(a) XRD studies about the 002-diffraction condition for (top to bottom) BaTiO3, Ba0.6Sr0.4TiO3, and compositionally graded heterostructures. (b) Off-axis RSM studies about the pseudocubic 103- and 332-diffraction conditions of a compositionally-graded heterostructure and the GdScO3 substrate, respectively, showing that the film is coherently strained to the substrate. (c) Rutherford backscattering spectrum for a compositionally graded heterostructure revealing a strong compositional gradient and the corresponding best fit for the data. (d) Low-resolution STEM image of a compositionally-graded heterostructure revealing no obvious defects within the films and pristine interfaces between layers. Scale bar, 50 nm. (e) Corresponding 2D maps of (left to right) in-plane (a axis) and out-of-plane (c axis) lattice parameters, and shear distortions (θ) of the compositionally-graded film extracted from local nanobeam diffraction studies.