Usually an assumption is made that transport of electrically charged species occurs only down their respective electrochemical potential gradients. This means if the transport is described using the Onsager formulation, the cross coefficients are zero (although there are some studies in which the cross coefficients are not assumed to be zero). The same equations, if written for the transport of the corresponding electrically neutral species, the cross coefficients are not zero. This means the origin of coupling lies in the electro-neutrality condition. In such a case, it is possible to write the Onsager coefficients in terms of the individual, partial conductivities.
Multi-species ionic conductors containing multiple phases can also be envisioned. For example, one may fabricate a two phase, contiguous mixture of Y-BaZrO3 and YSZ. When hydrated, all of the proton conduction will occur through the Y-BaZrO3 phase and most of the oxygen ion conduction will occur through the YSZ phase. Other examples of multi-species multi-phase ionic conductors include Na-beta”-alumina + YSZ (made by vapor phase conversion of a-Al2O3 + YSZ composite) and Na-rutile-beta-gallate + YSZ (made by vapor phase conversion of Ga2O3 + YSZ composite). Many other multi-species, multi-phase ionic conductors can be envisioned. These materials differ from the single phase materials in that their transport properties can be designed, to an extent, by suitably designing the corresponding microstructure. In Na-beta”-alumina + YSZ, sodium ion transport occurs through the Na-beta”-alumina phase while oxygen ion transport occurs through the YSZ phase. If an electrochemical cell can made with different thermodynamic activities of sodium and oxygen at the two electrodes, one can induce transport of two ionic species. The general transport equations continue to be applicable and electro-neutrality also continues to remain applicable. The difference from single phase materials, however, is that there is a physical separation of ionic fluxes which is on the order of the microstructural details. The typical grain size in these materials is on the order of a few microns. This means, assuming a one dimensional transport, the regions that transport sodium ions are physically separated by a lateral distance on the order of microns from the regions that transport oxygen ions. In single phase Y-BaZrO3, by contrast, the regions that transport protons and oxygen ions are not physically separate (more than at an atomic level).
The objective of this talk is to present similarities and differences between single phase and multi-phase ionic conductors capable of transporting two or more ionic species. Also, the objective is to discuss transport coefficients in these materials. Some preliminary experimental work conducted on some multi-phase materials will be discussed.
Acknowledgements: This work was supported by the US Department of Energy under Grant Number DE-FG02-06ER46086 and by the National Science Foundation under Grant Number DMR-1407048.