| In the Zn-rich Zn-Mg-RE alloys three groups of ternary hexagonal phases wereinvestigated: (Zn, Mg)58RE13 withα= 14.2-14.4(?), c=14.0-14.3(?); H-(Zn, Mg)5REwithα=8.9-9.1(?), c=9.2-9.4(?); and Z-Zn6Mg3RE withα≈14.6(?) c≈8.7(?). Theyhave been found to coexist with icosahedral quasicrystals. This has been determined bythe combination methods of TEM, X-ray powder diffraction and X-ray single-crystaldiffraction. Since these three phases have a high percentage of icosahedral coordinationthey are therefore crystalline approximants of the icosahedral i phase. In their <100>directions, there are either two or four mutually penetrated icosahedra, I2(P) or I4(P),within anαperiod. On the other hand, there is a pair of face-sharing icosahedra, I2(F),clusters in the [001] direction.By means of selected area electron diffraction (SAED) another hexagonal H' phasewithαH'=αH, cH'≈2cH has been found coexisting with the hexagonal H-(Zn, Mg)5Yin Zn-Mg-Y alloys. They have a parallel orientation relationship, such as [100]H'‖[100]H, (010)H'‖(010)H, (001)H'‖(001)H. A high-resolution electron microscopy(HREM) image has also been carried out to study the structural relationship between H'and H. In their [100] projection image, both H' and H phases have parallelogram unitsof which the bright image points in them correspond to the icosahedral center. Theirparallelogram units have the same hemline however the edge-length in the H' phase isabout double that in H. As a structural model of the H' phase, its <100> directionconsists of two penetrated icosahedra, I(2P), within anαperiod while there are twopairs of face-sharing ICO, I4(F), clusters forming a layer structure F1P1F2P2(f1p1f2p2) inthe [001] direction.Single phase regions of the icosahedral quasicrystal and the hexagonal(Zn,Mg)58Y13, (Zn,Mg)5Y, and Z (a ternary phase containing 6-8 at.% Y) in theZn-Mg(0-40 at.%)-Y(0-25 at.%) region have been determined. A tentative isothermalsection at 600℃was proposed. The (Zn, Mg)5Y and the icosahedral phase have wideranges of Mg solubility and are the dominant phases in these alloys. The hexagonal(Zn,Mg)58Y13 and (Zn,Mg)5Y result from the substitution of Mg for Zn in the respectivebinary Zn58Y13 and Zn5Y phases. Thus, they are isostructural with the respective binary phases. Reactions among the phases in this composition range were studied by means ofscanning electron microscopy. Similar phase reactions have also been observed in theZn-Mg-Ho/Er alloys.In AgxInxYb16-12 alloys, two cubic phases related to the icosahedral quasicrystal,(the 2/1 cubic approximant withα= 24.9 (?), and 1/1 cubic approximant withα= 15.4 (?))have been determined by means of SAED. The crystal structure of the 2/1 cubicapproximant Ag42In42Yb16 has been solved by single crystal X-ray diffraction. The basicbuilding blocks can be described as a 102-atom pseudo-Bergman cluster with threesuccessive shells of which the second shell consists of a dodecahedron and a 9-atompolyhedron thus breaking the icosahedral symmetry. It is different from the usual105-atom (with a center) or 104-atom (without a center) Bergman cluster whose secondshell consists of a dodecahedron and a 12-atom icosahedron. This is possibly owing tothe presence of illative large Yb atoms in this shell in the cubic 2/1 Ag-In-Yb phase.
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