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We outline a method to synthesize (ATiO3)nAO 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 (SrTiO3)50SrO 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 SrTiO3 (001) substrates, whereas up to 60% barium can be accommodated in films grown on TbScO3 (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. 

Homologous series are layered phases that can have a range of stoichiometries depending on an index n. Examples of perovskite-related homologous series include (ABO3)nAO Ruddlesden–Popper phases and (Bi2O2) (An−1BnO3n+1) Aurivillius phases. It is challenging to precisely control n because other members of the homologous series have similar stoichiometry and a phase with the desired n is degenerate in energy with syntactic intergrowths among similar n values; this challenge is amplified as n increases. To improve the ability to synthesize a targeted phase with precise control of the atomic layering, we apply the x-ray diffraction (XRD) approach developed for superlattices of III–V semiconductors to measure minute deviations from the ideal structure so that they can be quantitatively eradicated in subsequent films. We demonstrate the precision of this approach by improving the growth of known Ruddlesden–Popper phases and ultimately, by synthesizing an unprecedented n = 20 Ruddlesden–Popper phase, (ATiO3)20AO where the A-site occupancy is Ba0.6Sr0.4. We demonstrate the generality of this method by applying it to Aurivillius phases and the Bi2Sr2Can–1CunO2n+4 series of high-temperature superconducting phases.