Al-Co binary alloy system mystery of Al 13 Co 4 stability

1. Cohesive energies and phase stability in the Al-Co and Al-Co-Ni alloy systemsMarek Mihalkovic and Mike Widom Al-Co binary alloy systemmystery of Al13Co4 stability Al-Co-Ni ternary alloy systemmystery of stability for all compounds Above: Experimental phase diagram of Al-Co-Ni (adapted from Goedecke et al. (1998) Right: First-principles enthalpies calculated by VASP (meV/atom). Experimental phase diagram Goedecke and Ellner (1996) First-principles enthalpy of formation calculated by VASP. Note Al13Co4 is NOT stable at low temperature! COLORS: Black = minimum energy Blue = low energy Red = high energy SHAPES: Circles = equilibrium Diamonds = metastable Squares = hypothetical Al13Co4.mC102 structure Disagreements between experiment and calculation known crystal structures: Al(Co,Ni).cP2, Al3Ni.oP16, Al3Ni2.hP5, X-Al9Co2Ni2.mC26 and W-AlCoNi.mC534 are all believed stable but occur at positive energy. In each case we believe the phase is stabilized at high temperatures by the entropy of Co/Ni substitution. Estimates of available entropy support this conclusion. The bNi models are our best models of the basic Ni-rich decagonal phase. Note they are unstable by at least 20 meV/atom. To get their energies this low it is necessary to break the stacking periodicity from 4A to 8A. Flat layer partial occupancies confirmed by VASP energies Puckered layer predicted fully occupied by VASP energies 8A periodicity is also present in Co-rich structures such as the W-phase (Sugiyama (2002)). Here is our best realization of chemical occupancy in the W-phase. The shaded regions represent binary tile flips that relate one 4A layer to the other. We identify two basic clusters: The Pentagonal Bipyramid characteristic of Al-Co binaries; The 11-atom decagonal cluster characteristic of basic Ni-rich quasicrystal. 11-atom decagonal cluster Free energy including Al hopping entropy (black line). Vibrational free energy (red line). Combined hopping+vibration (green line) predicts stability above T=750K Vibrational densities of states note slight excess of low frequency modes in Al13Co4. Pentagonal bipyramid cluster Side, top and exploded view W-AlCoNi.mC534 single 4A layer