Three-dimensional reconstruction of the atomic arrangement of icosahedral quasicrystals by binary discrete tomography

Abstract

A three-dimensional reconstruction of the structure of icosahedral quasicrystals from high-resolution transmission electron microscope images observed along high-symmetry zone-axis projections is studied. As in discrete tomography, the quasicrystalline structure is treated as a discrete set of atoms arranged on the icosahedral lattice, including atom flip sites, which is a structural disorder originating from the degrees of freedom in the internal space. The occupancy of the atoms on each site of the lattice is determined using only the zone-axis projection images without any knowledge of the image intensity. Simulation studies using icosahedral model lattices composed of several thousands of atoms were carried out to test the present reconstruction method. In the case of the ideal icosahedral lattice, a reconstruction rate of 90% is achieved from 10 projection images and a reconstruction rate of 99% is achieved from 18 projections. The reconstruction rate degrades when the projection images are misaligned. Reconstruction of the three-dimensional distribution of the atom flips is discussed.

Keywords:

• electron microscopy
• electron tomography
• icosahedral quasicrystal
• phason