(Invited) Multi-Species Electrochemical Transport through Multi-Phase Materials
Authors: Virkar Anil V. 
Published: February 2020

Most of the solid state ionic conductors typically exhibit high ionic conductivity for only one ion. Examples include yttria-stabilized zirconia (YSZ), rare earth oxide doped ceria, Sr- and Mg-doped LaGaO3 (LSGM), etc. as oxygen ion conductors; Na-beta”-alumina, NaSICON as sodium ion conductors; LLZO, LiSICON as lithium ion conductors; CsH2PO4 as a proton conductor, etc. Alkaline earth cerates and zirconates when doped with rare earth oxides become mixed proton and oxygen ion conductors. In addition some electronic conduction also prevails. Thus, Y-BaZrO3 is an example of a single phase material that transports two ionic species; H+ and O2-. However, it is usually not possible to vary the conductivities for the two species independently; as the H2O content increases, the proton conductivity increases but the oxygen ion conductivity decreases. Multi-species transport in all of these systems can be given in terms of the gradients in electrochemical potentials of the individual species. The same equations can also be given in terms of the gradients in chemical potentials of neutral species if the assumption of local equilibrium is made. The assumption of local equilibrium implies that the electronic conductivity of the ionic conductors cannot be assumed to be identically (mathematically) zero. This is because such an assumption makes the local chemical potential of electrically neutral species indeterminate.
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.