It was noted that, in the phenomenon of mixed ionic-electronic conduction in the solid state, a flow of mobile ions (Ji) could be induced not only directly by their own electrochemical potential gradient, iη, but also indirectly by that of electrons (eη), and vice versa for a flow of electrons (Je) or Jm=−Lmnnη (m,n = i,e). A recent successful experimental determination of all 4 Onsager coefficients Lmn of the TiO2 system indicated that Onsager reciprocity was verified to within an error of 1.3% (Lie/Lei = 0.993). Contrary to received opinion, the cross-coefficient was not only non-negligible but was even larger than the direct one (1.5 ≤ Lie/Lii ≤ 3.7). An experimental technique was described which permitted measurement of all of the Onsager coefficients in a mixed-conductor oxide.

Measurement of the Onsager Coefficients of Mixed Ionic-Electronic Conduction in Oxides. Lee, D.K., Yoo, H.I.: Physical Review B, 2007, 75[23], 235110