Nano-Scaled Grain Growth

One of the main goals in sintering is to obtain dense compacts with retained grain sizes. Therefore, a detailed understanding of the phenomenon of grain growth and the parameters affecting it is of prime importance for a successful processing. In this chapter, two kinds of models (thermodynamic and kinetic ones) are constructed to explain the role of segregation playing in controlling the thermal stability and the grain growth of nanocrystalline materials. Thermodynamically, analogous to the Gibbs adsorption theorem, a concept that solute atoms segregating in GBs could decrease the GB energy is proposed, i.e. once the GB energy reduces to almost zero with solute segregation, the system approaches metastable equilibrium state. Kinetically, the difference of solute concentrations between the GBs and the bulk produces a drag force on the GB migration. Incorporating a constant drag term into the parabolic equation, a model describing the nanocrystalline growth kinetics subjected to the GB segregation is presented. Considering that the thermodynamic method cannot describe the process of grain growth and that the kinetic one could do nothing for predicting the metastable stability, a coupling of thermodynamic and kinetic ways seems particularly important to provide an insight for understanding the thermal stability and grain growth of nanocrystalline materials. On this basis, from Borisov’s empirical relationship, the rationality of coupling thermodynamic and kinetic ways has been demonstrated. Assuming a linear relationship between the GB energy and the average grain size, an analytical thermo-kinetic model with incorporating the reduced GB energy into the drag equation of grain growth is proposed.