Determination of the composition of the icosahedral phase in rapidly solidified AlMn quasicrystals at high spatial resolution

Abstract

Phenomenological models based on Landau theory with the point symmetry of the icosahedron and quasiperiodic or incommensurate translational order have been presented. These models accurately reproduce the observed diffraction patterns, but the position of the most intense peaks scale with tau/sup -1/ unlike the experiments where they scale with tau/sup -3/. An alternative approach is to interpret the experimental data as a projection in three dimensions of a six-dimensional regular crystal. Katz and Duneau and independently, Elser have computed the diffraction pattern of a three-dimensional Penrose pattern using an elegant projection scheme from a higher dimensional periodic lattice. The find delta-function peaks that are dense in reciprocal space, where the most intense peaks not only account for the peak positions in the Al-Mn diffraction patterns but also scale as tau/sup -3/. However, an understanding of the peak intensities is as yet non-existent, for this would entail a detailed knowledge of the distribution of the aluminum and manganese atoms in the quasilattice. In order to solve this problem, it is necessary to first determine the composition of the icosahedral phase as accurately as possible. This is complicated because the icosahedral phase is formed over a range of starting compositions (10-25 atom-percentmore » manganese) and the microstructure is such that these grains with icosahedral symmetry typically reach an average diameter of only 1-2 microns and they are embedded in an aluminum-rich matrix phase. Preliminary studies suggest an average optimal manganese content of 22 at%. In this report, the authors present the first results of determination of the composition of the icosahedral phase by energy dispersive x-ray spectroscopy measurements using convergent electron probes.« less