ESPEI, or Extensible Self-optimizing Phase Equilibria Infrastructure, is a tool for thermodynamic database development within the CALPHAD method. It uses pycalphad for calculating Gibbs free energies of thermodynamic models.

Installation Anaconda (recommended)

ESPEI does not require any special compiler, but several dependencies do. Therefore it is suggested to install ESPEI from conda-forge.

conda install -c conda-forge espei

What is ESPEI?

  1. ESPEI parameterizes CALPHAD models with enthalpy, entropy, and heat capacity data using the corrected Akiake Information Criterion (AICc). This parameter generation step augments the CALPHAD modeler by providing tools for data-driven model selection, rather than relying on a modeler's intuition alone.
  2. ESPEI optimizes CALPHAD model parameters to thermochemical and phase boundary data and quantifies the uncertainty of the model parameters using Markov Chain Monte Carlo (MCMC). This is similar to the PARROT module of Thermo-Calc, but goes beyond by adjusting all parameters simultaneously and evaluating parameter uncertainty.

Details on the implementation of ESPEI can be found in the publication: B. Bocklund et al., MRS Communications 9(2) (2019) 1–10. doi:10.1557/mrc.2019.59.

What ESPEI can do?

ESPEI can be used to generate model parameters for CALPHAD models of the Gibbs energy that follow the temperature-dependent polynomial by Dinsdale (CALPHAD 15(4) 1991 317-425) within the compound energy formalism (CEF) for endmembers and Redlich-Kister-Mugganu excess mixing parameters in unary, binary and ternary systems.

All thermodynamic quantities are computed by pycalphad. The MCMC-based Bayesian parameter estimation can optimize data for any model that is supported by pycalphad, including models beyond the endmember Gibbs energies Redlich-Kister-Mugganiu excess terms, such as parameters in the ionic liquid model, magnetic, or two-state models. Performing Bayesian parameter estimation for arbitrary multicomponent thermodynamic data is supported.


  1. Offer a free and open-source tool for users to develop multicomponent databases with quantified uncertainty
  2. Enable development of CALPHAD-type models for Gibbs energy, thermodynamic or kinetic properties
  3. Provide a platform to build and apply novel model selection, optimization, and uncertainty quantification methods

The implementation for ESPEI involves first performing parameter generation by calculating parameters in thermodynamic models that are linearly described by non-equilibrium thermochemical data. Then Markov Chain Monte Carlo (MCMC) is used to optimize the candidate models from the parameter generation to phase boundary data.


Cu-Mg phase diagram from a database created with and optimized by ESPEI. See the Cu-Mg Example.