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Thermodynamics of order and randomness in dopant distributions inferred from atomically resolved images

Lukas Vlcek1*, Shize Yang2, Yongji Gong3, Pulickel Ajayan4, Wu Zhou5, Matthew Chisholm6, Maxim Ziatdinov6, Rama Vasudevan6*, Sergei Kalinin6*

1 Joint Institute for Computational Sciences, University of Tennessee, Knoxville, Oak Ridge, TN 37831, U.S.A.

2 Center for Functional Nanomaterials, Brookhaven National Laboratory, New York, U.S.A.

3 School of Materials Science and Engineering, Beihang University, Beijing 100191, China

4 Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, U.S.A.

5 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge TN 37831, U.S.A.

6 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge TN 37831, U.S.A.

* Corresponding authors emails: lvlcek@utk.edu, vasudevanrk@ornl.gov, sergei2@ornl.gov
DOI10.24435/materialscloud:w8-k3 [version v1]

Publication date: Jan 26, 2021

How to cite this record

Lukas Vlcek, Shize Yang, Yongji Gong, Pulickel Ajayan, Wu Zhou, Matthew Chisholm, Maxim Ziatdinov, Rama Vasudevan, Sergei Kalinin, Thermodynamics of order and randomness in dopant distributions inferred from atomically resolved images, Materials Cloud Archive 2021.21 (2021), doi: 10.24435/materialscloud:w8-k3.


Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the material's processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of MoxRe1−xS2 at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures. This dataset includes STEM image data files and associated python code to perform statistical analysis of the images and simulations.

Materials Cloud sections using this data

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File name Size Description
15.0 MiB STEM image of Re_{x}Mo_{1-x}S_{2} with x = 0.05
7.5 MiB STEM image of Re_{x}Mo_{1-x}S_{2} with x = 0.55
7.5 MiB STEM image of Re_{x}Mo_{1-x}S_{2} with x = 0.78
7.5 MiB STEM image of Re_{x}Mo_{1-x}S_{2} with x = 0.95
1.6 MiB Python Jupyter notebook for processing included STEM image files
2.1 MiB R Jupyter notebook for running indicator Gaussian Process simulations of Re/Mo atom distributions based on STEM images
174.5 KiB Python Jupyter notebook for the analysis of GP simulations
29.6 KiB Utility functions needed by the included Jupyter notebooks


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.


scanning transmission electron microscopy statistical inference segregation dichalcogenide Monte Carlo simulation

Version history:

2021.21 (version v1) [This version] Jan 26, 2021 DOI10.24435/materialscloud:w8-k3