Icosahedral Boron‐Rich Solids

Disordered Icosahedral Boron-Rich Solids − A Theoretical Study of Thermodynamic Stability and Properties

This thesis is a theoretical study of configurational disorder in icosahedral boronrich solids, in particular boron carbide, including also the development of a methodological framework for treating configurational disorder in such materials, namely superatom-special quasirandom structure (SA-SQS). In terms of its practical implementations, the SA-SQS method is demonstrated to be capable of eff...

First-principles study of configurational disorder in icosahedral boron-rich solids

This thesis is a theoretical study of configurationally disordered icosahedral boronrich solids, in particular boron carbides, using density functional theory and alloy theory. The goal is to resolve discrepancies, regarding the properties of boron carbides, between experiments and previous theoretical calculations which have been a controversial issue in the field of icosahedral boron-rich sol...

Crystallography of Icosahedral Crystals

The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal can not in general be viewed as a space-filling ar...

More icosahedral fulleroids

Icosahedral coincidence rotations

The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In particular, we give a characterization of the possible coincidence indices …S-factors† and present a complete list of the possible rotations with S < 50.