Positron-annihilation studies on Al-Cu-Fe: their significance for the structural models of icosahedral quasicrystals

We have investigated the vacancy defects in samples of quasicrystalline Al-Cu-Fe using positron-lifetime measurements as a function of various heat treatments and alloy compositions. In general, a two-component positron-annihilation-lifetime spectrum seems characteristic of quasicrystalline Al-Cu-Fe and other icosahedral quasicrystals. This can be interpreted in terms of vacancy defects, whose concentrations are about three orders of magnitude more than what one usually observes in crystalline metals at room temperature. We discuss the significance of the results of our studies for the structure of icosahedral quasicrystals, for which several models have been postulated in the literature. The concentration of the vacancy defects observed by us seems incompatible with the icosahedral-twin model or, at first sight, with the space-filling Penrose tiling based models or random-tiling models