Dielectric permittivity and domain structures have been measured as functions of temperature, frequency and E‐field on a ⟨102⟩‐cut PMN‐31&percent;PT single crystal. By using relations of optical indicatrices and extinction, the unpoled PMN‐31&percent;PT crystal was evidenced to possess a rhombohedral phase at room temperature. As temperature increases, the extinction angles don’t exhibit apparent change until ∼350 K, indicating that the crystal keeps a mostly rhombohedral phase below ∼350 K. Above ∼350 K, the extinction angles begin to rotate through the monoclinic phase and then reach the tetragonal phase for most domains near 400 K. Near 410 K, the crystal transforms into the isotropic cubic phase. In addition, E‐field (along the [102] direction) dependent domain structures have also been observed at room temperature. The optical indicatrices of the domain matrix begin to rotate near E= 3.25 kV/cm through monoclinic polarizations. However, the crystal doesn’t exhibit total extinction even under an electric field of E= 37 kV/cm, indicating that a field‐induced single domain has not been reached. The domain structures show a strong hysteresis behavior during processes of increasing and decreasing E‐field. © 2003 American Institute of Physics