Ab initioTi-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals

The ab initio phase diagram determines the energetic stability of the icosahedral TiZrNi quasicrystal. The complete ab initio zero-temperature ternary phase diagram is constructed from the calculated energies of the elemental, binary and ternary Ti-Zr-Ni phases. For this, the icosahedral i-TiZrNi quasicrystal is approximated by periodic structures of up to 123 atoms/unit cell, based on a decorated-tiling model fR. G. Hennig, K. F. Kelton, A. E. Carlsson, and C. L. Henley, Phys. Rev. B 67, 134202 s2003dg. The approximant structures containing the 45-atom Bergman cluster are nearly degenerate in energy, and are all energetically stable against the competing phases. It is concluded that i-TiZrNi is a ground-state quasicrystal, as it is experimentally the low-temperature phase for its composition. In this work, we show that the i-TiZrNi quasicrystal sor a large unit cell crystal of nearly identical structure d is in fact a ground state. We determine the ternary ground-state phase diagram from ab initio energy calculations of 45 elemental, binary, and ternary crystalline phases in the Ti-Zr-Ni alloy system. The cohesive energy of the i-TiZrNi quasicrystal is estimated from eight different periodic approximants with 81 to 123 atoms per unit cell. The atomic structure of these approximants is given by our previously reported structure model, which is formulated as an atomic decoration of ca- nonical cell tilings, and was fit to a combination of diffrac- tion data and ab initio relaxations.11 Section II describes the ab initio method. In Sec. III ab initio relaxations determine the energies and structures of the crystalline Ti-Zr-Ni phases and allow the construction of the ground-state phase diagram. Comparing the calculated ener- gies and lattice parameters to experiments provides a mea- sure of the accuracy of the ab initio method. Section IV is the core of the paper; the energy of the quasicrystalline phase is estimated and found to be lower than the energy of the competing crystalline phase. Combining this result with the experimental findings that the quasicrystal is lower in energy than W-TiZrNi it is concluded that the quasicrystal is the ground state for its composition. The stability of the approxi- mants and the quasicrystal are explained in terms of the local atomic structure and the resulting electronic density of states.