Inelastic neutron scattering by quasi-crystals: A model for icosahedral Al-Mn; for Al-Mn-Pd comparison with the experimental results

Using the spectral moments method, we have studied the inelastic neutron scattering by phonons in an Al-Mn quasi-crystal. The structural model is derived from the work of Duneau and Oguey. For the dynamical model we assume an effective potential with force constants depending upon equilibrium distances. Calculations are performed with the first seven rational approximants of the quasi-periodic structure. Pseudo-acoustic dispersion curves associated with intense Bragg peaks are reported. Broadening of inelastic neutron scattering peaks with increasing phonon frequency is found in high-order approximants. We compare our results with experimental spectra obtained on an Al-Mn-Pd quasi-crystal where such a behaviour has been observed. The relation of the peak broadening to the critical character of the modes is discussed.