  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.
