Theory-guided discovery of pressure-induced transitions in the fast-ion conductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>BaSn</mml:mi> <mml:msub> <mml:mi mathvariant="normal">F</mml:mi> <mml:mn>4</mml:mn> </mml:m

Fast-ion conductors such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>BaSn</a:mi> <a:msub> <a:mi mathvariant="normal">F</a:mi> <a:mn>4</a:mn> </a:msub> </a:mrow> </a:math> are of significant interest for next-generation solid-state battery technologies due to their high ionic conductivity and chemical stability. However, the behavior of these materials under extreme conditions remains poorly understood, despite the relevance of pressure-induced modifications for tuning functional properties. In this study, we combine density functional theory (DFT) calculations with high-pressure experiments to investigate the structural evolution of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>BaSn</c:mi> <c:msub> <c:mi mathvariant="normal">F</c:mi> <c:mn>4</c:mn> </c:msub> </c:mrow> </c:math> up to 40 GPa. DFT predicts two pressure-induced phase transitions: from the ambient-pressure tetragonal <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>P</e:mi> <e:mn>4</e:mn> </e:mrow> </e:math> / phase to a monoclinic <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>P</f:mi> <f:msub> <f:mn>2</f:mn> <f:mn>1</f:mn> </f:msub> <f:mo>/</f:mo> <f:mi>m</f:mi> </f:mrow> </f:math> -I structure at 10 GPa, and subsequently to a denser monoclinic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>P</g:mi> <g:msub> <g:mn>2</g:mn> <g:mn>1</g:mn> </g:msub> </g:mrow> </g:math> /m-II phase at 32 GPa. The first transition is experimentally confirmed via angle-dispersive X-ray diffraction, Raman spectroscopy, and electrical resistivity measurements, all performed at ambient temperature. The second transition is supported by distinct changes in high-pressure Raman modes and resistivity behavior, consistent with a further structural reorganization. These findings not only clarify the high-pressure phase diagram of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>BaSn</h:mi> <h:msub> <h:mi mathvariant="normal">F</h:mi> <h:mn>4</h:mn> </h:msub> </h:mrow> </h:math> , but also shed light on the potential for pressure-tuned ionic transport in fluorostannate-based solid electrolytes.