Quantifying sintering activation en

Quantifying sintering activation energy. Linear shrinkage at different heating rates of the cold sintering and solid state sintering30 were plotted (Fig. 2a). The corresponding temperature of the maximum linear shrinkage rate shifts towards a lower region for both sintering methods, which can be related to heating rate dependent kinetic processes.39 Especially for the cold sintering, as a slower heating rate can retain the transient phase longer, allowing a higher degree of solution–assisted particle rearrangement, more linear shrinkage was then measured at temperature below 65◦C. Regarding anisothermal sintering activation energy estimation, the modified Woolfrey–Bannister method takes the data–driven approach based on Eq. 4 to empirically determine n and its relevant uncertainty (Fig. S7). It also needs to be noted that the shrinkage behavior can be roughly classified into three parts based on shrinkage rate, and only the middle portion, featuring the maximum shrinkage rate, was considered in this proposed analysis. Analogous to the solid state sintering case, that steep shrinkage is mainly related the densification during the cold sintering as the relative density evolves up to 93%. Therefore, the proposed method focuses on quantifying activation energy of anisothermal sintering, where powder densification generally happens. According to Eq. 3, the slope contains heating rate (α), experimental exponent (n) and activation energy (Q) (Fig. 2b),and final values are summarized in Table 1. For the cold sintering, Q converges around 49 kJ/mol, where the highest heating rate has diverging and higher Q, which may be related to the reduced degree of dissolution process, as the transient phase stays shorter in the system. In comparison, the solid state sintering shows that the slowest heating rate completely diverges from other two heating rates, which are within uncertainty range. Perhaps, such a low heating rate can provide sufficient thermal energy to drive grain coarsening through surface diffusion mechanism at low temperature region, also leading to decrease in surface area and thermodynamic driving force for sintering.39 Or, that specific heating rate may contain a possible experimental artifact as the shrinkage slope evolution is slightly aberrant from other two rates.