Modeling transformation paths of multiphase materials: The triple point of zirconia

We propose a general method for modeling transformation paths of multiphase materials such that elastic moduli can be fitted exactly. The energy landscape obtained in this way is global and automatically enjoys the correct symmetries. The method is applied to the triple point of zirconia, where tetragonal, orthorhombic (orthoI), and monoclinic phases meet. An explicit and relatively simple expression yields a phenomenological model in the two-dimensional space spanned by a set of order parameters. We also show how to extend this energy to a fully three-dimensional model with an exact fit of all given elastic moduli.