Ac conductivity of glassy Bi4-nPbnSr3Ca3Cu4Ox semiconductors (with n=0.0, 0.1, 0.5, and 1.0): Precursors for high-Tc superconductors.

Abstract

Experimental results are reported for the temperature- (T= 77--450 K) and frequency- (\ensuremath{\omega}=${10}^{2}$--${10}^{4}$ Hz) dependent (ac) conductivities (${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ac}}$) of Pb-doped ${\mathrm{Bi}}_{4\mathrm{\ensuremath{-}}\mathit{n}}$${\mathrm{Pb}}_{\mathit{n}}$${\mathrm{Sr}}_{3}$${\mathrm{Ca}}_{3}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{\mathit{x}}$ (n=0, 0.1, 0.5, and 1.0) semiconducting glasses. All these glasses show small clusters or grains of different sizes arising due to the phase separation as observed from the scanning electron microscopic study. The ac conductivities of these glasses follow the well-known relation ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ac}}$(\ensuremath{\omega})=A(T)${\mathrm{\ensuremath{\omega}}}^{\mathit{s}}$. In these glasses the electron-phonon interaction is strong enough to form small polarons and electrical conduction occurs by a small-polaron hopping mechanism. Like Li-doped ${\mathrm{Bi}}_{4}$${\mathrm{Sr}}_{3}$${\mathrm{Ca}}_{3}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ glasses, the exponents of all the present Pb-doped glasses are found to be a little higher than unity (1.1--1.2) in the low-temperature regime where ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ac}}$(\ensuremath{\omega}) also shows little nonlinear variation with temperature. Similar values of s (\ensuremath{\ge}1) have also been reported in the literature for glassy nonoxide semiconductors. The experimental ac conductivity data have been analyzed with different theoretical models based on quantum-mechanical tunneling through the barrier and classical hopping over the barrier mechanisms.The correlated barrier hopping (CBH) model is found to be most appropriate for these glasses, explaining the behavior of both ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ac}}$(\ensuremath{\omega},T) and its exponent s (except in the region where s>1). Other models, such as the quantum-mechanical tunneling model and the overlapping large-polaron tunneling model, are found to be inadequate to explain the general behavior of both temperature- and frequency-dependent ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{ac}}$ and s. The extended-pair approximation model and the percolation theoretical model are also found to fit the ac-conductivity data of these glasses (with s\ensuremath{\le}1). However, the fitting with the CBH model appears to be better. All the Pb-doped glasses are also found to be good precursors for superconductors with ${\mathit{T}}_{\mathit{c}}$ between 110 and 115 K in their crystalline phases obtained by annealing for optimum time of 24 h at 840 \ifmmode^\circ\else\textdegree\fi{}C. The thermoelectric powers of these superconductors are positive (hole-type superconductors).