Thermodynamic Modeling of Pure Elements from 0 K with Uncertainty Quantification using PyCalphad and ESPEI

Published

September 21, 2026

Author(s)

Alexander Richter, Abdulmonem Obaied, Irina Roslyakova, Boris Wilthan, Allison Beese, Zi-Kui Liu

Abstract

Thermodynamic modeling of pure elements is the foundation of the CALPHAD modeling of engineering materials. Recently, multiple physics-based models have been proposed to describe Gibbs energy of pure elements down to 0 K, extending from 298.15K in the current CALPHAD modeling. To enable their systematic and quantitative comparison and adoption, those thermodynamic models of pure elements are implemented into the open-source software packages PyCalphad and ESPEI in the present work for evaluation of model parameters and model fitness. PyCalphad and ESPEI are suitable tools for implementation of these models for high throughput CALPHAD modeling of multicomponent materials. Particularly, Markov Chain Monte Carlo used in ESPEI allows for uncertainty quantification of model parameters and model predications. Through the remodeling of 41 pure elements, the present work demonstrates the quantitative comparison of modeling of pure elements with different models and enables the efficient development of multicomponent systems with continuously improved CALPHAD description of pure elements.

Citation

Calphad-Computer Coupling of Phase Diagrams and Thermochemistry

Pub Type

Journals

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https://doi.org/10.1016/j.calphad.2026.103006

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Citation

Richter, A. , Obaied, A. , Roslyakova, I. , Wilthan, B. , Beese, A. and Liu, Z. (2026), Thermodynamic Modeling of Pure Elements from 0 K with Uncertainty Quantification using PyCalphad and ESPEI, Calphad-Computer Coupling of Phase Diagrams and Thermochemistry, [online], https://doi.org/10.1016/j.calphad.2026.103006, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=961531 (Accessed September 25, 2026)

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