A three-dimensional imaging study has found that oxygen dopants in a cuprate film were not spread evenly: sites with more space between neighboring copper atoms tended to contain more interstitial oxygen, and clusters appeared near a local Cu–Cu spacing of about 3.9 Å. Sites below 3.6 Å typically contained one to three interstitial oxygens per column. The finding is a spatial association in the film examined, not evidence that strain itself caused the oxygen to collect there.
The work, posted as an arXiv version 1 preprint dated 20 Aug 2026, used multislice electron ptychography to reconstruct oxygen positions at different depths. The images place the interstitial signal between Cu–O chains and show lateral displacements in neighboring copper and oxygen columns, giving the dopant-like features a structural context.
A three-dimensional view of the film
The material was a Sr2CuO3+δ film grown on a SrTiO3 substrate by molecular beam epitaxy. It was capped with Al2O3 and prepared as cross-section transmission-electron-microscopy lamellas using a focused ion beam, allowing the reconstructed data to include the film–substrate interface.
The experiment used scanning transmission electron microscopy at 300 kV, with four-dimensional scanning-transmission-electron-microscopy diffraction data collected by a pixelated EMPAD G2 detector. A multislice reconstruction algorithm was then used to recover the structure through the specimen’s depth.
Here, an interstitial oxygen is an oxygen atom identified at a position between the Cu–O chains rather than along the main chain columns. In the reconstruction, the positions of these features could be followed with depth, while nearby Cu and O columns shifted laterally.
The researchers also used simulations to calibrate the count. They reconstructed simulated four-dimensional microscopy data from structures containing different numbers of interstitial oxygens, then compared the resulting signal with the known input structures.
Turning reconstructed signal into oxygen counts
The analysis relied more heavily on relative oxygen intensity than on the absolute phase of the reconstructed object. That choice was intended to provide a more dependable way to compare the amount of oxygen-like signal from one site with another.
Not every feature was accepted as an interstitial column. A candidate had to rise above the noise, meet minimum requirements for lateral and depth size, and lie near the midpoint between neighboring Cu and O columns. These criteria were used to separate possible dopant signals from reconstruction background.
Features near the surfaces of the lamellas were left out because surface reconstructions or absorbates could create misleading dopant-like signals. The reported site counts therefore apply to the regions that passed the selection rules, rather than to every visible feature in the specimen.
More oxygen where the lattice opened up
After the candidate sites were identified, the study compared their interstitial counts with local Cu–Cu spacing. The relationship was positive: sites below 3.6 Å typically held one to three interstitial oxygens per column, while clusters were found near 3.9 Å. In ordinary terms, the larger-spacing sites carried more oxygen-like signal.
That pattern is the central result of the preprint. It supports the idea that oxygen interstitials are associated with the local lattice state in this film, but a comparison between sites does not establish a cause-and-effect mechanism. The result cannot by itself show that deliberately stretching the lattice would create more interstitial oxygen.
The relationship also appeared when the same dataset was reconstructed using depth-slice thicknesses of 4, 6 and 8 Å. Similar doping–strain correlations across those settings suggest that the reported pattern was not produced by one selected slice thickness, although the check remained within the same dataset.
The interface is part of the story
The three-dimensional reconstruction showed that the substrate surface was not perfectly flat. Its measured roughness was about 4 Å in height, approximately one SrTiO3 unit cell, and the interface contained visible steps.
Dislocation cores appeared in pairs near SrTiO3 step edges and coincided with regions under compressive strain. The images therefore place these defects in the same structural landscape as the local spacing changes, rather than showing oxygen distribution in an otherwise uniform interface.
Away from the interface, the imaging results suggested a small oxygen excess, expressed as δ approximately 0.005 for the Sr2CuO3+δ film. Because this value comes from the reconstructed oxygen signal, it should be read as an imaging-derived estimate rather than a complete count of every interstitial atom.
What the images may miss
Under the reported imaging conditions, the electron dose was 1.2 × 10^5 electrons per Å2. The minimum detectable signal corresponded to two interstitials per column, so isolated single interstitials below that level were not excluded.
That threshold limits what can be concluded about the film’s total oxygen population. The visible clusters are the interstitial signals that met the detection conditions; atoms producing a weaker signal could remain uncounted without contradicting the reported images.
Depth resolution was another unresolved issue. The authors proposed that nearby oxygen vacancies could form sub-nanometer orthorhombic twin domains, and said that improved multislice electron-ptychography depth resolution would be needed to distinguish that scenario from the interstitial interpretation.
The distinction matters because the observed contrast and lattice response do not identify a single structural explanation on their own. The preprint presents the interstitial-oxygen interpretation alongside an alternative involving vacancies and twin domains, leaving that question open for higher-resolution or complementary measurements.
A structural association, not a recipe
Taken together, the measurements provide a three-dimensional map of oxygen-like features, local copper spacing, interface roughness and dislocation locations in the described Sr2CuO3+δ/SrTiO3 structure. They show that the oxygen-interstitial count varied with local spacing and that the pattern survived the tested reconstruction settings.
They do not, however, turn that association into a general rule for cuprate materials. The strongest conclusion supported by the supplied analysis is narrower: in this film and under these imaging conditions, oxygen-interstitial signals were concentrated at sites with larger local Cu–Cu spacing, while the full population and exact structural identity of every oxygen-related feature remain uncertain.
Paper data and sources
Original title: Three-dimensional imaging of oxygen dopant distribution in Sr$_2$CuO$_{3+δ}$ by electron ptychography
Authors: Hongbin Yang, Jinkwon Kim, Desheng Ma et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text