Direct DFT Calculation of the Bulk and Nanoscale Stability of Icosahedral Quasicrystals

The discovery of quasicrystals forced solid-state chemists to revisit traditional assumptions about crystallinity, bonding, stability, and materials formation. Underlying all these questions is a fundamental question: are quasicrystals thermodynamically stable or metastable, but prefer nucleation due to a low surface energy? Density Functional Theory (DFT) is often used to evaluate thermodynamic stability, but quasicrystals are aperiodic and cannot be calculated under periodic boundary conditions. Here, we present a new technique to directly calculate the bulk and surface energies of quasicrystals in DFT. We compute the energies of large quasicrystal nanoparticles, and then fit the bulk and surface energies of the nanoparticles using a Gibbs-Thomson relationship. Using this technique, we evaluate the Tsai-type ScZn and YbCd icosahedral quasicrystals, whose structures have been resolved with atomistic resolution. From the bulk and surface energies, we construct size-dependent phase diagrams, enabling us to determine the bulk and nanoscale (meta)stability of icosahedral quasicrystals.