Data and code from: Bridging experiment and theory of relaxor ferroelectrics with multislice electron ptychography

Data files

Mar 25, 2026 version files 108.42 GB

PMNPT_0.5_newdata.tar.gz

15.87 GB
PMNPT_0.5_originaldata.tar.gz

14.92 GB
PMNPT_0.75_newdata_stabilitytest.tar.gz

15.91 GB
PMNPT_0.75_newdata.tar.gz

15.82 GB
PMNPT_0.75_originaldata.tar.gz

15.03 GB
PMNPT_1.0_newdata.tar.gz

15.79 GB
PMNPT_1.0_originaldata.tar.gz

14.97 GB
README.md

3.39 KB
SampleData_and_Notebooks.zip

109.78 MB

Abstract

Introducing structural and/or chemical heterogeneity into otherwise ordered crystals can dramatically alter material properties. Lead-based relaxor ferroelectrics, such as 0.68Pb(Mg_1/3Nb_2/3)O₃-0.32PbTiO₃, are prototypical examples. Here, we perform three-dimensional volumetric characterization using multislice electron ptychography (MEP) and bond valence molecular dynamics (BVMD) simulations. Real-space comparisons between the two under varying strain states reveal a coherent three-dimensional view of the "polar slush." Dipolar correlations from the atomic to domain scales are shown to be jointly modulated by strain and chemical configurations, with the best agreement found in a model accounting for both overall chemical disorder and residual short-range order. Together, MEP and BVMD demonstrate a framework for connecting atomic-scale heterogeneity in complex materials through complementary 3D imaging and predictive modeling.

https://doi.org/10.5061/dryad.tqjq2bw8j

Description of the data and file structure

PMN_PT_*.tar.gz

Four-dimensional scanning transmission electron microscopy dataset and metadata collected with EMPAD (.raw, .xml) and corresponding multislice electron ptychography reconstruction outputs, including the engine parameters (.mat).
The .raw file contains a 4D-STEM dataset that can be viewed using tools such as the 4D-STEM Explorer app for macOS, empad2 package, Fiji plugins, or custom Python scripts. The .xml file contains metadata for the collection of the .raw file and can be accessed with text edit tools.
Multislice electron ptychography reconstruction outputs, including the probe, object, and engine parameters are included in the .mat file following the stand output format of fold_slice.

SampleData and Notebooks.zip

The .npy files contains atomic positions, intensities and polar displacments fitted from the reconstructed ptychography image stack.
The python notebook examplifies the steps of loading the data and performing analysis, including polar color plot visualization, domain segmentation, polar correlation calculations, and principal component analysis as discussed in the Main Text and Supplementary Materials.
The .png files are the expected output from running the notebook
The file conda_env_setup.yaml specifies all dependencies required to execute the notebook. To create the environment, navigate to the project directory and run: conda env create -f conda_env_setup.yaml. Then activate the environment: conda activate relaxor-test. After activation, launch Jupyter and select the corresponding kernel before running the notebook.
The notebook has only been tested under the enviroment versions specified in conda_env_setup.yaml. Execution in other environments, with different Python versions or dependency versions, is not guaranteed to work or to produce identical results.

Files and variables

Each compressed archive contains three acquisitions of 4D-STEM data (.raw), its metadata generated by EMPAD at the time of acquisition (.xml), and its corresponding final reconstructed object, probes, and other outputs (.mat).

The folders are named in PMNPT_strainState_originaldata/newdata/stabilitytest. The originaldata were acquired for the initial submission and the newdata/stabilitytest were acquired for the review.

All other supporting data or codes including the molecular dynamics simulations are available from the authors upon reasonable request.

Code/software

Multislice electron ptychography is performed with the foldslice package (https://github.com/yijiang1/fold_slice) that is built upon the Matlab code developed by the Science IT and the coherent X-ray scattering (CXS) groups at Paul Scherrer Institut, Switzerland: https://www.psi.ch/en/sls/csaxs/software. Copyright and license issues should follow the agreements and/or refer to their website.