Solvent grain boundary diffusion in binary solid solutions: a new approach to evaluate solute grain boundary segregation

Abstract

A new method to estimate solute grain boundary (GB) segregation from solvent GB diffusion measurements in binary solid solutions is proposed for the systems with restricted solubility and intermediate stoichiometric phases. The method is based on the model of complex formation: solvent atoms (A) interact with solute ones (B) at GB with the formation of AB chemical bond. A description of solvent GB diffusion is then given. Using such an approach, a new equation for the dependence of solvent GB diffusion coefficient on solute bulk concentration is derived for the systems with simple atomic attraction with AB complex formation in GB. Theoretical results predict non-linear dependence of solvent GB diffusion coefficient on solute bulk content, which is in agreement with earlier published experimental data regarding the ease of grain boundary diffusion in alloys of different chemical compositions. More importantly, the equation deduced permits to evaluate, on one hand, the characteristics of solute GB segregation from solvent GB diffusion measurements and, one the other hand, GB diffusion coefficient in pure solvent. Such a numerical data analysis for Fe–Sn system is in agreement with experimental results. In special cases, such an analysis can be done analytically.

Keywords:

• grain boundary diffusion
• atomic interaction
• atomic complex
• segregation

Acknowledgements

Authors would like to thank one of the reviewers for his/her criticism that allowed to clarify significantly theoretical assumptions used in the work and to avoid errors.

Notes

1 Note, that the Equation (35(35) ) does not give for , as it is not valid for small solute concentration.