  Although extensive experimental and theoretical works have been conducted to
understand the ballistic and diffusive phonon transport in nanomaterials
recently, direct observation of temperature and thermal nonequilibrium of
different phonon modes has not been realized. Herein, we have developed a
method within the framework of molecular dynamics to calculate the temperatures
of phonon in both real and phase spaces. Taking silicon thin film and graphene
as examples, we directly obtained the spectral phonon temperature (SPT) and
observed the local thermal nonequilibrium between the ballistic and diffusive
phonons. Such nonequilibrium also generally exists across interfaces and is
surprisingly large, and it provides an additional thermal interfacial
resistance mechanism. Our SPT results directly show that the vertical thermal
transport across the dimensionally mismatched graphene/substrate interface is
through the coupling between flexural acoustic phonons of graphene and the
longitudinal phonons in the substrate with mode conversion. In the
dimensionally matched interfaces, e.g. graphene/graphene junction and
graphene/boron nitride planar interfaces, strong coupling occurs between the
acoustic phonon modes on both sides, and the coupling decreases with
interfacial mixing. The SPT method together with the spectral heat flux can
eliminate the size effect of the thermal conductivity prediction induced from
ballistic transport. Our work shows that in thin films and across interfaces,
phonons are in local thermal nonequilibrium.
