The phase diagram of solid argon and solid fluorine was determined by x-ray diffraction and the solidus and liquidus by thermal analysis. Although the high-temperature structures of oxygen and fluorine are very similar, their phase diagrams with argon are quite different. The addition of F2 does not change the fcc Ar structure to hcp as the addition of O2 does. In the solid, the miscibility gaps between the Ar-rich and the F2-rich solid solutions extend as two-phase regions from 25%±2% to 97%±2% F2 in the low-temperature (α) range at the eutectoid temperature (41°K). The presence of 22% F2 slightly contracts the fcc Ar lattice; the lattice constant at that concentration and 23°K is 5.295±0.010 Å compared with the Ar lattice constant, 5.318 Å. The solidus line is horizontal at 53°K from 37%±2% to 95%±2% F2, and there is a eutectic at 72%±2% F2; up to that concentration, the solidus and liquidus are widely separated. The β—α F2 transformation was observed visually; the β phase is soft and transparent, the α phase is pale yellow, opaque, very hard, and brittle. The transformation is frequently accompanied by a sharp click and an explosion blowing out the window of the sample holder.