Assessing Phase Diagram Accuracy

Axel Van De Walle,Qijun Hong

doi:10.1007/s11669-019-00711-5

Axel Van De Walle, Qijun Hong

Open Access

https://doi.org/10.1007/s11669-019-00711-5

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Abstract

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.

Highlights

One of the underlying assumption of the goal of achieving ‘‘predictive science’’ is the availability of suitable metric to quantify the accuracy of the predictions
We propose to quantify the difference between two phase diagrams f 1; f 2 in a region R of interest via the following figure-of-merit: f
We have described a formal methodology to quantify, in a single figure-of-merit, the level of agreement between two phase diagrams

Summary

Introduction

One of the underlying assumption of the goal of achieving ‘‘predictive science’’ is the availability of suitable metric to quantify the accuracy of the predictions. Phase boundaries cannot be considered single-valued functions: For instance, in a binary phase diagram, a phase boundary might cross a given vertical line (see label 1 on the figure) multiple times, precluding the use of simple ‘‘mean-square error along one axis’’ criteria. Boundary distance-based metrics are unable to handle the fact that, sometimes, phases are entirely absent from one phase diagram but present in another (label 6). Phase fractions have been put forward as powerful and fundamental descriptors of phase equilibria.[16] Phase fractions are scalar, dimensionless, everywhere defined and merely take the value 0 when a phase is not stable. These desirable properties solve all of the aforementioned problems. We illustrate the use of such a criterion to the study of the convergence of assessments performed on the same alloy system by different authors over time

Definition and Motivation

Application Example

Conclusion