  The 3D local atomic structures and crystal defects at the interfaces of
heterostructures control their electronic, magnetic, optical, catalytic and
topological quantum properties, but have thus far eluded any direct
experimental determination. Here we determine the 3D local atomic positions at
the interface of a MoS2-WSe2 heterojunction with picometer precision and
correlate 3D atomic defects with localized vibrational properties at the
epitaxial interface. We observe point defects, bond distortion, atomic-scale
ripples and measure the full 3D strain tensor at the heterointerface. By using
the experimental 3D atomic coordinates as direct input to first principles
calculations, we reveal new phonon modes localized at the interface, which are
corroborated by spatially resolved electron energy-loss spectroscopy. We expect
that this work will open the door to correlate structure-property relationships
of a wide range of heterostructure interfaces at the single-atom level.
