  Solid solutions, structurally ordered but compositionally disordered
mixtures, can form for salts, metals, and even organic compounds. The NaCl-KCl
system forms a solid solution at all compositions between 657{\deg}C and
505{\deg}C. Below a critical temperature of 505{\deg}C, the system exhibits a
miscibility gap with coexisting Na-rich and K-rich rocksalt phases. We
calculate the phase diagram in this region using the semi-grand canonical Widom
method, which averages over virtual particle transmutations. We verify our
results by comparison with free energies calculated from thermodynamic
integration and extrapolate the location of the critical point. The
calculations reproduce the experimental phase diagram remarkably well and
illustrate how solid-solid equilibria and chemical potentials, including those
at metastable conditions, can be computed for materials that form solid
solutions.
