Many-beam dynamical scattering simulations for scanning and transmission electron microscopy modalities for 2D and 3D quasicrystals

ABSTRACT

We present a general theory of electron scattering from both 2D and 3D quasicrystals, applicable to both transmission (forescatter) and scanning (backscatter) geometries. Specifically, simulations of conventional zone axis diffraction patterns, convergent beam diffraction patterns and electron backscatter diffraction for decagonal Al${}_{70}$Ni${}_{15}$Co${}_{15}$ are presented. As expected, the geometry of the diffraction pattern is similar to kinematical patterns, but the intensity distributions show strong dynamical effects in all the modalities. Experimental electron backscatter diffraction patterns for Al${}_{70}$Ni${}_{15}$Co${}_{15}$ are compared to simulated patterns for this 2D quasicrystalline structure as well as one of its crystalline monoclinic approximant phases, Co${}_4$Al${}_{13}$. While the simulated patterns from the quasicrystalline and approximant phases are very similar to the experimental patterns, direct comparison shows a better agreement with the decagonal phase.

KEYWORDS:

• Quasicrystal
• dynamical diffraction
• TEM
• EBSD
• pattern indexing

Acknowledgments

The authors acknowledge stimulating interactions with A. Shahani and M. Widom.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors acknowledge the financial support from an ONR/Vannevar Bush Faculty Fellowship program # N00014-16-1-2821 and grant MCF-677785 for use of the computational resources of the Materials Characterisation Facility at Carnegie Mellon University.