Abstract
The vacancy ordered phases observed in the AlCuNi system (τ phases) are described as one-dimensional vacancy ordered structures and can be looked at as rational approximants of one dimensional quasi-crystals. The different τ phases however do not belong to a single Fibonacci series. Three different Fibonacci series with different inflation rules have to be assumed in order to describe all the hitherto observed structures; some of these structures are reported here for the first time.
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