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Our Research Interests

Some big unit cells
Figure 1: Cu41Zn59,      Cu36.5Al63.5, and Cd3Cu4.

   Metals are important.  Three-quarters of the elements on the periodic table are metals, and when metallic elements are combined, they make more metals. These combinations of metals have some amazingly complicated structures,    some of which are shown here. Cu41Zn59 (Figure 1, left panel) has a crystalline  unit cell with 10 million atoms in it.  Cu36.5Al63.5    (Figure 1, center panel) has a cell axis of 1000 Å.  And while Cu    has 4 atoms in its cubic unit cell and Cd has 2, Cd3Cu4 (Figure 1, right panel) has 1124. And these are just a few examples.

Pd-Cd compounds
Figure 2: Pd59Cd217      and Pd105Cd343.
Perpendicular pseudo 5-fold 	     axes in Cd<sub>3</sub>Cu<sub>4</sub>
Figure 3: Perpendicular pseudo 5-fold      axes in Cd3Cu4.

Our group synthesizes intermetallic compounds with    complex crystal structures (including the Pd-Cd compounds shown in    Figure 2), and develops theoretical models to understand their structures. One structure of interest to us is that of Cd3Cu4. This compound has pseudo 5-fold symmetry along its [110] and [110] directions (Figure 3, in reciprocal space). This is interesting for two reasons. First, it’s interesting because 5-fold rotational symmetry is incompatible with crystalline translational symmetry, which has already been explored in the context of quasicrystals and their approximants.  Of more interest    to us is the fact that [110] and  [110] are perpendicular  to each other, but no 3-D point group has perpendicular 5-fold axes. How is it possible for Cd3Cu4 to have perpendicular pseudo 5-fold axes, when this feature is not consistent with any 3-D point    group?  If you’re interested in the answer, see our recent article. (Berger, R.F.; Lee, S.; Johnson, J.; Nebgen, B.; Sha, F.; Xu, J. “The mystery of perpendicular 5-fold axes and the fourth dimension in intermetallic structures”.  Chem. Eur. J. 2008,    14, 3908-3930.)

Ionic and metallic regions of NaCd<sub>2</sub>
Figure 4: Ionic and metallic regions of      NaCd2.

In another related mystery, we trace the complicated    structure of NaCd2 (with 1192 atoms in its cubic unit cell), as studied using simple electronic structure calculations, to periodic minimal surfaces (Figure 4).  You can read the full story in our recent article.  (Fredrickson, D.C.; Lee, S.; Hoffmann, R.            “Interpenetrating polar and nonpolar sublattices in intermetallics:  The NaCd2 structure”.  Angew. Chem. Int. Ed. 2007,    46, 1958-1976.)

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