Towards more realistic simulations of microstructural evolution in oxidic systems

Inge Bellemans, Nico Vervliet, Lieven De Lathauwer, Nele Moelans, Kim Verbeken


High temperature oxidic systems are encountered in nature (magma chambers) and pyrometallurgical processes. In these systems, the solidification of the oxidic liquids influences the flow, the cooling after tapping, the viscosity and rheological behaviour within the reactor and also the freeze lining behaviour. On the mesoscale, the phase field concept has proved to be a very powerful tool for modeling crystallizing microstructures. However, application of the method to slag solidification is still challenging. In this work, we present a phase field model to simulate the faceted crystallization of Fe3O4 in a quaternary FeO–Fe2O3–Cu2O–SiO2 melt under different partial pressures of oxygen to solve certain problems encountered related to more realistic simulations in oxidic systems. The ratio of FeO/Fe2O3 at the upper boundary is in equilibrium with the oxygen fugacity of the atmosphere, while conserving Fe. Two-dimensional simulations are performed with different varying oxygen fugacity in the atmosphere. For the considered composition range, the growth velocities of the spinel crystals increase with decreasing oxygen fugacity. One of the focus points in creating more realistic phase field models is the incorporation of the thermodynamic driving forces in multicomponent multiphase-field models by coupling to thermodynamic databases. The first part of this work used a tabular method. However, as the number of components in the system increases, the number of thermodynamic data points also increases exponentially, and so do the computational and memory requirements. A possible solution for this might be the use of a canonical polyadic decomposition of the tensors containing the thermodynamic data. In this way, the huge tensors are approximated well by compact multilinear models or decompositions. This promising solution has been applied in the second part of this work on the same oxidic liquid-solid system.

Code description

This package provides experiment files and auxiliary files requiredfor the computation of the CPD models for the thermodynamic datatensors of a FeO-Fe2O3-Cu2O-SiO2 system as described in the paper. Forboth the fourth-order and the third-order coupled cases, a computationfile and a file showing how to use the computed results is given.


I. Bellemans, N. Vervliet, L. De Lathauwer, N. Moelans, K. Verbeken, "Towards more realistic simulations of microstructural evolution in oxidic systems," Calphad, vol. 77, pp. 102402, June 2022.

Download code

This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from