  Calculation of phase diagrams is one of the fundamental tools in alloy
design---more specifically under the framework of Integrated Computational
Materials Engineering. Uncertainty quantification of phase diagrams is the
first step required to provide confidence for decision making in property- or
performance-based design. As a manner of illustration, a thorough probabilistic
assessment of the CALPHAD model parameters is performed against the available
data for a Hf-Si binary case study using a Markov Chain Monte Carlo sampling
approach. The plausible optimum values and uncertainties of the parameters are
thus obtained, which can be propagated to the resulting phase diagram. Using
the parameter values obtained from deterministic optimization in a
computational thermodynamic assessment tool (in this case Thermo-Calc) as the
prior information for the parameter values and ranges in the sampling process
is often necessary to achieve a reasonable cost for uncertainty quantification.
This brings up the problem of finding an appropriate CALPHAD model with
high-level of confidence which is a very hard and costly task that requires
considerable expert skill. A Bayesian hypothesis testing based on Bayes'
factors is proposed to fulfill the need of model selection in this case, which
is applied to compare four recommended models for the Hf-Si system. However, it
is demonstrated that information fusion approaches, i.e., Bayesian model
averaging and an error correlation-based model fusion, can be used to combine
the useful information existing in all the given models rather than just using
the best selected model, which may lack some information about the system being
modelled.
