The Local Structure of the Fibonacci Chain and the Penrose Tiling from X-Ray Fluorescence Holography

Abstract

Structural investigations based on X-ray fluorescence holography can add a new perspective to the research of aperiodic systems. This technique can reconstruct the average 3-dimensional (3-D) local structure around specific elements directly from the experimental data. However, these structures can be difficult to disentangle for the complex arrangements found in quasicrystals. Therefore, we illustrate this point of view by considering appropriate reference models with a 1-D model of a Fibonacci chain and a 2-D Penrose tiling. It is demonstrated that the holographic reconstructions correspond to a projection of the average structure. The results from X-ray fluorescence holography can then be interpreted as statistical information on inter-atomic connections in the system.