As the length-scales of materials decrease, heterogeneities associated with interfaces approach the importance of the surrounding materials. Emergent electronic and magnetic interface properties in superlattices have been studied extensively by both experiments and theory. $^{1-6}$ However, the presence of interfacial vibrations that impact phonon-mediated responses, like thermal conductivity $^{7,8}$, has only been inferred in experiments indirectly. While it is accepted that intrinsic phonons change near boundaries $^{9,10}$, the physical mechanisms and length-scales through which interfacial effects influence materials remain unclear. Herein, we demonstrate the localized vibrational response associated with the interfaces in SrTiO$_3$-CaTiO$_3$ superlattices by combining advanced scanning transmission electron microscopy imaging and spectroscopy and density-functional-theory calculations. Symmetries atypical of either constituent material are observed within a few atomic planes near the interface. The local symmetries create local phonon modes that determine the global response of the superlattice once the spacing of the interfaces approaches the phonon spatial extent. The results provide direct visualization and quantification, illustrating the progression of the local symmetries and interface vibrations as they come to determine the vibrational response of an entire superlattice; stated differently, the progression from a material with interfaces, to a material dominated by interfaces, to a material of interfaces as the period decreases. Direct observation of such local atomic and vibrational phenomena demonstrates that their spatial extent needs to be quantified to understand macroscopic behavior. Tailoring interfaces, and knowing their local vibrational response, provides a means of pursuing designer solids having emergent infrared and thermal responses.
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