Freezing of a two dimensional fluid in to a crystalline phase : Density functional approach

TL;DR

This study uses a density functional approach to analyze the crystallization of a two-dimensional fluid, showing how the symmetry broken part influences the free energy and explaining the success of certain functionals for different potentials.

Contribution

It applies a specific free-energy functional including symmetry broken parts to 2D fluid crystallization, clarifying its effectiveness for soft and hard potentials.

Findings

Agreement with experimental and simulation data for various potentials

Symmetry broken contribution increases with potential softness

Explains limitations of previous free-energy functionals

Abstract

A free-energy functional for a crystal proposed by Singh and Singh (Europhys. Lett. {\bf {88}}, 16005 (2009)) and which contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of a two-dimensional fluid. The results found for fluids interacting via the inverse power potential $ u(r)= \epsilon ({\sigma}/{r})^{n} $ for n= 3, 6 and 12 are in good agreement with experimental and simulation results. The contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is found to increase with the softness of the potential. Our results explain why the Ramakrishnan-Yussouff (Phys. Rev. B {\bf 19}, 2775 (1979)) free-energy functional gave good account of freezing transitions of hard-core potentials but failed for potentials that have soft core and/or attractive tail.