Out-of-plane thermal conductivity of the layered thermoelectric oxide ${\mathrm{Bi}}_{2-x}{\mathrm{Pb}}_x{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$

The out-of-plane thermal conductivity $\left({\kappa }_c\right)$ of ${\mathrm{Bi}}_{2-x}{\mathrm{Pb}}_x{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$ is measured and analyzed. A low value of $4–8\mathrm{mW}∕\mathrm{cm}\mathrm{K}$ is observed at $300\mathrm{K}$, which is close to the minimum thermal conductivity. This implies the phonon mean-free path is of the order of the $c$-axis lattice parameter. The temperature dependence is also anomalous, and the positive temperature coefficient $d{\kappa }_c∕dT>0$ is observed. These features can be understood semiquantitatively by a phenomenological expression of $\kappa$ including the contribution of optical phonons.

Figure 1

Crystal structure of ${\mathrm{Bi}}_{2-x}{\mathrm{Pb}}_x{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$.

Figure 2

(a) In-plane thermal conductivity of ${\mathrm{Bi}}_{1.6}{\mathrm{Pb}}_{0.4}{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$ measured by the Harman method and the steady method. The data for the Harman method are taken from Ref. 21. The inset shows the in- and out-of-plane thermal conductivities for a thick sample of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_8$ single crystals stacked along the $c$ axis with paste. (b) $c$-axis thermal conductivities of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$ measured for different samples.

Figure 3

Out-of-plane thermal conductivity of ${\mathrm{Bi}}_{2-x}{\mathrm{Pb}}_x{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$.

Figure 4

Anisotropic thermal conductivity of ${\mathrm{Bi}}_{1.6}{\mathrm{Pb}}_{0.4}{\mathrm{Sr}}_2{\mathrm{Co}}_2{\mathrm{O}}_y$.