Contents
1. Introduction..................................................................................................... 2
2. Nb3Sn.......................................................................................................... 3
2.1. Formation of Nb3Sn.......................................................................................... 3
2.1.1. Diffusion behavior of Nb3Sn in the presence of a small amount of Cu................................................ 4
2.1.2. Reaction behaviors of Nb3Sn wires in practical processes......................................................... 5
2.1.3. Interpretation of the reaction behavior of Nb3Sn in terms of Sn chemical potential...................................... 6
2.2. Potential for performance improvement............................................................................ 7
2.3. Effect of element addition on the formation behavior of Nb3Sn........................................................... 8
2.3.1. Grain refinement via internal oxidation of the parent Nb-Zr phase [14,15,113]......................................... 8
2.3.2. Grain refinement by the addition of Hf to the Nb parent phase..................................................... 8
2.3.3. Doping of Ti and Ta into Nb3Sn........................................................................... 10
2.3.4. Impact of Ti doping position on the formation of the Nb3Sn layer.................................................. 11
2.3.5. Strengthening of the matrix by element addition.............................................................. 12
3. Nb3Al.......................................................................................................... 12
3.1. Basic formation of Nb3Al....................................................................................... 12
3.1.1. Early days of Nb3Al research............................................................................. 12
3.1.2. Metastable reaction control at low temperatures............................................................... 12
3.1.3. Advanced transformation................................................................................ 14
3.2. Microstructural control of transformation-processed Nb3Al.............................................................. 15
3.3. Strain properties............................................................................................. 17
4. NbTi and Nb-alloy superconductors.................................................................................... 17
4.1. Microstructural control of NbTi.................................................................................. 18
4.2. Alternative artificial pinning in NbTi.............................................................................. 18
4.3. Application of HTT Nb-alloy superconductors in superconducting joints.................................................... 19
5. Summary........................................................................................................ 19
Declaration of Competing Interest..................................................................................... 19
Appendix A. Supplementary material..................................................................................... 19
References...................................................................................................... 19
1. Introduction
Low-temperature superconductors are typically defined as materials with critical temperature (Tc) values lower than approximately 20 K, which is the storage temperature of liquid H2. Nb-based superconductors, such as Nb3Sn and NbTi, and superconducting solders, including PbBi, are representative low-temperature superconductors. Liquid H2 has attracted attention due to its potential for realizing C neutrality. Thus, high-temperature superconductors whose Tc values are higher than the storage temperature of liquid H2 are of significant interest. However, superconductors that play important roles in almost all the high-field magnet applications, such as nuclear magnetic resonance (NMR) spectroscopy in biological science, medical magnetic resonance imaging (MRI) systems, high-speed magnetic levitation (Maglev) trains, fusion reactors, and accelerator magnets for high-energy physics, are low-temperature superconductors. Particularly, Nb3Sn exhibits substantial potential for performance improvement from the viewpoint of a gap between the actual microstructure and an ideal microstructure that maximizes flux pinning properties. Therefore, the improvement in the properties of low-temperature superconductors can lead to significant economic benefits, for example, compactness of the superconducting systems and saving of the operating costs in the cases of high-technology superconducting systems. Furthermore, He-free operation in certain applications is of environmental interest from the viewpoint of preservation of rare He also for A15-type superconductors, such as Nb3Sn.
Physical properties and growth kinetics of Nb3Sn have been reviewed by numerous prominent researchers. Echarri described fundamental characteristics of Nb3Sn during the early days of the emergence of Nb3Sn wires with multifilament assemblies [1]. He introduced the history of the discovery of A15-type superconductors (for instance, Nb3Sn) and their future applications such as in power transmissions. Binary Nb-Sn equilibrium phase diagram, diffusion rate, and coherence length were also reviewed. Dew-Hughes comprehensively described A15-type superconductors and discussed the potential limits of Tc and critical magnetic field, Bc2, in terms of interatomic distances and long-range atomic orders (LROs) [2]. Furthermore, he mentioned the basic pinning theory and provided substantial knowledge on the fundamental physical properties of A15-type superconductors. Suenaga reported several studies and reviews on the growth kinetics of the bronze method [3], [4], [5] and intrinsic physical properties of bronze-processed Nb3Sn [6], and his contributions have considerably benefited metallurgical scientists. Tachikawa invented the basic concept of the bronze method [7], [8] and developed interesting metallurgical processes of Nb3Sn from various new perspectives. Flükiger systematically discussed Tc, Bc2, and strain sensitivity from several viewpoints, specifically from the point of view of LRO [9], [10]. Moreover, he comprehensively reviewed martensitic transformation at approximately stoichiometric composition of binary Nb3Sn bulk. This crystallographic discussion offered a systematic understanding of Nb3Sn crystals. Powder-in-tube (PIT) process using Sn-based powders is another route for the synthesis of Nb3Sn, which is different from the bronze method and has been comprehensively reviewed by Godeke [11]. Additionally, he systematically discussed the general scaling law for physical properties and the performance boundary [12], [13]. Furthermore, significant contributions from many other researchers have laid the foundation for the current development of Nb3Sn wires.
Material scientists are focused on further deepening their understanding of the formation mechanism of Nb3Sn and thus realizing higher-performance Nb3Sn wires. After comprehensive optimization of the crystal growth kinetics and geometries of Nb3Sn wires, the performances of these wires in practical processes reached the limit until approximately 10 years ago. However, recently, some new breakthrough methods have been reported for grain refinement, which have attracted the interests of material scientists [14], [15], [16]. Moreover, recently, a substantial amount of new information has been obtained to broaden the understanding of the development behavior of Nb3Sn. Thus, the advancement of Nb3Sn is entering a new stage.
In this review, initially, growth kinetics of Nb/Sn diffusion and Nb3Sn development behavior during Nb/Sn diffusion are discussed. Since the discovery of the bronze method [7], [17], various routes have been explored for the fabrication of Nb3Sn. All recent practical routes for the synthesis of Nb3Sn need Cu addition. Cu plays a decisive role in formation reactions. Hence, as an example, herein, the effect of Cu addition on Nb3Sn development and the results of Nb/Sn diffusion experiments conducted in the presence of a small amount of Cu are demonstrated, and representative Nb3Sn formation behaviors are schematically summarized. These behaviors are qualitatively reviewed in terms of Sn chemical potential.
Subsequently, grain refinement mechanisms during artificial pinning [14], [15] and the incorporation of Hf into the Nb parent phase [16] are reviewed. Then, recent topics on the additions of Ti and Ta to Nb3Sn wires are introduced [18], [19]. The impact of the position of Ti doping in the Nb3Sn precursor wire on Nb/Sn diffusion is also discussed [20], [21]. Element doping is used not only as one of the effective techniques for Nb3Sn microstructural control, but also to impart certain functions (for example, high resistances of filament interfaces [22], [23], [24], [25], [26] and solid-solution strengthening of the matrix [27], [28], [29], [30], [31]), to Nb3Sn wires. Strengthening of the matrix of the Nb3Sn wire by element addition, which is of interest in large-magnet applications such as nuclear fusion and particle acceleration, is also outlined in this review [30], [31].
Nb3Al not only has essentially higher Tc and Bc2 than those of Nb3Sn (Tc and Bc2,4.2 K are 18.9 K and 29.5 T, respectively) [2], [32], but also exhibits lower strain sensitivity than that of Nb3Sn [10], [33]. Therefore, Nb3Al is expected to be employed in nuclear fusion magnets, in which significantly high electromagnetic forces are applied to the conductors [34], [35], [36], [37], [38], [39]. The fundamental features of Nb3Al were comprehensively reviewed by Takeuchi [40], [41]. Research on this material has steadily progressed with the development of Nb3Sn. Although Nb3Al wire materials have been constructed for practical applications, these materials did not reach the level of mass production. This is because achieving a stoichiometric composition of Nb3Al is inherently difficult, rendering the industrialization of Nb3Al challenging. Nevertheless, because of the high application potential of Nb3Al, the recent results achieved on the phase formation mechanism and microstructural control of this material are presented in this review.
In contrast, NbTi is an adequately investigated superconductor [42], [43]. Although Bc2 of optimized NbTi is approximately 11.5T [44], considerably lower than that of Nb3Sn, the ductility of NbTi is an attractive feature for many manufacturers, and thus, NbTi is used in major superconducting devices including MRI machines, Maglev vehicles, accelerators, and fusion magnets. Larbalestier and Lee have reported many studies and reviews on the development history and microstructure formation and control of NbTi, significantly contributing to the progress of NbTi [45], [46]. Accordingly, this review focuses on the fundamental microstructural control of NbTi and introduces some unique studies of Nb alloys. Precipitation of α-Ti is particularly important for magnetic flux pinning (Fp) in NbTi wires. Herein, initially, the microstructural control of NbTi is briefly summarized. Thereafter, a recently reported exceptional method of incorporating artificial nanoscale oxide pins into NbTi is introduced [47]. Additionally, a unique study of the application of high-temperature-tolerable (HTT) superconducting Nb alloys in superconducting joints between NbTi and Nb3Sn wires is presented [48].
2. Nb3Sn
Nb3Sn was discovered by Matthias et al. at Bell Laboratories in 1954 [49]. Tc and Bc2 of Nb3Sn are approximately 18 K and 30 T, respectively [9], and Nb3Sn is a major high-field superconductor for applications, including high-field NMR systems, nuclear fusion reactors, high-energy particle accelerators, and general-purpose high-field magnets for laboratories, where magnetic fields of over 10 T are employed. Nb3Sn belongs to the A15-type compounds according to the Strukturbericht classification [50]. A15-type compounds are sometimes called β-W-type compounds because the A15-type crystalline structure was initially reported to be the β-W structure: as β-W is a single-element system, at first, it was classified as an A-type compound. Thereafter, β-W was confirmed to be a misidentification of W3O, and therefore, it should have been categorized as an XmYn-type compound belonging to D-type compounds. Indeed, many attempts were made by crystallographers to rename β-W as the Cr3Si phase for A15-type compounds [2]; however, these attempts were unsuccessful. Interestingly, β-W was subsequently found to actually exist as a metastable phase [51].
Crystal structure of A15 Nb3Sn comprises two Nb atoms arranged in each lattice plane, and these Nb atoms form orthogonal chains along the three [100] directions (Fig. 1). From the viewpoint of long-range order, maintaining the integrity of this atomic arrangement is significantly important for obtaining higher Tc [2], [52]. Due to this Nb chain structure, Nb3Sn crystals exhibit superconducting properties without anisotropy. Furthermore, V3Si [53], [54], V3Ga [55], and Nb3Al [56] belong to this group of superconductors. Coherence length of Nb3Sn is approximately 3 nm, and the thickness of the Nb3Sn grain boundary (GB) is approximately 2 nm (in the cases of both Nb3Sn fabricated by the bronze method [57] and Nb3Sn synthesized by the internal Sn method [58]). Fig. 2 shows a representative three-dimensional atom probe tomography (3D-APT) image of Nb3Sn grains [58]. Unlike the cases of oxide superconductors, no weak link problem is noticed at the GBs of Nb3Sn, and thus, the GBs act as effective flux pinning centers. Therefore, most conventional research approaches related to the improvements of the superconducting performances of Nb3Sn wires involve quality modifications of the lattice constants, long-range orderings, and composition gradients of Nb3Sn grains and layers and enhancement of GB densities, increasing the number of flux pinning centers owing to grain refinement. Additionally, recently, Xu has reviewed the internal oxidation of the Nb parent phase [14], [15], and precipitation of nanoscale heterogeneous phases as artificial pins has been recognized as a crucial controlling factor for improving critical current density, Jc [59].
Fig. 1. Crystal structure of A15 Nb3Sn. Space group: Pm3n; A15 Nb3Sn is a primitive lattice, having mirror planes perpendicular to the [001] direction, three-fold rotational symmetry in the [111] direction, and n-glide planes perpendicular to the [110] direction. Wyckoff position 6c: Nb and 2a position: Sn. V3Si, V3Ga, and Nb3Al also belong to this crystal structure. |
Fig. 2. Representative three-dimensional atom probe tomography (3D-APT) image of Nb3Sn grains in an internal Sn wire [58]. |
2.1. Formation of Nb3Sn
Presently, the Nb3Sn layer is rarely synthesized directly via binary diffusion between Nb and Sn. Most practical strategies of Nb3Sn layer formation are based on the bronze method or a similar concept. The bronze method is a manufacturing method that promotes the growth of Nb3Sn (or V3Ga) layer at the reaction interface via interdiffusion between transition elements, such as Nb (or V), and Cu-Sn (or Cu-Ga) alloys [4], [7], [17], [60]. From the viewpoint of diffusion, Cu should also be considered an additive element even if it does not dissolve Nb3Sn. The practical reactions can be roughly classified according to the content of Cu (rather than that of Sn) in the mixed core of Sn and Cu. The formation behaviors of Nb3Sn were substantially different for each Cu content. Comparing and summarizing the development of Nb3Sn based on the Cu content in the mixed core should be of significant help in understanding the formation of Nb3Sn. Recently, the development behavior of Nb3Sn in practical processes has been clarified via systematic microstructural observations and synchrotron X-ray diffraction measurements, and sufficient information has been acquired to review the formation of Nb3Sn. According to these data, the effect of Cu addition to Nb3Sn on Nb/Sn diffusion is outlined here.
2.1.1. Diffusion behavior of Nb3Sn in the presence of a small amount of Cu
Generally, the approaches for the synthesis of Nb3Sn layer are categorized into the bronze (Nb/Cu-Sn alloy diffusion), internal Sn (Nb/Cu/Sn diffusion), and PIT (Nb/NbSn2 + Sn + Cu diffusion) methods [61], [62], [63], [64], [65], [66]. The internal Sn method is further subdivided into single-barrier internal Sn process [67], [68], Bruker OST restacked-rod process (RRP, multi-barrier internal Sn process) [69], Hyper Tech’s tube-type method [70], and distributed Sn (DT) method [71], [72]. Herein, referring to the design parameters reported in the literatures, the typical Cu contents in the cores (or submodules) of the samples prepared using the bronze method, RRP, tube-type method, and PIT method were calculated to be approximately 90 [73], 63 [74], [75], 36 [70], and 37 at%, respectively; in the case of the PIT method, 10 wt% Cu was added to NbSn2, and the Cu content was evaluated based on the Cu/(Cu + Sn) ratio [11], [62], [76]. Furthermore, in the case of RRP, Sn in the core and Cu at the Sn perimeter and in the Cu-Nb rod package were used for calculation.
At first, via a simple experiment, the events that occur during Nb/Sn diffusion when a small amount of Cu is added to the Sn side are demonstrated [77]. For simplification, plate-like diffusion couples of Nb and Sn-Cu were prepared. Initially, pure Sn and Sn-10at%Cu fabricated using an induction heating furnace were separately cold-worked into cylinders (outer diameters = 2.8 mm) and inserted into Nb tubes (outer/inner diameters = 5.8 mm/3 mm) with outer Cu tubes (outer/inner diameters = 8 mm/6 mm). The resulting composites were cold-drawn to single-core wires with diameters of 1.09 mm and flat-rolled into tapes with thicknesses of 0.2 mm. By chemically etching the Cu skins with nitric acid, samples with Nb/Sn diffusion couple structures on both sides were obtained. Next, the samples were heat-treated at 650 °C for 100 h (heating rate = 650 °C/4h), withdrawn at specific temperatures and times, and quenched with water. Each sample was encased in a glass tube with Ar gas during heat treatment. The reaction interfaces were analyzed by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) to determine the formed phases.
Fig. 3 depicts a comparison of phase changes in both samples. In the Cu-free sample, Nb was corroded by molten Sn at approximately 600 °C, and a thin phase (NbSn2) appeared at the interface. During holding at 650 °C, Sn diffused toward Nb, and NbSn2 grew. After 50 h, NbSn2 was also noticed inside the Sn side because NbSn2 grew inward into the Sn side. Even after 100 h, only NbSn2 continuously grew, and neither Nb6Sn5 nor Nb3Sn was developed.
Fig. 3. Scanning electron microscopy (SEM) images showing phase formation at the reaction interface for (a) Nb/Sn and (b) Nb/Sn-10at%Cu diffusion reactions. The yellow dotted lines are auxiliary lines used to clearly represent phase boundaries. |
When 10 at% Cu was introduced into Sn, island-like η-CuSn phases (Cu6Sn5), which were formed during melting, grew in Sn-10at%Cu during heating. At approximately 600 °C, Nb was corroded and NbSn2 developed at the Nb/Sn-Cu interface. At the initial stage of holding at 650 °C, NbSn2 began to grow. After heat treatment at 650 °C for 10 h, a large amount of Sn diffused toward the Nb side via the NbSn2 layer, and Nb6Sn5 started to form at the Nb/NbSn2 interface. Nb6Sn5 developed on the Nb side was very dense. SEM image of the microstructure formed after heat treatment at 650 °C for 10 h (650 °C/10 h) exhibited a strong contrast between Nb6Sn5 and NbSn2, where Cu at high concentrations was detected by EDS. This suggested that Cu also diffused to the reaction front with the growths of NbSn2 and Nb6Sn5. Lefranc et al. have clarified that Cu destabilizes NbSn2 and Nb6Sn5 [78], which implies that Cu also promotes reactions including Nb/NbSn2 → Nb6Sn5. According to the EDS results, this Cu-rich phase had an approximate composition of Nb-30at%Sn-60at%Cu. Furthermore, this phase is always located next to Nb6Sn5. Based on the phase diagram of Cu-Nb-Sn [79], [80], NbSn2 coexists with Nb6Sn5 and the Cu-Sn liquid phase at 588 and 670 °C, respectively. Therefore, this Cu-rich phase is deduced to be some Cu-rich liquid phase rather than Nausite.
At 650 °C/20 h, Nb6Sn5 further grew. Additionally, NbSn2 clearly decomposed into Nb6Sn5 and the Cu-Sn liquid phase, which acts as a Sn source for the formation of more Nb6Sn5 at the reaction front. At 650 °C/50 h, NbSn2 completely disintegrated into Nb6Sn5, and thin Nb3Sn began to develop at the Nb/Nb6Sn5 interface. At 650 °C/100 h, Nb3Sn grew thicker. Nevertheless, Nb6Sn5 remained thick.
Thus, notably, the addition of a small amount of Cu to the Sn core considerably changes the formation behavior of Nb3Sn, and a thick Nb3Sn layer is produced upon heat treatment, even at approximately 650 °C.
2.1.2. Reaction behaviors of Nb3Sn wires in practical processes
Recently, the reaction behaviors of Nb3Sn wires in practical processes have been revealed by detailed microstructural observations, in situ synchrotron X-ray diffraction measurements, and thermal analyses [81], [82], [83], [84], [85], [86], [87], [88], [89]. Fig. 4 shows the schematics of the designed cross-sections of representative unheated practical Nb3Sn wires. As the annealing conditions, including the heating rate and holding time, of Nb3Sn wires were different, a unified comparison could not be drawn; consequently, approximate qualitative reaction behaviors of Nb3Sn wires were demonstrated. Fig. 5 depicts a brief summary of the formation history of Nb3Sn at the reaction interface. For detailed microstructural changes, please refer to the individual studies cited in the figure.
Fig. 4. Schematics of the designed cross-sections of representative practical Nb3Sn wires before heat treatment: Nb3Sn wires synthesized by the (a) bronze method, (b) tube-type method, (c) powder-in-tube (PIT) method, and (d) restacked-rod process (RRP). |
(a)The bronze method
In the bronze method, Nb3Sn layer is directly developed at the interface between Nb filaments and Cu-Sn matrix. As the diffusion rate of Sn is substantially higher than that of Nb [90], [91], the Nb3Sn layer mainly forms on the Nb side. However, because of the solid solubility limit of Sn in Cu, a sufficient amount of Sn cannot be supplied, leaving unreacted Nb region in the filament. Uglietti et al. systematically observed the microstructure of the Nb3Sn layer and confirmed the following findings [81]. At first, crystal grains with sizes 50 nm or less are formed at the reaction interface followed by the growth of columnar crystals. Subsequently, the columnar phase decomposes into equiaxed grains, and the equiaxed grain region expands. Nevertheless, the columnar phase remains in the Nb3Sn layer until the end of heat treatment. Via electron backscatter diffraction (EBSD), Santra et al. demonstrated that the internal strain of the Nb3Sn layer was relaxed during the decomposition of the columnar phase into equiaxed grains [92].
(b)Tube-type method
Thereafter, the reaction behaviors of Nb3Sn formed by the tube-type method with a relatively simple diffusion couple structure were examined [88]. In the tube-type method, the submodule has a simple three-layer structure (Nb/Cu/Sn). Toward the beginning of the temperature increase to 600 °C, η-Cu6Sn5 develops. Then, at 400 °C, Nb is corroded in the core, generating the compound Cu-Nb-Sn (reportedly, Cu-20at%Nb-70at%Sn, as determined by EDS [88]) at the reaction interface. With further progress of the reaction, ɛ-Cu3Sn forms in the core, and Cu-Nb-Sn grows at the reaction interface. Moreover, at 550 °C, a thin NbSn2 layer appears at the reaction front. With the diffusion of Sn, NbSn2 grows, and the Cu-Nb-Sn layer eventually transforms into a NbSn2 layer. At 650 °C/0h, Nb6Sn5 is produced at the reaction front. At 650 °C/2h, upon further diffusion of Sn, Nb3Sn appears and grows at the reaction front. Finally, at 650 °C/48-200 h, Nb6Sn5 converts into Nb3Sn with a decrease in the Sn concentration in Nb6Sn5. Here, note that Nb3Sn originated from Nb6Sn5 has coarse grains and less intergranular connections, and it hardly contributes to Jc [93]. Increase in the areas of these coarse Nb3Sn grains is a serious problem in the tube-type method.
(c)PIT method
The PIT method involving the use of NbSn2 powder was developed by the Netherlands Energy Research Foundation (ECN) (the first report was on the synthesis of V3Ga using V2Ga3 powder) and then acquired by ShapeMetal Innovation followed by Bruker EAS [11], [61], [62], [87]. Cu5Sn4 powder can also be employed as a Sn source [66]. The submodules for this method are relatively simple and typically have the diffusion interface structure Nb/Cu/NbSn2 + Sn + Cu [13]. The basic interfacial phase generation is the same as that in the tube-type method [86]. Cu is essential even in the PIT method, and at least 3 at% Cu is required to form Nb3Sn [76]. Initially, a Nb-Cu-Sn layer develops, which is called Nausite [82], [94] and has the composition (Nb0.75Cu0.25)Sn2 [95]. Ultimately, fine Nb3Sn is generated at the interface between Nb and Nb6Sn5, and Nb6Sn5 transforms into coarse Nb3Sn as in the case of the tube-type method. Similar to that in the case of the tube-type method, the volume ratio of the coarse Nb3Sn layer is large.
(d)RRP
In RRP, the Cu-Nb-Sn reaction is significantly more complicated because the submodule is composed of Nb multifilamentary wires. The reaction behavior of Nb3Sn formed by this method has been systematically investigated by Pong et al., Scheuerlein et al., and Sanabria et al. [82], [83], [84], [85], [96]. The Cu-Nb-Sn reaction, particularly at low temperatures, has been analyzed by Hopkins et al. [89]. The latest detailed Cu-Nb-Sn phase diagram (isothermal sections) considering Nausite was investigated by Lachamann et al. [80]. In Fig. 5, the reaction behavior of Nb3Sn inside the Nb filamentary area is not comprehensively depicted for convenience. At the beginning of the heat treatment at 215 °C or less, Sn and the surrounding Cu interdiffuse to produce mainly η-Cu6Sn5 and partly ɛ-Cu3Sn [85]. From 215 to 300 °C, Nausite forms at the inner surface of the Nb filamentary area ahead of NbSn2 formation. Furthermore, slightly above 400 °C, η-Cu6Sn5 starts to decompose into ɛ-Cu3Sn [80], [85]. Simultaneously, Nb is corroded in the core side, and Nausite grows at the reaction interface. At 586 °C, Nausite decomposes into NbSn2 [80], [89]. Even during the mixing of Sn and Cu at the core, Cu in the filamentary region flows inward to the Sn core side [85]. Then, similar to the cases of the tube-type and PIT methods, Nb6Sn5 is formed at the reaction front. Subsequently, Nb3Sn is generated at the interface between Nb6Sn5 and Nb filaments. Finally, the Nb3Sn filaments are almost completely connected to construct a Nb3Sn cylinder. However, RRP produces less amount of Nb6Sn5, resulting in lower concentration of coarse Nb3Sn.
2.1.3. Interpretation of the reaction behavior of Nb3Sn in terms of Sn chemical potential
If there is a concentration gradient in the constituent elements of a system, diffusion fluxes of the elements occur from higher concentrations to lower concentrations. This is termed Fick’s first law, and it is always applicable to binary systems that do not generate compounds. In this case, concentration of elements is one of the important variables in describing diffusion. Nevertheless, in the case of the bronze method where the Sn diffusion flux occurs from the Cu alloy with a Sn concentration of approximately 9% to Nb3Sn with a higher Sn concentration of approximately 25%, diffusion cannot be explained only by the Sn concentration. This type of diffusion is also called uphill diffusion. To correctly understand these phenomena, considering the chemical potentials of elements is necessary. The concept of chemical potential has been described in many studies. Briefly, it is defined as the Gibbs energy per mole of a substance (element or compound) when the substance is present in a mixture. Comparison of the magnitudes of the Gibbs energies per mol of the original and product phases reveals the strength and direction of the reaction. Hence, the chemical potential gradient acts as a driving force for diffusion. After the discovery of the bronze method [7], [17], [60], numerous experimental [97], [98] and theoretical [79], [91], [99] studies have been reported on the ternary equilibrium diagram of Nb-Cu-Sn to gain a deeper understanding of the mechanism of Nb3Sn formation. Kajihara et al. created an activity diagram of Sn from the viewpoint of the Sn chemical potential and explained uphill diffusion during the production of Nb3Sn [99]. The chemical potentials of Sn in different phases of Nb3Sn at approximately 650 °C are schematically shown in Fig. 6(a) according to the results obtained to date for phase formation. A schematic of the routes for the representative diffusions of Nb/Cu-Sn considering the initial Cu-Sn composition is depicted in Fig. 6(b).
Using the chemical potential concept, Nb/Sn diffusion can be described as follows. Without Cu, the chemical potential of Sn is considerably high, and NbSn2 with the next highest Sn chemical potential is formed (Fig. 3(a)). Moreover, the Sn chemical potential of liquid Sn remains high throughout the reaction, and NbSn2 continuously grows without the development of Nb6Sn5. With an increase in the concentration of Cu in the core, the Sn chemical potential in the core decreases, and the difference between the Sn chemical potentials of liquid Sn and NbSn2 decreases. NbSn2 grows in the same way as that in the absence of Cu; however, on the Sn alloy side, the Cu concentration increases due to the diffusion of Sn. With the depletion of Sn, the growth rate of NbSn2 decreases, and Nb6Sn5 is generated at the interface between NbSn2 and Nb. With further progress of the reaction, the chemical potential of Sn in the core further decreases, and NbSn2 transforms into Nb6Sn5 in sequence. When the NbSn2 layer disappears, Nb3Sn is produced at the interface between Nb6Sn5 and Nb. Previous studies on the Nb-Cu-Sn ternary equilibrium diagram have demonstrated that Nb3Sn directly forms when the Cu content is approximately 75 at% or higher or the Sn content is 25 at% or lower (Fig. 6(b)) [80], [91], [98].
The Nb3Sn samples generated via the tube-type and PIT methods are believed to have higher initial Sn chemical potentials than those of the Nb3Sn samples produced by the other processes considering the initial Sn concentration in the core. High Sn chemical potential leads to a high Sn diffusion driving force, which enables the formation of a thick Nb3Sn layer in a short time, reduction of the heat-treatment temperature, and suppression of grain coarsening in the small grain layer. Indeed, the heat-treatment time in the case of the PIT method is approximately 3 days. Nevertheless, the high Sn diffusion driving force promotes the growth of the Nb6Sn5 layer, thereby increasing the volume ratio of the coarse Nb3Sn layer, which is disadvantageous. Reduction of the volume ratio of this coarse Nb3Sn layer is one of the critical issues in the cases of the tube-type and PIT methods [87], [88]. In RRP, the submodule comprises Nb multifilamentary wires, and a sufficient amount of Nb3Sn layer is produced even if the Sn chemical potential is low. This adequate balance between the diffusion length and chemical potential of Sn is the reason for the high Jc characteristics of RRP wires. The reason for the emergence of NbSn2 in the case of Nb3Sn produced by RRP is due to a high Sn chemical potential of the core at the early stage of the reaction. Unlike the PIT and Tube-type methods, in the RRP, a large amount of Cu exists in the Cu/Nb filamentary region and has to diffuse into the Sn core. That causes temporally a high Sn concentration in the core at the early stage of the reaction. More specifically, in the low-temperature stage, Nausite ring is developed around the Sn core. The Nausite ring inhibits Sn diffusion into the Cu/Nb filamentary region [85]. The control of Nausite thickness is significantly important to increase the Cu inflow while minimizing the increase in Nausite thickness, because the Nausite changes ultimately into coarse Nb3Sn grains [85]. Increasing the Cu inflow helps to reduce the amount of η-Cu6Sn5 that liquefies at 408 °C.
In the bronze method, although a fine Nb3Sn layer can be directly formed, the solubility of Sn in Cu-Sn bronze is limited to approximately 10 at%, rendering substantial increase in the Sn chemical potential challenging.
2.2. Potential for performance improvement
During the solid-phase diffusion of Sn into Nb, the diffusion rate of Sn is considerably higher than that of Nb, and the Nb3Sn layer is mainly generated on the Nb side [90], [91]. The Nb3Sn layer is polycrystalline, and GB diffusion plays a significant role in Sn diffusion, whose rate is substantially higher than that of bulk diffusion [100], [101]. However, a composition gradient always exists in the Nb3Sn layer for a realistic heat-treatment time. These composition gradients directly reflect the distribution of Tc. Via specific heat measurements, Senatore et al. revealed the presence of a large Tc distribution, even in practical wires [102]. Results of the specific heat measurements indicated the actual importance of a composition gradient in accurately determining the distribution of Tc in the layer even when there is a shielding effect on the superconducting filaments, for example, in the cases of DT wires [72], during electromagnetic measurements such as measurements performed using a superconducting quantum interference device (SQUID).
Compositional gradients vary widely depending on the wire design. Fig. 7 depicts some examples of the Sn composition distributions in the Nb3Sn layers measured by compositional microchemical analysis in the different wire designs (the bronze method [103], RRP [104], PIT method [105], and tube-type method [70]), showing clear differences.
Fig. 7. Sn composition distributions across the A15 layers for the bronze Nb3Sn wires fabricated by adding 7.5 wt% Ta and 1 wt% Ti to Nb [103], RRP wires synthesized by introducing 7.5 wt% Ta into Nb [104], PIT wires [105] presumably constructed by adding 7.5 wt% Ta to Nb [11]), and tube-type wires developed by incorporating 7.5 wt% Ta into Nb and 1.5 at% Ti into Sn [70]. |
In the sample prepared by the bronze method, the Sn composition gradient is significantly higher than those in the samples fabricated via other methods, suggesting that the driving force for Sn diffusion is an extremely crucial factor in improving compositional uniformity. Notably, among all composition gradients, the composition gradient in the sample synthesized by RRP is clearly lower. In the case of RRP, the Nb module consists of a multifilament structure. Thus, Sn diffusion over a very short distance (∼a few microns) is achieved at the beginning of Nb3Sn formation; when the Nb rods completely react, the Nb3Sn layer develops at the end of heat treatment. This is considered to be the major reason for the very small Sn composition gradient in the sample prepared by RRP despite lower Sn diffusion driving force in this case than those in the samples synthesized by the PIT and tube-type methods.
The composition gradient is dependent on the heat-treatment condition. The diffusion coefficient, D can be expressed by an Arrhenius-type function (=D0 × exp(−Q ∕ (R × T)), where D0, Q, R, and T are the pre-exponential factor, activation energy, universal gas constant, and absolute temperature, respectively). Hence, the decrease in the heat-treatment temperature, which is desirable for grain refinement, decreases D and thus results in a steeper Sn composition gradient. In contrast, diffusion layer thickness is proportional to n-square root of time [106]. Therefore, a longer heat-treatment time should mitigate the steepening of the Sn composition gradient.
Nevertheless, Xu et al. analytically demonstrated that the Sn composition gradient in the Nb3Sn layer barely changed even when the Nb3Sn layer grew over time, and a bronze-type wire was considered in this analysis [59]. This was owing to the dominance of the GB diffusion of Sn within the Nb3Sn layer, in which Sn reached the reaction front faster than diffusing into the grains [59].
All of the samples in Fig. 7 are doped with Ti or Ta or both; Ti and Ta have long been known as additives that improve the Bc2 of Nb3Sn [107], [108], [109], [110], in which the Sn compositional gradient is believed to be improved, and these elements are now added to all practical wires. The Sn compositional gradient is not significantly affected by whether Ti or Ta is added [103], [111], but it does affect the homogeneity of Nb3Sn layer, as discussed in Section 2.3.3.
In type-II superconductors, the magnetic field is quantized [112], and the vortices are randomly arranged within the superconductor due to both vortex-vortex and vortex-pin interactions. The flux pinning force is believed to be maximum when the pinning centers are as large as the coherence length of Nb3Sn and the spacing of the pinning centers overlaps the flux-line lattice (FLL). The magnetic flux quantum is expressed as φ0 (=h/2e) (where h is the Planck’s constant and e is the electron charge), which is equivalent to 2.06783385 × 10-15 Wb. Considering B (Wb/m2) as the external magnetic flux density, the square FLL spacing (Fig. 8) as an average value, a, can be presented by
$a=\sqrt{\frac{\varphi_{0}}{B}}$
Fig. 8. Schematic of a triangular magnetic flux-line lattice. |
At B = 5, 12, and 16 T, a was estimated to be approximately 20, 13, and 11 nm, respectively. A typical grain size of 100-200 nm is considerably large when compared with the abovementioned a values. Variation of the maximum pinning force as a function of reciprocal grain size has been summarized by Godeke, revealing a universal monotonically increasing trend of the maximum pinning force with an increase in the grain size to 35 nm [12]. This indicates that the conventional Nb3Sn wires have still high potential margins in terms of grain size.
2.3. Effect of element addition on the formation behavior of Nb3Sn
Element addition is one of the effective techniques for realizing microstructural control and increase of Bc2, thereby improving the in-field Jc performance. Generally, the term “element addition” is often employed to imply that the element dissolves in a certain phase and changes its physical properties. However, the diffusion of Nb3Sn suggests that the added element does not always dissolve in the phase and remains in the matrix in some cases. This type of element addition is important for imparting certain functions (for example, high resistance at the interface between filament and matrix [22], [23], [24], [25], [26] and solid-solution strengthening of the matrix [27], [28], [29], [30], [31]), to the wire.
This section explains particularly interesting topics such as refinement of Nb3Sn microstructure by element addition [14], [15], [16], substitution sites of Ti and Ta [18], [19], impact of Ti doping position on the formation behavior of Nb3Sn [20], [21], and enhancement of the mechanical strengths of wires by element addition [58].
Internal oxidation of Zr is currently attracting the most attention for improving the performances of Nb3Sn wires. Historical background of the development of internal oxidation is provided in the review reported by Xu [15]. Using this method, grain morphology can be substantially refined (typically down to less than half when compared with that acquired using the conventional method). Moreover, the wires with high Jc values obtained via internal oxidation satisfy the performance requirements for application in the Future Circular Collider (FCC) project [114]. Recently, the addition of Hf to the Nb parent phase instead of that of Zr has been confirmed to have the same internal oxidation effect on the formation behavior of Nb3Sn [115]. The basic concept of this method is to add Zr to Nb followed by the addition of SnO2, which serves as an O supply source, to the Sn core side. As the incorporation of Zr alone cannot lead to a high Bc2, a small amount of Ta is simultaneously added to improve Bc2 [116].
Fig. 9(a) shows a schematic of internal Zr oxidation in the PIT method. Nb, Ti, Ta, and Zr are easily oxidizable, and Zr has the highest affinity for O among them (see Ellingham diagram)) [15], [117]. Zr is preferentially oxidized in the Nb-Zr matrix and precipitates as a nanoscale oxide phase (particle size of typically 1-10 nm [59], which is quite close to the coherence length of Nb3Sn). Here, note that appropriate intermediate annealing is required to promote the diffusion of O into Nb3Sn [14]. At low temperatures (500 °C or less), the diffusion rate of O is low, and NbSn2 and other phases develop at the reaction interface. The formation of these phases can be a concern as these phases may act as O diffusion barriers. To overcome this issue, a preheat treatment at 450 °C was proposed, and sufficient O diffusion was achieved even with a compound layer.
SEM, transmission electron microscopy (TEM), and APT results have verified that nano-oxide particles exist not only at GBs, but also inside the Nb3Sn grains (Fig. 9(b)) [59]. This deposition of nano-oxide particles has two primary effects. The first effect is the so-called Zener pinning effect. If there are fine precipitates in the parent phase, they promote the nucleation of Nb3Sn and suppress grain growth. The second effect is the impact of point pinning on magnetic flux quanta [59], [118], [119]. Due to the influence of this artificial point-type pinning, the peak position of the Fp curve for the internal oxidation-type wire shifts to the high magnetic field range as compared to that in the case of GB pinning [120] (Fig. 7(c)). As this shift decreases the low magnetic field Jc, it also reduces the magnetization hysteresis loss [59].
2.3.2. Grain refinement by the addition of Hf to the Nb parent phase
Hf addition was reported for the first time in 1979, where Hf was added along with Ga to the Nb core [121]. Thereafter, the effect of Ti addition to the Nb parent phase was investigated [107], and less attention was paid to Hf addition. Nevertheless, Balachandran et al. have recently reported that the simultaneous addition of Hf and Ta (which is added to improve Bc2)) to Nb substantially refines the grain size [16]. Consequently, Hf addition has attracted significant attention again as it can be facilely applied to the existing wire drawing process because Nb is simply doped with Hf. According to the first report on Hf addition, fine grain morphology remained in the unreacted Nb-Hf-Ta parent phase even after the formation of Nb3Sn [16]. Therefore, it was speculated that fine crystal defects, including dislocations, introduced into the Nb parent phase became nucleation sites and promoted grain refinement.
However, recently, elemental distribution analysis at the atomic level by APT for this sample has revealed the presence of numerous nanocrystalline HfO2 phases within the grains (Fig. 10) [122]. The use of Cu-Sn powder as the Sn source in the synthesis of the sample in the first report [16] is one of the reasons for the existences of these phases, and the oxide layer on the powder surface must have decomposed and diffused during Nb3Sn formation. Based on the Ellingham diagram, the O affinity of Hf is equal to or higher than that of Zr. Thus, it is possible that grain refinement and additional Fp effect may have occurred by the same mechanism as that of internal oxidation.
Nevertheless, the following basic experiments have demonstrated that the grain morphology of the Nb parent phase definitely affects the Nb3Sn microstructure development [123]. At first, two Cu/Nb composite wires with a core of Nb, to which 1at%Hf-4at% Ta was added, were prepared by cold drawing. Simultaneously, the Nb-Ta-Hf core was in a true strain state of 242.5%. Then, one sample was left untreated, and the other sample was heat-treated at 1010 °C for 5 h to ensure complete recrystallization and grain growth. Next, approximately 30 at% Sn was electroplated around both samples. Subsequently, heat treatment was conducted at 685 °C for 100 h to form a Nb3Sn layer at the Nb-Ta-Hf core interface. The recrystallization temperature of Nb-Ta-Hf was approximately 850-950 °C [123], and thus, the recrystallization of the Nb-Ta-Hf matrix hardly progressed during heat treatment at 685 °C. Therefore, the fine Nb-Ta-Hf grain morphology of the unannealed specimen was preserved during the formation of the Nb3Sn layer. By comparing the developed Nb3Sn grain morphologies of both samples, the influence of the original Nb-Ta-Hf microstructure on the Nb3Sn grain morphologies was clearly revealed. Fig. 11 depicts the EBSD grain orientation maps (inverse pole figure (IPF)) with GBs and kernel average misorientation (KAM) maps of the Nb-Ta-Hf phases of both samples and SEM images of the Nb3Sn layer formed on the Nb-Ta-Hf phase. KAM indicates a slight difference between the orientations of crystals inside the grain, and the acquired value can reflect the internal strain state. Thus, by measuring KAM, the states of residual strain and stress can be determined.
Fig. 11. SEM images of Nb3Sn grain morphology (right) formation on the parent Nb-Ta-Hf phase (a) without intermediate annealing and (b) with intermediate annealing at 1010 °C for 5 h. The grain orientation (Inverse pole figure (IPF)) and kernel average misorientation (KAM) maps of the parent Nb-Ta-Hf phase are presented on the left side [123]. |
In the completely annealed Nb-Ta-Hf phase, grain coarsening was observed: the average KAM over the measurement area was approximately 0.428°. The average grain size of the Nb3Sn layer generated on this phase was approximately 160 nm. In contrast, the cross-section of the unannealed Nb-Ta-Hf phase demonstrated a strong texture in the [001] direction because of wire drawing, and the average KAM in the measurement range was as high as 0.793°. This implied that the unannealed Nb-Ta-Hf phase was in a higher internal strain energy state due to shear deformation. The average grain size of the Nb3Sn layer formed on this parent phase was approximately 81.5 nm, which was almost half that of the Nb3Sn layer developed on the fully annealed Nb-Ta-Hf phase. This result indicates that the internal strain state of the Nb-Ta-Hf parent phase considerably affects the nucleation of Nb3Sn.
These effects of internal strain energy on the nucleation of Nb3Sn can be approximately represented by the classical nucleation model [123]. By hypothesizing that a spherical phase is nucleated on a parent phase, the Gibbs energy change ΔG can be expressed as [124](2)ΔG=-4πr33Δgv+4πr2σwhere Δg, r, v, and σ denote the chemical potential difference, radius of the precipitate particle, volume of the precipitate particle per mole, and surface energy density, respectively. Fig. 12 shows a schematic of the ΔG curve. The first term on the right side of equation (2) is the volume free energy term, and the second term is the surface free energy term. When a phase nucleates, the volumetric energy of the original phase is reduced by the nucleation volume, and the surface energy increases with an increase in the surface area. The sum of these energies results in a maximum in ΔG at rc = 2συ / Δg. Here, ΔGc, which is the peak value of ΔG, is the activation energy, and rc is the critical nuclear radius.
Fig. 12. Schematic curve of the Gibbs energy difference (nucleation driving force) when a completely spherical particle nucleates from the parent phase. |
The accumulated internal strain energy should be used for nucleation, and the grain size is supposed to monotonically decrease with an increase in the internal strain energy. Therefore, the simplest way to consider this additional energy is adding this energy to Δg. This reduces ΔG and shrinks the critical nucleus needed for nucleation. This effect of internal strain energy was also observed during the transformation of Nb3Al to the supersaturated solid-solution Nb(Al)SS [125]. During the transformation of Nb3Al, the grain size reduced by half with 730% true strain deformation to the supersaturated solid-solution phase. In the case of Hf-added Nb3Sn, the grain size is estimated to be reduced to half at a true strain of approximately 243% [123]. From the viewpoint of nucleation, the internal strain energy should be as high as possible.
However, Nb, Ta, and Hf are all high-melting-point metals with melting points higher than 2000 °C. Particularly, homogenizations, refinements, and attainment of uniform control over the grain sizes of these alloys are extremely difficult. Furthermore, the hardnesses of these alloys are high. The microstructure of the hard-alloy core surface tends to freely deform under the soft Cu skin in the Cu/hard-alloy composite, causing microscopic irregularities at the Cu/hard-alloy interface. Uniform wire drawing requires precise control of the fine grain morphology of Nb-Ta-Hf [126].
2.3.3. Doping of Ti and Ta into Nb3Sn
Ti dissolves in Nb3Sn and increases Bc2 [107], [108], [109]. Although Ta exhibits a similar effect [110], approximately double amount of Ta is needed to obtain the same effect as that of Ti [5]. Additionally, Ti diffuses into Nb3Sn even from the Sn side when it is added to the Sn core side [127]. In contrast, Ta dissolves in Nb3Sn only when it is introduced into the Nb side. Based on the Ginzburg-Landau-Abrikosov-Gorkov (GLAG) theory [128], [129], Bc2 is derived as follows
$B_{\mathrm{c} 2}(0)=3.11 \times 10^{3} \rho_{\mathrm{n}} \gamma T_{\mathrm{c}}$
where ρn is the residual resistivity of the normal state, γ is the electronic specific heat coefficient, and Tc is the critical temperature. The improvement of Bc2 by the addition of Ti and/or Ta is believed to be due to the increase in ρn [6], [9], [130]. Moreover, in the case of the perfect binary phase Nb3Sn, Bc2 rapidly decreases when the Sn concentration exceeds 24 at%, approaching the stoichiometric composition (25 at%). This is because rapid lattice softening near the stoichiometric composition causes martensite transformation (crystal lattice change without atomic diffusion). Flükiger has comprehensively explained that long-range order is closely related to martensite transformation [8]. Addition of a small amount of Ti or Ta to Nb3Sn suppresses this martensite transformation [131].
Specific heat measurements confirmed that the introduction of Ti into Nb3Sn led to a sharper distribution of Tc than that in the case of Ta addition to Nb3Sn; that is, Nb3Sn with higher stoichiometry was formed [18], [111]. This suggests that the Tc distribution acquired after the incorporation of Ti into Nb3Sn can be further improved. Very recently, Heald et al. and Tarantini et al. investigated the substitution sites of Ti and Ta in the Nb3Sn crystal lattice via extended X-ray absorption fine structure measurements. Fig. 13 depicts schematics of the substitution sites of Ti and Ta in the Nb3Sn structure [18], [19]. Ti substitutes for Nb sites regardless of the formation temperature of Nb3Sn, whereas Ta substitutes for not only Nb sites, but also Sn sites. Furthermore, substitution of Ta exhibits temperature dependence, and Sn site substitution decreases at higher temperatures (Sn site substitution ratio decreases from 43 ± 7% at 634 °C to 11 ± 4% at 666 °C) [19]. Additionally, depending on the substitution element, antisite occupancies of Nb and Sn occur (Fig. 13) [18]. With the addition of transition elements, Nb3Sn tends to exhibit high Bc2 [132]; thus, elucidation of the site substitution effect remains an important issue in enhancing the performance of Nb3Sn.
2.3.4. Impact of Ti doping position on the formation of the Nb3Sn layer
Diffusion of Ti into the Nb3Sn layer regardless of whether Ti is added to the Nb or the Cu-Sn matrix is one of the characteristics of Ti addition. Nevertheless, the development of the Nb3Sn layer is affected by the doping position of Ti [20], [92], [133], [134]. A clear difference in microstructure change was observed particularly at the reaction interface in the internal Sn method with a high Sn chemical potential on the Cu-Sn side [21].
Senatore et al. determined Tc distributions via specific heat measurements on the wires constructed by the bronze method and reported that although there was no significant difference between the Tc distributions obtained by adding Ti to different positions, a higher Jc was achieved when Ti was added to the bronze side [133]. Popova et al., Deryagina et al., and Santra et al. demonstrated that the addition of Ti to the bronze matrix reduced the fraction of the coarse columnar grain region in the Nb3Sn layer and increased the fraction of the fine equiaxed grain region [20], [92], [134]. Consequently, the introduction of Ti into Nb decreased Jc [134]. In the case of the bronze method, addition of Ti to the bronze matrix is more advantageous.
In the simplest case of the internal Sn method with the Nb/Cu/Sn diffusion couple, Ti can be doped into three positions: Nb, Sn core, and Cu matrix. A closer observation of the interdiffusion behaviors of Cu/Sn and Nb/Cu-Sn with respect to the Ti doping position revealed a considerable difference between these behaviors than those in the case of the bronze method. Fig. 14 shows the EDS composition maps at around the reaction interface after heat treatment (500 °C/100 h + 685 °C/100 h) when Ti is separately added to the Nb and Sn cores [21]. When Ti was doped into the Nb core, almost no compound phase was observed at the interface between the Nb3Sn layer and the Cu-Sn layer. In contrast, when Ti was added to the Sn core, a clear Ti-rich layer (the quaternary compound phase NbCuSnTi) was noticed at the abovementioned interface. The same phenomenon was observed when Ti was doped into the Cu matrix. A liquid phase and CuSnTi coexist at 572 °C in the Cu-Sn-Ti reaction system [135]. However, in the presence of Nb, the liquid phase is supposed to promote the corrosion of Nb, resulting in the formation of NbCuSnTi. Moreover, the thickness of the Nb3Sn layer in the Sn-Ti core sample was approximately two-third of that in the Nb-Ti core sample, implying that NbCuSnTi acted as a Sn diffusion barrier.
Fig. 14. Energy-dispersive X-ray spectroscopy (EDS) maps of the elements around the Nb3Sn reaction area for the cases of Ti addition to (a) Nb and (b) Sn cores [21]. |
The way of Ti addition in the case of the RRP is slightly different from that of other internal Sn method. In RRP Nb3Sn wires, some Nb filaments are replaced with Nb-47wt%Ti filaments as the Ti source, which are sparsely distributed in the Nb filament bundle [136]. After heat treatment, the original Nb-47wt%Ti filaments transform into Ti-rich Nb-Sn-Ti surrounded by Cu, whereas the rest of Ti is homogeneously diffused across the Nb3Sn layer [111].
2.3.5. Strengthening of the matrix by element addition
Among various additive elements, Zn is one of the elements that exhibit characteristic diffusion behaviors. Wada et al. reported that the doping of Zn into the bronze matrix during the bronze method promoted the formation of Nb3Sn [27]. Additionally, Zn barely dissolves in Nb3Sn and remains in the matrix, which causes solid-solution strengthening of the matrix; thus, high-strength Nb3Sn wires for nuclear fusion reactors are also developed by the bronze method [28]. Nevertheless, a problem arises in the case of the bronze method: the solubility limit of Sn in Cu decreases owing to the addition of Zn.
Zn addition was also applied to the internal Sn method [30], and similar diffusion behaviors as those in the case of the bronze method were noticed [31]. However, work hardening of the Cu-Zn matrix can be an issue. Nevertheless, substantially less number of intermediate annealing cycles are required for the Cu-Zn matrix than that in the case of the Cu-Sn bronze matrix. Therefore, if the Nb and Sn modules are separately manufactured followed by their combination in the final drawing process (DT method), intermediate annealing will not be needed at the final stage of wire drawing [31], [137], [138], [139]. Nb3Sn wire as a candidate wire for particle accelerators and prototype reactors was also produced by the DT method using a Cu-Zn brass matrix, which demonstrated adequate stress tolerance [140], [141].
Zn doping has another important effect on the internal Sn method. Typically, heat treatment during the internal Sn method consists of two steps: Cu/Sn mixing step and Nb3Sn layer formation. ɛ-Cu3Sn develops before the generation of the Nb3Sn layer during Cu/Sn interdiffusion (Fig. 4). The formation of ɛ-Cu3Sn is accompanied by the production of large Kirkendall voids at the reaction front. This is caused by the difference between the diffusion rates of Cu and Sn (the Cu diffusion rate is considerably higher) and volume reduction induced by the development of ɛ-Cu3Sn [58], [85], [142], [143], [144]. Kirkendall voids may physically block the diffusion of Sn and may also be the starting points of crack generation when stress/strain is applied [145], [146]. Therefore, suppression of these voids during Cu/Sn interdiffusion is crucial.
Addition of Zn is characterized by the production of a tight phase (β-CuZn) between ɛ-Cu3Sn and α-Cu, which significantly suppresses the Kirkendall voids [58], [147]. Fig. 15 depicts the phase formation in DT Nb3Sn wires at 400 °C/200 h and 400 °C/200 h + 480 °C/50 h with and without Zn addition. Apparently, in the absence of Zn, the voids are concentrated at the reaction front of ɛ-Cu3Sn in the Nb module, which inhibits Sn diffusion. In contrast, in the presence of Zn, a tight β phase is generated at the reaction front of ɛ-Cu3Sn in the Nb module, and Sn smoothly diffuses in the Nb module.
Fig. 15. Phase formation in DT Nb3Sn wires at 400 °C/200 h and 400 °C/200 h + 480 °C/50 h: (a) Cu/Sn − 1.6 wt%Ti and (b) Cu−12 wt%Zn/Sn-1.6 wt%Ti diffusion couples [138]. |
3. Nb3Al
Nb3Al was discovered in 1958 [56]. Nb3Al has intrinsically higher Tc and Bc2 (18.9 K and 29.5 T at 4.2 K, respectively) than those of Nb3Sn [2], [32] and is characterized by lower strain sensitivity [10], [33]. However, unlike Nb3Sn, Nb3Al does not exist in equilibrium with the stoichiometric composition at room temperature (Fig. 16) [148]. Stoichiometric Nb3Al is stable only at approximately 1940 °C. At other temperatures, Nb-rich Nb3Al and Nb2Al (σ) stably coexist. Nb3Ge and Nb3Ga exhibit similar equilibrium phase diagrams. Nevertheless, compared to the case of Nb3Al, Nb3Ge and Nb3Ga do not have a temperature region where their stoichiometric compositions are stable.
Fig. 16. Nb-Al equilibrium phase diagram [148]. |
Furthermore, to date, no catalytic element has been reported to preferentially form Nb3Al, like Cu in the Nb/Sn diffusion. NbAl3 and Nb2Al are adequately stable at low temperatures. Therefore, reducing the chemical potential of Al to stimulate the production of Nb3Al does not seem to be an essential approach. Even in the case of diffusion between Cu-Al and Nb, more stable ternary compounds (μ and C14 phases) than Nb3Al would form, and the development of Nb3Al would not proceed [149]. This is another feature in the formation of Nb3Al.
This section briefly summarizes the fundamental production mechanism of Nb3Al and focuses on the important topics related to microstructural control.
3.1. Basic formation of Nb3Al
3.1.1. Early days of Nb3Al research
Because of the difficulty in achieving the equilibrium stoichiometric composition of Nb3Al, sputter quenching has been the primary method to obtain Nb3X (X = Al, Ge) since the early days [150], [151], [152], [153]. In this process, Nb3Al is synthesized at high temperatures and immediately quenched, resulting in high-quality Nb3Al. At a high deposition rate (>1000 Å/mm) during sputter quenching, initially, a supersaturated solid-solution (Nb(Al)SS) is formed, and then, it is converted into nearly stoichiometric Nb3Al with considerably small grain sizes of approximately 250 nm by moderate-temperature annealing at 700 °C, compared with high-temperature synthesis [154]. The Tc of Nb3Al acquired via this way is slightly lower (approximately 17.2 K) than that of Nb3Al bulk achieved via high-temperature synthesis [32], [155]. However, this method could not produce long wires for practical applications.
3.1.2. Metastable reaction control at low temperatures
As abovementioned, during the formation of Nb3Al, attention should be paid to the production of the Nb/Al binary system, in which Nb-rich Nb3Al and σ (Nb2Al) stably coexist. Stable Al-rich compound phases, such as σ and NbAl3, act as diffusion barriers and strongly prevent the development of Nb3Al during Nb/Al diffusion. Fig. 17(a) and (b) depict the estimated ΔG curves for the compositions of the Nb/Al binary system at 1940 and 800 °C, which were obtained by referring to the enthalpy curves reported in the literature [40], [156]. At 1940 °C, the common tangent lines of the ΔG curves of Nb3Al and σ meet at 25 at% Al, indicating the development of Nb3Al with stoichiometric composition and 25 at% Al. Nevertheless, naturally, grain growth occurs at these high temperatures, resulting in the losses of GBs that serve as pinning centers. Thus, the key to acquiring high-quality Nb3Al is to suppress the formation of σ and achieve a stoichiometric composition at low temperatures.
Fig. 17. Curves of the Gibbs energy change (ΔG) for the compositions of the Nb-Al binary system at (a) 1940 and (b) 800 °C and (c) for rapid heating, quenching, and transformation of the Nb/Al diffusion couple, which were obtained by referring to the enthalpy curves reported in the literature [40], [156]. |
Based on the principle of minimum ΔG, the equilibrium compositions of two phases are determined by the tangent points to the common tangent lines of the corresponding ΔG curves. For example, according to the ΔG curves acquired for the Nb/Al binary system at 800 °C (Fig. 17(b)), the Nb3Al contact contains 22 at% Al, whereas σ comprises 30 at% Al. The equilibrium volume fractions of these two phases are evaluated by the ratio of the two distances from the target compositions to the tangent points. For instance, if the tangent point approaches the Nb3Al contact, Nb3Al becomes dominant in the mixed phase, and the composition of Nb3Al remains constant. The phase diagram implies that at 800 °C, stoichiometric Nb3Al cannot be achieved at equilibrium. However, if ΔG of σ is increased, as expressed by the dotted line in Fig. 17(b), the tangent point of Nb3Al can possibly be moved closer to the stoichiometric composition. Similar to the case of the classical nucleation mechanism, ΔG can be controlled by regulating the surface free energy.
Ceresara et al. successfully fabricated Nb3Al wires for the first time using the jelly-roll (JR) technique [157]. They synthesized JR wires with 0.2 mm diameters by wire drawing followed by overlapping Nb and Al sheets, wounding them around a thin Cu rod, and placing them in a metal tube. In this study, reportedly, only Nb3Al formed at the interface when the thickness of the Al layer was less than 200 nm; the average Al content of the laminating section was 14 at%. When the thickness of the Al layer was higher than 200 nm, the fraction of Nb3Al decreased and other Al-rich phases emerged. This was explained by the following growth mechanism: with a decrease in the Al layer thickness, the initially produced phase NbAl3 becomes unstable, σ begins to form at the reaction front immediately after the depletion of the Al layer, and Nb3Al develops at the reaction front with the depletion of NbAl3.
Thereafter, Borman et al. fabricated Nb/Al multilayer thin films by sequential sputtering and discovered that the body-centered-cubic (bcc) supersaturated solid-solution phase Nb(Al)SS formed after heat treatment of these films at 700 °C for 2 h when the Al layer thickness was 9.2 nm (Nb layer thickness: 30 nm and overall Al composition: 25 at%) [156]. This bcc phase transformed into the A15 phase upon heat treatment at higher temperatures of approximately 800 °C. Subsequently, Barmak et al. comprehensively investigated the development of Nb-Al on multilayer thin films at Al layer thicknesses of 34 and 120 nm (Nb/Al periodicity: 143 and 500 nm, respectively) by differential thermal analysis (DTA), TEM, and X-ray diffraction [158]. Then, they concluded that the formation of Nb3Al occurred in the following sequence:
1. Nb + Al → Nb + NbAl3
2. Nb + NbAl3 → Nb + Nb3Al + Nb2Al + NbAl3
3. (Nb/Al periodicity: 500 nm)
Nb + Nb3Al + Nb2Al + NbAl3 → Nb3Al + Nb2Al
(Nb/Al periodicity: 143 nm)
Nb + Nb3Al + Nb2Al + NbAl3 → Nb3Al
Thus, reduction in the thickness of the Al layer in the diffusion couple destabilizes the Al-rich compound phase and promotes the production of Nb3Al even after heat treatment of the diffusion couple at approximately 800 °C.
Moreover, one of the very valuable aspects of the study reported by Ceresara et al. is that it reveals that single Nb3Al can form even with a realistic Al layer thickness of 200 nm from the viewpoint of wire manufacturing. This has significantly increased the application prospects of Nb3Al. In fact, after their study, long Nb3Al wires have been extensively developed using several methods including the rod-in-tube (RIT) [159], PIT [160], [161], and clad-chip extrusion [162], [163] methods, in addition to the JR method [34], [164], [165], [166]. Among these, the JR method leads to the most uniform and thinnest Al layers. Tc and Bc2 of the wires achieved by the JR method were approximately 15.8 K and 21 T, respectively [40]. Fig. 18 shows the images of the cross-sections of a Nb3Al precursor wire (before heat treatment) manufactured by Hitachi Cable, Ltd. using the JR method. The development of Nb3Al wires for practical use has made considerable progress, specifically in Japan. Promotion of the development of Nb3Al as a new candidate material for fusion magnets by the Japan Atomic Energy Research Institute has significantly boosted the advancement of Nb3Al wires [34], [35], [36].
Fig. 18. Optical microscopy and SEM images of the cross-section of the Nb3Al precursor wire (before heat treatment) manufactured by Hitachi Cable, Ltd. using the jelly-roll (JR) process: the lower and right images are the magnified images of a JR filament. |
In the case of wire drawing of Nb/Al composites, intermediate annealing is not possible because Nb and Al easily react even at low temperatures. Therefore, to obtain an Al layer with a thickness of approximately 100 nm from the starting billet, the total reduction in the area of the composite material reaches 105 for the JR method and 1010 for RIT [40]. Homogeneous cold drawing of the composites consisting of hard and soft materials is inherently difficult, and wire drawing requires precise control of the reduction rates of the composite areas and other factors. Adhesion between individual parts is a factor that particularly affects the workabilities of composite materials and often determines the risk of wire breakage. In this regard, hydrostatic extrusion is highly effective in improving the adhesion between individual parts. Nevertheless, extrusion in the case of the JR method needs to be paid close attention to because it can result in uneven deformations of Nb and Al sheets due to the presence of small gaps in the billet. Only after carefully regulating these factors, a relatively uniform Al layer thickness of approximately 100 nm can be achieved without wire breakage (Fig. 18).
3.1.3. Advanced transformation
Metastable low-temperature diffusion has been further developed by incorporating phase transformation into it. Inoue et al. and Iijima et al. successfully transformed Nb3Al wires into nearly stoichiometric Nb3Al wires with Nb matrices having high melting points by the following rod-in-tube process: the precursor wires were processed via continuous high-temperature ohmic heating and rapid cooling with molten Ga, followed by heat treatment at a moderate temperature of 800 °C [167], [168]. The resulting wires were the first Nb3Al superconducting wires with Tc values of 17.3 K and Bc2 values of approximately 25 T (at 4.2 K). The Tc and Bc2 values of JR-processed wires were slightly higher (17.8 K and 26 T, respectively) [169]. The Jc per Nb3Al layer for the Nb3Al wire fabricated using rapid heating, quenching, and transformation (RHQT) at 15 T was 1000 A/mm2, which was substantially higher than that of the Nb3Al wire prepared by low-temperature diffusion using the JR method (approximately 280 A/mm2).
Another major advantage of RHQT is the transformation of the supersaturated solid solution into a flexible bcc phase after rapid heating and quenching [170], [171]. Thus, the wind and react technique, in which the coil is wound and then heat-treated, can be applied to this flexible bcc phase, as in the case of general Nb3Sn coils. To date, Nb3Al wires with long lengths of ∼1.3 km have been realized using RHQT [172], and a magnet capable of generating a magnetic field of more than 19 T has been developed using these wires [173], [174]. Fig. 19 depicts the rapid heating and quenching equipment installed at the National Institute for Materials Science.
Fig. 19. Rapid-heating and quenching (RHQ) equipment installed at the National Institute for Materials Science: reel-to-reel-type RHQ equipment (left) and short wire-type RHQ equipment (right). The wire is ohmic-heated. The movies produced during the operation of the equipment are provided in the supplementary files (A and B). |
Furthermore, Nb(Al)SS can be obtained by quenching the bulk maintained at high temperatures [175]. However, this bulk does not exhibit appropriate ductility observed in the cases of sputter-quenched and RHQT-processed Nb(Al)SS. This may be owing to the fact that the bulk is a hard, brittle polycrystalline material that undergoes twinning during processing, which may cause cracks at the GBs [40].
After the availability of relatively uniform and long Nb3Al wires, research on the formation of Nb3Al microstructures and the microstructures and properties of Nb3Al has made significant progress. Similar to those of the wires acquired using sputter quenching, Tc values of the wires obtained by RHQT were less than or equal to 18 K. Fig. 17(c) shows a schematic of the mechanism of Nb3Al formation via phase transformation. The Nb/Al diffusion couples undergo diffusion during rapid heating to form NbAl2 and off-stoichiometric Nb-rich Nb3Al. Then, at high temperatures of approximately 1940 °C, NbAl2 is consumed and Nb3Al with a single stoichiometric composition emerges; moreover, upon further heating, Nb3Al converts into Nb(Al)SS (upper schematic in Fig. 17(c)). Buta et al. experimentally confirmed the occurrence of an endothermic reaction during this phase transformation [176]. Subsequently, by quenching Nb(Al)SS to room temperature, a metastable supersaturated solid-solution phase can be frozen while retaining its high energy. Then, when this frozen phase is heated to approximately 800 °C, its massive transformation to more stable Nb3Al takes place via the release of the energy corresponding to the energy difference between Nb(Al)SS and Nb3Al (lower schematic in Fig. 17(c)). Nevertheless, based on the principal of minimum ΔG, this phase transforms into slightly Nb-rich Nb3Al rather than into full stoichiometric Nb3Al owing to growth kinetics. This may be the reason for the slightly lower Tc and Bc2 of Nb3Al obtained by phase transformation than those of Nb3Al with stoichiometric composition.
This phase separation can be considerably suppressed by performing higher-temperature phase transformation after freezing the supersaturated solid solution [177], [178]. Takeuchi et al. discovered that upon increasing the temperature of Nb(Al)SS at a faster heating rate, self-heating of Nb(Al)SS occurred because of the energy difference between Nb(Al)SS and Nb3Al [177]. In this method, even if the furnace temperature is maintained below 1000 °C and self-heating is triggered by quickly heating the sample, the generated heat sequentially propagates similar to the case of combustion synthesis, and high-temperature transformation is realized [179] (supplementary file: C). This high-temperature phase transformation increases Tc and Bc2 of Nb(Al)SS to 18.3 K and more than 28 T at 4.2 K, respectively. The high-field Jc shifts toward the high-field side by approximately 2.5 T.
Relationship between the input energy during RHQ and the type of compound phase formed is systematically described in the literature [180]. Fig. 20 depicts the dependences of Tc and Jc per Nb3Al layer on the heating current. All the samples were heat-treated at 800 °C for 10 h after RHQ for the transformation and long-range ordering of the formed Nb3Al. Although Tc of Nb3Al was the highest, when Nb3Al was quenched before Nb(Al)SS, the Nb3Al layer directly developed at high temperatures demonstrated a large grain size and did not exhibit high Jc characteristics. Beyond this boundary input energy, Tc demonstrated a nearly plateau region with respect to the input energy. Jc was also the highest in this range. Even when the wire was quenched under this optimum condition, the as-quenched bcc phase still exhibited a slightly inhomogeneous microstructure, in which some unreacted Nb was observed [181]. Beyond this input energy region, Tc and Jc rapidly decreased due to solid-liquid separation. Further increase in energy resulted in a fully liquid phase. However, during the quenching of the liquid phase, the cooling rate was not sufficiently high to freeze the phase without separating it into Nb-rich and Al-rich bcc phases. Although these phases also converted into Nb3Al, Jc was more than half lower than that acquired in the plateau region of Tc.
Fig. 20. Tc and Jc per compound area of the transformed Nb3Al (RHQT) wire as a function of heating current in RHQ [180]. The samples were heat-treated at 800 °C for 10 h after RHQ. |
Nb-Al-Ge ternary phase diagram suggests a miscibility gap between the Al- and Ge-rich σ phases [2]. This miscibility gap is believed to move the A-15 phase boundary up toward the stoichiometric composition at an appropriate Al:Ge ratio (Fig. 21) [2], [182]. RHQT was also applied to Ge-, Si-, or Cu-added Nb3Al multifilamentary wires. Nevertheless, although Nb(Al, Ge) supersaturated solid solution has been obtained by sputter quenching [153], [183], to date, freezing of the bcc phase has not been achieved in the case of RHQT [184], [185], [186]. Particularly, uniform cold workings of Al-Ge and Al-Si, which are eutectic alloys, are challenging. New technological developments are needed to achieve Al layers with thicknesses of 200 nm or less.
Fig. 21. Al-Ge-Nb ternary phase diagram [182]. σ regions were schematically outlined. |
However, Hitachi Cable, Ltd. (The only manufacturer of RHQT wires in Japan) withdrew from the superconducting wire business in 2016. Now, a Chinese superconducting wire manufacturer, Western Superconducting Technologies Co., Ltd. is trying to reproduce the RHQT wires [190].
3.2. Microstructural control of transformation-processed Nb3Al
Enhancement of Jc by plastic deformation of the supersaturated bcc phase has been noticed in studies on the workabilities of the as-quenched wires and Cu stabilization [171], [191]. Then, bcc deformation has been verified to promote the transformation of the supersaturated bcc phase to Nb3Al [125]. Fig. 22 shows the DTA curves for the transformation of the supersaturated bcc phase to Nb3Al. The peaks in the curve represent the exotherm associated with phase transformation. Apparently, the phase transformation temperature decreases with a decrease in the degree of deformation. Similar to the mechanism described in Section 2.3.2, deformation stimulates the nucleation of Nb3Al, which also reduces the grain size of Nb3Al (Fig. 23) [125].
Fig. 22. Differential thermal analysis (DTA) curves of the degree of deformation of a typical transformed Nb3Al (RHQT) wire with respect to phase transformation temperature. Inset: transformation vs. logarithmic strain of rapidly quenched bcc Nb(Al)SS [125]. DTA peaks indicate the bcc-to-Nb3Al transformation. |
Fig. 23. Dependences of grain size and filament Jc at 20 T of the transformed Nb3Al (RHQT) wire on area reduction of bcc Nb(Al)SS [125]. |
Nevertheless, note that Jc is slightly dependent on grain size, and Jc tends to saturate with a decrease in grain size. Initially, Bc2 also increases by approximately 1 T with an increase in deformation degree and then remains almost constant [192]. The GBs do not act as pinning centers because they are extremely sharp, and little compositional changes occur across them [193]. Fig. 24(a) and (b) depict high-angle annular dark-field (HAADF)-scanning TEM (STEM) images and STEM-EDS maps and atom maps obtained by APT at GBs for the transformed Nb3Al (RHQT) wire, respectively. The GBs are significantly sharp with slight crystal disorders: the thickness appears to be less than 1 nm, which is considerably smaller than the coherence length of Nb3Al. Stacked planar defects that occur during phase transformation are possible pinning centers. Wang et al. have demonstrated that stacking fault (SF) exists in Nb3Al transformed from the sputter-quenched bcc phase [154]. Subsequently, the presence of SF was also confirmed in the RHQT wire (Fig. 25) [192], [194], [195], [196]. The crystal structure of the planar defect was directly verified to be identical to the Zr4Al3-type crystalline architecture expanding on the {100} plane via HAADF-STEM and STEM-EDS [193]; as indicated by Rong, the planar defect is believed to act as an embryonic nucleus for the precipitation of Nb2Al [197]. HAADF-STEM image of the transformed Nb3Al grain with planar defects and the EDS maps for one planar defect are shown in Fig. 24(c) [193]. Usually, the planar defects are present in a single layer or are stacked in two layers. Thus, the thickness of the planar defect was in the range of approximately 1-2 nm, in which the Al composition distributes. That was comparable to the coherence length of Nb3Al. A three-dimensional APT image of the planar defect is provided in the supplementary file D [196].
Fig. 24. (a) High-angle annular dark-field (HAADF)-scanning TEM (STEM) image and EDS maps and (b) 3D-APT maps of the transformed Nb3Al (RHQT) wire around the GB [193]. (c) HAADF-STEM image of the transformed Nb3Al grain with planar defects and the EDS maps for one planar defect. Usually, the planar defects are present in a single layer or are stacked in two layers [193]. |
Fig. 25. Bright-field TEM image of the transformed Nb3Al (RHQT) wire [192]. |
Fig. 26 depicts the dark-field TEM images of the samples with high and low planar defect densities and their pinning characteristics: the low planar defect densities were obtained by phase transformation in a short time at high temperatures [196]. The distance between planar defects was 5-20 nm (Fig. 25, Fig. 26(a)), which was close to the FLL spacing at 12 T. The samples with high planar defect densities exhibited high pinning forces at low magnetic fields, and the corresponding curves were relatively close to that of GB pinning (surface pinning). In contrast, the samples with low planar defect densities demonstrated lower pinning forces, and the Jc peak was acquired in the higher field region. This is similar to the peak effect that occurs in superconductors with weak pinning forces [198], [199]. Thus, a strong correlation exists between Jc and planar defect density in the phase-transformed Nb3Al wire.
Fig. 26. Dark-field TEM images of the Nb3Al grains of the samples with (a) crowded planar stacking fault (40% area reduction + 800 °C transformation) and (b) uncrowded planar stacking fault (40% area reduction + 1200 °C transformation). (c) Curves of flux pinning as a function of magnetic field for various samples with different area reductions and heat-treatment conditions [196]. |
3.3. Strain properties
Strain properties of A15-type superconductors are closely related to the LRO (Sa), as comprehensively described by Flükiger et al. [9], [10]. Nb3Sn wire has an almost perfect regularity (Sa = 1), whereas the Nb3Al wire produced by powder diffusion at low temperatures [149] is relatively off-stoichiometric: Sa = 0.95. Fig. 27(a) shows the intrinsic strain dependence of normalized critical current (Ic) at 4.2 K obtained by Flükiger [9], [10]. The normalized external magnetic field range is 0.57 ≤ B/Bc2 ≤ 0.68. Notably, the strain sensitivity of Ic increases with an increase in Sa. Fig. 27(b) depicts a comparison between the strain dependences of normalized Ic at 17 T for the Nb3Al wires fabricated by RHQT and Nb3Sn wires [200]: B/Bc2 is approximately 0.67. The improved stoichiometry results in a slightly stronger strain sensitivity of Nb3Al, suggesting improvement in the Sa of Nb3Al. Sa of the RHQT Nb3Al wire is estimated to be approximately 0.98 (Fig. 27(a)).
Fig. 27. Normalized critical current at 4.2 K as a function of intrinsic strain for (a) various A15-type superconductors obtained from literature [10] and (b) comparison between the variations of normalized critical current as a function of intrinsic strain for RHQT Nb3Al and Nb3Sn wires at 17 T [200]. |
As mentioned earlier, the GB of phase-transformed Nb3Al is very sharp, and the Nb3Al layer exhibits an intragranular fracture when fractured. This indicates strong connectivity between grains. The diameter of the Nb3Al filament is relatively large (∼50 μm); therefore, once a crack forms in the wire when strain is applied, it rapidly propagates and leads to rupture [201]. Although this is a serious problem in magnet design, rapid rupture can be prevented by reducing the filament diameter or placing a Ag layer between filaments [201], [202], [203], [204].
4. NbTi and Nb-alloy superconductors
Compared to other Nb-alloy superconductors, NbTi was spotlighted relatively later [205]. Until the advent of NbTi, Nb-25%Zr was the predominant superconducting Nb alloy with transition elements doped around Nb [206]. NbZr has attracted attention as a material for nuclear reactors for a long very time. After the prediction of the high Bc2 potential of NbTi in 1962 [207], NbTi wire development has significantly progressed. Compared to NbZr, NbTi exhibits superior adhesion to Cu during processing, which is one of the major factors stimulating the advancement of NbTi wires. The long history of NbTi development has been systematically reported in the literature [45], [46]. Tc and Bc2 of the ternary system Nb-Ti-Ta have also been comprehensively investigated [44]. Bc2 of the optimized binary system Nb-Ti is approximately 11.5 T, obtained at a composition of 60 at% Ti, and Tc is approximately 9.3 K.
4.1. Microstructural control of NbTi
The precipitation effect of α-Ti, which is currently the most important factor for Jc of NbTi wire, was discovered in 1965 at Atomics International [208] using Nb-78at% Ti (65 wt% Ti) alloy and heat treatment at 400 °C for several hours in the final process. Subsequently, microstructural optimizations were extensively conducted [209], [210], [211], [212]. Fig. 28(a) shows the Nb-Ti binary equilibrium phase diagram with a schematic of α-Ti precipitation [213]. When NbTi with Ti uniformly dissolved at high temperatures is heat-treated at moderate temperatures below the solvus, α-Ti containing 1-2 at% Nb precipitates from β-NbTi. α-Ti precipitation is also governed by thermodynamics including those of the nucleation mechanisms; consequently, the size of the precipitated phase is determined by the degree of deformation and heat-treatment conditions of the parent phase. A more detailed control process is clearly summarized in the literature [214]. Nowadays, Nb-47 wt%Ti is generally employed for superconducting applications. Typically, after heat treatment of Nb-47 wt%Ti at 380-420 °C for 40-80 h in the final process, 330-450% strain is applied to the resulting material [43].
Microstructure of the NbTi layer with optimized pinning force is depicted in Fig. 28(b) [43]. The optimal α-Ti ribbon thickness is approximately 5 nm, and the spacing is approximately 10-30 nm, which is very close to the coherence length of NbTi (approximately 5 nm) and the FLL spacing at 5 T, resulting in a nearly ideal pinning force [43], [215]. Because of this optimized inherent high performance and ductility of NbTi, NbTi wires are currently the dominant materials for superconducting applications.
4.2. Alternative artificial pinning in NbTi
Furthermore, attempts have been made to introduce artificial pinning centers (APC) into NbTi to further improve the performances of NbTi wires [216], [217], [218]. Compared to α-Ti precipitation, artificial pinning has the advantage of enabling facile control of the pin size, density, and shape. However, the materials used for artificial pinning are limited to those that can withstand severe plastic working including extrusion and wire drawing. Recently, Mousavi et al. reported a unique and simpler method of incorporating artificial pins into NbTi based on a powder method with mechanical alloying [47]. To date, they have achieved fine microstructures and bulk Jc (2.9 kA/mm2 at 5 T) equivalent to those of conventional NbTi wires with α-Ti by the powder method [219]. In this study, high-energy ball millings of Nb, Ti, and Y2O3 powders were utilized to produce bcc β-Nb with solid solutions of Ti and Y2O3. Reportedly, Ti promotes the dissolution of the solid solution of Y2O3 in Nb. The resulting ball-milled powder was hot-pressed (400 °C, 40 MPa) into pellets with densities of 97%. Subsequent heat treatment at 800 °C resulted in the deposition of Y2Ti2O7 particles with sizes ranging from 2 to 5 nm. Fig. 29 depicts a high-resolution TEM image of the microstructure of bulk NbTi-Y2O3 after annealing at 800 °C. This microstructure acts as a volume pin according to the Dew-Hughes pinning model [47].
Fig. 29. High-resolution TEM image of the microstructure of bulk NbTi-Y2O3 after annealing at 800 °C [47]. |
4.3. Application of HTT Nb-alloy superconductors in superconducting joints
Nb alloy also follows the GLAG theory, in which the upper Bc2 at 0 K is presented by equation (3). Critical deformation of the bcc Nb-alloy develops a dense dislocation cell structure in the grain morphology of the polycrystalline Nb alloy following the formation of a preferred orientation or texture. This fine nanoscale microstructure increases ρn, thereby increasing Bc2. In the case of NbTi, Bc2 increases from approximately 1.5 T (for fully annealed bulk NbTi) to 11 T (for NbTi with a fine nanoscale microstructure). The fine microstructure and α-Ti ribbon contribute to the flux pinning force. Nevertheless, from the perspective of phase equilibrium (Fig. 28(a)), this fine microstructure coarsens after heat treatment at temperatures higher than 650 °C, accompanied by redissolution of α-Ti in the Nb parent phase, decreasing the Jc.
However, HTT superconducting Nb alloys whose fine microstructures can be maintained even after exposure to temperatures higher than 650 °C can be applied to unique superconducting joints as intermedia between NbTi and Nb3Sn wires based on metallurgical bonding instead of conventional intermedia (Pb-alloy solders) [48], [220]. Pb-free superconducting jointing is crucially important from the viewpoint of environmental regulations and has been strongly pursued for many years. In this regard, the most promising HTT Nb-alloy is Nb-Hf. Although the phase diagram of Nb-Hf is similar to that of Nb-Ti, the solvus of bcc Nb-Hf is considerably higher than that of bcc Nb-Ti. The recrystallization temperature of Nb-Hf is > 800 °C [123]. The Bc2 at 4.2 K of Nb-3at%Hf is more than 1.1 T, and its Jc remains significantly steep with respect to the magnetic field. Fig. 30 shows EBSD IPF maps of the microstructures of an as-deformed Nb-Hf alloy (Nb-4at%Ta-1at%Hf) before and after annealing at 800 °C for 3 h [48]. Nb-4at%Ta-1at%Hf retained its fine microstructure after annealing, implying high Jc of this alloy.
Fig. 30. Electron backscatter diffraction IPF and image quality maps of the transverse cross-sections of the bulk Nb-4at%Ta-1at%Hf tape with severe deformation before and after annealing at 800 °C for 3 h [48]. |
Using the HTT Nb-alloy intermedia, a superconducting joint was established between Nb3Sn filaments and one end of the Nb-Hf alloy by forming a superconducting Nb3Sn layer at the interface of the Nb3Sn filaments and Nb-Hf alloy via a chemical reaction at approximately 650 °C. The other end of the Nb-Hf alloy was cold-pressed along with the NbTi filament to connect their active new surfaces to each other, generating a superconducting junction. Finally, a superconducting joint was achieved between NbTi and Nb3Sn wires. The joint resistances were in the order of 10-14-10-13 Ω under the magnetic fields of 0-0.9 T, which confirmed the superconducting states of the joints [48], [220].
5. Summary
In this review, the fundamental formation of Nb3Sn is discussed. Cu is an important element in controlling the chemical potential of Sn, which substantially changes the Nb/Sn diffusion behavior depending on its amount. High driving force of Sn diffusion is a crucial factor promoting the production of the Nb3Sn layer. Nevertheless, high driving force also causes the formation of Nb6Sn5, which increases the volume fractions of coarse Nb3Sn layers that barely contribute to Jc property. Optimization of the cross-sectional geometric assembly, including the structure of diffusion couple, of the wire is important to achieve high Jc. Formation of nanoprecipitates into the Nb parent phase and utilization of the internal strain energy of the parent phase for nucleation are new concepts that have recently attracted attention in the field of Nb3Sn wire development. These concepts are expected to be breakthroughs for further improvement of Jc in the future. Another interesting feature of adding elements to the matrix metal is that element addition endows the matrix metal with additional functionalities such as mechanical strength. Mechanical strengthening would reduce the additional burden of protecting the wire during its application in high-field magnets where a large electromagnetic force is applied to the conductors.
Catalytic methods, for example, introduction of Cu into the Nb/Sn diffusion system, are not applicable in the case of Nb/Al diffusion. Thus, during the formation of Nb3Al, attention should be paid to the Nb/Al binary system, in which Nb-rich Nb3Al and σ (Nb2Al) stably coexist at low temperatures. In low-temperature reactions, control of the Gibbs energy of σ is a critical factor in obtaining high-quality Nb3Al. Transformation of bcc Nb(Al) supersaturated solid solution frozen at high temperatures to Nb3Al by heating the supersaturated solid solution at a suitable temperature of approximately 800 °C is the most effective way to achieve nearly stoichiometric Nb3Al wires with superior pinning characteristics. The GBs in transformed Nb3Al are considerably sharp with almost no composition gradients. As the thickness of the GB is very small as compared to the coherence length of Nb3Al, the contribution of the GB to the flux pinning property is probably small. Instead, planar stacking defects may be the dominant pinning centers because there are distinct Al compositional variations in the planar defect area and the size of the area where planar defects are concentrated is comparable to the coherence length of Nb3Al. The strain sensitivity of Nb3Al is slightly increased by the improved stoichiometry.
NbTi is already a well-developed superconductor whose microstructure is nearly ideal in terms of the sizes and spacings of the pinning centers inserted by α-Ti precipitation. Herein, recently reported yttrium oxide precipitation based on a powder method has been introduced as a simple process of APC incorporation that can replace α-Ti precipitation. This type of APC introduction has the advantages of enabling facile control of pin size, density, and shape. Finally, a unique study of the application of HTT Nb superconducting alloys in the production of Pb-free superconducting joints between NbTi and Nb3Sn wires has also been discussed. Pb-free superconducting jointing is crucially important from the standpoint of environmental regulations.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Institute for Materials Science.
Appendix A. Supplementary material
Supplementary data to this article can be found online at https://doi.org/10.1016/j.supcon.2023.100047.
