Improved Grain Boundary Conductivity By Post Annealing: Minimizing Vacancy Depletion through Non-Equilibrium Distribution of Immobile Species
Authors: Zhang Lei , Zhu Liangzhu , Liu Feng , Virkar Anil V. 
Published: February 2020

Typical electrolyte materials in solid oxide fuel cells (SOFC) and solid oxide electrolyzer cells (SOEC) are yttria-stabilized zirconia (YSZ), Sr and Mg-doped LaGaO3 (LSGM) or doped cerium oxide. These solid oxides exhibit good oxygen ion conductivity at elevated temperatures, ranging between 600oC and 800oC. It is preferable to lower the operating temperature to 600oC, and possibly even lower. During the last two decades, considerable effort has been devoted to lower the ohmic resistance, primarily by using thin electrolyte film, anode-supported cell design. Over the past decade, considerable effort has also been devoted to lowering the cathode polarization resistance. This has led to the development of a number of excellent cathodes, so that at least in many cell designs, the cathode is no longer the component which limits cell performance. Our recent work [1] has shown that the ohmic loss may actually be the dominant loss even in anode-supported thin electrolyte cells, necessitating additional efforts to further reduce the ohmic contribution to the net cell resistance. It is known that at low temperatures, the electrolyte resistance is dominated by grain boundary resistance, which in turn is often dictated by space charge effects.
The purpose of the present work was to examine the role of space charge on grain boundary contribution to the electrolyte resistance. Figure 1 shows that grain boundary resistance dominates the overall ohmic resistance of a typical electrolyte (in this case GDC) at medium-to-low temperature range. Thus, it is deemed necessary to determine parameters that control ion transport across grain boundaries. It is known that grain boundary resistance usually is attributed to either a silicate phase and/or oxygen vacancy depletion. As the purity of raw materials has been improved greatly over the years, oxygen vacancy depletion is considered to be the primary reason for the grain boundary resistance [2]. The objective of this work is to explore the effect of space charge on conduction properties when one of the defects is far more mobile than the other defects. In such a case, at low temperatures, only the mobile defects can move, but the less mobile defects are essentially frozen from the high temperature annealing step. The present work first examines an example of a simple, undoped NaCl system. Later, the work will be extended to YSZ and other oxide systems of interest. This work is based on the classic work of Kliewer and Koehler [3]. Figure 2 shows that in order to maintain charge neutrality in the grain interior of a grain of sufficiently large thickness, the electrostatic potential inside the grain should be negative for NaCl, which is realized by anion vacancy depletion near the surface. Supposing both cations and anions are mobile and have reached their equilibrium spatial positions at each temperature, Figure 2 shows that, as the temperature increases, the grain boundary thickness (the region of space charge) decreases and both cation and anion vacancy concentrations increase. If, however, the anion vacancies are less mobile and thus are frozen when the sample is cooled to a lower temperature, equilibrium will be attained by the re-distribution of cation vacancies to minimize the free energy.
Figure 3 shows the corresponding cation vacancy profile as a function of distance from the crystal surface (grain boundary) at various temperatures. Assuming much of the ionic transport occurs by cation vacancies (this for NaCl), the grain boundary resistance is expected to be different in the two cases. Similar calculations are conducted on oxygen ion conductors such as doped zirconia and ceria. The results of the calculations and the corresponding experimental results will be presented.

Funded by DOE EFRC Grant Number DE-SC0001061 as a flow-through from the University of South Carolina.

References:
1. Liangzhu Zhu, Lei Zhang, Feng Zhao, Virkar A.V., ECS transcription (2014)
2. X. Guo, J. Maier, J. Electrochem. Soc., 145, E121, 2001
3. K. L. Kliewer, J. S. Koehler Physical Review, 140, 4 (1965)
Fig. 1A and 1C: Electrochemical impedance spectra on a GDC electrolyte; 1B and 1D: Arrhenius plots of grain and grain boundary resistance.
Fig. 2: Simulated anion vacancy distribution. Both cations and anions are assumed mobile and to have reached equilibrium distributions at each of the temperatures.
Fig. 3: Simulated cation vacancy distribution assuming the anion vacancies to be frozen at the highest annealing temperature.