Magnetoelectric coupling has attracted interest due to its potential to write magnetic information with electric fields. In the model system of Fe islands on Cu(111), electric fields can induce martensitic phase transitions between ferromagnetic body-centered cubic and antiferromagnetic face-centered cubic phases. Here, we present a detailed study of the dynamics and energetics of the phase transition in the electric field of the junction of a scanning tunneling microscope. Statistical measurements allow us to reveal the influence of both the electric field and the crystallographic strain on the energy landscape of the two competing phases.