Non-isothermal phase-field models and evolution equation

Phase transitions between two phases are modelled as space regions where a phase field, or order parameter, changes smoothly. The literature shows a seeming contradiction in that some papers lead to the use of the reduced chemical potential through the temperature, others do not. The paper has a threefold purpose. First, to revise the arguments of known approaches and possibly generalize the associated schemes. Secondly, to show that a further approach is possible which involves the phase field as an internal variable. Thirdly, to contrast the various schemes and the corresponding results. It follows that differences arise because different fields enter the models and different forms are considered for the balance of energy and the second law of thermodynamics.