Self-Diffusion in Tellurium. II. Grain Boundary and Dislocation Effects

Abstract

Self-diffusion in tellurium has been determined directly and unambiguously using a ${\mathrm{Te}}^{127m}$ radiotracer in polycrystalline and dislocated single-crystal tellurium samples. The data along the grain boundaries between 280 and 390°C can be represented by $D_{\mathrm{GB}}=7.47\mathrm{}\times {10}^{-4\mathrm{}} \exp \left[\frac{(-0.87\mathrm{}\pm 0.08 \mathrm{eV})}{\mathrm{kT}}\right]$ ${\mathrm{cm}}^2$/sec, whereas those along the edge (between 253 and 401°C) and screw (between 275 and 380°C) dislocations are described by $D_{\mathrm{ED}}=9.67\mathrm{}\times {10}^{-6\mathrm{}} \exp \left[\frac{(-0.65\mathrm{}\pm 0.02 \mathrm{eV})}{\mathrm{kT}}\right]$ ${\mathrm{cm}}^2$/sec and $D_{\mathrm{SD}}=7.12\mathrm{}\times {10}^{-3\mathrm{}} \exp \left[\frac{(-0.98\mathrm{}\pm 0.10\mathrm{eV})}{\mathrm{kT}}\right]$ ${\mathrm{cm}}^2$/sec, respectively. From these data, in conjunction with the available lattice-diffusivity data in single crystals, it is estimated that the activation energy of the motion of vacancies in tellurium is about 0.7 eV along [0001] and 1 eV along $〈10\overline{1}0〉$ or $〈11\overline{2}0〉$. The use of Fisher's analysis of Harrison's type-B diffusion kinetics, along with the directly measured data along dislocations and grain boundaries, substantiated the model of grain boundaries as a single-line array of dislocations. But the values of effective grain-boundary thickness and dislocation diameters obtained using the same analysis (1.5×${10}^{-5\mathrm{}}$ cm) is about two orders of magnitude higher than usually assumed in grain-boundary diffusion studies.