This page describes the methods used to generate the alloy database.

Our main calculational tool is the plane-wave electronic density functional program VASP. We use VASP to relax atomic coordinates and lattice parameters and report the final cohesive energy. The calculations reported in this database primarily employ PAW potentials using the Perdew-Wang (1991) GGA. Some additional runs using LDA or the PBE GGA, or using ultrasoft pseudopotentials can be found via special search options.

We choose k-point grids to fill space nearly isotropically with sufficient density to achieve convergence with a precision of 10 meV/atom for highly unstable structures and 1 meV/atom for structures within 20 meV/atom of the convex hull. Mainly we use MP smearing (ismear=1, sigma=0.2). Occasionally for structures on or near the convex hull we recalculate the final structure using the tetrahedron method to verify we have achieved our 1 meV/atom convergence goal.

Plane wave energy cutoffs for "medium precision" were used by default, leading to inconsistent energy cutoffs in the database. Inconsistency in the cutoff energies typically shifts enthalpies of formation by a few meV/atom. We have not found a case where stabilities are qualitatively affected. For our published multicomponent works we employ a constant energy cutoff equal to medium precision for the "hardest" atomic potential (e.g. B in B-Fe-Y-Zr).

Spin polarization is used for Fe-, Ni- and Co-rich compounds and in other special cases where we find it appropriate. We use the Vosko-Wilkes-Nussair XC interpolation.

Frequently crystallographic structure determinations reveal mixed chemical occupancy or vacancies on certain atomic sites. In these cases we usually test alternate realizations individually and report only the best. Occasionally we employ "fixed site Monte Carlo" to anneal the occupancy of the atomic sites prior to our VASP calculation. These methods utilize interatomic pair potentials that can be Lennard-Jones or other forms (e.g. GPT) chosen to realistically model the compound.

Subtracting cohesive energies of compounds from cohesive energies of the pure elements yields T=0K enthalpies of formation. The result is an enthalpy because the volume relaxation implies pressure P=0 is held constant. The result is at T=0K because we report fully relaxed minimum energy structures. The convex hull of enthalpy versus composition is found using the program qhull.

Calculations are performed on an in-house computer cluster and at the Pittsburgh Supercomputer Center.