New phases in the Al-Co-Cu alloy system : Marked variations from the “true” decagonal phase

The decagonal phase in the Al-Co-Cu alloy system was first discovered by He et al. We shall call this phase the “true” decagonal phase (TD) phase because it is the one most commonly observed in the Al-Co-Cu alloy system. It is well known that quasicrystalline phases such as the TD phase contain the phason defect peculiar to incommensurate phases that causes subtle variations from perfect decagonal symmetry. In this paper we report on the existence of new phases in the Al-Co-Cu alloy system, that are related to the TD phase but yet show marked variations from the TD phase. These variations are too drastic to be caused by phason defects alone.Figure 1(a) is a selected area diffraction pattern (SADP) recorded from a TD phase single “crystal” showing near perfect decagonal (tenfold) symmetry. This SADP agrees very well with the first published SADP of the TD phase in Al-Co-Cu that also shows almost perfect decagonal symmetry. In a previous paper we have reported several kinds of deviations from perfect decagonal symmetry, but none of these deviations involved the observation of perfect pentagonal (fivefold) symmetry. Figure 1(b) is an SADP recorded from a phase in Al-Co-Cu that exhibits perfect pentagonal symmetry instead of the expected decagonal symmetry. This breakdown of true tenfold symmetry into true fivefold symmetry is caused by unequal intensities of equal and opposite reflections. This example is a clear violation of Friedel's law, which states that the intensities of equal and opposite diffraction vectors must be equal.