where t is the required time to achieve the thermal equilibration, t ( is incubation time which before no conversion happens, x ( is initial converted thickness, D 9;; is effective diffusion coefficient, K 9;; is effective interface coefficient. In this study, the conversion time is considered as the dwell time once the conversion temperature is achieved (1250 °C). It is noteworthy that due to the high partial vapor pressure of Na " O at temperatures below 1250 °C, there is an expected initial converted thickness at the surface on the order of a few microns at T :,?B ≤ T CD9== ≈ 1250 °C. Therefore, before reaching the conversion temperature, the extrapolation of the polynomial fit does not meet at zero but is slightly greater than zero ( x ( > 0 at t = 0). In some other cases, it is also possible that a negative extrapolation of polynomial fit for x ( (x ( < 0 at t = 0) occurs. Such a condition can be the case provided that some morphological changes at the surface occur (i.e., grain boundary grooving) prior to incorporation of Na " O at the three-phase boundaries (TPBs). The polynomial fit of data points proves the conversion of Ga " O ' + YSZ happen to have a lower kinetic rate, although the extrapolation of the x-axis before reaching conversion temperature is almost in the same order of a few microns for both alumina and the gallia systems. The mathematical reason for the lower conversion rate is attributed to the lower mobility of the mobile species since