Anomalously low thermal conductivity in superhard cubic Si3N4

Superhard bulk materials with large bulk modulus like diamond and cubic BN (c-BN) show high thermal conductivity (\ensuremath{\kappa}) reaching 2000--3000 $\mathrm{W}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. The large modulus means large group velocity, which contributes to high lattice thermal conductivity. However, whether the hardening of phonon bands would increase or decrease the phonon scattering rate through the phonon-phonon scattering phase space is not evident and should depend on the material type. In this work, we target cubic silicon nitride ($\mathrm{c}\text{\ensuremath{-}}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$), which was recently developed and found to be the third superhardest material next to the diamond and c-BN. The \ensuremath{\kappa} of polycrystalline $\mathrm{c}\text{\ensuremath{-}}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$ was measured with the time-domain thermoreflectance method, and thermal conductivity of 23 $\mathrm{W}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ was obtained at room temperature. The first-principles thermal conductivity calculations identified that this translates to a single-crystal value of about 88 $\mathrm{W}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$, which is more than an order of magnitude smaller than those of diamond and c-BN. The calculation further identified that difference arises from the large scattering phase space and anharmonic amplitude of $\mathrm{c}\text{\ensuremath{-}}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$, which are two to three times larger than the values of diamond. It is found that the scattering phase space of $\mathrm{c}\text{\ensuremath{-}}\mathrm{S}{\mathrm{i}}_{3}{\mathrm{N}}_{4}$ optical phonons with small dispersion anomalously increases with the frequency.