Assessing Phase Diagram Accuracy

Assessing the predictive power of any computational model requires the definition of an appropriate metric or figure-of-merit (e.g. mean square error, maximum error, etc). However, quantifying errors in an alloy phase diagram with a single figure-of-merit is a considerably more complex problem. The “distance” between phase boundaries is not a uniquely defined concept and different phase diagrams may differ in the possible stable phases which they predict, making it unclear which “distance” to measure. Given the difficulty associated with such metrics, we instead propose to use differences in predicted phase fractions between different phase diagrams as the basis of a suitable metric. We prove that our criterion satisfies all the properties of the mathematical notion of a norm or of a metric, in addition to other properties directly relevant to phase stability problems. We illustrate the use of such criterion to the study of the convergence of assessments performed on the same alloy system by different authors over time.