The thermodynamic properties of the binary Cu-Mg system are examined with a focus on equilibria involving the liquid phase, which is described with a four-species association model, incorporating a two-state treatment for the pure component liquids below their respective melting temperatures. The terminal and intermediate crystalline phases are described as substitutional solid solutions, employing two sublattices for the latter. Model parameters are fitted using available experimental data, and the resulting phase diagram is reported over the full range of compositions in the binary system. We also report the associated T 0 curves, indicating the limits of partitionless crystallization and compare these with reports of amorphous solid formation during rapid solidification processing.