Ga 4 [Ga(Mg)] 8 Cu 12 Sc 12 Cu 32 Ga 32 A New Route to Quasicrystals and their Approximants: Electronic Tuning of Mg 2 Cu 6 Ga 5 John D. Corbett, Iowa State University, DMR and Searches for quasicrystals and their nearby approximants, which are normal crystalline relatives, generally proceed via either chemical similitude or trial and error. However, quasicrystals (and evidently their approximants) are known to exhibit pseudogaps in their electronic structures, energies at which the valence electrons are bound more tightly. We have discovered that we can predict new and favorable compositions to gain both phase types by means of prior electronic structure calculations. Shown below is the multiply endohedral structure of the approximant achieved by tuning the title compound with the electron-richer Sc. Its new quasicrystalline neighbor is obtained similarly.

Quasicrystals (QC) are a novel form of matter, highly ordered but without the translational symmetry and therefore the simple unit cells of traditional compounds. The detailed structure of any QC is not yet known, but they occur in metal- rich systems with low electron counts per atom (~2), are closely related to Hume-Rothery intermetallic phases, and exhibit 5-fold as well as more traditional rotational axes (s.g. m-3-5). Fortunately, all such systems evidently also contain crystalline approximant (AC) phases with quite similar compositions and characteristic cluster building blocks that ideally exhibit -5 improper rotational axes, i.e., icosahedra and pentagonal dodecahedra among others. We have broadened the search for AC and QC, starting with more distant structures that exhibit promising cluster- based networks of similar elements. The rare Mg2Zn11 structure and its isotypes such as Mg2Cu6Ga5 have proven to be fruitful sources of new QC and AC materials. Theoretical calculations on these frequently reveal a pseudogap above the highest filled state (Fermi level), and changing the compositions to achieve that point have nearly always led us to the AC sought, sometimes after fine tuning with the aid of X-ray powder patterns. Similar calculations on and tuning of the new ACs have led to the corresponding QCs. These methods have also been successfully applied in the Sc-Mg- Zn, Ca-Au-In and Yb-Au-In systems, giving QCs from new elements as well, In and Au. Qisheng Lin has been the lead investigator in all of this work. A New Route to Quasicrystals and their Approximants: Electronic Tuning of Mg 2 Cu 6 Ga 5 John D. Corbett, Iowa State University, DMR and

Broader Impacts Studies of AC and QC systems have generally been carried out in the physics and metallurgy communities. At the same time, we have been broadly exploring the chemistry of binary and ternary intermetallic systems involving combinations of electropositive, transition, and post-transition metals, originally featuring the triel elements Ga, In, Tl in the last role. These new systems are too electron-poor to contain Zintl (valence) compounds. Such intermetallic systems are generally poorly studied, yet there is clearly much new chemistry in them. Some feature cluster and condensed cluster polyhedra containing pseudo 5-fold axes. Two discoveries years ago have afforded especially promising starting points for QC work– Na 3 K 8 Tl 13 with Tl-centered icosahedra and a cation sheath closely resembling the last frame of the structure in slide one, and Na 15 K 6 Tl 18 M (M=Mg, Zn, etc.), which is a polar example of the Mg 2 Zn 11 -type structure discussed earlier. Conversion of the second to more likely elements led to the discoveries described here and elsewhere. * The success of the new calculational approach to locate pseudogaps in likely starting materials and the resultant AC and QC is a little surprising inasmuch as this is being applied across structural changes. However, AC and QC are known to have very similar compositions and related structures. We are broadly exploring new elements, new QC systems, and cluster-based models therefor. Many of these results have broadened considerably examples of the third type among AC and QC – the symmetry-breaking icosahedral version in addition to the longer known Bergman and Mackay types. The first frame in the previous picture represents one characteristic member of this type, a 3-fold disordered Ga 4 tetrahedron that is clearly incompatible with the cubic space group Im-3. Large polyhedra that lie within well-ordered and common cation sheaths have also been discovered following more intuitive approaches in numerous electron-poor intermetallics, e.g., alkali, alkaline-earth, rare-earth metal – Ni, Cu, Ag, Au, Zn, Cd – Ga, In, Tl. These provide more evidence regarding the general importance of tight polyhedral packing, diverse (delocalized) metal-metal bonding, bonding and structural regularities, and possible cluster-based QC models. ________ * Qisheng Lin, John D. Corbett, Inorg. Chem. 44, 572 (2005); Philos. Mag. accepted; JACS, submitted. July 2005