Radiation is a form of energy that can damage materials at an atomic level. This has implications for the mobility of radioactive waste through containment materials. We are characterizing atomic defects in materials by using Electron-Positron Annihilation Lifetime Spectroscopy (EPALS). When an electron and positron come into contact with each other, they annihilate and release two antiparallel 511-keV gamma rays. In a pristine crystalline sample, positrons can easily annihilate with electrons, but in a sample with vacancies/defects in the crystal structure, positrons take longer to annihilate. Therefore, the more vacancies in a sample, the longer the average lifetime of a positron in the sample. We measure the lifetime by detecting the time between the emission of a 1274-keV gamma ray when the positron is created and the emission of the 511-keV gamma ray. We have experimentally measured pure, single-crystal MgO samples and found that our results are within the range of past published results (120 ps - 280 ps) with average lifetimes at 258±34.8 ns and 266±12.1 ns. We have also made measurements that span over the course of 1-3 days, resulting in similar lifetimes of 265±2.62 ns. In future experiments, we plan on analyzing pure Fe and Aluminum-doped MgO and then comparing these positron lifetimes with radiation-damaged versions of the same samples.