Periodic and quasiperiodic crystals
Abstract
Icosahedral diffraction symmetry is analyzed in terms of proper periodicity and multiple twinning. The generation of periodic crystals with increasing lattice parameters and of quasi-periodic lattices using the cut and projection method is described; a two-dimensional quasi-periodic structure is examined. The diffraction patterns of an icosahedral structure generated from a six-dimensional lattice by a slice parallel to a three-dimensional plane with irrational indices involving tau, and of a cubic structure formed by replacing tau with a series of rational approximants are studied. The relation between diffraction pattern symmetry and crystal symmetry, and the long range order of crystals are investigated.
- Publication:
-
Scripta Metallurgica
- Pub Date:
- September 1986
- Bibcode:
- 1986ScM....20.1193G
- Keywords:
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- Crystal Lattices;
- Crystallography;
- Icosahedrons;
- Metal Crystals;
- Periodic Variations;
- Cubic Lattices;
- Diffraction Patterns;
- Lattice Parameters;
- Solid-State Physics