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 neutr on scattering by phonons in an Al-Mn quasi-crystal. The structural mod el is derived from the work of Duneau and Oguey. For the dynamical mod el we assume an effective potential with force constants depending upo n equilibrium distances. Calculations are performed with the first sev en rational approximants of the quasi-periodic structure. Pseudo-acous tic dispersion curves associated with intense Bragg peaks are reported , Broadening of inelastic neutron scattering peaks with increasing pho non frequency is found in high-order approximants. We compare our resu lts with experimental spectra obtained on an Al-Mn-Pd quasi-crystal wh ere such a behaviour has been observed. The relation of the peak broad ening to the critical character of the modes is discussed.