  We resolve issues that have plagued reliable prediction of relative phase
stability for solid-solutions and compounds. Due to its commercially important
phase diagram, we showcase Al-Li system because historically density-functional
theory (DFT) results show large scatter and limited success in predicting the
structural properties and stability of solid-solutions relative to ordered
compounds. Using recent advances in an optimal basis-set representation of the
topology of electronic charge density (and, hence, atomic size), we present DFT
results that agree reasonably well with all known experimental data for the
structural properties and formation energies of ordered, off-stoichiometric
partially-ordered and disordered alloys, opening the way for reliable study in
complex alloys.
