Pressure-Induced Phase Transitions in the Cd-Yb Periodic Approximant to a Quasicrystal

The phase study of a Cd-Yb $1/1$ approximant crystal over a wide pressure and temperature range is crucial for the comparison study between periodic and quasiperiodic crystals. The ${\mathrm{Cd}}_4$ tetrahedra, the most inner part of the atomic clusters, exhibited various structural ordering in the orientation sensitive to pressure and temperature. Five ordered phases appeared in a $P\mathrm{\text{−}}T$ span up to 5.2 GPa and down to 10 K. The propagation direction of ordering alternated from $[110]$ to $⟨111⟩$ at about 1.0 GPa and again to $[110]$ at 3.5–4.3 GPa. The primarily ordered phases that appeared by cooling to 210–250 K between 1.0–5.2 GPa further transformed to finely ordered ones at 120–155 K. Besides the original short-range type interaction, a long-range type interaction was likely developed under pressure to lead to the primary ordering of ${\mathrm{Cd}}_4$ tetrahedra. Coexistence of these interactions is responsible for the complicated phase behavior.

Figure 1

Successive shells of the atomic cluster in Cd-Yb $1/1$ approximant and quasicrystal: (a) ${\mathrm{Cd}}_4$ tetrahedron, (b) ${\mathrm{Cd}}_{20}$ dodecahedron, (c) ${\mathrm{Yb}}_{12}$ icosahedron, and (d) ${\mathrm{Cd}}_{30}$ icosidodecahedron. The first shell Cd tetrahedron in the approximant bcc crystal ($a=15.64\AA$, space group: $Im\overline{3}$ [3]) is separated by 13.54 Å from the neighboring tetrahedra and orientationally disordered at ambient temperature and pressure.

Figure 2

X-ray oscillation photographs of Cd-Yb $1/1$ approximant crystal measured for the bcc phase (a), phase I at ambient pressure and 50 K (b), phase II at 2.7 GPa and 170 K (c), phase III at 2.7 GPa and 50 K (d), phase IV at 5.2 GPa and 170 K (e), and phase V at 5.2 GPa and 50 K (f). Each photograph shows the reciprocal space around the $hk1$ zone for (a) and (c)–(f), and the $hk0$ and $hk\frac{1}{2}$ zones for (b). Arrows indicate representative superlattice spots that appear by cooling in the isobar process.

Figure 3

(a) Phase diagram outline of the Cd-Yb $1/1$ approximant crystal. Besides the well-defined phases, slight modifications (${\mathrm{III}}^{\prime },{\mathrm{IV}}^{\prime }$) seem to appear. (b) Schematic drawing of the main ordering structure of the first shell Cd tetrahedra in phases II and III. Arrows represent the propagation direction of ordering along the $⟨111⟩$ directions. The two orientations are represented by white and gray tetrahedra. (c) A plausible candidate [17] for the main ordering structure in phases I, IV, and V. Gray planes represent the same phase zone of structural modulation propagating along the $[110]$ direction.

Figure 4

Temperature dependence of the integrated intensity of superlattice spots on heating for phase I at ambient pressure (a), phases II and III at 2.7 GPa (b), and phases IV and V at 5.2 GPa (c).