The formation factor measurements were performed using an aqueous solution of potassium chloride as the pore solution because the conductivity of a few standard concentrations of this electrolyte are known to a high precision [11]. A range of concentrations were used to ensure that the surface conduction component was properly accounted for. The specimens were first vacuum saturated with one of the KCl electrolyte concentrations and then mounted, using rubber o-rings and clamps, between two glass vessels, each containing a platinum electrode. The setup is shown schematically in Fig. 1(a). The apparatus, in the absence of a sample and holder, had a conductivity cell constant of 0.3567 cm−1.
To determine the formation factor of the saturated specimen, both sides of the cell were filled with the same solution as was used to saturate the specimen and then the entire system was allowed to thermally equilibrate in the environmental chamber. The direct current (dc) resistance of the sample and cell was then determined using a commercial impedance spectrometer that sampled frequencies between 10 Hz and 1 MHz. The bulk conductivity of each specimen was calculated from the cell constant and the specimen geometry. The formation factor was calculated from the ratio of the known pore solution conductivity to the calculated bulk conductivity. The procedure was repeated for the other KCl concentrations to investigate the effect of surface conduction.
Potassium chloride pore solution concentrations of 0.01 mol·kg−1, 0.10 mol·kg−1, and 1.00 mol·kg−1 were used to determine the specimen conductivity and to assess the contribution from surface conduction. Due to surface conduction contributions, the formation factor increases with increasing pore solution conductivity, converging to the correct value as the concentration increases. The specimen conductivity measured using the 0.01 mol·kg−1 solution was approximately 85 % of the value using the 1.0 mol·kg−1 solution, and the specimen conductivity using the 0.10 mol·kg−1 solution was approximately 98 % of the value using the 1.0 mol·kg−1 solution. Therefore, the formation factor calculated at 1.0 mol·kg−1 was used as the best estimate. An estimate of the formation factor at infinite conductivity can be estimated from a Padé approximation [12]. Unfortunately, the approximation contains four parameters, and only three conductivity measurements were taken. Nonetheless, the reported result represents a lower bound to the true formation factor. Since the change in formation factor was only 2 % for a ten fold increase in concentration, the true value is probably not more than a fraction of percent larger than the values reported.
Since the ceramic specimens are the result of a controlled commercial process, they have relatively little variation among specimens. The four specimens used in this experiment had formation factors ranging from 10.6 to 10.9. These values were determined after each sample was allowed sufficient time to reach thermal equilibrium, and then the values of the dc resistance varied by less than 1 %. The corresponding calculated formation factor varied by approximately 2 %.