Thermodynamics of microstructure evolution: Grain growth

It is gradually getting clear that the macroscopic description of microstructure evolution requires additional thermodynamic parameters, entropy of microstructure and temperature of microstructure. It was claimed that there is “one more law of thermodynamics”: entropy of microstructure must decay in isolated thermodynamically stable systems. Such behavior is opposite to that of thermodynamic entropy. This paper aims to illustrate the concept of microstructure entropy by one example, the grain growth in polycrystals. The grain growth is treated within the framework of a theory which is a modification of Hillert theory. The modification is made in order to reach simultaneously two goals: to get a coincidence of theoretical predictions with experimentally observed results and to obtain the equations that admit analytical solutions. Due to these features, the modified theory is of independent interest. In the modified Hillert theory one observes the decay of total microstructure entropy when the system approaches the self-similar regime. The microstructure entropy per one grain grows indicating a chaotization of grain sizes. It is shown also that there exits an equation of state of grain boundary microstructure that links entropy of microstructure, energy of microstructure, average grain size and a characteristic of the inhomogeneity of the large grain distribution.