Calculation of diffusion coefficient in Au diffusion-doped Bi$_{1.8}$Pb$_{0.35}$Sr$_{1.9}$Ca$_{2.1}$Cu$_{3}$O$_{y}$ by EDXRF measurements*

Gold (Au) diffusion in superconducting Bi$_{1.8}$Pb$_{0.35}$Sr$_{1.9}$Ca$_{2.1}$Cu$_{3}$O$_{y}$ was investigated over the temperature range 500-800 \r{ }C by the EDXRF technique. It is found that the Au diffusion coefficient decreases as the diffusion-annealing temperature decreases. The temperature dependences of Au diffusion coefficient in grains and over grain boundaries are described by the relations D$_{1}$=6.7 x 10$^{-5}$exp(-1.19eV/k$_{B}$T) and D$_{2}$=9.7 x 10$^{-4}$exp(-1.09eV/k$_{B}$T), respectively. The diffusion doping of Bi-2223 by Au causes a significant increase of the lattice parameter c by about 0.19{\%}. For the Au-diffused samples, transport measurements indicated the T$_{c}$ increased from 100 to 104K and the J$_{c}$ increased from 40 to 125Acm$^{-2}$, in comparison with those of undoped samples. From SEM and XRD measurements it is observed that Au doping of the sample also improved the surface morphology and increased the ratio of the high-T$_{c}$ phase to the low-T$_{c}$ phase. The possible reasons for the observed improvement due to Au diffusion are also discussed.