Abstract: We investigate the effects of post-growth annealing on the structural and magnetic properties of BaFe2As2. Magnetic susceptibility measurements, which exhibit a signal corresponding to the magnetic phase transition, and high-resolution x-ray diffraction measurements, which directly probe the structural order parameter, show that annealing causes the ordering temperatures of both the phase transitions to increase, sharpen and converge. In the as grown sample, our measurements show two distinct transitions corresponding to structural and magnetic ordering, which are separated in temperature by approximately 1 K. After 46 days (d) of annealing at 700 °C, the two become concurrent in temperature. These measurements demonstrate that the structural phase transition is second-order like when the magnetic and structural phase transitions are separated in temperature, and first-order like when the two phase transition temperatures coincide. This observation indicates that annealing causes the system to cross a hitherto undiscovered tricritical point. In addition, x-ray diffraction measurements show that the c-axis lattice parameter increases with annealing up to 30 d, but remains constant for longer annealing times. Comparisons of BaFe2As2 to SrFe2As2 are made when possible.