A model for the compositions of non-stoichiometric intermediate phases formed by diffusion reactions, and its application to Nb3Sn superconductors

TL;DR

This paper develops a mathematical model for the composition of non-stoichiometric intermediate phases formed by diffusion reactions, specifically applied to Nb3Sn superconductors, to better understand and control their properties.

Contribution

The paper introduces a new mathematical framework for analyzing non-stoichiometric phases in diffusion reactions, including effects of bulk and grain boundary diffusion, applied to Nb3Sn superconductors.

Findings

The model accurately predicts composition profiles and growth rates.

Bulk and grain boundary diffusion lead to distinct composition characteristics.

The approach offers strategies to control Nb3Sn superconductor compositions.

Abstract

In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and inter-phase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that frozen bulk diffusion leads to unique composition characteristics quite distinct from equilibrium expectations; then the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose the approaches to control their compositions.