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[Nobuya Banno](https://orcid.org/0000-0002-7141-541X)

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Role of elemental additions in Nb3Sn phase formation in wiresSuperconductorScience andTechnology     TOPICAL REVIEW • OPEN ACCESSRole of elemental additions in Nb3Sn phaseformation in wiresTo cite this article: Nobuya Banno 2026 Supercond. Sci. Technol. 39 083002 View the article online for updates and enhancements.You may also likeAsymmetric diffusion and crystallographicinheritance: unveiling microstructureformation mechanisms in internal-tinNb3Sn wiresYuxuan Wang, Juntao Zou, Yujia Yan etal.-The impact of Cu/Sn precursor tin contenton the properties and growth mechanismof Nb3Sn thin films via bronze methodsMing Lu, Jing Zhang, Didi Luo et al.-Cu diffusion in Nb3Sn internal tinsuperconductors during heat treatmentIan Pong, Luc-Rene Oberli and LucaBottura-This content was downloaded from IP address 144.213.253.16 on 12/08/2026 at 08:57https://doi.org/10.1088/1361-6668/ae922b/article/10.1088/1361-6668/ae694b/article/10.1088/1361-6668/ae694b/article/10.1088/1361-6668/ae694b/article/10.1088/1361-6668/ae694b/article/10.1088/1361-6668/ae694b/article/10.1088/1402-4896/adf893/article/10.1088/1402-4896/adf893/article/10.1088/1402-4896/adf893/article/10.1088/1402-4896/adf893/article/10.1088/0953-2048/26/10/105002/article/10.1088/0953-2048/26/10/105002/article/10.1088/0953-2048/26/10/105002Supercond. Sci. Technol. 39 (2026) 083002 https://doi.org/10.1088/1361-6668/ae922bOPEN ACCESSRECEIVED9 March 2026REVISED25 June 2026ACCEPTED FOR PUBLICATION29 July 2026PUBLISHED11 August 2026Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe authors (s) and thetitle of the work, journalcitation and DOI.TOPICAL REVIEWRole of elemental additions in Nb3Sn phase formation in wiresNobuya Banno∗Research Center for Energy and Environmental Materials (GREEN), National Institute for Materials Science, Tsukuba, Japan∗ Author to whom any correspondence should be addressed.E-mail: banno.nobuya@nims.go.jpKeywords:Nb3Sn, thermodynamics, elemental addition, growth kinetics, zinc addition, titanium additionAbstractNb3Sn remains an indispensable core material for high-field applications, including fusion reac-tors, particle accelerators, and nuclear magnetic resonance systems, owing to its manufacturabil-ity and superior high-field performance, making it a key enabling material for advanced energytechnologies required for a sustainable and decarbonized future. The enduring appeal of Nb3Snstems from the incomplete elucidation of its phase formation more than 70 years after its discov-ery, which suggests significant potential for further performance enhancement. This article reviewsrecent progress in Nb3Sn conductor development from the perspectives of thermodynamics, diffu-sion kinetics, and microstructural control via elemental additions. In contrast to previous reviewsthat primarily focused on conductor performance, processing routes, or artificial pinning centertechnologies, the present review places particular emphasis on phase formation during diffusionreactions and on the mechanisms by which elemental additions modify reaction pathways, inter-mediate phases, diffusion behavior, and microstructural evolution. This review focuses on the con-trol of the Sn chemical potential through Cu addition, Sn concentration gradient within the Nb3Snlayer resulting from slow bulk diffusion, and Cu diffusion along the Nb3Sn and Nb grain bound-aries. The unique role of Cu in facilitating the bronze process is discussed alongside the chemicalreactivity of Cu with Nb and Sn. Furthermore, this review systematically summarizes the effects ofTi and Zn additions, including variations in interfacial compound formation depending on the Tiaddition site, grain-boundary pinning and grain size modification associated with Cu segregation,and effective multielement addition strategies. Finally, the strengthening of the tin core throughelemental additions as a primary method for achieving optimal drawability in advanced Nb3Snconductors is addressed. This review provides a thermodynamic and kinetic framework for under-standing Nb3Sn layer formation through elemental-addition strategies.1. IntroductionBefore the discovery of NbTi superconductors [1, 2, 3], Matthias et al discovered Nb3Sn superconduc-tors (A15-type compound superconductors) in 1954 at Bell Laboratories (figure 1) [4]. Despite a historyspanning 70 years, these materials continue to fascinate superconducting materials scientists. As a type-IIsuperconductor, Nb3Sn possesses a coherence length that exceeds the grain boundary thickness, whichallows crystal defects such as grain boundaries to function as effective flux-pinning sites without weakcoupling issues [5–11]. High-performance Nb3Sn superconductors are comprised of dense compoundpolycrystals, for which low-temperature diffusion synthesis using Nb and Sn alloys is well-suited to pro-duce refined, dense crystal structures. The superconducting properties depend on a comprehensive rangeof crystallographic factors, including the homogeneity (concentration gradient) of the superconductinglayer, grain boundary density, and the precipitation of impurities. Complex thermodynamics, governedby the geometric arrangement of precursor cross-sections, composition ratios, diffusion reaction condi-tions, elemental additions, and other factors, control the formation of these dense polycrystalline layers.Thus, the synthesis of the Nb3Sn superconducting layer offers considerable scope for leveraging materi-als science expertise. This fundamentally different development philosophy remains distinct from that of© 2026 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/1361-6668/ae922bhttps://crossmark.crossref.org/dialog/?doi=10.1088/1361-6668/ae922b&domain=pdf&date_stamp=2026-8-11https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-7141-541Xmailto:banno.nobuya@nims.go.jpSupercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 1. Crystal lattice of Nb3Sn.rare-earth barium copper oxide (REBCO) superconductors, which require highly oriented single-crystalsuperconducting layers, further contributing to the scientific interest in the Nb3Sn system. In addition,the wire-fabrication processes for Nb3Sn conductors are well suited to large-scale production, represent-ing a further advantage over REBCO conductors for many practical magnet applications.Numerous review articles on Nb3Sn conductors have been published over the past decades.Representative recent reviews include the review by Godeke, which summarized composition and mor-phology effects, strain sensitivity, Cu/Ti/Ta additions, and grain-size-related issues [12]; the review byXu, which focused on phase fractions, stoichiometry, Sn content, Ti addition, artificial pinning centers(APCs) based on internal oxidation, and reaction pathways toward high-Jc conductors [13]; and thereview by Barzi, which reviewed the historical development of Nb3Sn wires and conductors from theperspective of magnet applications, including magnetothermal instabilities and subelement deformation[14]. For a broader overview of previous reviews, readers are referred to [15].Although a substantial body of knowledge on Nb3Sn superconductors has been accumulated and sys-tematically reviewed over many years, achieving precise control of Nb3Sn layer formation remains chal-lenging, even for materials specialists. This difficulty arises from the strong interplay among thermody-namics, diffusion kinetics, phase evolution, and microstructural development during the reaction pro-cess. To provide a unified perspective on these interrelated phenomena, the author previously publisheda review in 2023 focusing on the relationships among processing, microstructure, and superconduct-ing performance, together with introductory discussions on growth kinetics, nucleation theory, chemicalpotential, elemental additions, and matrix strengthening [15].Nb3Sn superconductors possess a critical temperature exceeding 18 K [16], and a critical magneticfield of approximately 23 T at 4.2 K [17]. Ti and Ta additions significantly enhance the critical magneticfield (Bc2) to approximately 27 T [17]. Beyond these intrinsic properties, its manufacturability estab-lishes Nb3Sn wire as the primary candidate for next-generation particle accelerators, such as the FutureCircular hadron-hadron Collider (FCC-hh) and prototype DEMOnstration Power Station (DEMO) mag-net conductors. Estimated total shipments for both applications are expected to reach several thousandtons. Furthermore, Nb3Sn wire remains essential for nuclear magnetic resonance systems with resonancefrequencies of 400 MHz or higher (corresponding to magnetic fields of 9.4 T or greater) in drug discov-ery and related fields. Demand for this wire is projected to remain robust.The recent development of high-performance Nb3Sn conductors is being driven by the demand-ing requirements of future large-scale projects, including the FCC-hh at CERN [18] and various globalfusion-energy programs. These programs encompass Q-DEMO, an ITER-sized demonstration reactorproject led by QST in Japan [19], EU-DEMO [20, 21], DTT (Divertor Tokamak Test facility) in Italy[22], and two Chinese fusion projects: CFETR (China Fusion Engineering Test Reactor) [23] and CFEDR(China Fusion Energy Demonstration Reactor) [24]. These demanding projects have stimulated Nb3Sndevelopment activities worldwide, involving Japan [25, 26], the European Union, the United States ofAmerica [27–29], South Korea [30, 31], China [32], and Russia [33]. The broader research and develop-ment community encompasses universities, national laboratories, and industrial suppliers working acrossmultiple countries and regions. Major institutions include CERN, Fermilab, LBNL, NHMFL, ACIPP,KEK, QST, NIFS, NIMS, and leading universities such as the University of Geneva, the University ofOxford, the University of Twente, TU Wien, Ohio State University (OSU), and Tohoku University. Theseorganizations are actively investigating superconducting properties such as Bc2 [34–37], stress–straintolerance [38–45] and thermo-magnetic instability [46, 47], and neutron irradiation effects [48–50], aswell as phase formation and microstructural evolution.2Supercond. Sci. Technol. 39 (2026) 083002 N BannoA primary performance target for next generation Nb3Sn conductors is a critical current density (Jc)of 1200–1500 A mm−2 at 15 T, corresponding to the target specification for FCC-hh magnets [18, 51].To achieve this target, wire manufacturers and research institutions worldwide are vigorously pursuingconductor optimization. Bruker-OST/Bruker USA Restacked Rod Process (RRP) wires have long servedas a benchmark for high-performance conductors [52] and have been widely adopted by major institu-tions such as CERN. A notable example of project-driven conductor development is provided by KAT(Kiswire Advanced Technology), which developed Nb3Sn wires meeting the more demanding perfor-mance requirements of the DTT project, beyond those specified for ITER conductors [30]. Furthermore,OSU/Fermilab/Hyper Tech’s APC Nb3Sn wires have recently demonstrated critical current densitiesexceeding the FCC target specification, representing a significant advance in high-performance conduc-tor development [29]. In parallel, recent compact-fusion reactor concepts have increased the demand forhigh-Jc Nb3Sn conductors. Consequently, achieving high Jc within increasingly limited magnet volumeshas become one of the most important objectives in contemporary Nb3Sn wire development.Enhancing wire strength is also essential for large-scale magnets to withstand increased electromag-netic forces. The FCC-hh magnet requires resistance to lateral compressive stresses of 200 MPa [53–55].Similarly, the DEMO magnet requires high-strength, high-performance wires capable of withstandingcomplex stress–strain distributions, including bending, tension, and compression, arising from intricatewire trajectories in the multistage twisted cables [45, 56–58].Additionally, reduction of the effective superconducting filament diameter in Nb3Sn wires isrequired under time-varying magnetic fields to mitigate hysteresis losses and improve stability [59,60]. Consequently, next-generation Nb3Sn superconducting wires must simultaneously satisfy three keyrequirements, namely, high Jc, high mechanical strength, and a low effective filament diameter.Against this backdrop, and building upon the author’s previous review [15], this paper reviews recentresearch in Nb3Sn conductor development from the perspectives of thermodynamics and growth kineticsto elucidate the Nb3Sn layer formation mechanism and to achieve simultaneous critical current densityand mechanical strength improvements. The present review places greater emphasis on phase formationduring diffusion reactions and on the role of elemental additions in controlling reaction pathways, inter-mediate phases, diffusion behavior, and microstructural evolution in superconducting wires. Comparedwith previous reviews, this article provides a more in-depth discussion of these topics and incorporatesseveral insights emerging from recent studies.This review outlines the diffusion-based formation of Nb3Sn layers, emphasizing chemical potentialas a vital concept for understanding phase formation and layer growth. Furthermore, this article explainshow elemental additions establish interfacial diffusion barriers or accelerate phase formation. This paperdemonstrates that elemental additions facilitate matrix microstructural control and that wires possess-ing both high strength and superior performance result from appropriate element selection and cross-sectional microstructural regulation. Finally, this paper introduces recent findings demonstrating thatelemental additions control the Nb3Sn grain boundary composition, thereby modifying the contributionof elemental pinning to the grain-boundary pinning force.2. Fundamental issues in Nb3Sn layer formationA summary of representative Nb–Sn–Cu phases related to the Nb3Sn diffusion reaction is provided intable 1 [61–63]. These phases appear during different stages of the reaction process and play importantroles in controlling diffusion pathways, reaction kinetics, and Nb3Sn layer formation.As discussed throughout this review, industrial Nb3Sn conductors are fabricated through diffusionreactions between Nb and Sn–containing Cu alloys. The conductor architectures used to realize thesediffusion reactions can be broadly classified into the bronze-route, internal-tin (single-barrier, RRP, tube-type, and distributed-Sn designs), and powder-in-tube (PIT) processes. Representative conductor archi-tectures are schematically illustrated in figure 2(a).Compared with the bronze-route process, the internal-tin and PIT processes separate the Sn sourcefrom the Cu matrix, thereby avoiding the limitation of Sn supply inherent to bronze-route conductorsand enabling higher Nb3Sn volume fractions and higher non–Cu Jc values. Another important charac-teristic of RRP and PIT conductors is that Ti or Ta is introduced from the Nb-module side, which con-tributes to the formation of a more homogeneous Nb3Sn layer, as discussed in later sections.Since the present review focuses on thermodynamics, diffusion kinetics, and phase formation duringNb3Sn layer growth, it is useful to first identify the principal issues associated with diffusion reactionsin multifilamentary conductors. Therefore, figure 2(b) summarizes several representative microstructural3Supercond. Sci. Technol. 39 (2026) 083002 N BannoTable 1. Representative Nb–Sn–Cu phases involved in the Nb3Sn diffusion reaction.Phase RemarkBronze Cu–Sn solid solution containing typically 8–9 at% Sn, used as the Sn source during reaction heat treatment.Nausite [61, 62] Nb–Cu–Sn ternary compound ((Nb0.75Cu0.25)Sn2) formed at∼360 ◦C–550 ◦C, subsequently decomposinginto NbSn2 and Nb6Sn5.NbSn2 [63] Sn-rich intermediate intermetallic phase (Tc≈2.68 K), generally regarded as an undesirable precursor phaseduring Nb3Sn formation.Nb6Sn5 [63] Sn-rich intermediate intermetallic phase (Tc≈2.07 K), formed prior to Nb3Sn and generally undesirable forconductor performance.Nb3Sn A15-type superconducting compound (Tc≈18 K), serving as the primary current-carrying phase in practicalsuperconducting wires.Figure 2. (a) Representative Nb3Sn conductor architectures. (b) Representative microstructural and diffusion-reaction-relatedissues in a single-barrier internal-tin conductor.and reaction-related issues using a single-barrier internal-tin conductor as an example. Elemental addi-tions are among the most effective approaches for addressing many of these issues and are therefore acentral focus of this review.This section reviews several classical models relevant to Nb3Sn layer formation alongside recent find-ings by the author on elemental diffusion phenomena.2.1. Role of Cu in the Sn diffusion driving forceAs shown in the equilibrium phase diagram, the melting point of completely molten Nb3Sn exceeds2200 ◦C; such elevated temperatures induce significant grain growth within the Nb3Sn layers. For con-text, in other A15-type compound superconductors, such as Nb3Al, the grain size produced directlyfrom the molten state via electron beam melting typically reaches several hundred nanometers or larger[64]. This coarsening is detrimental to Nb3Sn superconductors, where grain boundaries serve as the pri-mary flux-pinning sites. Conversely, the formation of a binary Nb/Sn diffusion couple at low tempera-tures primarily yields the NbSn2 compound phase at the interface, which inhibits the formation of thedesired Nb3Sn phase [15].The bronze-route reaction process was developed as a strategic solution to this problem. This methodfacilitates a diffusion reaction between a bronze alloy, in which Sn (or Ga) is solidified in Cu and Nb4Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 3. Schematic diagram illustrating the relationship between the Gibbs energy (G) and the Sn chemical potential (µ) at agiven Nb3Sn formation temperature. Here, µSn, Nb6Sn5 denotes the Sn chemical potential under equilibrium conditions whereNb6Sn5 and Nb3Sn coexist, µSn, Cu–Sn denotes the Sn chemical potential in the Cu–Sn system when the Sn composition is slightlyless than 25 at%, µSn, Nb3Sn denotes the Sn chemical potential of stable Nb3Sn, and∆g denotes the molar free-energy changeassociated with Nb3Sn formation. Reproduced from [68]. © IOP Publishing Ltd all rights reserved.Figure 4. Schematic diagram illustrating the Sn chemical potentials in the Nb–Sn compound and Sn–Cu phases at approximately650 ◦C. The dashed line represents the Sn chemical potential along a Nb3Sn grain boundary. Reprinted from [15], Copyright(2023), with permission from Elsevier.(or V), thereby enabling the synthesis of thick Nb3Sn (or V3Ga) layers [65–67]. Heat treatment is gen-erally conducted at 650 ◦C −750 ◦C, producing Nb3Sn grain sizes in the range of 100−200 nm. Thismanufacturing protocol remains the industrial standard for producing Nb3Sn wires. Chemical potentialserves as a critical conceptual framework for understanding the thermodynamics of Nb3Sn layer forma-tion facilitated by Cu additions.While Fick’s first law dictates that elemental diffusion fluxes proceed from regions of higher concen-tration to lower concentration, this principle does not apply to systems where intermediate phases format the interface. In the bronze-route reaction, the Sn diffusion flux proceeds from the Cu alloy with a Snconcentration of approximately 9% to the Nb3Sn phase with a higher Sn concentration of approximately25%. This phenomenon, historically characterized as ‘uphill diffusion’ [40], is governed by the chemi-cal potential, which describes the movement of elements as a release of free energy between two phases.The chemical potential is defined as the Gibbs energy per mole of a substance (element or compound)when present in a mixture. The magnitude of the difference in Gibbs free energies per mol between theprecursor and product phases determines the reaction strength and direction; consequently, the chemicalpotential gradient acts as the driving force for diffusion.Figure 3 schematically illustrates the relationship between the Sn chemical potential and the Gibbsenergy of Nb3Sn within the Nb–Sn system at a Nb3Sn formation temperature of 685 ◦C. Furthermore,figure 4 provides a conceptual illustration of this relationship regarding the compound phases and theSn chemical potential.5Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 5. Role of Cu in the Nb/Sn diffusion reaction. Scanning electron microscope (SEM) images of (a) Nb/Sn and (b) Nb/Cu–Sn heat-treated at 650 ◦C. During the Nb/Sn diffusion reaction, NbSn2 forms predominantly, whereas phase formation inNb/Cu–Sn proceeds through Nb6Sn5 and subsequently to Nb3Sn. Reprinted from [15], Copyright (2023), with permission fromElsevier.Figure 5 compares the actual interfacial microstructure in the Nb/Sn and Nb/Sn-10at%Cu diffusioncouples after the reaction [15]. In the absence of Cu, the chemical potential of Sn remains extremelyhigh, indicating a strong Sn diffusion driving force, preferentially forming NbSn2, which has a relativelyhigh Sn chemical potential. In pure Sn, this high Sn chemical potential persists, facilitating the continu-ous growth of NbSn2 and precluding the formation of Nb6Sn5. Conversely, the addition of a small quan-tity of Cu to the Sn core initially produces NbSn2, but subsequently decreases the Sn chemical poten-tial, thereby slowing the growth rate of NbSn2. Subsequently, Nb6Sn5 with a lower Sn chemical potentialemerges at the reaction front. As the reaction proceeds, the growth rate of Nb6Sn5 decreases, allowingthe fine-grained Nb3Sn phase to nucleate and grow at the reaction front. Eventually, Nb6Sn5 decomposesto form coarse-grained Nb3Sn while simultaneously liberating Sn, which contributes to the formation offine-grained Nb3Sn [69, 70]. Furthermore, the solid solution of Cu into NbSn2 and Nb6Sn5 destabilizesthese intermediate phases [71]. This destabilization effectively increases the Sn chemical potential, furtherpromoting the growth of the Nb3Sn layer.In the bronze-route process, the Sn chemical potential within Cu–Sn is lower than that in NbSn2and Nb6Sn5, leading to the development of Nb3Sn while bypassing the formation of these intermedi-ate phases. However, a reduced Sn chemical potential induces a pronounced Sn concentration gradientacross the Nb3Sn layer [15].Reducing the dimensions of the diffusion couple provides an alternative strategy to promote Nb3Snphase formation. In the Nb/Al diffusion reaction, the energetically stable Nb2Al typically develops at thereaction interface and functions as a diffusion barrier that inhibits Nb3Al formation [72, 73]. Conversely,minimizing the multilayered Nb/Al diffusion pair to the nanoscale enables Nb3Al formation via diffusionreactions at temperatures below 800 ◦C [72, 74]. This phenomenon results from the destabilization ofthe generated Nb2Al as the reduction in the diffusion couple structure increases the surface energy ofthe phase. Following this mechanism, reducing the Nb/Sn(Cu) diffusion couple destabilizes intermediatecompound phases such as NbSn2, thereby enhancing Nb3Sn phase formation.During the Cu and Sn mixing stage, the formation of the NbCuSn compound nausite((Nb0.75Cu0.25)Sn2) at approximately 400 ◦C influences the Nb3Sn phase formation [61, 62, 75, 76].6Supercond. Sci. Technol. 39 (2026) 083002 N BannoNausite forms at 360 ◦C −550 ◦C [77], and significantly influences the mutual diffusivity of Cu andSn, particularly during the Cu–Sn mixing stage [62]. Controlling nausite formation may contribute toimproving the homogeneity of Sn distribution during the early stages of reaction. Since nausite subse-quently decomposes into NbSn2 and Nb6Sn5 [62], its formation may also influence the subsequent for-mation of Nb3Sn at higher temperatures.2.2. Nb3Sn growth kineticsGrain boundaries substantially affect both flux pinning and the Nb3Sn layer growth rate. Crystal defectssuch as grain boundaries generally have low activation energy for atomic migration, facilitating themovement of atoms along grain boundaries, as compared to bulk diffusion. In the polycrystalline Nb3Snlayer, a large amount of Sn diffuses to the reaction front through the Nb3Sn grain boundaries. Moleculardynamics simulations have revealed that Sn grain boundary diffusion in Nb3Sn has been estimated to beapproximately 7–14 orders of magnitude faster than bulk diffusion over the temperature range relevantto Nb3Sn reaction heat treatments (∼923–1023 K) [78]. The difference decreases with increasing temper-ature because bulk diffusion generally exhibits a stronger temperature dependence than grain boundarydiffusion. This indicates that during the Nb3Sn layer growth process, once Nb3Sn grains are formed, theSn composition in the grain varies minimally via bulk diffusion, resulting in an essentially unchangedSn concentration gradient across the Nb3Sn layer [79, 80]. These findings suggest that enhancing the Sndiffusion driving force while simultaneously minimizing the Nb/Sn diffusion couple length is essentialfor maximizing the improvement in the Sn concentration gradient within the Nb3Sn layer. This accountsfor why RRP wire achieves a smaller Sn concentration gradient, as compared to the tube-type and PITwires [15].Instead of the concentration-gradient form of Fick’s first law, the diffusion flux can be expressed interms of the chemical-potential gradient asJi =−CiMi∂µi∂x(1)where Ji, Ci, Mi and µi denote the net flux, concentration, mobility, and chemical potential of com-ponent i, respectively [81]. This expression indicates that the diffusion flux is determined by both thechemical-potential gradient and the atomic mobility. Therefore, both an increased chemical-potentialgradient and enhanced atomic mobility are expected to contribute to improved Sn transport and conse-quently to a more homogeneous Sn concentration profile within the Nb3Sn layer.2.3. Copper diffusion through Nb3Sn and Nb grain boundariesPrevious elemental analyses of grain boundaries using atom probe tomography (APT) and scanningtransmission electron microscopy (STEM) coupled with energy-dispersive x-ray spectroscopy (EDS) haverevealed the presence of Cu at the grain boundaries after the reaction [68, 82–84]. This suggests thatCu also migrates towards the reaction front along with Sn through Nb3Sn grain boundaries, therebyinfluencing Nb3Sn formation at the reaction interface. However, the precise stage at which Cu dif-fuses remains a fundamental question, as a limited number of studies have thoroughly investigated Cudiffusion.STEM-EDS analysis at the reaction interface between the Nb and Nb3Sn layers clearly reveals themigration of Cu. Figure 6 shows a STEM-EDS elemental map of the reaction front between Nb andNb3Sn in a Nb/Cu–12 wt%Zn–0.2 wt%Mg/Sn–1.6 wt%Ti diffusion couple heat-heated at 650 ◦C for150 h [85]. These results demonstrate that Cu preferentially diffuses along Nb grain boundaries uponreaching the reaction front, followed by Sn diffusion. This observation supports the hypothesis that theprior presence of Cu at the reaction front reduces the chemical potential of the subsequently arriving Sn,thereby suppressing Nb2Sn and Nb6Sn5 formation while promoting Nb3Sn nucleation. These findingsprovide valuable insights into Cu diffusion within the Nb3Sn layer. Regarding the grain boundary diffu-sion of Sn and Cu, the Sn chemical potential at the Nb3Sn grain boundary is schematically representedby the dotted line in figure 4.Furthermore, in Nb filament structures where a Ti source, such as Nb − 47 wt%Ti, is positioned atthe Nb center (figure 7(a)), Cu diffusivity increases due to mutual diffusion with Ti. Figures 7(b) and (c)show SEM images of the Nb filaments and the corresponding compositional profiles after heat treatmentat 650 ◦C for 10 h. Elevated Cu concentrations were detected within the NbTi core (details providedin section 3.6.), indicating that a large amount of Cu reaches the NbTi core more rapidly than the Sndiffusion rate permits. Notably, Cu was detected by EDS in the NbTi core even after heat treatment at550 ◦C for 100 h. Copper and Ti reportedly undergo mutual diffusion in Cu-based NbTi wires duringheat treatment at approximately 650 ◦C [86, 87]. This phenomenon suggests that Ti diffuses efficiently7Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 6. Copper diffusion along the Nb grain boundary prior to Sn diffusion. STEM-EDS elemental maps at the reaction inter-face between Nb3Sn and Nb in a Nb/Cu–12 wt%Zn–0.2 wt%Mg/Sn–1.6 wt%Ti diffusion couple heat-treated at 650 ◦C for150 h. © (2025) IEEE. Reprinted, with permission, from [85].Figure 7. Promotion of Cu diffusion into Nb in the presence of an artificial Ti source at the center of Nb. (a) SEM-backscatteredelectron image (BSE) image of a multifilmentary Nb3Sn precursor with a distributed-tin (DT) configuration, incorporating aNb− 47 wt%Ti core as a Ti source at the center of Nb, (b) SEM-BSE image of the Nb filament after heat treatment at 650 ◦C for10 h, and (c) compositional distribution within the Nb filament after heat treatment at 650 ◦C for 10 h. A large Cu flux clearlyreaches the Ti source at the center. The yellow line in (b) indicates the trajectory used for the concentration analysis.within the Nb module, even in cross-sectional architectures such as RRP wires, where NbTi filaments aredispersed as the Ti source [88].Why is Cu so special? The significance of Cu in Nb3Sn layer formation is attributed to two primarycharacteristics:1. Copper exhibits negligible solubility in Nb and2. The solubility of Sn in Cu, including the formation of Cu–Sn compound phases, moderately adjuststhe Sn chemical potential.In addition to Cu, Ag also exhibits a comparable effect on phase formation behavior, as observed inthe bronze method [89, 90]. Although an equilibrium phase diagram for the Nb−Ag system is currentlyunavailable, investigations into equilibrium reactions and Ag-matrix Nb3Al wires indicate that Nb andAg exhibit negligible mutual solid solubility [91, 92], suggesting that the Nb−Ag phase diagram is simi-lar to that of the Nb−Cu system.Cu diffusivity may depend on the chemical potential of Cu in the surrounding Cu–Sn matrix.Because the thermodynamic state of Cu differs among bronze-route, PIT, and internal-tin conductors,the driving force for Cu diffusion may also vary with conductor architecture. For example, the Cu-richmatrix in bronze-route conductors may provide a different chemical environment from that in PIT orinternal-tin conductors. Such differences could influence the extent of Cu diffusion into the Nb3Sn layerand thereby affect subsequent phase formation and microstructural evolution.8Supercond. Sci. Technol. 39 (2026) 083002 N Banno2.4. Nucleation and grain growth: grain refinement and formation of APCsNb3Sn phase formation via diffusion reactions may be characterized as a thermodynamic nucleationprocess, wherein Nb3Sn nuclei precipitate within the Nb matrix at the reaction front. In regimes dom-inated by grain boundary diffusion, refining the Nb3Sn grain structure increases the Sn diffusion flux.This enhanced Sn transport accelerates growth kinetics.Nucleation theory facilitates the understanding of Nb3Sn formation and the precipitation ofnanoparticles that serve as artificial flux pinning centers in superconducting materials, including Nb3Snand REBCO [29, 93–97]. In contrast to REBCO conductors, where APCs are widely utilized, flux pin-ning in conventional Nb3Sn conductors is generally dominated by grain boundaries. Therefore, grainrefinement remains one of the most effective approaches for enhancing Jc. Recent APC and internal-oxidation approaches have shown promising improvements in conductor performance; however, theextent to which oxide nanoparticles directly contribute to flux pinning remains under active investigation[98].Generally, the magnetic flux pinning force is maximized when precipitate dimensions are commen-surate with the coherence length. Furthermore, the optimal grain size is considered comparable to themagnetic flux lattice spacing, as this condition maximizes the magnetic flux pinning force. Assuminga square magnetic flux lattice [99–101], the lattice spacing is defined as a= √(φ 0/B), where φ0 is themagnetic flux quantum and B is the external magnetic flux density. For example, as a guideline, atB = 5, 12, and 16 T, a is estimated at approximately 20, 13, and 11 nm, respectively. Godeke corre-lated the maximum pinning force with the reciprocal grain size, demonstrating a universal, monotonicincrease in the maximum pinning force down to a grain size of 35 nm [11].Classic nucleation theory posits that nucleation occurs when the reduction in volume energy duringphase precipitation exceeds the corresponding increase in surface energy [102]. The Gibbs energy change(∆G) is expressed as ∆G =(−4π r3/3)(∆g/v) + 4π r2σ, where, ∆g, r, v and σ represent the molar free-energy change (i.e. the chemical potential difference driving phase formation), precipitate radius, precip-itate molar volume, and surface energy density, respectively. The first term on the right-hand side of theequation represents the volume free energy, while the second term accounts for the surface free energy.This relationship yields a concave energy curve with a peak value (∆Gc) occurring at the critical nucleusradius, rc = 2συ/∆g.Although the classical homogeneous-nucleation model provides a useful framework for understand-ing the role of interfacial energy in nucleation, Nb3Sn formation in practical conductors generally pro-ceeds through heterogeneous nucleation at existing interfaces. Furthermore, the subsequent phase evo-lution and layer growth are largely governed by diffusion processes rather than by nucleation kineticsalone. Meanwhile, for oxide precipitation associated with internal oxidation, the thermodynamic drivingforce originates primarily from the corresponding chemical reactions, although interfacial energy remainsan important factor governing nucleation.As ∆g increases, the critical radius decreases and the nucleation rate increases, leading to grainrefinement. The chemical potential difference is influenced by the internal strain state and crystal defects,such as dislocations and grain boundaries, within the parent phase prior to precipitation, which serveas preferential nucleation sites. Hafnium additions to Nb exemplifies this effect. Figure 8 shows micro-graphs of the Nb3Sn phase formed from a Nb–4at%Ta–1at%Hf matrix in the as-deformed condition andafter preheating at 1000 ◦C [15, 103]. The recrystallization temperature of Hf-doped Nb exceeds the typ-ical Nb3Sn formation temperature of approximately 650 ◦C, allowing the retention of a fine microstruc-ture during Nb3Sn formation. Consequently, the Nb−Hf system accumulates internal strain energy,which provides an additional driving force for Nb3Sn phase formation and subsequent grain refinement[103–106].The temperature dependence of the nucleation rate follows an Arrhenius-type relationship, wherethe rate increases exponentially with temperature once the minimum activation energy threshold issurpassed [107, 108]. While elevated temperatures enhance diffusion rates and compositional unifor-mity, in Nb3Sn layer formation dominated by grain-boundary diffusion, compositional homogenizationwithin the grains is negligible over relevant timescales. This activation energy concept also governs graingrowth, consistent with previous reports indicating that grain size varies exponentially with temperature[93, 109]. As reference data, the grain sizes reported for tube-type Nb3Sn wires using Nb − 7.5 wt%Taare approximately 80, 110, 140, and 180 nm at 615 ◦C, 650 ◦C, 700 ◦C, and 750 ◦C, respectively [93,109]. This relationship is approximately expressed as dGS = 0.5918e0.0056T, where dGS is the grain size(nm) and T is the temperature (K). Thus, balancing layer growth and grain growth through optimizedheat treatment is therefore vital for enhancing the critical current density of Nb3Sn.The Zener pinning effect also significantly influences the formation of Nb3Sn polycrystalline layers[110]. This effect has recently garnered significant attention, particularly in the Nb internal oxidation9Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 8. Grain refinement via the formation of Nb3Sn on a fine Nb− 4at%Ta− 1at%Hf parent phase. Inverse pole figure (IPF)map, kernel average misorientation (KAM), and SEM image of the fractured surface of a Nb3Sn layer (a) reacted on as-drawnNb−Ta−Hf and (b) reacted on fully annealed Nb−Ta−Hf [103]. High KAM values suggest a matrix featuring high internalstrain. Reprinted from [15], Copyright (2023), with permission from Elsevier.technique for Nb3Sn [29, 93, 106]. This effect occurs when finely dispersed, energetically stable second-phase particles within the reaction layer suppress grain boundary migration, thereby inhibiting graincoarsening (grain growth). The empirical relationship can be expressed as R∼= 4/3 · r/f, where R is thefinal grain size, f is the fraction of the total volume occupied by inclusions, and r is the size of thesecond-phase particles [111–113]. Precipitates that induce this effect are not limited to oxides. Santrareported the existence of β-(Ti, Nb) particles at grain boundaries and noted that these particles inducethe Zener pinning effect [84]. Similarly, the solute drag effect, characterized by the segregation (or con-centration) of specific solute elements at grain boundaries, further hinders grain boundary migration[114–116].3. Effect of elemental additionsDuring the formation of Nb3Sn layers via solid-state diffusion, elemental additions influence polycrys-talline Nb3Sn layer formation and the overall phase formation, including that of the matrix materialssurrounding the superconducting filaments. Based on the fundamental principles of thermodynamicsand growth kinetics outlined above, this section discusses the effects of elemental additions on the for-mation of Nb3Sn layers via complex diffusion reactions using several examples and incorporating ourrecent research results.The internal oxidation approach reported by Xu et al is also relevant to the present discussion ofelemental-addition strategies because it involves the addition of oxygen-gettering elements such as Zror Hf to Nb [106]. Therefore, a brief overview of its underlying mechanism is provided here. In thisapproach, nanoscale oxide precipitates (e.g. ZrO2 or HfO2) formed during internal oxidation suppressgrain growth through the Zener pinning effect, resulting in significant refinement of the Nb3Sn grainstructure [13, 29, 93, 106, 109, 117]. In addition, these oxide nanoparticles have been reported to pro-vide an additional contribution to flux pinning. Detailed descriptions of the internal oxidation approachand APC conductors can be found in the review by Xu et al [13, 118, 119]. The present review there-fore focuses primarily on the thermodynamics and growth kinetics through which elemental additionsinfluence phase formation and microstructural evolution.3.1. Variation in the Nb3Sn phase formation behavior depending on the Ti addition siteTi and Ta are widely recognized as additive elements that improve Bc2 in Nb3Sn [17, 120, 121]. At 4.2 K,Ti or Ta doping increases Bc2 by 3 and 4 T relative to undoped samples, reaching approximately 27 T.Within the dirty-limit (l ≪ ξ0, where l is the electron mean free path and ξ0 is the BCS coherencelength) approximation of the Ginzburg–Landau–Abrikosov–Gor’kov theory [122–124], Bc2 (0) can beexpressed as Bc2(0) = 3.11× 103ρnγTc, where ρn is the residual resistivity of the normal state, γ is the10Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 9. Comparison of the segregation of Ti at a grain boundary when (a) Ti was added to Nb and (b) when Ti was added toSn. This comparison was facilitated by APT maps and elemental distribution across the grain boundary. Reproduced from [83].© IOP Publishing Ltd all rights reserved.electronic specific heat coefficient, and Tc is the critical temperature. The disproportionally large changein Bc2, as compared to Tc, is attributed to a significant increase in normal-state resistance caused by theshortening of the mean free path resulting from increased electron scattering [16, 125–127]. The optimalTi addition amount is approximately 1.5–2 at%, whereas Ta requires approximately double the concen-tration of Ti to achieve a comparable effect. The extended x-ray absorption fine structure findings byTarantini, which indicate that Ti preferentially substitutes at Nb sites more readily than Ta [88], mayexplain this discrepancy. APT analyses have further revealed that Ti does not form a complete solid solu-tion within the Nb3Sn phase; instead, trace amounts of Ti segregate at the grain boundaries [82, 83].The site of the elemental additions in the precursor wires is a critical consideration for Nb3Sn layerformation via diffusion reactions. In the internal-Sn process, Ti dissolves into the Nb3Sn phase regardlessof whether it is added to a Nb, Cu matrix or Sn core. Conversely, Ta exhibits minimal dissolution, exceptwhen added to Nb. This behavior is attributed to the lower diffusion driving force of Ta in the Sn–Taphase.Figure 9 compares the elemental concentration distributions at grain boundaries obtained via APTfor Ti doping with Nb and Ti doping within Sn cores [83]. The addition of Ti to the Sn core results inhigher Ti concentrations. Santra reported the presence of β-(Ti, Nb) at the grain boundaries in bronze-processed wires, noting that the amount of β-(Ti, Nb) is likely higher when Ti is doped into the Cu–Sn bronze than when it is added to Nb [84]. Santra further highlighted the contribution of β-(Ti, Nb)to grain refinement via the Zener pinning effect. Popova reported the presence of fine Ti6Sn5 particleswithin Nb3Sn grains when Ti doped to Nb, which may purify the grain boundaries and induce localgrain coarsening near these particles [128]. Thus, the site of Ti doping can influence both the Nb3Sngrain size and Sn diffusivity within the Nb3Sn layer.In the internal Sn method, the site of Ti addition significantly influences the interfacial reaction. Theaddition of Ti to the Sn cores represents the simplest case and is employed in JASTEC and KAT wires[25, 31]. When Ti is added to Sn cores, a distinct multinary Nb–Sn–Cu–Ti compound layer develops atthe interface [129].Figure 10 shows micrographs comparing the interfacial reaction behavior at 685 ◦C when Ti is addedto a Sn core, the Cu intermediate layer, or the Nb matrix within a Nb/Cu/Sn single-core wire [129].When Ti is added to Nb, no compound layer is observed. However, adding Ti to either the Sn core orCu layer results in the formation of a distinct Ti-containing compound layer. Recent STEM-EDS anal-yses of Nb/Cu–15Zn/Sn–1.6Ti diffusion-couple samples indicated that the composition of this com-pound corresponds to the values listed in table 2 [85]. Considering only the Nb:Sn ratio, the compoundappears stoichiometrically similar to Nb6Sn5. This quaternary compound forms at approximately 500 ◦C11Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 10. Segregation of the Ti compound at the interface between Nb3Sn and the Cu–Sn core for three Ti doping concentra-tions after heat treatment at 685 ◦C. (a) Titanium doped into Sn, (b) Ti doped into Nb, and (c) Ti doped into Cu. Titaniumdoping to Nb suppresses the formation of the Ti compound. Reprinted from [129], Copyright (2022), with permission fromElsevier.Table 2. Composition of the NbSnCuTi phase analyzed usingSTEM-EDS (at%).Nb Sn Cu(Zn) Ti38.5 33.6 13.2 14.7and decomposes at approximately 685 ◦C. Consequently, this quaternary compound clearly differs fromnausite in both composition and formation temperature [61, 75, 77].Within the Cu–Sn–Ti reaction system, a liquid phase and CuSnTi compound coexist at 572 ◦C[130]. At the Nb interface, the liquid phase facilitates Nb dissolution, which initiates the formationof NbSnCuTi compound phases. The deduced Sn chemical potential within this phase subsequentlyreduces the Sn diffusion driving force. As shown in figure 10, the thickness of the Nb3Sn layer formedin the Sn–Ti core sample decreased to approximately two-thirds of the thickness observed in the Nb–Tisheath sample, suggesting that the NbSnCuTi compound phase functions as a diffusion barrier for Sn. Incontrast to the bronze process, the internal-tin method induces grain refinement in Ti-added Nb [85].Furthermore, in multifilamentary wires, this compound phase persists as a diffusion barrier between Nbfilaments within the Nb module, which serve as Sn diffusion pathways, thereby inhibiting the diffusionof both Sn and Ti to the module center. This results in compositional inhomogeneity within the finalNb3Sn filament [25, 131].3.2. Optimization of Ti doping positionFrom the perspective of Nb3Sn layer formation, the internal-Sn method is optimized by locating the Tisource within the Nb module, a configuration currently implemented in RRP wires. In our laboratory-scale fabrications, a multifilamentary wire employing Nb alloy filaments containing 0.8 wt. % Ti exhib-ited an approximately 30% improvement in non-Cu Jc at 16 T, as compared with Ti additions to the Sncore (figure 11) [83]. Although these results were obtained from laboratory-scale samples, Ti addition toNb represents a significant potential for further enhancing superconducting performance.Furthermore, strategic placement of Ti sources within the Nb module may be achieved by substitut-ing some Nb rods with NbTi rods, as demonstrated in the RRP design, or by artificially incorporating aTi source directly into the Nb filaments, as illustrated by the structure shown in figure 7. This effect willbe discussed in detail in section 3.6.3.3. Enhancement of growth kinetics by Zn additionAmong various additive elements [132], Zn addition offers several unique advantages for microstructuralmodification not found in other elements, as follows:1. During the Cu/Sn mixing process, β-CuZn or γ-CuZn phases form at the interface, which suppressesCu diffusion into Sn and inhibits the formation of Kirkendall voids [83, 133].2. In the Nb/Cu–Zn–Sn diffusion process, the Sn chemical potential increases, which promotes thegrowth of the Nb3Sn layer [85, 134]12Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 11. Improvement of Jc through the addition of Ti to Nb in multifilamentary internal-Sn Nb3Sn wires. Cross-sectionalimages of wires with (a) Ti doping into Nb and (b) Ti doping into Sn. (c) Non-Cu Jc as a function of the magnetic field for thesewires. Reproduced from [83]. © IOP Publishing Ltd all rights reserved.Figure 12. Formation of the solid phase at the Cu–Sn reaction front with Zn addition to Cu during heat treatment at 400 ◦C.SEM-BSE images with (a) no Zn addition and (b) Zn addition. Reproduced from [83]. © IOP Publishing Ltd all rights reserved.3. Zinc remains primarily within the Cu matrix with minimal diffusion into the Nb3Sn layer, resulting insolid-solution strengthening of the Cu matrix [45, 135, 136].Figure 12 shows a micrograph illustrating the effects of Zn addition at the reaction interface afterheat treatment at 400 ◦C in a Cu/Sn single-core structure [83]. Generally, during mutual solid-state dif-fusion in the Cu/Sn system, the faster diffusion of Cu in Cu–Sn induces the Kirkendall effect, resultingin interface migration and void formation [137]. Moreover, the formation of Cu–Sn compounds inducesvolume contraction, which exacerbates void development. As shown in figure 12(a), ε-Cu3Sn forms atthe reaction front between pure Cu and Sn at 400 ◦C, accompanied by large voids; the volume contrac-tion associated with ε-phase formation is estimated to be approximately 5.3% based on density varia-tions. Previous studies reported that at 500 ◦C, the δ phase predominates and large voids persist [138].These voids can act as physical barriers to Sn diffusion, particularly in Nb modules with architecturescomprising numerous fine filaments embedded in the matrix, such as the ultra-fine multifilamentaryassemblies used in commercial wires. Conversely, the addition of Zn to Cu or Sn results in the formationof a dense CuZn phase at the interface without voids (figure 12(b)) [83, 133].13Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 13. (a) Nb3Sn layer thickness and (b) grain size as a function of the Zn composition in Cu. The layer thickness increaseswith an increasing amount of Zn, while the grain size exhibits a concave trend. Reprinted from [134], Copyright (2025), withpermission from Elsevier.3.4. Variation in the pinning force dependent on elemental concentration at the grain boundaryRecent research regarding the optimization of Zn addition have yielded intriguing results, indicating thatZn addition influences both Nb3Sn layer formation and the elemental pinning force at grain boundaries[134]. An overview of these results is provided below. The experimental samples consisted of single-corewires with a Nb/Cu/Sn diffusion-couple structure, where 10–15 wt. % Zn was added to the Cu inter-mediate layer. A wire featuring a pure Cu intermediate layer was also prepared as a reference. To elimi-nate the formation of unnecessary compound layers and isolate the effect of the Zn addition, Ti was notintroduced. The sample designations were:1. N-10Z-S: Nb/Cu-10 wt%Zn/Sn,2. N-12Z-S: Nb/Cu-12 wt%Zn/Sn,3. N-15Z-S: Nb/Cu-15 wt%Zn/Sn, and4. N–C–S: Nb/Cu/Sn.For BSE cross-sectional images at the interface following heat treatment at 650 ◦C, the reader isreferred to [134]. Figure 13(a) shows the dependence of the Nb3Sn layer thickness on the Zn content,as obtained through image analysis. The Nb3Sn layer thickness increased monotonically with an increas-ing Zn addition, suggesting that Zn enhances the Sn diffusion driving force. Conversely, the Nb3Sn grainsize, as shown in figure 13(b), did not monotonically change with an increasing Zn addition; instead, itexhibited a convex trend with a minimum observed at 10 wt. %.Figures 14(a) and (b) show the layer Jc and flux pinning characteristics per superconducting volume,respectively, derived from the magnetization curves measured using a vibrating sample magnetometerand analyzed using the critical state model [134, 139, 140]. As the Zn content increases, Bc2 tends toincrease, resulting in an enhanced Jc and pinning force under high magnetic fields. A particularly signif-icant improvement in high-field Jc characteristics occurs at 15 wt. % Zn. Microstructural observation ofthe interface confirmed that Nb6Sn5 formed during the reaction only in the 15 wt. % Zn sample. Theformation of Nb6Sn5, as detailed in section 2.1, suggests an increased Sn diffusion driving force; conse-quently, the 15 wt. % Zn concentration represents a threshold at which the reaction behavior changesrapidly. Conversely, the maximum pinning force exhibited a monotonic decrease with an increasing Zncontent (figure 14(b)). When compared to the convex relationship between the grain size and Zn con-centration shown in figure 13(b), these results indicate that the pinning characteristics do not correlatedirectly with grain boundary density. This suggests that the elemental pinning force at grain boundariesis influenced by additional factors.Examination of the Sn concentration ratio distribution within the Nb3Sn layer (figure 15(a)) [134]shows that the Sn concentration approaches stoichiometric compositions with an increasing Zn con-tent. This stoichiometric progression may account for the observed improvement in the high-field Jccharacteristics at higher Zn contents. Conversely, the average Cu concentration decreased at 10 wt. %Zn and subsequently increased with further Zn additions, as shown in figure 15(b) [134]. Figure 1614Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 14. (a) Layer Jc and (b) pinning force per superconducting volume as a function of the magnetic field with respect to theZn composition. The high-field layer increases with an increasing amount of Zn, while the maximum pinning force decreases.The pinning force values reported in [134]. contain a scaling error due to a coefficient error in the calculation; the values shownin the present figure have been corrected accordingly. The relative trends and overall conclusions are unaffected. Reprinted from[134], Copyright (2025), with permission from Elsevier.Figure 15. (a) Tin concentration ratio and Cu concentration distribution in the Nb3Sn layer [134]. The Sn concentrationincreases with an increasing amount of Zn, while the Cu concentration does not exhibit a linear trend. Reprinted from [134],Copyright (2025), with permission from Elsevier.summarizes the dependence of the maximum magnetic flux pinning force on both the grain size andCu concentration [134]. The relationship between grain size and Zn content, obtained from elec-tron backscatter diffraction (EBSD) analyses, also exhibits convex characteristics, as further detailed infigure 17. These results clearly indicate that the decrease in maximum flux pinning force with an increas-ing Zn addition correlates more significantly with Cu concentration than with grain size. APT [82–84]and STEM-EDS results [85] indicated that Cu preferentially segregates at grain boundaries. Therefore, anincrease in the average Cu concentration within the Nb3Sn layer suggests a corresponding enrichment ofCu at the grain boundaries. Based on these results, it is hypothesized that the elemental pinning force atthe grain boundaries is dependent on the Cu concentration at the grain boundaries.Grain boundary misorientation is another factor affecting the elemental pinning force at grainboundaries. Figure 17 shows the IPF maps and rotational grain boundary angle maps of the Nb3Snlayer on each sample obtained via EBSD. Cross-sectional specimens were prepared for the EBSD analysisthrough mechanical polishing using a polycrystalline diamond slurry, followed by mechanochemical pol-ishing using colloidal silica. Although the grain size approaches the resolution limit of the EBSD equip-ment (approximately 50 nm), which makes complete noise removal difficult, the overall trend indicatesthat all samples were dominated by high-angle grain boundaries with misorientation angles of approxi-mately 15◦, and no significant differences were observed among the samples. Accordingly, the contribu-tion of grain boundary misorientation to the variation in pinning force can be excluded. These resultsindicate that the anomalous elemental pinning force characteristics are primarily influenced by elementconcentrations at the grain boundaries.15Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 16. Relationship between the maximum pinning force (Fp, max), grain size of Nb3Sn, and Cu concentration in the Nb3Snlayer. The pinning characteristics do not follow a typical grain boundary pinning mechanism; instead, Fp, max correlates morewith the Cu concentration. The overall pinning characteristics are determined by the grain boundary density and elementalconcentration at the grain boundaries. The Fp, max values reported in [134] contain a scaling error due to a coefficient error in thecalculation; the values shown in the present figure have been corrected accordingly. The relative trends and overall conclusionsare unaffected. Reprinted from [134], Copyright (2025), with permission from Elsevier.Figure 17. EBSD IPFs and rotational grain boundary angle maps of (a) N–C–S, (b) N-10Z-S, (c) N-12Z-S, and (d) N-15Zn-S. Grain size analyses indicated a trend similar to that shown in figure 13(b). In all samples, grains with a misorientation angleof⩾ 5◦ are dominant.In conclusion, the overall magnetic flux pinning force is governed by two synergistic factors, namely,grain boundary density and the elemental concentration at those boundaries. As shown in figure 16, theCu concentration increases when the Zn addition exceeds 10 wt. %, while the maximum pinning forcesimultaneously decreases. This behavior likely reflects the dominant influence of grain coarsening at ele-vated Zn concentrations.Figure 16 further suggests a strong correlation between grain size and Cu concentration, where largergrain sizes occur at higher Cu concentrations. As discussed earlier, Cu diffuses along the Nb3Sn grainboundaries alongside Sn toward the reaction front, where Nb3Sn subsequently precipitates. The Cuconcentration at the grain boundaries is expected to influence the localized Sn chemical potential. Anenrichment in Cu reduces the Sn diffusion driving force, which subsequently increases the critical radiusof Nb3Sn nuclei. These experimental results demonstrate that Zn addition modifies the Cu concentration16Supercond. Sci. Technol. 39 (2026) 083002 N Bannoat the grain boundaries and serves a crucial role in both grain boundary pinning and regulation of theNb3Sn grain morphology.Previous studies have demonstrated that elemental segregation at grain boundaries affects both thegrain size and magnetic flux pinning force [84, 128, 141]. However, to the best of our knowledge, fewstudies have comprehensively examined the specific influence of elemental concentration. It remains pos-sible that the Ti concentration at Nb3Sn grain boundaries, as shown in figure 9, affects the elementalpinning force at grain boundaries. While grain refinement is traditionally the guideline for improvingJc, these results provide new insights indicating that the elemental composition at grain boundaries alsoinfluences the Jc characteristics. Further detailed investigations are required to elucidate this mechanism.3.5. Multiple elemental additionsMultiple elemental additions do not necessarily result in a simple superposition of their effects. Forexample, Mg is reportedly effective for grain refinement [142–144]. Wu employed high-resolution Augerspectroscopy to analyze bronze-processed Nb3Sn wires and reported that Mg preferentially diffuses intoNb3Sn grains rather than segregating at grain boundaries [145], although the underlying refinementmechanism has not yet been fully elucidated. Conversely, within the internal-Sn process, the addition ofTi to the Sn core may suppress the grain-refinement effect of Mg in specific instances [85]. Our groupreported [85] that heat treatment of a single-core wire with a diffusion couple, comprising a Nb fil-ament, a Cu intermediate layer co-added with 12 wt. % Zn and 0.2 wt. % Mg, and a Sn core dopedwith 1.6 wt. % Ti, at 650 ◦C resulted in the formation of a highly stable multinary compound phaseat the interface. Magnesium was entrapped within this compound phase, thereby preventing its contribu-tion to grain refinement. Similarly, although Ge doping in bronze-route Nb3Sn wires reportedly inducesNb3Sn grain refinement [146, 147], in the internal Sn process, the addition of Ti to the Sn core report-edly leads to the formation of a Ge–Ti-rich multinary compound phase at the interface [132]. To avoidsuch effects, it is necessary to carefully determine the additive location by considering the Gibbs energiesof the resulting phases, thereby ensuring that no stable, undesirable compound phases are formed.This section discusses the effective co-addition of Zn and Ti. Based on the preceding discus-sion, the combined addition of Zn to Sn and addition of Ti to Nb appears to be an optimal strat-egy for suppressing interfacial compound phase formation while maximizing Nb3Sn layer formation.Accordingly, the effect of this co-addition was demonstrated using a diffusion-couple structure consist-ing of Nb − 0.8 wt%Ti, Cu − 15 wt%Zn and Sn (NT-CZ-S). The following four single-core samples,including a reference sample [85], were prepared:1. N-C-ST: Nb/Cu /Sn − 1.6 wt%Ti,2. N-CZ-ST: Nb/Cu − 15 wt%Zn/Sn − 1.6 wt%Ti,3. NT-C-S: Nb − 0.8 wt%Ti/Cu /Sn, and4. NT-CZ-S: Nb − 0.8 wt%Ti /Cu − 15 wt%Zn/Sn.The wires had a diameter of 0.92 mm and consisted of seven modules, each containing a singleNb/Cu/Sn diffusion couple. The Sn/(Cu + Zn + Sn) compositional ratio, an important parameter gov-erning the driving force for Sn diffusion, was designed to be approximately 26 at% to avoid the forma-tion of Cu–Nb–Sn phases at the diffusion interface [148, 149]. In addition, the Nb layer was intention-ally made sufficiently thick to prevent complete reaction of the Nb during heat treatment.Figure 18 compares the SEM-EDS elemental maps (Sn and Ti overlay) of the Nb3Sn layers foreach sample after heat treatment at 650 ◦C. The addition of Zn to the Cu intermediate layer com-bined with Ti alloying in Nb maximizes the Nb3Sn layer thickness, even though the isolated qua-ternary Ti-containing compound phase remains at the Nb3Sn/Cu–Sn interface (approximatelyNb:Sn:Cu(Zn):Ti = 25:20:50:5).Figures 19(a) and (b) show the pinning force (Fp) per superconducting volume derived from themagnetization curves and the Sn compositional ratio distribution in the Nb3Sn layer, respectively.Compared with N-CZ-ST, NT-CZ-S exhibited a higher Bc2 and improved high-field Jc; however, its Fpwas lower than that of NT-C–S across the entire magnetic field range. Figure 19(b) shows that the Snconcentration gradient in NT-CZ-S was steeper than that in NT-C-S. This steeper concentration gradientis attributed to the reduced Sn diffusion driving force caused by the presence of the interfacial quater-nary phase. Such a pronounced concentration gradient may contribute to the reduced Fp in NT-CZ-S.Meanwhile, the Sn concentration near the Cu–Sn/Nb3Sn interface in NT-CZ-S remained comparableto that in NT-C-S. This observation suggests that differences in the chemical-potential gradient alone17Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 18. Overlapping elemental maps of Sn (red) and Ti (blue) for (a) N-C-ST, (b) N-CZ-ST, (c) NT-C-S and (d) NT-CZ-S. The combined addition of Zn to Cu and Ti to Nb maximizes the Nb3Sn layer formation, reducing the formation of theNbSnCuTi quaternary compound phase.Figure 19. (a) Pinning force per superconducting volume as a function of the magnetic field and (b) Sn concentration ratio inthe Nb3Sn layer for samples with different Ti doping locations.may not fully account for the steeper Sn concentration gradient observed in NT-CZ-S. According toequation (1), diffusion flux is governed by both the thermodynamic driving force and atomic mobil-ity. Therefore, the present result raises the possibility that Zn addition influences not only the thermo-dynamic driving force but also the effective mobility governing Sn transport, for example through Znsegregation at Nb3Sn grain boundaries (figure 6). A more detailed analysis, including quantitative grainsize evaluation, is currently underway, and the results will be reported in a future publication.3.6. Arrangement of Ti source in NbmodulesIn the internal-Sn method, the addition of Ti to Nb offers the potential to enhance the performance ofNb3Sn wires. When introducing the Ti source into Nb modules, Ti may be uniformly alloyed with theNb filaments; alternatively, isolated Ti sources may be distributeabled within the Nb module, as observedin RRP-type wire designs. Additionally, a double-layered structure for each Nb filament is conceivable,wherein a Ti source is artificially placed at the center of the filament. Here, two types of laboratory-scalemultifilamentary wires with distinct Ti addition configurations were prepared. The sample featuring Tiuniformly alloyed with Nb was designated as Multi-NT-CZ-S, while the sample with Nb − 47 wt%Tipositioned at the Nb filament center was designated as Multi-NNT-CZ-S. Figure 20 shows cross-sectionalSEM images of the precursor wires, and table 3 summarizes their specifications. The subsequent sectionsdescribe and discuss the changes in Nb3Sn layer formation and the resulting superconducting character-istics. Both samples employed cross-sectional assemblies similar to those of DT-type wires, with 15 wt.% Zn added to the Cu matrix.18Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 20. Cross-sectional SEM images of as-drawn (a) Multi-NT-CZ-S and (b) Multi-NNT-CZ-S wires. Multi-NNT-CZ-S wasassembled with Sn cores and Nb modules composed of Nb filaments artificially incorporated with Nb−47 wt%Ti.Table 3. Specifications of DT-type Nb3Sn precursor wires with different Ti dopingconfigurations to the Nb filament.Multi-NT-CZ-S Multi-NNT-CZ-SWire diameter (mm) 0.7 0.7Nb module diameter (µm) 49.7 49.7No of Nb modules 12 12No of Nb filament in the module 19 19Nb filament diameter (µm)) 9.3 9.3No of Sn modules 7 7Sn core diameter (µm) 42.2 42.2Ti/(Nb+ Ti) ratio (wt%) 0.8 1.62Figures 21(a) and (b) show cross-sectional SEM images of the Nb3Sn module following reactionat 650 ◦C. In both instances, the absence of multinary compound phases between the Nb filaments,which serve as Sn diffusion pathways, suggests that smooth Sn diffusion occurred. However, the reactionmicrostructure revealed significant differences. The Nb filaments with uniform Ti doping (Multi-NT-CZ-S) failed to undergo full reaction, leaving unreacted Nb at the center. In contrast, Multi-NNT-CZ-Sreceived a sufficient Sn supply to the filament center. This phenomenon is attributed to the enhanced Sndiffusion kinetics driven by the mutual diffusion between Cu and Ti as shown in figure 6. Figures 21(c)and (d) plot the radial distribution of the Sn concentration ratio (Sn/(Nb + Sn + Ti)) and the Ti con-centration within the Nb3Sn layer for each sample. EDS analysis identified the contrast observed at thecenter of the Multi-NNT-CZ-S sample as a multinary compound phase of Nb − Sn − Ti − Cu(Zn)resulting from the reaction between Sn and residual NbTiCu compounds. Multi-NNT-CZ-S seem-ingly achieved Sn concentration ratios closer to the stoichiometric composition, as compared withMulti-NT-CZ-S.Figures 22(a) and (b) show the magnetic field dependence and the reaction temperature depen-dence of the non-Cu Jc for each sample heat-treated at 650 ◦C, respectively. Following heat treatment at650 ◦C, Multi-NNT-CZ exhibited significantly higher Jc properties than Multi-NT-CZ-S. Given that thegrain sizes evaluated from the fracture surfaces were approximately 125 nm for both Multi-NT-CZ-S andMulti-NNT-CZ-S, the observed difference in Jc is primarily attributed to differences in the stoichiome-try of the formed Nb3Sn. The comparable Nb3Sn grain sizes in both samples imply that the Sn chemicalpotential at the Cu–Sn site was also similar. Consequently, the lower stoichiometry of the Nb3Sn layerin Multi-NT-CZ-S results mainly from reduced Sn diffusion kinetics. This behavior is likely associatedwith the absence of Cu–Ti mutual diffusion. Additionally, the segregation of Ti-related compounds dur-ing the early stage of grain boundary diffusion as shown in figure 18(d) is considered to influence the Sndiffusion kinetics [84, 128].19Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 21. SEM-BSE images of the Nb modules in (a) Multi-NT-CZ-S and (b) Multi-NNT-CZ-S after reaction at 650 ◦C for150 h. Concentration distributions of (c) Sn and (d) Ti in the Nb3Sn filaments. The yellow line indicates the EDS analysis line.Figure 22. (a) Non-Cu Jc ersus magnetic field of Multi-NT-CZ-S and Multi-NNT-CZ-S reacted at 650 ◦C for 250 h and 4.2 Kand (b) temperature dependence of non-Cu Jc at 16 T for both wires.3.7. Elemental doping to Sn coreIn the internal Sn method, the necessity of drawing composite wires comprising materials with markedlydifferent hardnesses constitutes a major challenge for industrial applications. One approach to enhancingthe hardness balance involves increasing the hardness and homogeneity of the Sn core. Alloying elementssuch as Zn, Cu, Ti and Mg can be introduced to achieve a relatively uniform dispersion of precipitatesduring casting under near-thermodynamic equilibrium conditions [76, 133, 150, 151]. Copper readilyforms intermetallic compounds with Sn, and the η and ε phases tend to grow during solidification; how-ever, at concentrations up to approximately 20 wt. % Cu, a microstructure featuring a finely dispersedη phase can be obtained (figure 23(a)) [151]. Regarding Ti additions, stable Ti6Sn5 precipitates are dis-persed throughout the core, although a tendency toward coarsening is observed (figure 23(b)). A notablecharacteristic of Zn addition is its complete immiscibility with Sn, which results in a uniform dispersionof Zn after melting and drawing (figure 23(c)). The co-addition of Cu is effective for further refiningand homogenizing the dispersion (figure 23(d)). However, an increase in the relative Zn ratio is likely toincrease the size of the precipitated particles (figure 23(e)). Copper preferentially bonds with Zn ratherthan Sn, leading to the formation of Cu–Zn compounds. Even at a total Cu + Zn content of 50 wt. %,these compounds form preferentially, yielding a dispersed microstructure devoid of significant precipitate20Supercond. Sci. Technol. 39 (2026) 083002 N BannoFigure 23.Microstructure of Sn cores with different additive elements: (a) 20 wt%Cu, (b) 1.6 wt%Ti, (c) 20 wt%Zn, (d)20 wt%Cu−5 wt%Zn, and (e) 5 wt%Cu−5 wt%Zn. © (2025) IEEE. Reprinted, with permission, from [151].crystal growth [151]. From the perspective of homogenization, previous research indicates that atomizedSn–Cu–Ti powders can be consolidated via cold isostatic pressing [31].The Vickers hardness of Sn is approximately 7.5 HV [152], whereas that of Sn–20at%Cu, Sn–3.9at%Ti (Sn–1.6 wt%Ti), Sn–31at%Zn (Sn–20 wt%Zn), Sn–20at%Cu–5at% Zn, and Sn–5at%Cu–5at%Zn increases to approximately 19.4, 11, 20.7, 22.6, and 11 HV, respectively. Ensuring a sufficientSn content in the core is essential for promoting Nb3Sn layer formation, and thus future studies shouldfocus on detailed investigations of alloying elements and compositions that enable sufficient hardnessenhancement with reduced addition levels.4. Summary: perspective for high-performance Nb3Sn wiresTable 4 summarizes the representative additive elements discussed throughout this review and their prin-cipal effects on Nb–Sn diffusion reactions.In light of the FCC project and the recent move toward compact DEMO reactors, Nb3Sn wires fea-turing superior Jc performance fabricated via the internal Sn method are essential for achieving superiorcoil magnetic field performance under space-limited conditions. Concurrently, these applications increas-ingly require enhanced mechanical strength to withstand extreme electromagnetic force environments. Ifhybrid designs employing both high-performance Nb3Sn wires and bronze-route wires prove feasible forNb3Sn coils, sustained demand for high-strength bronze-route Nb3Sn wires is anticipated [26, 43, 153].Furthermore, applications requiring fast magnetic field ramping, including the FCC-hh and tokamakmagnets, necessitate the mitigation of hysteresis losses. This can be realized through the further reduc-tion of the effective filament diameter and lowering of low-field Jc [27, 154, 155]. From a stability per-spective, increasing the specific heat of the conductor to mitigate temperature rise is also considered aneffective strategy [156, 157].Accordingly, the future development of Nb3Sn wires demands not only the further enhancement ofJc but also increased multifunctionality. Achieving these goals requires a comprehensive approach to themicrostructural control of all constituent materials within the conductor, rather than focusing exclu-sively on Nb3Sn phase formation. Elemental additions constitute a primary strategy for comprehensivemicrostructural control and, when applied with a thorough fundamental understanding, are expected tofacilitate the realization of high-performance Nb3Sn wires with novel and advanced functionalities.The key topics regarding the elemental additions discussed in this paper and their implications forfuture conductor development are summarized as follows:1. Control of the Sn chemical potential through Cu addition.→ Efficient Nb3Sn layer formation requires a high Sn chemical potential while maintaining the Sncontent in the Cu–Sn matrix below 25 at%, thereby suppressing the formation of Sn-rich Nb–Sn com-pounds and facilitating Sn transport toward the growing Nb3Sn layer.21Supercond. Sci. Technol. 39 (2026) 083002 N BannoTable 4. Representative additive elements discussed in this review and their principal effects on Nb–Sn diffusion reactions.Element RemarkCu Reduces Sn chemical potential, destabilizes Sn-rich Nb–Sn intermediate phases, suppresses their formation,and facilitates Sn diffusion during Nb3Sn layer growth.Ti Enhances Bc2 of Nb3Sn. Ti source location is critical because Ti additions on the Sn side promote interfacialNb–Sn–Cu–Ti compound formation, while Ti additions on the Nb side suppress these phases and improvelayer homogeneity.Ta Enhances Bc2 of Nb3Sn. Approximately twice the Ta concentration is required to achieve a comparable effectto Ti because Ta substitutes for Nb sites less readily. Owing to its limited diffusivity, Ta is generally added tothe Nb precursor.Zn Increases the Sn diffusion driving force and alters grain-boundary composition, thereby modifyinggrain-boundary elemental pinning characteristics.Zr Forms oxide nanoparticles through internal oxidation, leading to grain refinement via the Zener pinningeffect.Hf Increases the recrystallization resistance of Nb, promotes grain refinement, and contributes to higher Jc.Similar to Zr, Hf can also form oxide nanoparticles through internal oxidation, resulting inZener-pinning-induced grain refinement.Mg Reported to promote Nb3Sn grain refinement. Its effectiveness may depend strongly on conductorarchitecture because Mg can be incorporated into interfacial quaternary compounds when added togetherwith Ti on the Sn side.2. The Sn concentration gradient within the Nb3Sn layer originating from the slow bulk diffusion of Sn.→ Minimizing the Nb/Sn diffusion distance in the precursor is an effective strategy for reducing theSn concentration gradient and improving Nb3Sn layer homogeneity.3. Copper diffusion at Nb3Sn and Nb grain boundaries.4. Changes in pinning force and grain size at Nb3Sn grain boundaries induced by grain-boundary Cuconcentration (Zn addition is discussed as a representative example).→ Grain-boundary Cu concentration may be controlled through elemental-addition strategies, provid-ing a potential route to optimize grain-boundary pinning and grain-size control.5. Variation in interfacial compound phase formation depending on the Ti addition site.→ Thermodynamic assessment of possible interfacial compound phases is essential prior to elementaladdition, since such phases can significantly alter diffusion pathways, reaction kinetics, and Nb3Snlayer formation. The Ti-addition example demonstrates that introducing Ti from the Nb-module sideis preferable because it minimizes the formation of undesirable interfacial compound phases.6. Effective strategies for multielement addition.→ The Zn-addition example demonstrates that conductor optimization should not focus exclusivelyon the Nb3Sn layer. Zn addition is also effective in suppressing void formation during the Cu–Sninterdiffusion stage. Comprehensive microstructural control of both the Nb3Sn layer and the sur-rounding matrix is essential for achieving multifunctional conductor performance.7. Fundamental theories of nucleation and grain growth.→ Grain refinement can be promoted by increasing the thermodynamic driving force for nucleation.From this perspective, increasing the Sn chemical potential and introducing internal strain energy arepromising approaches for enhancing nucleation frequency and refining the Nb3Sn grain structure. Inaddition, the ability of additive elements to provide a Zener pinning effect should also be considered,since suppression of grain growth is equally important for achieving fine-grained microstructures.8. Strengthening of the Sn core through elemental additions.→ Improved wire drawability requires fine and homogeneous compound dispersions while minimiz-ing the formation of coarse brittle phases.Despite substantial progress in understanding Nb3Sn layer formation, several important scientificquestions remain unresolved.First, the relationship between grain-boundary chemistry and elemental pinning behavior remainspoorly understood. A quantitative understanding of this relationship may provide important guidelinesfor maximizing grain-boundary pinning and further enhancing Jc.Second, the effects of elemental additions on Nb3Sn layer formation, including diffusion drivingforce, diffusion kinetics, and microstructural evolution, require further clarification. Similar challenges22Supercond. Sci. Technol. 39 (2026) 083002 N Bannoexist in the design of high-strength matrix materials. Additional beneficial elements may remain undis-covered, and the exploration of such effects is expected to benefit significantly from thermodynamicdatabases, CALPHAD-based calculations, diffusion simulations, and AI-assisted materials design.Third, although APC conductors have demonstrated outstanding superconducting performance, fur-ther understanding of the underlying mechanisms remains desirable, including the respective roles ofgrain refinement and direct nanoparticle pinning, as well as the optimization of nanoparticle precipita-tion conditions, size, and density. Furthermore, whether APC concepts can be generalized beyond cur-rent internal-oxidation-based PIT conductors and successfully implemented in other Nb3Sn conductorarchitectures remains an open question. 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Introduction 2. Fundamental issues in Nb3Sn layer formation 2.1. Role of Cu in the Sn diffusion driving force 2.2. Nb3Sn growth kinetics 2.3. Copper diffusion through Nb3Sn and Nb grain boundaries 2.4. Nucleation and grain growth: grain refinement and formation of APCs 3. Effect of elemental additions 3.1. Variation in the Nb3Sn phase formation behavior depending on the Ti addition site 3.2. Optimization of Ti doping position 3.3. Enhancement of growth kinetics by Zn addition 3.4. Variation in the pinning force dependent on elemental concentration at the grain boundary 3.5. Multiple elemental additions 3.6. Arrangement of Ti source in Nb modules 3.7. Elemental doping to Sn core 4. Summary: perspective for high-performance Nb3Sn wires References