  Solid solutions occur when multiple chemical species share sites of a common
crystal lattice. Although the single site occupation is random, chemical
interaction preferences bias the occupation probabilities of neighboring sites,
and this bias reduced the entropy of mixing below its ideal value. Sufficiently
strong bias leads to symmetry-breaking phase transitions. We apply the cluster
variation method to explore solid solutions on body centered cubic lattices in
the context of two specific compounds that exhibit opposite ordering trends.
Employing density functional theory to model the energetics, we show that CuZn
exhibits an order-disorder transition to the CsCl prototype structure, while
AlLi instead takes the NaTl prototype structure, and we evaluate their
temperature-dependent order parameters, correlations and entropies.
