Plasma energies forBaPb1−xBixO3

Recent room-temperature infrared reflectivity studies on polycrystalline $\mathrm{Ba}{\mathrm{Pb}}_{1-x}{\mathrm{Bi}}_x{\mathrm{O}}_3$ samples by Tajima et al. have determined the $x$ dependence of the optical parameters for these materials in the composition range $0\le x\le 0.25$, including the free-carrier plasma energies ${\Omega }_p\mathrm{}\left(x\right)\mathrm{}$. These results are of considerable interest since they represent a useful measure of the alloy electronic structure near the $x$-dependent Fermi energy $E_F\mathrm{}\left(x\right)\mathrm{}$. In combination with thermopower data, these observed plasma energies ${\Omega }_p\mathrm{}\left(x\right)\mathrm{}$ provide for the first time a detailed test of the calculated electronic properties near $E_F\mathrm{}\left(x\right)\mathrm{}$ for this alloy system, as derived from recent self-consistent linear augmented—plane-wave calculations and the virtual-crystal approximation. By assuming a rigid-band model based on the cubic Ba${\mathrm{Pb}}_{0.7}$ ${\mathrm{Bi}}_{0.3}$ ${\mathrm{O}}_3$ results, it is shown that the $\mathrm{Ba}{\mathrm{Pb}}_{1-x}{\mathrm{Bi}}_x{\mathrm{O}}_3$ conduction band yields calculated plasma energies ${\Omega }_p\mathrm{}\left(x\right)\mathrm{}$ that are within 5-10% of these observed values. The larger discrepancy between the calculated and thermopower-derived values for the $x$-dependent density of states at $E_F$ is consistent with an appreciable electron-phonon enhancement.