Fig. 5: Linear fitting analysis of the metal concentration to determine the composition of the four material phases in CGO-CFO MIEC system.

Fe vs. Co (a). Gd vs. Co (b). Ce vs. Co (c). Gd vs. Ce (d). For each panel, the data for EP1 are shifted vertically by 0.1 to provide good data visibility. The solid lines are the linear fits to the data. The following is the summary of the linear fitting results. For CFO, [Fe] = 0.48 + [Co]/3, [Gd] = 0.51–4[Co]/3, and [Ce] = 0.01 ± 0.01 for 0.27 < [Co] < 0.37. For CGO, [Fe] = 2[Co], [Gd] = 0.13 ± 0.13, and [Ce] = 0.88–3[Co] for 0 < [Co] < 0.19. For EP1, [Fe] = 2[Co], [Gd] = 0.61–3[Co]/2, and [Ce] = 0.39–3[Co]/2 for 0.05 < [Co] < 0.16. For EP2, [Fe] = 0.28 + 3[Co]/2, [Gd] = 0.42-[Co], and [Ce] = 0.3–3[Co]/2 for 0.02 < [Co] < 0.16. Typical fitting errors are ~0.02 for the linear term and ~0.03 for the constant term. Determinming the composition of EP1 and EP2 is somewhat tricky since EP1 and EP2 do not contain any element with a constant concentration. In addition, the correlation between Gd and Ce is too poor to perform the reliable fitting. By fitting the datasets with better linear correlations (Fe vs. Co, Gd vs. Co, and Ce vs. Co), we deduce the linear trend between Gd and Ce shown in d, over which the data points are highly scattered.