Where are the atoms in quasicrystals? Experimental and theoretical studies of ternary and quaternary approximants

Problems concerning complete structural characterization of quasicrystals involve locating the atomic positions as well as determining the distribution of elements at each site. Quasicrystalline approximants provide models for potential building units of quasicrystals, but a clear determination of the elemental decorations in such approximants also remains incomplete. We report experimental and theoretical studies of new, quaternary Bergman phases in the Li-Mg-Zn-Al system and a new, quasicrystalline approximant Li₁₀Mg₆Zn₃₁Al₃ (A₁₆M₃₄-type). A theoretical model using averaged Mulliken populations provides a means to track the segregation of elements (and vacancies) onto different sites as a function of valence electron concentration. As the Li content decreases, vacancies begin to occur at a specific site in the Bergman structure. The new approximant demonstrates how truncated tetrahedra can play an important role in forming clusters with possible fivefold symmetry in quasicrystalline structures.