__Katz and Gratias Model__

This bulk
model of icosahedral Al–Pd–Mn is Katz and Gratias' simplest
model of Al–Pd–Mn.
The underlying model of atomic positions was developed for icosahedral
Al–Cu–Fe in references [1,2]. It is the primitive tiling ^{P} decorated by Bergman (and therefore automatically Mackay) polyhedra. The
atomic positions in the model are deterministic.

The
deterministic atomic positions of this model are defined uniquely by the
polyhedral windows (atomic surfaces) W_{bc}, W_{n'}, and
W_{n} in
the coding space E_{⊥}shown
below [1,2]. Each window defines a quasilattice from a corresponding copy
of an icosahedrally projected D_{6} module. These windows corresond
to the windows W_{a},
W_{q},
and W_{b} respectively, for the Papadopolos and Kasner model. The
model of atomic positions describes both *i*-Al–Pd–Mn and *i*-Al–Cu–Fe.

Atomic
surfaces (windows)
W |

Appropriate normals to 2-fold, 5-fold and 3-fold planes in "Katz-Gratias AlPdMn.dat" are as follows:

(0,
0, 1) is 2-fold

(1, τ,
0) is 5-fold

(0, τ, τ-1)
is a 3-fold

If you need instructions on how to determine atomic 2-fold, 3-fold, and 5-fold planes orthogonal to the given directions, click HERE.

The file available for downloading is in ASCII format. Specific information about the format can be found at the top of the file.

[1] A. Katz
and D. Gratias J. Non-Cryst. Solids, 1993, 153&154, 187.

[2] A. Katz and D. Gratias in Proceedings of the 5th International
Conference on Quasicrystals, Ed. by C. Janot and R. Mosseri, World Scientific,
Singapore,
1995, 164.