PROPERTIES OF RANDOM TILINGS IN 3 DIMENSIONS

Three-dimensional icosahedral random tilings with rhombohedral cells a re studied in the semientropic model. We introduce a global energy mea sure defined by the variance of the quasilattice points in orthogonal space and justify its physical basis. The internal energy, the specifi c heat, the configuration entropy, and the sheet magnetization las def ined by Dotera and Steinhardt [Phys. Rev. Lett. 72, 1670 (1994)]) are calculated. Since the model has mean-field character, no phase transit ion occurs in contrast to matching-rule models. The self-diffusion coe fficients closely follow an Arrhenius law but show plateaus at interme diate temperature ranges, because there is a correlation between the t emperature behavior of the self-diffusion coefficient and the frequenc y of vertices which are able to Aip (simpletons). We demonstrate that the radial distribution function and the radial structure factor depen d only slightly on the random tiling configuration. Isotropic interact ions lead to an energetical equidistribution of all configurations of a canonical random riling ensemble and do not enforce matching rules.