Melting in Two Dimensions
T. Kaplan, K. Chen, and M. Mostoller (ORNL)
F. Somer and G. Canright (U Tennessee)
Melting is a fundamental process everyone has observed, as in the melting
of ice. Yet in three dimensions, the process is understood only on
a macroscopic thermodynamic level, not at the atomistic level. In
two-dimensions (2D), an elegant theory for melting has been proposed by
Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) in a series of
papers in the 70's. It predicts that a new phase, called the
hexatic, exists between the solid and liquid in a certain portion of the
phase diagram. In the hexatic phase, the 2D system has no
long-range translational order but does retain quasi-long-range
orientational order. More than two decades of intensive study
including a great many experiments and simulations have provided
ambiguous evidence on the nature of the transition.
In 1995, we published [1] a study in which molecular dynamics (MD)
simulations were performed that confirmed the existence of the hexatic
phase predicted by KTHNY. These simulations utilized the ORNL Intel
Paragon computers and were the first that involve system sizes and time
scales adequate to test the theory. In addition to this greater
computer power, a recently developed exact MD scheme was used to generate
a correct constant temperature and pressure statistical ensemble that is
essential in a proper treatment of the melting process. These simulations
provided the strongest evidence yet for the validity of the KTHNY
theory.
Following this work, we have investigated the inherent structures
associated with the equilibrium phases of this 2D system [2,3].
Stillinger and Weber, in 1984, predicted that there are underlying
potential energy minimum structures that a phase is connected to via
steepest decent paths. It is these structures that are referred to
as “inherent structures.” Our results provide strong support both
for the inherent structure theory of classical fluids, and for the KTHNY
theory of melting. This support comes from the observation of three
qualitatively distinct phases of inherent structures: a crystal, a
“hexatic glass”, and a “liquid glass.” We also observe, in the
inherent structures, analogs of the defect unbinding mechanisms predicted
by KTHNY to mediate the two-phase transformations.
For a non-technical review of the molecular dynamics simulations and
the KTHNY theory of 2D melting see
"How Solids Melt".
[1] Kun Chen, Theodore Kaplan, and
Mark Mostoller, "Melting in Two-Dimensional Lennard-Jones Systems:
Observation of a Metastable Hexatic Phase," Phys Rev Lett.
74, 4019 (1995)
[2] F. L. Somer, G. S. Canright, T. Kaplan, Kun
Chen, and M. Mostoller, "Inherent structures and two-stage melting in
two dimensions," Phys. Rev. Lett. 79, 3431 (1997)
[3] F.
L. Somer, G. S. Canright, and T. Kaplan, "Defect-unbinding transitions
and inherent structures in two dimensions," Phys. Rev. E
58, 5748 (1998)