A contribution to the analysis of grain boundary diffusion measurements

Abstract

The Whipple and Suzuoka exact solutions of the grain boundary diffusion problem have been extended to the Gruzin method. The penetration curves for these two solutions were evaluated numerically using the method of penetration depth measurement, the sectioning method, and the Gruzin method. With the results obtained, relationships are given which make the evaluation of grain boundary diffusion coefficients in the low concentration range (up to 0.005%) comparatively easy. For all three experimental methods the Whipple and Suzuoka solutions have been compared. The comparison for the method of penetration depth measurement was only possible in the low concentration range. When evaluating the data in the low concentration range, using Whipple's or Suzuoka's solutions, approximately the same values of grain boundary coefficient are obtained, irrespective of the experimental method used. A comparison of the solutions using the sectioning and the Gruzin methods in the high concentration range (100%–0.1%) shows that the Gruzin method is not sensitive to the mathematical model used for treating the experimental data. The application of Whipple's solution to the data corresponding to Suzuoka's model gives higher values of the volume diffusion coefficient and slightly higher values of the grain boundary diffusion coefficient in the sectioning method and vice versa.