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The effective piezoelectric coefficients of BaTiO₃ ferroelectric films epitaxially grown on different single crystal substrates with finite thickness have been theoretically analyzed. The effective longitudinal converse piezoelectric coefficients d₃₃ of film and "film-substrate" heterostructure all monotonously increased with increase of the film thickness fraction k, and the latter is always larger than the former at the range of 0 < k < 1. Meanwhile, we also found that the effective piezoelectric coefficients d₃₃ were affected by the substrates due to different elastic constants. These results show that the elastic deformation and clamping effect of substrate have significant impacts on the piezoelectric behavior of bilayer heterostructure.
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