Cohesive energies and phase stability in the Al-Co and Al-Co-Ni alloy systems Marek Mihalkovic and Mike Widom. Al-Co binary alloy system mystery of Al 13 Co 4 stability. Al-Co-Ni ternary alloy system mystery of stability for all compounds.
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
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.
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
single 4A layer