Thermal conductivity of polycrystalline ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$

We have measured the thermal conductivity κ and the thermal diffusivity a of a dense bulk ceramic polycrystalline sample of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ (1:2:4) in the temperature range 30–300 K. We find κ≊10 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$ at 100 K, significantly higher than in ceramic ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (1:2:3) and approaching the in-plane value for single-crystal 1:2:3, and decreasing to 7.6 W ${\mathrm{m}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}1}$ at 300 K. The data for this sample can be described by standard theories for phonon thermal conductivity of crystalline materials with boundary, phonon, and electron scattering. The higher κ in 1:2:4 as compared to 1:2:3 is, in this model, due to the smaller point defect scattering in the former. The fitted parameters for the three scattering mechanisms all agree with independent estimates based on simple models; inserting data for electric resistivity, grain size, carrier density, and lattice properties we can predict κ and its T dependence to within about 20%. We also discuss models for the phonon and electron thermal conductivities in some detail, including some second-order effects such as inelastic electron scattering and a T-dependent carrier density.