Abstract
This structural study of quasicrystals is based on extremely dense icosahedral unit cells that are systematically and consistently measured for the first time. The structure and pattern indexation are 3-dimensional. A formula is given for scattering from atoms in hierarchic arrangement and geometric series. The Quasi-Bragg law is a new law in physics, with possible applications beyond crystallography. The structure is compared with previous, unsuccessful, and contradictory, attempts at analysis.
Highlights
The structural solution for icosahedral quasicrystals has been described in several journal publications [1] [2], monographs [3]-[7] and warmly received at several conferences e.g. [8]
We find that with the edgesharing unit cells, with 3-dimensional indexation, with the Quasi-Bragg law, the structure is solved and a new law of physics is discovered
An illustration can be given for the relationship between those Fibonacci sequences and the single geometric series, base τ, that is proper in quasicrystals
Summary
The structural solution for icosahedral quasicrystals has been described in several journal publications [1] [2], monographs [3]-[7] and warmly received at several conferences e.g. [8]. The structural solution for icosahedral quasicrystals has been described in several journal publications [1] [2], monographs [3]-[7] and warmly received at several conferences e.g. Electron microscope images showed that, though the diffraction peaks were sharp, the real structure was not periodic. It was called “quasi-periodic” and the solids were referred to as “quasicrystals”. We find that with the edgesharing unit cells, with 3-dimensional indexation, with the Quasi-Bragg law, the structure is solved and a new law of physics is discovered. This follows from the multiple interplanar spacings in geometric series.
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