Ti0.5Al0.5N alloy films, typically 1.5-mu-m thick, were grown on MgO(001) at temperatures T(s) between 400 and 850-degrees-C by ultra-high-vacuum reactive magnetron sputtering in pure N2. Films grown at T(s) between congruent-to 480 and 560-degrees-C were single crystals in which the lattice misfit strain was partially relieved by glide of <001> misfit dislocations, with Burgers vector = a0/2<011>, on {011BAR} planes. Cross-sectional transmission electron microscopy investigation showed no evidence of residual extended defects in the films until thicknesses of congruent-to 150 nm at which point threading dislocations, oriented along the [001] growth direction, were observed. Surface-initiated spinodal decomposition, resulting in the formation of compositionally modulated NaCl-structure platelets along [001] with width congruent-to 1 nm, occurred over a narrow growth temperature range between 540 and 560-degrees-C as a precursor to bulk phase separation of wurtzite-structure AlN at T(s) greater-than-or-equal-to 560-degrees-C. The alloy was continuously depleted of AlN at higher growth temperatures until the equilibrium two-phase structure, cubic TiN and wurtzite AlN, was obtained at T(s) greater-than-or-equal-to 750-degrees-C.