  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.
