Thermodynamically stable one-component quasicrystals: A density-functional survey of relative stabilities

A combination of classical density-functional theory and thermodynamic perturbation theory is applied to a survey of finite-temperature trends in the relative stabilities of one-component crystals and quasicrystals interacting via effective metallic pair potentials derived from pseudopotential theory. Splitting the pair potential into a strongly repulsive short-range core and a relatively weak oscillating tail, the Helmholtz free energy functional of specified solid structures with Gaussian density distribution is computed for given thermodynamic states, and variationally minimized with respect to the width of the distribution. Comparing the free energies of several periodic crystals and rational approximant models of quasicrystals over a range of pseudopotential parameters, thermodynamically stable quasicrystals are predicted for parameters approaching the limits of mechanical stability of the crystal structures. Quasicrystalline stability is attributed to vibrational stiffness and energetically favorable medium- and long-range interactions. The results support and significantly extend conclusions of previous ground-state lattice-sum studies.