The description of morphologically stable regimes for steady state solidification based on the maximum entropy production rate postulate

Abstract

The maximum entropy production rate (MEPR) in the solid–liquid zone is developed and tested as a possible postulate for predicting the stable morphology for the special case of steady state directional solidification (DS). The principle of MEPR states that, if there are sufficient degrees of freedom within a system, it will adopt a stable state at which the entropy generation (production) rate is maximized. Where feasible, the system will also try and adopt a steady state. The MEPR postulate determines the most probable state and therefore allows pathway selections to occur in an open thermodynamic system. In the context of steady state solidification, pathway selections are reflected in the corresponding morphological selections made by the system in the solid–liquid (mushy) zone in order to cope with the required entropy production. Steady state solidification is feasible at both close to, and far from equilibrium conditions. Based on MEPR, a model is proposed for examining the stability of various morphologies that have been experimentally observed during steady state directional solidification. This model employs a control volume approach for entropy balance, including the entropy generation term (Sgen), which depends on the diffuse zone and average temperature of the solid–liquid region within the control volume. In this manner, the model takes a different approach from the successful kinetic models that have been able to predict key features of stable morphological patterns. Unstable planar interfaces, faceted cellular arrays, cell–dendrite transitions, half cells both faceted and smooth, and other transitions such as the absolute stability transition at high solid/liquid velocities are examined with the model. Uncommon solidification morphological features such as non-crystallographic dendrites and discontinuous cell-tip splitting are also examined with the model. The preferred morphological change-direction for the emergence of the stable morphological feature is inferred with the MEPR postulate in a manner analogous to the free energy minimization principle(s) when used for predicting phase stability and metastable phase formation. Aspects of mixed-mode order transformation characteristics are also discussed for non-equilibrium solidification containing a diffuse interface, in contrast to classifying solidification as purely a first order transformation. The MEPR model predictions are shown to follow the experimental transitions observed to date in several historical studies.