Electrical properties of the protonic conductor 1 mol% Y-doped ${\hbox{BaZr}}{{\hbox{O}}_{{3 - \delta }}}$

Abstract

Much attention has been paid to barium zirconates because their high protonic conductivity and chemical stability are excellent properties for solid electrolytes. However, most studies have focused on highly doped materials such as 10 or 20 mol% Y-doped barium zirconates. In this study, the bulk and the grain boundary electrical properties of 1 mol% Y-doped barium zirconate are investigated as a function of temperature, water partial pressure, and oxygen partial pressure. At low temperatures and in wet atmospheres, the bulk of the barium zirconate predominantly conducts protonic defects, whereas, at high temperatures and in dry conditions, it is mixed oxygen ionic and electron-hole conducting. In the grain boundary, the protonic conductivity is a few orders of magnitude lower than the protonic conductivity in the bulk. In this study, possible causes for the low protonic conduction at the grain boundaries are considered.

Appendix

The ${P_{{{{\rm{H}}_2}{\rm{O}}}}}$-dependence of the protonic conductivity is defined as the ENC. I consider three cases.

• (1) ENC: $2\left[ {{\hbox{V}}_{\rm{O}}^{{ \bullet \bullet }}} \right] \approx \left[ {{\hbox{Y}}_{\rm{Zr}}^{\prime }} \right]$

In this case, the protonic defect and the corresponding protonic conductivity strongly depend on the water partial pressure as shown below.

$$ \left[ {OH_O^{ \bullet }} \right] = {\left( {K\left[ {{\hbox{V}}_{\rm{O}}^{{ \bullet \bullet }}} \right]\left[ {{{\hbox{O}}_{\rm{O}}}} \right]} \right)^{{1/2}}}P_{{{{\rm{H}}_2}{\rm{O}}}}^{{1/2}} $$

(A1)

$$ {\sigma_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} = \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right]e{\mu_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} \propto P_{{{{\rm{H}}_2}{\rm{O}}}}^{{1/2}}\left( {\because {c_{{{\rm{v}}\bullet \bullet }}} \sim {\hbox{constant}}} \right). $$

(A2)

• (2) ENC: $2\left[ {{\hbox{V}}_{\rm{O}}^{{ \bullet \bullet }}} \right] + \left[ {OH_O^{ \bullet }} \right] \approx \left[ {{\hbox{Y}}_{\rm{Zr}}^{\prime }} \right]$

In perovskite materials (ABO₃), the site restriction is given by

$$ \left[ {{\hbox{V}}_{\rm{O}}^{{ \bullet \bullet }}} \right] + \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right] + \left[ {{\hbox{O}}_{\rm{O}}^{\rm{x}}} \right] = 3. $$

(A3)

Considering Eq. A3 and Eq. 4, the protonic defect can be estimated as following.

$$ \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right] = \frac{{3K{P_{{{{\rm{H}}_2}{\rm{O}}}}} - \sqrt {{K{P_{{{{\rm{H}}_2}{\rm{O}}}}}\left( {9K{P_{{{H_2}O}}} - 6K{P_{{{H_2}O}}}S + K{P_{{{H_2}O}}}{S^2} + 24S - 4{S^2}} \right.}} }}{{K{P_{{{{\rm{H}}_2}{\rm{O}}}}} - 4}} $$

(A4)

where S denotes an effective dopant concentration (Ref. 4). Thus, in this condition,

$$ {\sigma_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} = \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right]e{\mu_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} \propto P_{{{{\rm{H}}_2}{\rm{O}}}}^{{0\sim 1/2}} $$

(A5)

• (3) ENC: $\left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right] \approx \left[ {{\hbox{Y}}_{\rm{Zr}}^{\prime }} \right]$

The protonic conductivity hardly depends on the water partial pressure owing to the fixed concentration of the acceptor.

$$ \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right] = \left[ {Y_{\rm{Zr}}^{\prime }} \right] = {\hbox{constant}} $$

(A6)

$$ {\sigma_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} = \left[ {{\hbox{OH}}_{\rm{O}}^{ \bullet }} \right]e{\mu_{{{\rm{O}}{{\rm{H}}^{ \bullet }}}}} \propto P_{{{{\rm{H}}_2}{\rm{O}}}}^0 $$

(A7)