Greetings from the Fredrickson Group! We are a research group in the Chemistry Department at the University of Wisconsin-Madison focusing on the structural chemistry of alloys and intermetallic compounds. When we think about metals, images of simple sphere packings usually come to mind, such as the body-centered cubic, face-centered cubic and hexagonally close-packed structures. Such images describe well the structures of most of the elemental metals, but do little justice to the structural diversity that arises when we start mixing these metals together to form compounds - a diversity which rivals that of molecular chemistry. A few examples: the unit cells of NaCd2, Cd3Cu4, and Al3Mg2 all contain more than 1000 atoms, while the structure of the quasicrystal YbCd5.7 defies all attempts at reduction to a 3D unit cell.

In the following paragraphs, you can find more examples of this diversity and complexity in the descriptions of some specific projects we are working on. All of these projects involve a close interplay between electronic structure theory, solid state synthesis, and crystallography. All of them also point toward the two intertwined goals of our group's research: an understanding of the chemical bonding principles underlying these structures and a theoretical framework for the design of new metallic materials.

Electronics vs. sterics: How chemical pressure shapes intermetallic structures

CHEMICAL PRESSURE GALLERY

Atomic size has long been evoked in rationalizing the preferred structures of metals and alloys. A fundamental difficulty in using this concept in materials design, however, is that it is inherently empirical. We have devised a way of adapting the notion of atomic size to theoretical calculations: In the dense atomic packing of metals, correlations between interatomic distances mean that contacts often cannot be independently optimized. When bond formation at one point is stunted by repulsion at other points where there is insufficient electronic support, we encounter the classic molecular theme of electronics vs. sterics. Local chemical pressures (CPs) might be expected to emerge at such contacts, and we have developed tools for visualizing these pressures: the μ2-Hückel and DFT CP analyses. This approach has already offered intuitive explanations of, for example, the unusual structure of Ca2Ag7, and we are extending it to a diverse range of systems, such as quasicrystal approximants.

Analogies between intermetallics and coordination complexes

Since the pioneering work of Hume-Rothery, electron count has also been known as a key factor involved in the structures of metals and alloys. However, with notable exceptions such as Zintl phases, the ways in which electron count influences intermetallic structure remain largely mysterious. Our recent synthetic work has led to structures opening new connections to molecular bonding schemes. Gd13Fe10C13 adopts a new carbometallate structure type, featuring unique H-shaped C2FeFeC2 units with short Fe-Fe distances of ca. 2.37 Å. DFT-calibrated Hückel calculations reveal that multiple-bonds occur at these Fe-Fe contacts, and the overall geometry of this fragment can be understood by analogies to coordination complexes. In Fe8Al17.4Si7.6 and the incommensurately modulated Co3Al4Si2, a more general connection is found. Their complex structures (based on the fragmentation of the fluorite type into columns) provide the TM atoms with 18 electron configurations, through bonding schemes that are nearly isolobal to those of molecular 18 electron TM complexes. Using these observations, we are developing new electron counting rules for TM-based intermetallics.

Structural acid-base chemistry in the metallic state

The concept of acidity has a rich history that mirrors the growth of chemistry as a science, but its power for understanding intermetallics has been far from fully recognized. In our theoretical work adapting the Method of Moments to bonding analysis, we have derived a new model for acidity that is accounting for an increasing number of structural aspects of transition metal (TM) intermetallics. In this scheme, atoms are classified as μ3-acidic or -basic when they are electron-poor or -rich, respectively, relative to an ideal electron count determined by the third moment of their electronic density of states curves (μ3). Combining μ3-acidic and basic atoms into intermetallic phases neutralizes the deviations between their actual and ideal electron counts. Using this simple model, we have explained the stabilities of 24 binary phases, and created structure maps for the CsCl and Laves types forming between 3d TMs. Most exciting, however, has been this approach's potential for explaining structural features: In Ti21Mn25, acid-base interactions drives the structure's segregation into MgZn2-type columns and Ti-rich matrix, as well as the formation of helical tubes of Ti intertwined with helices of Mn.