Historical Overview
V.
Elser in reference [1] stated that the Katz and Gratias model [2,3] of
icosahedral Al–Cu–Fe and the Boudard and de Boissieu model
[4,5] of icosahedral Al–Pd–Mn can both be explained as a
decoration of the primitive icosahedral tiling 
P [6] by the Bergman and therefore automatically by Mackay polyhedra. Elser
introduced in [1] a unifying model that is partly deterministic and partly
probabilistic, i.e. some atomic positions are fixed and another occupied
with certain probabilities. Z. Papadopolos introduced an analogous unifying
model as a decoration by Bergman polyhedra of an F-phase tiling *(2F) [7,8],
using the fact that the tiling P is locally derivable from the tiling *(2F) [7].
She constructed the windows in [8] for the unifying model formulated
in [1]. The Papadopolos and Kasner model [9,10] is a deterministic model
with polyhedral windows, somewhat different from the Katz and Gratias
windows.
[1] V. Elser
Phil. Mag. B, 1996, 73, 641.
[2] A. Katz and D. Gratias J. Non-Cryst. Solid, 1993, 153&154, 187.
[3] 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.
[4] M. Boudard, M. de Boissieu, C. Janot, G. Heger, C. Beeli, H.-U. Nissen,
H. Vincent, R. Ibberson, M. Audier and J. M. Dubois J. Phys.: Condens.
Matter, 1992, 4, 10149.
[5] M. de Boissieu, P. Stephens, M. Boudard, C. Janot, D. L. Chapman and
M. Audier J.
Phys.:Condens. Matter, 1994, 6, 10725.
[6] P. Kramer and R. Neri Acta Cryst. A, 1984, 40, 580.
[7] P. Kramer, Z. Papadopolos and D. Zeidler in Symmetries in Science
V: Algebraic Structures, their Representions, Realizations and Physical Applications,
Ed. by B. Gruber, L.
C. Biedenharn and H. D. Döbner, Plenum Press, New York, 1991, 395.
[8] Z. Papadopolos, P. Kramer and W. Liebermeister in Aperiodic '97, Ed.
by M. de Boissieu, J.-L. Verger-Gaugry and R. Currat, World Scientific, Singapore,
1998, 173.
[9] G. Kasner, Z. Papadopolos, P. Kramer and D. E. Bürgler Phys. Rev.
B, 1999, 60, 3899.
[10]
Z. Papadopolos, P. Kramer, G. Kasner and D. E. Bürgler Mat.
Res. Soc. Symp., 1999, 553, 231.
The
shortest interatomic distances in the model, along the 5-fold, 2-fold and
3-fold axes are τ-1
,
τ-1
and
τ-1
, respectively.
The standard distances , ,
and are
related by /√3
= /(τ+2)1/2 =
/2,
where τ =
(1 + √5)/2. The standard distance =
1 / √2
in E|| is
set to be 4.561 Å for i-Al–Pd–Mn and 4.465 Å for
i-Al–Cu–Fe.
All files available for download are in TEXT format (*.txt .dat???). Specific details about the file format can be found in the header of each file. If you use these files and publish the results please cite the authors of the model appropriately. References are available in the "More Info" section for each model.