Doppler broadening measurements of the 511 keV positron annihilation line-shape have been carried out to study the nature of vacancy-type defects in samples of cadmium mercury telluride. Results from annealing in the temperature range 300-450 K indicate an unusual, reversible variation with temperature which is attributed to the role of impurities or native defects in the sample. Further annealing (to 570 K) produces an increase in the vacancy concentration due to the formation of a new type of defect. Extensive annealing at this temperature gradually changes the sample to a coral structure of CdTe as Hg and Te are lost from the sample.