Structure and lattice dynamics of rational approximants to icosahedral Al-Cu-Li.

Abstract

We present a detailed theoretical investigation of the structure and the dynamical properties of icosahedral Al-Cu-Li alloys. Structural models of the quasicrystalline structure have been constructed on the basis of three-dimensional Penrose- and canonical-cell tilings. We show that the periodic approximants (up to \ensuremath{\tau}\ensuremath{\sim}5/3) are stable under molecular-dynamics (MD) annealing with realistic pair forces and that the partial-pair-correlation functions, powder- and single-crystal and neutron- and x-ray diffraction data are in good agreement with experiment, with a slight preference for the canonical-cell models. The vibrational spectrum (spectral functions, densities of state) and inelastic neutron-scattering intensities have been calculated using a real-space recursion technique and the same interatomic forces as used in the MD annealing. Well-defined propagating longitudinal and transverse acoustic modes are found in the vicinity of quasiperiodically distributed special points in k space, the \ensuremath{\Gamma} points of the reciprocal quasilattice. At higher energy, a hierarchy of stationary modes is predicted around other high-symmetry points corresponding to quasi-Brillouin-zone boundaries. For the propagating low-energy modes, the predictions are in very good agreement with inelastic neutron-scattering experiments on single crystals of i-Al-Cu-Li. However, certain discrepancies subsist between the predicted vibrational density of states (DOS) and the experiments with powdered samples. Quite generally, the calculated DOS shows more structure (with again only minor differences between the Penrose- and canonical-cell models) than the experimental result. This is probably to be attributed to the influence of phason disorder in the real quasicrystals.