Phase change materials (PCM) can exist in two different states, namely, as amorphous and crystalline solids, which can have markedly different physical properties. This is the basis for the usage of PCM for data storage applications. The ternary alloy of germanium, antimony and tellurium (GST) has been intensely studied, because at the stoichiometric composition Ge2Sb2Te5, the amorphous phase can rapidly crystallize without change in composition. This makes it a material of choice for random access memory devices (PCRAM). The amorphous phase spontaneously crystallizes at relatively low temperature, 160 °C. For numerous applications, this temperature has to be increased, for example by enriching the stoichiometric GST with germanium. However, then the phase change is accompanied by a composition change: upon crystallization, the additional Ge segregates into the amorphous phase. This can lead to the nucleation and growth of a new crystalline phase which is rich in Ge. For the development of new materials, it is important to better understand this complex microstructure formation process. A grand-canonical multi-phase-field model for the crystallization of GST has been developed, which takes into account three phases: the amorphous state, stoichiometric GST and a Ge-rich crystalline phase. Within a pseudo-binary approximation of the phase diagram, the phase fields are coupled to a single concentration field. The grain structure of the polycrystalline material is described using orientation fields. The kinetic parameters of the model are determined from data on stoichiometric GST available in the literature. Combining this model with the equations for thermal and electric conduction, we have constructed a multiphysics model for simulations of memory operations. The microstructure and composition distribution observed in real memory cells can be qualitatively reproduced, and semi-quantitative agreement with several calibration curves used in the semiconductor industry can be reached.