How Proton Incorporation Reshapes Lattice Dynamics In BaSnO₃-Type Proton Conductors

Proton conduction in acceptor-doped perovskites is fundamentally a vibronic process: mobile $H^{+}$ and $D^{+}$ do not move independently, but dynamically co-vibrate with the surrounding oxygen-metal framework. Direct experimental evidence for this behavior is presented using in situ ${}^{119}Sn$ nuclear resonance vibrational spectroscopy (NRVS) on hydrated, deuterated, and dry $BaS{n}_{1-x}{Y}_x{O}_{3-\delta }$ . Hydration induces systematic redistributions in the Sn-projected phonon density of states (PDOS), including an upshift of the first spectral moment by about 0.4 meV, indicating a stiffening of the extended Sn-O network. H/D isotopic substitution leaves the Sn-projected PDOS largely unchanged, with only subtle isotope-dependent spectral reweighting, demonstrating that protonic degrees of freedom are not localized oscillators but are embedded in collective lattice modes. These results are rationalized using a classical coupled proton-phonon oscillator model that links the observed PDOS variations to changes in effective force constants and vibrational mass terms. The model captures how $H^{+}$ and $D^{+}$ participate in cooperative lattice dynamics rather than forming isolated OH/OD entities. Overall, NRVS probes proton-lattice coupling in ceramic proton conductors and quantitatively describes how protonic defects modulate host lattice dynamics to enable phonon-assisted long-range proton transport.