  Phase diagrams for multi-component systems represent crucial information for
understanding and designing materials but are very time consuming to assess
experimentally. Computational modeling plays an increasingly important role in
this regard but has been largely focused on systems with matching lattice
structures and/or stable boundary phases. Here, using a combination of density
functional theory calculations, alloy cluster expansions, free energy
integration, and Monte Carlo simulations, we obtain the phase diagram of W-Ti,
a system that features metastable boundary phases on both sides of the phase
diagram. We find that the mixing energy on the body-centered cubic (BCC)
lattice is asymmetric and negative with a minimum of about -120 meV/atom,
whereas for the hexagonal closed packed (HCP) lattice the mixing energy is
positive. By combining these data with a model for the vibrational free energy,
we propose a revision of the W-rich end of the phase diagram with a much larger
solubility of Ti in BCC-W than previous assessments. Finally, by comparison
with the W-V and W-Re system we demonstrate how strongly asymmetric phase
diagrams can arise from a subtle energy balance of stable and metastable
lattice structures.
