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Updated: Aug 2, 2026

Microcrystallography of Protein Crystals and In Cellulo Diffraction
Published on: July 21, 2017
A multigrid approach to the average lattices of quasicrystals
J L Aragón1, Gerardo G Naumis, M Torres
1Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 1-1010, 76000 Querétaro, Mexico. joselouis@fisica.unam.mx
Abstract:
An average structure associated with a given quasilattice is a system composed of several average lattices that in reciprocal space produces strong main reflections. The average lattice of a quasicrystal is a useful concept closely related to the geometric description of the quasicrystal to crystal transformation and has been proved to be structurally significant. Here we calculate average structures for arbitrary two- and three-dimensional quasilattices using the dual generalized method. Additionally, closed analytical expressions for the coordinates of the average structure, the quasiperiodic lattice and its diffraction pattern are given.
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