Ac conductivity of tungsten phosphate glasses

Abstract

The electrical conductivity in tungsten phosphate glasses of three different compositions (67 mole% of W${\mathrm{O}}_{3}$-33 mole% ${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$, 70 mole% M${\mathrm{O}}_{3}$-30 mole% ${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$, and 81 mole% W${\mathrm{O}}_{3}$-19 mole% ${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$) has been measured in the frequency range 100 Hz to 3.60 GHz and in the temperature range 77-500\ifmmode^\circ\else\textdegree\fi{}K. The measured ac conductivity at low temperature is almost independent of temperature but shows strong dependence on frequency according to the relation $\ensuremath{\sigma}(\ensuremath{\omega})=A{\ensuremath{\omega}}^{s}$ where the exponent $s$ has been observed to be less than unity. At higher temperatures the frequency dependence becomes weak at low frequencies and remains strong at higher frequencies. The weak frequency dependence is due to the contribution of dc conductivity to the measured ac conductivity. A clear Debye-type dielectric relaxation loss peak is observed by taking out the contribution of dc conductivity, but the frequency dependence of conductivity remains less than quadratic at low frequencies indicating some distribution of relaxation times. This behavior is confirmed by the variation of dielectric constant with frequency and temperature. The temperature and frequency dependence of ac conductivity can be adequately explained in W${\mathrm{O}}_{3}$-${\mathrm{P}}_{2}$${\mathrm{O}}_{5}$ systems by considering the contributions from two mechanisms, one giving an almost linear dependence of conductivity on frequency, and the other having a narrower distribution of relaxation times giving rise to clear but broad dielectric loss peaks.