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A free-energy functional for a crystal proposed by Singh and Singh (Europhys.Lett. {\bf {88}}, 16005 (2009)) and which contains both the symmetry conservedand symmetry broken parts of the direct pair correlation function has been usedto investigate the crystallization of a two-dimensional fluid. The resultsfound 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 experimentaland simulation results. The contribution made by the symmetry broken part tothe grand thermodynamic potential at the freezing point is found to increasewith the softness of the potential. Our results explain why theRamakrishnan-Yussouff (Phys. Rev. B {\bf 19}, 2775 (1979)) free-energyfunctional gave good account of freezing transitions of hard-core potentialsbut failed for potentials that have soft core and/or attractive tail.

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