2014•Acta Physica Polonica AOpen access

Coincidences of a Shifted Hexagonal Lattice and the Hexagonal Packing

Jeanine Concepcion H. Arias, E.D. Gabinete, Manuel Joseph C. Loquias

Abstract

A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices and coincidence site modules, respectively.Recently, coincidences of shifted lattices and multilattices (i.e.nite unions of shifted copies of a lattice) have been investigated.Here, we solve the coincidence problem for a shifted hexagonal lattice.This result allows us to analyze the coincidence isometries of the hexagonal packing by viewing the hexagonal packing as a multilattice.

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Key concepts: Hexagonal crystal system, Coincidence, Hexagonal lattice, Lattice (music), Crystallography, Hexagonal tiling, Condensed matter physics, Close-packing of equal spheres