The Al-Mn decagonal phase Part 3. Diffraction pattern simulation based on a new index scheme

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Abstract
A proposal to abandon the current sophisticated index scheme of the Al-Mn decagonal phase has recently been advanced (Fitz Gerald, Withers, Stewart and Calka 1987), in favour of a new straightforward description. This description is based on a periodic stacking of Penrose lattices which are two-dimensional, using the natural in-plane (quasi-periodic) a 6 (n = 1 to 5) and (periodic) a 6 vectors as its basis. It affords a simpler description than the currently adopted system which is based on the lower and upper edge vectors of a (distorted icosahedral) pentagonal bipyramid model, with useful advantages for example in comparing vectors of identical quasiperiodic but different periodic components. Computing the diffraction pattern is straightforward in our description, and our simulations show excellent agreement with patterns recorded experimentally at various projection angles.