Crystal structure of the hexagonal (Zn, Mg)4Ho and (Zn, Mg)4Er

The crystal structure of the hexagonal (Zn, Mg)4Ho/Er was determined by single crystal X-ray diffraction analysis. For the Zn68.4Mg12.7Ho18.9, the structural model, refined to a final R-value of 0.0672, has the composition of Zn69.34Mg12.01Ho18.65, a = 14.259 Å and c = 14.007 Å, and the space group P63/mmc (No. 194). Among the 10 Zn, 2 Mg, and 4 Ho independent sites, 3 Zn sites are icosahedral coordinated whereas 1 Mg is located at the center of a CN15 Kasper deltahedron enclosed by 26 triangles and 15 vertices. In the 〈1 0 0〉 directions, there are four interpenetrated icosahedra, I4(P), within an a period, constituting an icosahedral (0 0 1) layer block in half of the unit-cell. In the [0 0 1] direction, in addition to the two face-sharing icosahedra, I2(F), there is still a CN15 Kasper deltahedron. For the Zn70.8Mg10.6Er18.6, the final refinement led to a R-value of 0.0708. The atom coordinates are very close to those of above (Zn, Mg)4Ho, the largest difference between two corresponding coordinates being only 0.00086. Thus (Zn, Mg)4Er is iso-structural with (Zn, Mg)4Ho. This hexagonal (Zn, Mg)4RE phase has also been found in RE = Y, Sm, Gd, Dy, and Yb cases and they are probably also iso-structural with (Zn, Mg)4Ho/Er. This structure is icosahedrally closely related to the other two known, hexagonal, Zn-rich (Zn, Mg)nRE structures, namely, the Zn6Mg3Y/Sm/Gd [H. Takakura, A. Sato, A. Yamamoto, A.P. Tsai, Phil. Mag. Lett. 78 (1998) 263; K. Sugiyama, K. Yasuda, T. Ohsuna, K. Hiraga, Z. Kristallogr. 213 (1998) 537] and the Zn3MgY [D.W. Deng, K.H. Kuo, Z.P. Luo, D.J. Miller, M.J. Kramer, D.W. Dennis, J. Alloys Compd. 373 (2004) 156]. All these three hexagonal phases coexist with the icosahedral quasicrystal in the Zn–Mg–RE alloys.