Dynamics of the AlPdMn icosahedral phase

Abstract

A centimetre-sized single grain of the perfect AlPdMn icosahedral phase was grown by slow cooling from the melt. It has been fully characterized to be of perfect icosahedral symmetry, i.e. without any frozen-in phason strain. The dynamical properties of this icosahedral phase have been studied by means of inelastic neutron scattering measurements on a triple-axis spectrometer. The response function S(Q, omega ) was measured around several Bragg reflections and along the high-symmetry twofold, threefold and fivefold axes of the icosahedron. In the long-wavelength limit there are well defined phonons whose width is limited by the instrumental resolution. The isotropy of acoustic modes is verified and the corresponding sound velocities are in good agreement with ultrasonic measurements made on the same sample. At shorter wavelengths, gaps are expected. By analogy with 1D models and electron density of states calculations, the positions in reciprocal space where the strongest gaps are expected may be estimated. This defines a set of three main pseudo-Brillouin zones which are quasiperiodically stacked around each strong Bragg reflection chosen as the zone centre. In the limit of the instrumental resolution no gap could be detected, even when two branches crossed.