The orthorhombic approximant phases of the decagonal phase

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Abstract
Two distinct orthorhombic phases form in the Al65Cu20Fe10Cr5 and Al63Cu17.5Co17.5Si2 alloys and represent an important class of approximant structures of the decagonal phase. Their structural units (convex pentagon, concave pentagon and rhombus) as revealed by high resolution electron microscopy (HREM) images can also be used to construct the Penrose tiling. We propose that one single orthorhombic phase may not be able to account for the transformation towards the high-temperature decagonal phase. For this transformation to be possible, the microcrystalline structure must satisfy a delicate balance among building blocks that is required to achieve a Penrose tiling. Two concepts are distinguished: the approximant phase and the approximation state. An analysis of the orientation relationships between a CsCl type of structure and orthorhombic phases suggests that such orthorhombic phases are three-dimensional superstruc-tures based on the CsCl unit cell. Furthermore, this relationship leads to the definition of Penrose tiling-like subnetworks inside the orthorhombic unit cells so that these orthorhombic phases can be considered as the periodic patchworks of quasiperiodic subnetworks.