  We calculate the cohesive energies of Fe-based glass-forming alloys in the
B-Fe-Y-Zr quaternary system. Our {\it ab-initio} calculations fully relax
atomic positions and lattice parameters yielding enthalpies of mixing at T=0K.
We examine both the known equilibrium and metastable phases as well as a
selection of plausible structures drawn from related alloy systems. This
method, generally reproduces experimentally determined phase diagrams while
providing additional information about energetics of metastable and unstable
structures. In particular we can identify crystalline structures whose
formation competes with the metallic glass. In some cases we identify
previously unknown structures or observe possible errors in the experimental
phase diagrams.
