  Phase fractions, compositions and energies of the stable phases as a function
of macroscopic composition, temperature, and pressure (X-T-P) are the principle
correlations needed for the design of new materials and improvement of existing
materials. They are the outcomes of thermodynamic modeling based on the
CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD
predictions vary widely in X-T-P space due to experimental error, model
inadequacy and unequal data coverage. In response, researchers have developed
frameworks to quantify the uncertainty of thermodynamic property model
parameters and propagate it to phase diagram predictions. In previous studies,
uncertainty was represented as intervals on phase boundaries (with respect to
composition) or invariant reactions (with respect to temperature) and was
unable to represent the uncertainty in eutectoid reactions or in the stability
of phase regions. In this work, we propose a suite of tools that leverages
samples from the multivariate model parameter distribution to represent
uncertainty in forms that surpass previous limitations and are well suited to
materials design. These representations include the distribution of phase
diagrams and their features, as well as the dependence of phase stability and
the distributions of phase fraction, composition activity and Gibbs energy on
X-T-P location - irrespective of the total number of components. Most
critically, the new methodology allows the material designer to interrogate a
certain composition and temperature domain and get in return the probability of
different phases to be stable, which can positively impact materials design.
