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Assessment of Uncertainty in CALPHAD Descriptions


This project addresses the development of methods for uncertainty quantification for CALPHAD descriptions.


Knowledge of phase equilibria and phase transformations is absolutely essential for the development of new materials and processing methods. The CALPHAD (CALculation of PHAse Diagrams) method is a proven, indispensable tool in this endeavor. It combines thermodynamic descriptions of binary and ternary systems to predict phase equilibria and phase transformation temperatures in multicomponent systems.  Further, thermodynamic calculations can be coupled with diffusion mobility descriptions for the simulation of diffusion induced phase transformations. 

For materials and process developers, the knowledge of the uncertainty associated with the results from CALPHAD is crucial.  Currently, however, the reliability of these predictions is inferred by comparing CALPHAD results to experimental phase equilibria data of commercial alloys.  This limits the region of confidence to known composition and temperature regimes.  Isolated attempts at evaluating confidence intervals for unary self-diffusion data and binary phase diagrams have been made, but no attempt has been made to evaluate uncertainties that originate from the descriptions of the unary, binary and ternary systems that constitute a multicomponent system.

Major Accomplishments

Our project includes the following components:

  1. Development of a systematic approach for rigorous assessment of uncertainties in CALPHAD results, using the principles widely adopted in metrology and statistics, and in harmony with NIST uncertainty guidance documents (NIST Tech Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Tech Note 1900: Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results, and the ISO Guide the Uncertainty in Measurements (GUM)).
  2. Development of new, state of the art optimization methods for use in CALPHAD software (OpenCalphad). The new optimization methods will be more efficient and are more likely to produce global optimum results. 
  3. Development of a web-based tool, somewhat akin to the NIST UNCERTAINTY MACHINE (, to assist researchers in applying the methods we develop to uncertainty assessments for their own CALPHAD work.

We will follow the general CALPHAD approach to first develop uncertainty quantification methods for unary, binary, and ternary systems, and then to extend the methods to multicomponent systems.

Upon successful addition of an NRC post doctoral fellow to our team we will be able to assemble available experimental data from the published research which will form the basis for CALPHAD computations and associated uncertainties.

Created October 24, 2017, Updated March 25, 2019