The cyclic growth and shrinkage of solid oxides (i.e. wollastonite) in CaO–SiO2-based slags is investigated in-situ by means of High-Temperature Confocal Scanning Laser Microscopy (HT-CSLM). The compositions of the slags are carefully selected to induce different phase transformation conditions, i.e. congruent and incongruent melting/solidification. To complement the experimental results, the kinetics of growth and shrinkage of oxide crystals is investigated by means of a sharp interface model where the interfacial reaction and diffusion in the liquid bulk are considered as possible rate-controlling processes. The modelling approach combined with data analysis from key experiments reveals the underlying dissipative processes of solidification and melting phenomena, here, diffusion in the liquid bulk material and/or the interfacial reactions. The modelling approach is likely to be applicable for future materials design and processing problems from this perspective.