Abstract
The tiling and covering of images derived from the experimental technique of high-resolution transmission electron microscopy (HRTEM) has been a fruitful avenue in studies of bulk quasicrystal structures. In particular, the quasi-unit-cell model has been successfully applied to the 2-dimensional decagonal AlNiCo (d-AlNiCo) quasicrystal (see Sect. 8.3.1). However, HRTEM is a bulk technique and can only be used to observe the average structure over the thickness of the sample. On the other hand, scanning tunneling microscopy (STM) is a purely surface technique. Hence, if high-quality images of quasicrystal surfaces can be obtained, then the possibility arises of applying tiling and covering methodologies to these surfaces, with a view to elucidating their structure and determining whether or not they are terminations of the bulk. A corollary of this approach is that such studies would provide independent verification of current bulk tiling and covering models. In this chapter, we describe our attempts to apply tilings and coverings to images of surfaces of quasicrystals obtained using STM [1, 2, 3, 4, 5, 6, 7].
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McGrath, R., Ledieu, J., Cox, E.J., Diehl, R.D. (2002). Tilings and Coverings of Quasicrystal Surfaces. In: Kramer, P., Papadopolos, Z. (eds) Coverings of Discrete Quasiperiodic Sets. Springer Tracts in Modern Physics, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45805-0_8
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