melting because of the cooperative nature ofthe transition. However, at lower temperatures this is the defect that should be created thermodynamically.…”