The Quasicrystal Model as a Framework for Order to Disorder Transitions in 2D Systems

Proceedings

Cherkas, Sergey L.¹  Cherkas, Nadezhda L.² 

[1] Institute for Nuclear Problems, Belarus State University, 220030 Minsk, Belarus;Military Academy of the Republic of Belarus, 220057 Minsk, Belarus

关键词: order to disorder transitions;    2D objects;    radial distribution function;    quasicrystal model;    wavelet;    porous aluminium oxide;    hard disks in a plane;   

DOI  :  10.3390/IECC_2018-05251

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

Order to disorder transitions are important for 2D objects such as oxide films with a cellular porous structure, honeycomb, graphene, and Bénard cells in liquid and artificial systems consisting of colloid particles on a plane. For instance, solid films of the porous alumina represent an almost regular quasicrystal structure (perfect aperiodic quasicrystals discovered in 1991 is not implied here). We show that, in this case, the radial distribution function is well described by the quasicrystal model, i.e., the smeared hexagonal lattice of the two-dimensional ideal crystal by inserting a certain amount of defects into the lattice. Another example is a system of 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, a 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 short distances. Dependences of the lattices constants, smoothing widths, and impurity on the filling parameter are found. Transition to the order occurs upon an increasing of the hexagonal lattice contribution and decreasing of smearing.

【 授权许可】

CC BY