General Results Non-AI-based QCs

The discussion above reveals that there has been considerable attention paid to Al-based QC and CMA surfaces. Naturally, the question arises as to the surface science of the non-Al-based QCs and CMAs. The two main QC famihes in this category are i-Zn-Mg-RE (rare earth) and i-Cd-Yb. The difflculty in applying surface science techniques to either of these families is that surface preparation in UHV is extremely difflcult due to the presence of the high-vapor-pressure elements 

Zn and Cd. For the Zn-based family, this has proved to be an insurmountable barrier [60], 

In the case of i-Cd-Yb, a solution has been found through the substitution of equal amounts of Ag and In for Cd, leading to a QC with stoichiometry Ag42ln42Ybij, which is isostructural to i-Cd-Yb. The building block of i-Cd-Yb is a 44-atom regular triacontahedron or Tsai-cluster [201]. The six-dimensional hyperlattice is P type or primitive, whereas the Al-based icosahedral QCs are described by a six-dimensional F type of face-centered hypercube. The surfaces of isostructural i-Ag-In-Yb thus differ in structure and chemistry from aU previously investigated QC surfaces. 

Regarding techniques of data analysis, the most fundamental challenge in QCs is the inabihty to apply periodic boundary conditions. In general terms, there are three possible solutions (i) analyze long-range structure in a nonperiodic manner, (ii) focus on local stmcture in a way that makes boundary conditions unnecessary, or (iii) use periodic approximants as surrogates. 

Using these techniques, it has generally been found that both QCs and CMAs are stable against reconstruction or surface segregation they are usually found to be bulk-terminated, except for interplanar relaxation. The terminating plane, or set of closely spaced planes, is usually rich in the element with the lowest elemental surface energy (A1 in the case of Al-rich QCs and CMAs). These conclusions draw heavily on comparison with bulk structural models. However, using bulk models as benchmarks to interpret surface structure for a QC usually involves subtleties and pitfalls that are not present for a more typical crystalline material. Chemical decorations of local motifs is one of the main such features. 

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