Interfaces between functional ceramics, such as Pb(Zr0.5Ti0.5)O-3 or PZT, and metal electrodes, such as Pt, are important for many devices. Maintaining an interface that is free of secondary phases is necessary for the efficient transfer of electrons and device function. However, there are instances where unstable transient phases form at the interface due to atomic diffusion, such as Pt3Pb. Here, we investigate the migration barriers for the diffusion of Pb across the PZT/Pt and PZT/Pt3Pb interfaces using density functional theory (DFT) and the climbing image nudge elastic band (c-NEB) method. Our calculation models take into account the influence of atmospheric conditions on Pb diffusion through the preferential stabilization of defects near the interface as a result of changes to the Pb and O chemical potentials. In addition, the PZT structures that are stable above and below the Curie temperature are considered. The migration barriers are predicted to be strongly dependent on atmospheric conditions and the phase of the PZT, tetragonal or cubic. In particular, an inversion of the Pb diffusion direction at the PZT/Pt interface is predicted to take place as the oxygen partial pressure increases. This prediction is confirmed by experimental insitu X-ray diffraction measurements of a PZT/Pt interface.