The TPBs length per unit area of the gas/solid interface is inversely proportional to the average grain diameter of both phases, d w . Therefore, a decrease in the average grain size (d w ) results in a longer TPB and hence, a shorter diffusion distance and subsequently higher conversion thickness. Later, at sufficiently high temperatures (~800 -900 °C), O "# conduction is provided through the YSZ phase and Na ! conduction takes place through the newly formed NZGO phase at the three-phase boundaries (TPBs) toward the interface between NZGO + YSZ and Ga " O ' + YSZ Since gallia is a refractory compound with a melting point of ~1725 °C, low vapor pressure at conversion temperature (1250 °C) was expected. Moreover, due to the low diffusivity of gallium ions in aluminum ions there isn't a considerable exchange of Ga 3+ and Al 3+ . Additionally, no evidence of diffusion of Y in NZGO or Ga in YSZ has been observed by the EDS in agreement with prior work .