Uncertainty quantification and propagation in CALPHAD modeling

Abstract

Design is about making decisions bounded by a quantifiable degree of certainty. In the context of alloy design, Integrated Computational Materials Engineering (ICME) provides the framework whereby performance requirements are ultimately transformed into alloy/processing specifications through the combination of (complex) computational models connecting processstructure-property-performance relationships and experiments. Most ICME approaches consider the models used as deterministic and thus do not provide the means to make alloy design decisions with proper confidence measures. At the root of ICME lie CALPHAD models that describe the thermodynamics and phase stability of phases under specific thermodynamic boundary conditions. To date, the vast majority of efforts within the CALPHAD community have been deterministic in that thermodynamic models and the resulting thermodynamic properties and phase diagram features do not explicitly account for the uncertainties inherent in the model formulation or in the experimental/computational data used. In this contribution, we provide an overview of the state of the field. We review major efforts thus far and we then provide a (brief) tutorial on basic concepts of uncertainty quantification and propagation (UQ/UP) in CALPHAD. We discuss the major features of frequentist and Bayesian interpretations of uncertainty and proceed with a discussion of recent case studies in which UQ has been used to parameterize models for the thermodynamic properties of phases. We follow our discussion by presenting frameworks and demonstrating the propagation of uncertainty in

Uncertainty Quantification of First Principles Computational Phase Diagram Predictions of Li-Si System Via Bayesian Sampling

“…For example, we can say that solid Li is stable at low temperatures and Li 12 Si 7 is very unlikely to be stable according to the c-value of the UQ phase diagram. In the previous uncertainty phase diagram found in literature, 9,45 only the uncertainty range of a specific phase is given. Therefore, in this uncertainty phase diagram, it can not only give the uncertainty range but also give the occurrence probability compared with the uncertainty phase diagrams in P. Honarmandi et al's work 9 .…”

“…In CALPHAD, the uncertainty can be propagated from the model parameters to Gibbs free energy, then to the phase diagram. In previous work incorporating uncertainty within phase diagram predictions, as discussed above, Markov Chain Monte Carlo (MCMC) sampling approach has conventionally been used to obtain plausible optimum values and uncertainties of the parameters 9,45 . This propagation of uncertainty assumes that the errors in the prediction of two materials from DFT are independent of one another.…”

Applications of Data Driven Methods in Computational Materials Design

“…CALPHAD assessments have mostly been deterministic, giving a single value for the parameters, without specifying any uncertainty of the parameters. Although there have been some early works, the topic of uncertainty quantification and propagation in CALPHAD has only gained momentum in recent years, often adopting the Bayesian framework [11]. As the accuracy of the thermodynamic database determines the reliability of the calculated results, the determination of the uncertainty in CALPHAD helps to understand how strongly one can rely on results from thermodynamic simulations.…”

Equilibrium Phase Relations of a SiO2–Al2O3–FeOx System with 10 wt % CaO Addition for the Production of Continuous Basalt Fibers

“…However, the predicted thermodynamic properties are mainly reliable for lower binary and ternary systems such as CaO–SiO 2 , 33 CaO–SiO 2 –Al 2 O 3 , 34 CaO–SiO 2 –ZrO 2 , 35 and SiO 2 –Al 2 O 3 –TiO 2 , 36 while the calculated thermodynamic information for high-order systems is still far from sufficient due to the lack of accurate experimental data. 37 , 38 It is then necessary to conduct basic thermodynamic studies to lay the foundation for further comprehensive construction of the basalt oxide thermodynamic databases.…”

“…21 The optimized industrial parameters corresponding to the varying oxide 36 while the calculated thermodynamic information for high-order systems is still far from sufficient due to the lack of accurate experimental data. 37,38 It is then necessary to conduct basic thermodynamic studies to lay the foundation for further comprehensive construction of the basalt oxide thermodynamic databases. Therefore, a long-term project for the fundamental thermodynamic investigation of the equilibrium phase relations has been proposed for the efficient production of CBFs.…”