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BaTiO3/SrTiO3(001) epitaxial thin films were prepared at various growth rates by pulsed laser deposition, and their heterostructures were evaluated by synchrotron x-ray diffraction measurements and cross-sectional scanning transmission electron microscopy observations. In a film grown at a low deposition rate (0.01 nm/s), misfit dislocations are found near the interface and a fully relaxed BaTiO3 thin film grows epitaxially on the substrate. On the other hand, a film grown at a high deposition rate (0.04 nm/s) consists of strained and relaxed BaTiO3 lattices. Our results showed that the critical thickness of BaTiO3/SrTiO3(001) epitaxial thin films can be controlled by the deposition rate and that the critical thickness increases with increasing the deposition rate, and by adjusting the deposition rate we were able to prepare epitaxial thin films consisting of fully strained BaTiO3, partially strained BaTiO3 or fully relaxed BaTiO3. We have also achieved the growth controlling of BaTiO3 thin films on SrTiO3(001) substrates with SrRuO3 bottom electrode layer.