The 'random' square-triangle tiling: simulation of growth

Some alloy systems, such as Ni-Cr, V-Ni-Si and Ta-Te, have quasicrystalline phases with 12-fold symmetry. These structures may be described in terms o f dodecagonal tilings by equilateral triangles and squares. The formation o f quasicrystals still poses a problem, since local information is insuffici ent for the construction of a perfect quasiperiodic structure. The growth o f real quasicrystals may be due to several mechanisms. We have simulated th e growth of a quasicrystal from a melt, consisting of squares and equilater al triangles of equal edge length. We are interested in the abundancies of the vertex configurations formed, both regular and defective. Unrestricted random growth tends to result in segregation of triangles from squares. Fav oring triangles to attract squares and vice versa brings about nearly perfe ct patterns with nearly perfect vertex abundancies, as well as realistic de fect concentrations. We have also calculated the exact vertex frequencies o f the ideal square-triangle tiling by relying on inflation symmetry. (C) 20 00 Elsevier Science B.V. All rights reserved.