We describe how the nature of defects may be investigated by positron 2D-ACAR measurements. We show that it is possible to identify a specific distribution for each defect. Focusing on GaAs, we characterize negative ions, identified as antisites, as well as As and Ga vacancies in various charge states. We find that each 2D-ACAR distribution is different, hence providing 2D “fingerprints” of the defects which might be used for the characterization of real materials. We also show that 2D-ACAR measurements provide information on the atomic relaxations around vacancies: we infer that VAs⁻ has a smaller open volume than VAs⁰. This finding is in agreement with results from positron lifetime experiments and molecular dynamics calculations.