Heat Treatment Optimization on Nb$_{3}$Sn Strands Based on Electrical and Physical Properties

Abstract

The electrical and physical properties of Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> Sn strands are strongly dependent on the heat treatment during which tin diffuses into niobium by solid-state diffusion. During diffusion, Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> Sn grains grow at the Nb/bronze interface. The shape and size of the grain depend on the temperature of the last step of the heat treatment, its duration and the size of the Nb filaments. The volume of reacted Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> Sn together with the grains’ structure influence the non-copper critical current density J <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{c}$</tex-math></inline-formula> and the magnetization. Therefore, an optimization of the heat treatment with respect to J <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{c}$</tex-math></inline-formula> and hysteresis loss is important when working on the design of superconducting cables. This contribution presents the results of a heat treatment optimization performed on a 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\,$</tex-math></inline-formula> mm diameter, internal Sn Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> Sn strands produced by Kiswire Advanced Technology (KAT) for two React&Wind conductor prototypes for the Toroidal Field Coil of the EUROfusion DEMO: a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {66}\,$</tex-math></inline-formula> kA/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {12}\,$</tex-math></inline-formula> T and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {105}\,$</tex-math></inline-formula> kA/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {12}\,$</tex-math></inline-formula> T prototype. For the optimization, four heat treatment schemes were considered and their evaluation based on I <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{c}$</tex-math></inline-formula> measurements at 4.2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\,$</tex-math></inline-formula> K, in the range of 9 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\,$</tex-math></inline-formula> T to 15 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\,$</tex-math></inline-formula> T, on SEM micrographic studies on grain size and shape and on hysteresis loss measurements on a vibrating sample magnetometer (VSM). Based on these results, a heat treatment schedule is proposed for the prototype DEMO conductor and the scaling law for J <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{c}$</tex-math></inline-formula> is updated.