Geometrically Frustrated Element: Boron

March Meeting 2010

Badwater in Death Valley, California, where borax are found on the ground. The underlying frustrated Ising model for boron in the left, and the geometry of partial occupancy in a boron crystal in the right


Tadashi Ogitsu
John Reed
Eric Schwegler
Condensed Matter and Materials Division
Physical and Life Sciences Directorate
Lawrence Livermore National Laboratory
Livermore, California, USA

François GygiCenter for Applied Scientific Computing
Lawrence Livermore National Laboratory
Livermore, California
and
Department of Applied Science
University of California, Davis
Davis, California, USA

Masafumi Udagawa
Yukitoshi Motome

Department of Applied Physics
University of Tokyo
Tokyo, Japan

Giulia Galli
Department of Chemistry
University of California, Davis
Davis, California, USA
and
Condensed Matter and Materials Division
Physical and Life Sciences Directorate
Lawrence Livermore National Laboratory
Livermore, California, USA

Geometrically Frustrated Element: Boron

Could an elemental crystal prefer to be defective rather than perfectly ordered? A recent study shows that this is indeed the case for Boron, and that its defects arrange in a very peculiar geometry. This geometry and the way defects interact are related to a very well know concept in the physics of disordered systems: frustration. So boron is not only a defective solid, but a frustrated element.

In general chemistry classes we learn that all elements, with the exception of helium, solidify into an ordered crystal structure at low temperature and that defects destabilize ordered solids, making their energy higher. Therefore it has been a mystery for decades why the fifth element, boron, has a phenomenally complicated crystal structure with 4 percent atomic defects.

Ogitsu et al. have shown that it is precisely the presence of these defects that stabilizes the phenomenally complex phase of boron against all the other allotropes, providing a geometry where the number of bonds is commensurate to the number of electrons. Most surprisingly, the geometrical arrangement of these defects forms a very specific two-dimensional geometrical lattice: a double layer expanded kagome lattice. The hopping of boron defects between its nearly degenerate configurations has been related to the peculiar transport properties of boron reported over the past four decades.

References

Ogitsu et al. Phys. Rev. B 81, 020102(R) (2010)

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Jason Bardi
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