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Low- and high-angle X-ray diffraction patterns have been obtained from one-dimensional superlattice crystals prepared artificially by alternately depositing predetermined thicknesses of GaAs and AlAs, on the (001) face of a GaAs single-crystal by molecular-beam epitaxy. The positions and intensities of several superlattice reflections obtained along the 00l, 11l and 02l reciprocal lattice rows have been recorded. The structure of the superlattice can be approximated by a model which incorporates elastic strains in the unit cell due to the lattice mismatch between GaAs and AlAs. The number of Ga and Al layers in the superlattice unit cell can be accurately determined from the low-angle scattering data while the relative intensities of the high-angle superlattice reflections are a sensitive measure of the elastic strain present in the lattice. It is shown that the elastic strain agrees with the value computed theoretically on the assumption that the strain is not relieved by dislocations at the GaAs-AlAs interfaces.