We have investigated the out-of-plane lattice relaxation related to the ferroelectric transitions in epitaxial BaTiO3 (BTO) films using synchrotron X-ray diffraction. Under either compressive strain or tensile strain, there is evidence for two structural phase transitions as a function of temperature. The transition temperature TC is a strong function of strain, which can be as much as 100 K above the corresponding TC in bulk. Under compressive strain, the tetragonality of BTO unit cell implies that the polarization of the first ferroelectric phase is out-of-plane, while under tensile strain, the polarization is in-plane. The transitions at lower temperature may correspond to the aa → r or c → r transitions, following the notations by Pertsev et al. The orientations of the domains are consistent with theoretical predictions. PACS numbers: 77.55.+f, 68.55.Jk, 68.35.Rh Perovskite films have received a great deal of interest lately due to the potential for creating working technologies based on a variety of interesting properties such as high-T c superconductivity, colossal magneto-resistivity, ferroelectricity, and variable dielectric constants. These properties can be quite different in thin films versus nominally similar bulk crystals. The primary reasons for the property changes are believed to be strain and defects. [1] Bulk BrTiO 3 (BTO) undergoes three phase transitions at 393 K, 278 K and 183 K, from cubic paraelectric phase at high temperature to three ferroelectric phases at lower temperature, with tetragonal, orthorhombic and rhombohedral symmetries, respectively. At each transition the lattice parameters change drastically. Thus in bulk, the lattice parameters can be used to identify the phase transitions. In strained BTO films, theoretical calculations based on either first-principles method or Landau-Devonshire-type thermodynamic theory predict that there are two successive phase transitions for many values of film strain. [2,3,4,5,6] The high-temperature, paraelectric-to-ferroelectric transition has been identified by electrical measurements. [7,8] However, lattice parameter measurements on epitaxial BTO films have not been consistent. Terauchi et al reported that both the outof-plane and in-plane lattice parameters increase linearly with temperature from 15 K to 800 K, with no indications of the transitions. [7,9]. On the contrary, recent experiments revealed that, the temperature dependence of the lattice parameters do show slope changes associated with the ferroelectric transition. [10,11] Experimental evidence for the transition at lower temperature has not been reported for BTO films. This may be because this transition involves only a slight change in the orientations of the polarization, thus the signature is too subtle for electrical measurements or Raman * Present Address:Canadian Light Source, University of Saskatchewan, Saskatoon, SK S7N 0X4, Canada. † Electronic address: wells@phys.uconn.edu scattering. Inspired by the recent experimental observations and theoretical results [12] and o...