Chemical Potential Diagrams (CPDs)
Overview of how chemical potential diagrams (CPDs) are constructed and visualized. These are available as part of the Phase Diagram App.
Introduction
The chemical potential diagram is the mathematical dual to the compositional phase diagram. To create the diagram, convex minimization is performed in energy (E) vs. chemical potential (μ) space by taking the lower convex envelope of hyperplanes. Accordingly, “points” on the compositional phase diagram become N-dimensional convex polytopes (domains) in chemical potential space.
For more information on this specific implementation of the algorithm, please cite/reference the paper below:
Methodology
Constructing hyperplanes
Calculating lower convex envelope (halfspace intersection)
Visualizing the chemical potential diagram
Relationship to predominance diagrams
Citations
Methodology
Todd, P. K., McDermott, M. J., Rom, C. L., Corrao, A. A., Denney, J. J., Dwaraknath, S. S., Khalifah, P. G., Persson, K. A., & Neilson, J. R. (2021). Selectivity in Yttrium Manganese Oxide Synthesis via Local Chemical Potentials in Hyperdimensional Phase Space. Journal of the American Chemical Society, 143(37), 15185-15194. https://doi.org/10.1021/jacs.1c06229
References
[1] Yokokawa, H. “Generalized chemical potential diagram and its applications to chemical reactions at interfaces between dissimilar materials.” JPE 20, 258 (1999). https://doi.org/10.1361/105497199770335794
[1] Todd, P. K., McDermott, M. J., Rom, C. L., Corrao, A. A., Denney, J. J., Dwaraknath, S. S., Khalifah, P. G., Persson, K. A., & Neilson, J. R. (2021). Selectivity in Yttrium Manganese Oxide Synthesis via Local Chemical Potentials in Hyperdimensional Phase Space. Journal of the American Chemical Society, 143(37), 15185-15194. https://doi.org/10.1021/jacs.1c06229
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