A simple unique 6D atomic structural model for both $i\text{−}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ and $i\text{−}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ is proposed that is built with an unique and simple set of atomic surfaces and chemical subcells. The model has accurate compositions with respect to the best experimental estimates of both structures and fit reasonably well the experimental diffraction data of x-rays and neutrons spectra with no fitting parameters. It presents a surprisingly small number of chemical configurations for the basic $B$ (Bergman) and $M$ (Mackay) type clusters as compared to what could be expected for quasiperiodic ternary systems. Finally, because of its relative simplicity, the present model is well adapted for being used in discussing the physical properties of either $i\text{−}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ or $i\text{−}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ that are essentially dependent on the local atomic arrangements of the various chemical species.

• Received 9 June 2006

DOI:https://doi.org/10.1103/PhysRevB.74.214205