Oxide-ion transport at low and high electric fields in brownmillerite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Sr</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>Fe</mml:mi> <mml:mn>2</mml:mn>

Strontium iron oxide undergoes a voltage-driven topotactic phase transition between an insulating brownmillerite (BM) and a conductive perovskite (PV) structure. Understanding this redox-based transition requires, first, a detailed characterization of and, second, a detailed description of field-driven oxide-ion transport in both phases. In this study, we used classical molecular dynamics (MD) simulations to determine the oxide-ion mobility <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>u</a:mi> <a:mi mathvariant="normal">O</a:mi> </a:msub> </a:math> in anisotropic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>Sr</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi>Fe</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mrow> <c:mn>5</c:mn> <c:mo>±</c:mo> <c:mi>δ</c:mi> </c:mrow> </c:msub> </c:mrow> </c:math> (BM phase) and in isotropic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>SrFeO</e:mi> <e:mrow> <e:mn>2.5</e:mn> <e:mo>±</e:mo> <e:mi>δ</e:mi> <e:mo>/</e:mo> <e:mn>2</e:mn> </e:mrow> </e:msub> </e:math> (PV phase) as a function of electric field strength, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mn>0.5</f:mn> <f:mo>≤</f:mo> <f:mi>E</f:mi> <f:mo>/</f:mo> <f:mi mathvariant="normal">M</f:mi> <f:mi mathvariant="normal">V</f:mi> <f:mspace width="0.16em"/> <f:mi mathvariant="normal">c</f:mi> <f:msup> <f:mi mathvariant="normal">m</f:mi> <f:mrow> <f:mo>−</f:mo> <f:mn>1</f:mn> </f:mrow> </f:msup> <f:mo>≤</f:mo> <f:mn>10</f:mn> </f:mrow> </f:math> , and as a function of temperature, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mn>1300</l:mn> <l:mo>≤</l:mo> <l:mi>T</l:mi> <l:mo>/</l:mo> <l:mi mathvariant="normal">K</l:mi> <l:mo>≤</l:mo> <l:mn>3000</l:mn> </l:mrow> </l:math> . The use of oxygen-excess ( <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mo>+</n:mo> <n:mi>δ</n:mi> </n:mrow> </n:math> ) and oxygen-deficient ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mo>−</o:mo> <o:mi>δ</o:mi> </o:mrow> </o:math> ) BM systems permits, respectively, interstitialcy and interstitial migration, and vacancy migration, to be probed. From <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:msub> <p:mi>u</p:mi> <p:mi mathvariant="normal">O</p:mi> </p:msub> </p:math> results obtained at low fields (i.e., within the linear regime), we obtain the activation enthalpies and effective attempt frequencies of oxygen-vacancy migration and oxygen-interstitial/oxygen-interstitialcy migration; and, together with literature data for tracer diffusivities, we determine Haven ratios <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:msub> <r:mi>H</r:mi> <r:mi mathvariant="normal">r</r:mi> </r:msub> <r:mrow> <r:mo>(</r:mo> <r:mi>T</r:mi> <r:mo>)</r:mo> </r:mrow> </r:mrow> </r:math> for BM and PV phases. At higher fields (i.e., within the nonlinear regime), <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:msub> <t:mi>u</t:mi> <t:mi mathvariant="normal">O</t:mi> </t:msub> <t:mrow> <t:mo>(</t:mo> <t:mi>E</t:mi> <t:mo>)</t:mo> </t:mrow> </t:mrow> </t:math> data shows a strong nonlinear response for all three migration mechanisms. In each case, the behavior is described within an existing analytical framework that uses as input the zero-field activation enthalpies and effective attempt frequencies. Interstitialcy migration displays a stronger nonlinear response compared with interstitial or vacancy migration, and this is ascribed to its longer effective charge displacement arising from its collective nature. Finally, the MD simulations at high field strengths indicate a field-driven BM-to-PV phase transition (at constant oxygen stoichiometry).