  Are quasicrystals stable or metastable? Density functional theory (DFT) is
often used to evaluate thermodynamic stability, but quasicrystals are
long-range aperiodic and their energies cannot be calculated using conventional
ab initio methods. Here, we perform first-principles calculations on
quasicrystal nanoparticles of increasing sizes, from which we can directly
extrapolate their bulk and surface energies. Using this technique, we determine
with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7
are ground-state phases--revealing that translational symmetry is not a
necessary condition for the T = 0 K stability of inorganic solids. Although we
find the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a
mixed thermodynamic and kinetic phase diagram that its solidification from the
melt is nucleation-limited, which illustrates why even stable materials may be
kinetically challenging to grow. Our techniques here broadly open the door to
first-principles investigations into the structure-bonding-stability
relationships of aperiodic materials.
