Quasicrystal model as framework for an order to disorder transitions in 2D systems.

An order to disorder transitions are important for 2D objects such as oxide films with cellular porous structure, honeycomb, graphene, Bénard cells in liquid and artificial systems consisting of colloid particles on a plane. For instance, solid films of the porous alumina represent almost regular quasicrystal structure. We show that in this case the radial distribution function is well described by the quasicrystal model [1], i.e. the smeared hexagonal lattice of the two dimensional ideal crystal with inserting some amount of defects into the lattice. Another example is a system of the hard disks in a plane which illustrates the order to disorder transitions. It is shown, that the coincidence with the distribution function, obtained by the solution of the Percus-Yevick equation is achieved by the smoothing of the square lattice and injecting the defects of the vacancy type into it. However, better approximation is reached when the lattice is a result of a mixture of the smoothened square and hexagonal lattices. Impurity of the hexagonal lattice is considerable at the short distances. Dependences of the lattices constants, smoothing widths and impurity on the filling parameter are found. Transition to the order looks as an increasing of the hexagonal lattice contribution and decreasing of smearing.

           [1] Cherkas, N.L. & Cherkas, S.L. Crystallogr. Rep. (2016) 61: 285. https://doi.org/10.1134/S106377451506005X