Sensitivity estimation for calculated phase equilibria

Richard Otis, Brandon Bocklund, Zi‐Kui ‐K Liu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The development of a consistent framework for Calphad model sensitivity is necessary for the rational reduction of uncertainty via new models and experiments. In the present work, a sensitivity theory for Calphad was developed, and a closed‐form expression for the log‐likelihood gradient and Hessian of a multi‐phase equilibrium measurement was presented. The inherent locality of the defined sensitivity metric was mitigated through the use of Monte Carlo averaging. A case study of the Cr–Ni system was used to demonstrate visualizations and analyses enabled by the developed theory. Criteria based on the classical Cramér–Rao bound were shown to be a useful diagnostic in assessing the accuracy of parameter covariance estimates from Markov Chain Monte Carlo. The developed sensitivity framework was applied to estimate the statistical value of phase equilibria measurements in comparison with thermochemical measurements, with implications for Calphad model uncertainty reduction. [Figure not available: see fulltext.]

Original languageEnglish (US)
Pages (from-to)140-150
Number of pages11
JournalJournal of Materials Research
Issue number1
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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