Orientation relation between icosahedral and crystalline phases in Al-Mn alloys

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Abstract
A transmission-electron-microscope investigation of the orientation relations between faceted icosahedral quasicrystals and crystalline f.c.c. matrix in rapidly cooled alloys of Al-Mn reveals three different orientation relations: In the third relation the f.c.c.[111] axis cannot be exactly parallel to the twofold axis i2 because of geometrical restrictions. Most of the observed relations can be ideally classified into these three classes (with deviations smaller than 4°). The point-symmetry elements common to the two structures in these three orientation relations are subgroups of m35 (icosahedral phase) as well as of m3m (f.c.c. phase). For the three orientation relations, the corresponding subgroups are 2,222 and 32 respectively, whereby the last case is slightly idealized.