Orientation relationship between the T structure and the icosahedral quasicrystal in the Zn-Mg-Al alloy system

To understand the crystallographic relation between the Bergman-type icosahedral quasicrystal and its approximant-T structure, we have investigated the crystallographic features of prepared Zn-Mg-Al alloy samples, mainly by transmission electron microscopy. It was found that there existed three kinds of regions: that is, C14-Laves, approximant-T, and icosahedral-quasicrystal regions, in Zn-Mg-Al alloy samples with the composition of Zn-36at.%Mg-9at.%Al. Among these regions, in particular, we tried to determine an orientation relationship between neighboring icosahedral-quasicrystal and approximant-T regions. Based on the determined relationship, for instance, four threefold rotatory-inversion axes in the T structure were found to be parallel to four of ten threefold rotatory-inversion axes in the icosahedral quasicrystal. It was thus understood that the atomic arrangements of the Bergman-type icosahedral quasicrystal and its approximant-T structure are likely to resemble each other.