Dislocation-mediated melting in two dimensions

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Authors: David R. Nelson and B. I. Halperin

Date: 1 March 1979

Physical Review B, Vol 19, No 5

Melting transition sequences for a solid on different substrates: (a)smooth substrate (b) fine mesh (c) course mesh
Elementary dislocation in (a) triangular lattice (b) square lattice.
Speculative phase diagram for material of circularly symmetric molecules in an attractive potential.


This paper discusses and develops rigorously the mathematical theory for a melting solid on smooth and periodic substrates, focusing primarily on solids with a triangular lattice. Solids on a smooth substrate undergo a two-stage melting process. First the dislocation pairs (defects) in a solid dissociate, destroying the symmetry of the crystal. This causes it to enter a liquid crystal state. Further increase in temperature causes the material to melt fully into a liquid. Solids on a periodic substrate may bypass the liquid crystal state because of the influence of the structure of the substrate.

Connection to Soft Matter

There are many relations this paper can claim with soft matter. Firstly, soft matter physics is particularly characterized by high sensitivity to temperature. The realm of the squishy physics is dominated by the limitations imposed by thermal equilibrium, and many examples of soft matter will undergo drastic changes in properties when their temperature is elevated or depressed. Therefore it is vital to have a strong intuition regarding thermodynamic phenomena such as melting and other phase transitions.

One important category of soft matter is liquid crystals. This article attempts to delineate the conditions that lead to a liquid crystal state, an existence in between the solid phase and isotropic fluid phase. Liquid crystals are various in both nature and technology. Naturally occurring liquid crystals include many proteins and cell structures. Artificial liquid crystals include LCDs (liquid crystal displays) and detergents. Much research in soft matter concerns materials that exhibit the liquid crystal phase at room temperatures, but heating the material above or below this temperature would cause it to change phase, by affecting its order and orientation.

More information: Single component phase diagrams, Phase transitions in liquid crystals