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

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 that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose approaches to control their compositions.

A review and prospects for Nb3Sn superconductor development

“…The assumptions and derivations for the governing equations, which are based on Fick's laws and mass conservation, for this diffusion reaction system are described in details in [74].…”

“…The μSn(XSn) curve for Cu-Sn calculated from the thermodynamic data given in [79], and a rough μSn(XSn) curve for Nb3Sn speculated based on the phase formation relation between for the μSn profiles of the Sn source/Nb3Sn/Nb system for two different Sn sources are shown in Figure 14 (a). Based on the calculations using the model in [74], it is known that larger μSn in the Sn source causes both larger μSn drop across the Nb3Sn layer and larger (μSn II -μSn l ), which cause larger diffusion rate and larger reaction rate, respectively. This explains the fact that increase in the activity of Sn in the Sn source (e.g., increasing Sn content of Cu-Sn) leads to higher Nb3Sn layer growth rate.…”

Atomic-scale analyses of Nb3Sn on Nb prepared by vapor diffusion for superconducting radiofrequency cavity applications: a correlative study

“…Therefore, Sn-deficient regions with 17-19 at.% Sn can decrease the T c of Nb 3 Sn coatings to below that of Nb, 9 K. The formation of Sn-deficient regions is particularly undesirable near the top surface of Nb 3 Sn cavities where radiofrequency currents flow. The growth mechanism and compositional variation of Nb 3 Sn have been rigorously investigated in Nb 3 Sn samples prepared for superconducting wire applications by a solid-diffusion process using Cu-Sn and Nb diffusion couples, the bronze process [1,[21][22][23][24][25]. The compositional variation in Nb 3 Sn prepared by soliddiffusion was investigated utilizing a composition gradient between a Sn-rich phase (Nb 6 Sn 5 ) and bulk Nb, originating from the diffusion process [21,[25][26][27].…”

GLAG theory for superconducting property variations with A15 composition in Nb3Sn wires

“…Various experiments 11 – 13 and models 14 , 15 have recently been conducted to investigate the dependence of the superconductivity and magnetic properties of Nb 3 Sn samples on Sn content and disorder. The underlying physics for the superconducting properties variation with the A15 composition in Nb 3 Sn is however still not very clear.…”