Evolution of cellular morphology in pure materials

The evolution of cellular morphology during interfacial instability for liquid–solid transition for pure unary material systems is studied using the maximum entropy production (generation) rate principle (MEPR) for steady-state directional solidification. This approach is dependent on a quantity called maximum entropy production rate density which inherently contains key solidification parameters that governs cellular evolution for liquid–solid transformation. The maximum entropy production rate density is computationally measured from the solid–liquid interface in diffuse form and considers steady-state solidification at low velocities for both near and far from equilibrium conditions. The results are presented in mathematical expressions for morphological instability that corresponding to the evolution of a cellular morphology which emanates from the solid–liquid interface. The model is formulated to evaluate the solid–liquid interface thickness, the solidification velocity, grain boundary energy, and the size of the cellular morphological at instability. The results are tested with a number of pure single element materials at different temperature gradients which compare well with available experimental data.