We have studied the cubic to tetragonal phase transition in epitaxial SrTiO3 films under various biaxial strain conditions using synchrotron X-ray diffraction. Measuring the superlattice peak associated with TiO6 octahedra rotation in the low temperature tetragonal phase indicates the presence of a phase transition whose critical temperature is a strong function of strain, with TC as much as 50K above the corresponding bulk temperature. Surprisingly, the lattice constants evolve smoothly through the transition with no indication of a phase change. This signals an important change in the nature of the phase transition due to the epitaxy strain and substrate clamping effect. The internal degrees of freedom (TiO6 rotations) have become uncoupled from the overall lattice shape.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, ferro-electricity, and variable dielectric constants. These properties can be quite different in thin films versus nominally similar bulk samples. The primary reasons for the changes in properties are believed to be strain and defects. There is also an emerging theoretical effort to treat the effects of strain. To understand the mechanisms for these changes we must be able to conduct detailed microscopic measurements of the atomic and electronic structure.SrTiO 3 (STO) is a nearly ferroelectric material with a large dielectric nonlinearity and low dielectric loss at cryogenic temperature, making it ideal for tunable microwave devices [1]. STO is also a good model system for studying structural phase transitions. Bulk STO crystals are cubic at room temperature, with space group Pm3m(O 1 h ), but become tetragonal, space group I4/mcm(D 18 4h ), below about 105K. This phase transition involves the rotation of TiO 6 octahedra and has been featured historically in the study of structural phase transitions as the classic example of a soft-mode phase transition [2]. The unit cell of the tetragonal phase has a volume four times that of the cubic unit cell, with approximate unit cell of √ 2a× √ 2a×2a, where a is the lattice parameter of cubic unit cell. In this paper we describe the tetragonal phase as pseudo-cubic, in order to compare the structure before and after the phase transition. In this pseudo-cubic frame, the tetragonal phase has additional superlattice peaks at half integer index positions. These superlattice peaks disappear as the temperature is raised through the tetragonal-cubic phase transition. * Present Address: HASYLAB at DESY, Notkestr. 85, 22603 Hamburg, GermanyIn the bulk, the deviation from cubic symmetry is directly related to the rotation angle of the TiO 6 octahedra. This rotation angle has been identified as the order parameter for this phase transition [3]. Correspondingly, the intensities of the superlattice peaks are proportional to the square of the order parameter and can be used to track the phas...