The generalized vibrational density of states (GVDOS) of polycrystalline Al9Co2 has been investigated by inelastic neutron scattering at 300 K at the Institute Laue–Langevin in Grenoble. The data are compared to the GVDOS of the decagonal phase Al71.5Co15.5Ni13 (J. Non-Cryst. Solids 205–252 (1999) 860) and the crystalline phase Al13Co4. In contrast to the decagonal phase, the GVDOS of Al9Co2 shows a pronounced band structure. This band structure shows the same characteristics as the GVDOS of the phase Al13Co4.

A comparative investigation of the atomic dynamics of an icosahedral and a decagonal quasicrystal from the same alloy family, here the ZnMgRE/Y Frank–Kasper type of quasicrystals, has been performed for the first time. The i- and d-alloy were studied at 296 and 200 K, respectively at the ISIS neutron spallation source (UK) in a large region of energy and momentum transfers using neutron inelastic scattering (NIS). The quantitative comparisons of the single particle dynamics of the two ZnMgY samples via the generalized vibrational density of states shows a considerable difference in the intensity of the sub-bands constituting the main energy bands, but only small shifts of these bands and subbands in energy. We attribute the differences observed in the single particle dynamics more to differences in the short range structure of decagonal and icosahedral ZnMgY, leading to a stronger grouping of the local density of the states in the case of the decagonal alloy, than to their different aperiodic long range order.

We consider colour symmetries for planar tilings of certain n-fold rotational symmetry. The colourings are such that one colour occupies a submodule of n-fold symmetry, while the other colours encode the cosets. We determine the possible numbers of colours and count inequivalent colouring solutions with those numbers. The corresponding Dirichlet series generating functions are zeta functions of cyclotomic fields. The cases with φ(n)⩽8, where φ is Euler’s totient function, have been completely presented in previous publications. The same methods can be employed to extend the classification to all cases where the cyclotomic integers have class number one. Several examples for symmetries with φ(n)>8 are discussed here.

The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and determines the actual colour symmetry groups. Continuing previous work, we present the results of the combinatorial part for planar patterns with n-fold symmetry, where n=7, 9, 15, 16, 20, 24. This completes the cases with φ(n)≤8, where φ is Euler’s totient function.

The generalised vibrational density of states (GVDOS) of polycrystalline Al74Pd22Mn4 (ξ′) has been investigated by inelastic neutron scattering at the temperatures 296, 600, 800 and 1000 K. The GVDOS shows two broad main maxima near 14 and 32 meV, which are shifted to lower energies with increasing temperature. The data are compared to the GVDOS of the icosahedral phase [J. Non-Cryst. Solids 156–158 (1993) 872; Mater. Sci. Eng. A 226–228 (1997) 479; J. Non-Cryst. Solids 250–252 (1999) 855] in this system, the structure of which is strongly related to this crystalline phase [Philos. Mag. B 68 (1993) 607; Philos. Mag. A 74 (1996) 939]. At energies below 9 meV, the GVDOS of the ξ′-phase shows higher densities and a much more harmonic behaviour than that of the icosahedral phase. Thermodynamic quantities like the heat capacity are calculated and compared to measured values.

We have investigated a structure model of the high temperature Ni-rich decagonal phase 'basic' in Al-Co-Ni generated by the cut & projection method. The acceptance domains are very simple and describe a structure which exhibits small decagonal clusters with a twofold centre and a diameter of 6.5 Angstrom and results in a small number of atoms per cluster. The density of the structure model is 3.91 g/cm(3) and the stoichiometry (72.36 at.% Al) matches to the existence region of the decagonal phase.

Concerning different variants of quasicrystalline phases we present quasiperiodic tilings which combine properties of superstructures with those of modulated structures or nanostructured domains of approximants.

In contrast to the magnetic transition metal ions in other quasiperiodic alloys, the RE (RE=rare earth) ions in icosahedral Zn–Mg–RE show localised magnetic moments due to localised 4f electrons. Long range as well as short range order of these moments are still under discussion. To investigate the magnetic properties of these fci-structures of Frank–Kasper type, we performed inelastic neutron scattering experiments at temperatures between 1.6 and 25.0K and measured the DC magnetic susceptibility. The results show mainly paramagnetic scattering of the samples. Comparison with the data of Zn–Mg–Y ensures, that the observed scattering is not of phononic or phasonic nature. The lineshape of the quasielastic peak can be modeled by a shifted Lorentzian. The observed shift is small (approximately 0.6meV) and shows no dispersion. The linewidth is constant in Q and increases with temperature. A possible interpretation of this behaviour is the existence of a crystal field splitting.

Quenched samples of the icosahedral alloy of the ternary system Al–Pd–Mn contain a high amount of vacancies depending on the annealing temperature and the quench rate. As shown before [M. Scheffer, R. Lück, Proceedings Aperiodic ’97, 1998, pp. 469–472], these vacancies result in a change from a diamagnetic to a paramagnetic state at room temperature. We investigated the behaviour of the magnetic moments at low temperatures of a quenched and an annealed sample. At this temperatures a strong decrease of the total magnetic moment after the annealing was observed. The number and the magnitude of the magnetic moments were determined by measurements of the field and temperature dependence of the total magnetic moment. Evaluation of the data yields only a small number of magnetic moments. We relate the observed moments to a high amount of vacancies and to a disorder of Al and Mn, respectively.