Why a master sintering curve model can be applied to the sintering of nano-sized particles?

The master sintering curve model (MSC) has been widely applied to both the analysis and prediction of the sintering behavior of many powder materials, including nanocrystalline powder. However, since the conventional sintering theories are only true for submicron-sized or larger particles, it should not be applicable to the sintering of nano-sized particles. This work aims to provide an explanation as to why the MSC is capable of predicting nano-sized particle sintering. A comparison with another kinetic model, i.e., the master kinetics curve (MKC), which was derived from general chemical kinetic equation, reveals that MSC is almost identical except for a 1/T term in the equation. The analysis of sintering data also shows that the ability of both MSC and MKC are almost equal, and that the values of apparent activation energy provided by both two models are similar too. In previous researches, it is also found that the MSC can be applied to non-sintering systems. These results show that the ability of prediction of the MSC is strongly related to the integration of an Arrhenius type equation. However, because the MSC cannot determine the mechanism of the sintering process, the apparent activation energy Qa may not represent any physical meaning. In summary, MSC may be a “universal” analytical tool for many reaction systems, and its success is definitely not due to its sintering origin but rather to its Arrhenius type form.