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   We outline a method to synthesize ( ATiO 3 ) n AO Ruddlesden–Popper phases with high- n, where the A-site is a mixture of barium and strontium, by molecular-beam epitaxy. The precision and consistency of the method described is demonstrated by the growth of an unprecedented (SrTiO 3 ) 50 SrO epitaxial film. We proceed to investigate barium incorporation into the Ruddlesden–Popper structure, which is limited to a few percent in bulk, and we find that the amount of barium that can be incorporated depends on both the substrate temperature and the strain state of the film. At the optimal growth temperature, we demonstrate that as much as 33% barium can homogeneously populate the A-site when films are grown on SrTiO 3 (001) substrates, whereas up to 60% barium can be accommodated in films grown on TbScO 3 (110) substrates, which we attribute to the difference in strain. This detailed synthetic study of high n, metastable Ruddlesden–Popper phases is pertinent to a variety of fields from quantum materials to tunable dielectrics. 

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