Journal of Materials Research


Indexing of icosahedral quasiperiodic crystals

John W. Cahna1, Dan Shechtmana2 p1 and Denis Gratiasa3

a1 Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland, 20899

a2 Department of Materials Engineering, Israel Institute of Technology, Technion, 32000 Haifa, Israel

a3 C.E.C.M./C.N.R.S., 15 rue Georges Urbain, 94400 Vitry-sur-Seine, France


Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

(Received November 13 1985)

(Accepted December 10 1985)


p1 Center for Materials Research, The Johns Hopkins University, Baltimore, MD 21218; also a guest worker at the National Bureau of Standards, Gaithersburg, MD 20899.