Theoretical Modeling of Defect Segregation and Space-Charge Formation in Proton-Conducting Barium Zirconate

Introduction

Acceptor-doped barium zirconate (BaZrO₃) shows considerable potential as an electrolyte material for intermediate temperature solid oxide fuel cells due to its high bulk proton conductivity and chemical stability. However, in polycrystalline materials the grain boundaries (GBs) display high proton resistivity, severely limiting the overall proton transport in the material. The low GB conductivity has been thought to be due to an intrinsic mechanism, and recently the so called space charge model has been used to interpret and model the GB blocking behavior in BaZrO₃ by several research groups [1-5].

Modeling

According to the space charge model, charged defects accumulate in the structurally distorted region at the GB plane, the GB core. The resulting core charge gives rise to an electrostatic potential barrier and causes depletion of mobile charge carriers of the same polarity in the regions adjacent to the core, the space charge layers.

The existence of a positive core charge is crucial to the application of the space charge model to BaZrO₃. In a previous study, we used density functional theory (DFT) to investigate oxygen vacancy segregation to a symmetric tilt GB and we found that oxygen vacancies segregate to the GB and create a positive core charge [4].

Here, we extend our previous studies [4,6] to several other tilt GBs. Segregation energies of both oxygen vacancies and protons are determined and used in a one-dimensional thermodynamic space charge model. We also investigate the effect of segregation of dopants as well as interaction between oxygen vacancies in the GB core. Our first-principles electronic-structure calculations are performed within the framework of DFT using the generalized gradient PBE functional to approximate exchange and a layer-by-layer space charge model [6] is employed to determine the potential barrier and core charge resulting from defect segregation.

Results and Discussion

Using DFT proton and oxygen vacancy segregation have been investigated for an extensive set of tilt GBs. Both defect species are found to segregate to the GB core, with typical segregation energies of -1.5 eV and -1.0 eV for oxygen vacancies and protons, respectively. Below 900 K and at wet conditions potential barrier heights around 0.6V are obtained, which is consistent with experimental results. For many GBs we find the protons to be responsible for the major part of the excess core charge and thereby the electrostatic potential.

We have also investigated dopant segregation and its effect on the potential barrier. Experimental evidence suggests that an increased dopant content should decrease the potential barrier and that this effect should be especially pronounced if the dopants are able to segregate to the GB. Indeed, we find that if low-energy sites in the core are saturated with positive defects, an increase in the dopant concentration does lower the potential barrier. However, if the low-energy sites are not saturated an increased dopant concentration in the core could also lead to an increase in the concentration of positive defects and the core concentration is instead limited by the electrostatic potential. An increase in the number of negative defects is therefore followed by an increase in the number of positive defects, keeping the total core charge constant. 

Furthermore, our results suggest that interactions among oxygen vacancies may effectively reduce the number of available sites in the GB core. This has consequences for the effects of dopant segregation since it implies that the core can become saturated with positive defects at an earlier stage and segregation of dopant ions may then actually decrease the core charge, and reduce the potential barrier height.

Conclusions

To conclude, segregation of oxygen vacancies and protons plays an important role in the formation of space charge potentials at the grain boundary interface. Additionally, our results show that protons may be the main source to the space-charge potentials under conditions relevant for fuel cell applications.

References

[1] C. Kjølseth, et al., Solid State Ionics 181, 268 (2010).

[2] R. A. De Souza, Z. A. Munir, S. Kim, M. Martin, Solid State Ionics 196, 1 (2011).

[3] F. Iguchi, C. Chen, H. Yugami, S. Kim, J. Mater. Chem. 21, 16517 (2011).

[4] B. J. Nyman, E. E. Helgee, G. Wahnström, Appl. Phys. Lett. 100, 061903 (2012).

[5] M. Shirpour, et al., J. Phys. Chem. C116, 2453 (2012).

[6] E. E. Helgee, A. Lindman, G. Wahnström, Fuel Cells, 13, 19 (2013).