Atomic scale analysis of Nb3Sn on Nb prepared by a vapor-diffusion process for superconducting radiofrequency cavity applications

We report an atomic-scale analysis of the microstructure of Nb3Sn coating on Nb prepared by vapor diffusion process for superconducting radiofrequency (SRF) cavity application using transmission electron microscopy (TEM). Epitaxial growth of Nb3Sn on the Nb substrate is found and four types of orientation relationships at the Nb3Sn/Nb interface are identified by electron diffraction or high-resolution scanning transmission electron microscopy (STEM) analysis. Thin Nb3Sn grains are observed in regions with low Sn flux and they have the specific orientation relationship, Nb3Sn (1-20)//Nb (-111) and Nb3Sn (002)//Nb (0-11). The Nb3Sn/Nb interface of thin grains had a large lattice mismatch, 12.3 at.%, and a high density of misfit dislocations was observed by HR-STEM. Based on our microstructural analysis of the thin grains, we conclude that the thin regions are probably a result of a slow interfacial reaction with this particular orientation relationship at the interface. The Sn-deficient regions are seen to form initially at the Nb3Sn/Nb interface and remain in the grains due to the slow diffusion of Sn in bulk Nb3Sn. The formation of Sn-deficient regions and the effects of strain and interfacial energies on the formation of Sn-deficient regions at various interfaces were also estimated by first-principle calculation. The finding of orientation relationships at the Nb3Sn/Nb interface provides important information about the formation of defects in Nb3Sn coatings such as large thin regions, Sn-deficient regions, which are critical to the performance of Nb3Sn superconducting radiofrequency cavities for accelerators.


Introduction
Nb 3 Sn is an A15-type superconductor that has been actively studied and used in superconducting wire applications [1]. A number of studies have employed Nb 3 Sn coatings on Nb for superconducting radiofrequency (SRF) cavity applications and these studies were motivated by the high critical temperature (T c ) and quality factor (Q 0 ) of the superconductor at a given temperature, compared to Nb [2][3][4], where the quality factor (Q 0 ) is defined by the surface resistance (R s ) and the geometric factor (G) of a cavity as G/R s . Nb 3 Sn has lower surface resistance and higher T c than the Nb currently used in accelerators [5,6], and an Nb 3 Sn SRF cavity is considered to be a promising candidate to replace the current Nb SRF cavities in accelerator applications. Recently, studies in Cornell [7,8] reported a high Qfactor (~10 10 ) at 4.2 K with a maximum accelerating electric field gradient up to 17 MV/m for ~2 μm thick Nb 3 Sn coatings on Nb prepared by a vapor diffusion process. Active research in vapor diffusion Nb 3 Sn films is now on-going at Fermilab, Cornell, and Jefferson Lab [9].
It should be noted that Nb 3 Sn-coated cavities have been seen to quench of superconductivity in the [14][15][16][17] MV/m range and some cavities still display Q-slope, the increase of surface resistance as a function of accelerating field, as seen in Fig.1. However, the surface magnetic field at which quench occurs, ~70 mT, is significantly lower than the superheating field of Nb 3 Sn ~400 mT, the ultimate limit predicted by theory for RF superconductivity with an ideal surface [10][11][12]. These limits have been suggested to be a consequence of defects on the surface of Nb 3 Sn coatings [13] including surface roughness, thin regions, Sn-deficient regions, grain boundaries, and surface chemistry.
Specifically, microstructural analysis has focused on two defects of Nb 3 Sn coatings on Nb that are expected to have significant detrimental effects on the performance of Nb 3 Sn coated cavities: thin grain regions [14][15][16] and Sn-deficient regions [14,17]. Abnormally large thin grains with a thickness of ~200 nm (compared to a normal value of ~2 μm) were observed in some regions of Nb 3 Sn cavities coated at Cornell. Significantly, the presence of thin grains was strongly correlated to a decrease in the performance of Nb 3 Sn SRF cavities [9,14,18]. The penetration depth of magnetic flux of Nb 3 Sn is ~111 nm [12] and Nb 3 Sn coatings require a thickness of at least ~500 nm to avoid any detrimental effects from the Nb 3 Sn/Nb interface. The formation of thin grains (< ~500 nm) in the Nb 3 Sn coating has been reported to be affected by a number of factors including the supply of Sn [19], pre-anodization of the Nb substrate [18], and orientation of Nb [15]. It provides some evidence that the texture and nucleation of Nb 3 Sn grains could play a role but the detailed mechanism and origin of the formation of thin grains are still not understood. Also, Sn-deficient regions are currently one of the primary concerns in Nb 3 Sn superconducting radiofrequency cavities [17]. The proportion of Sn in Nb 3 Sn ranges widely from ~17 to 26 at.% as can be seen in Fig. 1 [1,20], and the critical temperature (T c ) of Nb 3 Sn also varies from 6K at ~17 at.% Sn to 18.3K at ~26 at.%. It follows that Sn-deficient regions with 17-19 at.%Sn could decrease the T c of Nb 3 Sn coatings to below that of Nb, 9K, and the formation of Sn-deficient regions is particularly undesirable near the top surface of Nb 3 Sn where magnetic current flow. The growth mechanism and compositional variation of Nb 3 Sn have been rigorously investigated in Nb 3 Sn samples prepared for superconducting wire applications by a solid-diffusion process using Cu-Sn and Nb diffusion couples, so called bronze technique [1,[21][22][23][24][25]. The compositional variation in Nb 3 Sn prepared by the solid-diffusion process was investigated in terms of a compositional gradient between the Sn-rich phase (Nb 6 Sn 5 ) and Nb bulk originating from the diffusion process [21,[25][26][27]. Low levels of Sn in Nb 3 Sn have been attributed to the low formation energy of Nb antisite defects, Nb sitting on Sn sites [26]. However, there is little information about how Sn-deficient regions are formed during vapor diffusion preparation of Nb 3 Sn coating or about the critical role that the interface between Nb 3 Sn/Nb, may play in Nb 3 Sn grain growth and the formation of thin grains. The objective of the current studies was to investigate the origin of the formation of thin grains and Sn-deficient regions in Nb 3 Sn coatings on Nb prepared by vapor-diffusion process and the role of Nb 3 Sn/Nb interface on the formation of such defects.
Here, we report atomic scale analysis of Nb 3 Sn coatings on Nb using transmission electron microscopy (TEM) and first-principle calculations. In particular, we found that orientation relationships at the Nb 3 Sn/Nb interface of the Nb 3 Sn coating on Nb are correlated with the formation of thin grains and Sndeficient regions. Through the use of electron diffraction and high-resolution S/TEM, we could identify four types of orientation relationships between Nb 3 Sn and Nb at the interface. Notably large thin Nb 3 Sn grains were highly correlated with a certain type of grain orientation relationship, Nb 3 Sn (12 ̅ 0)//Nb (1 ̅ 11) and Nb 3 Sn (002)//Nb (01 ̅ 1). The thin grains have a large lattice mismatch with the Nb substrate, and we suggest that this results in the formation of an Sn-deficient layer at the Nb 3 Sn/Nb interface, possibly in order to minimize the lattice mismatch. Our findings provide clues towards understanding the formation of defects in Nb 3 Sn coating on Nb, and may be used to improve the performance of Nb 3 Sn SRF cavities.

Experimental procedures
Nb 3 Sn coatings were prepared at the Fermi National Accelerator Laboratory (FNAL) and Cornell University by a vapor diffusion process developed through work at Siemens, Wuppertal University, and Cornell University as seen in Fig. 1(c) [2,3,9,10,28,29]. Nb samples, tin source, and SnCl 2 nucleation agent were placed in a vacuum furnace and heated to 500 ˚C to create nucleation sites of Nb 3 Sn on the Nb surface. The furnace temperature was then raised to 1100 ˚C for 3.5 h to allow a Nb 3 Sn coating to form on the Nb surface. The tin source was maintained at 1200 o C so that sufficient Sn could continue to be provided to the top surface of the Nb 3 Sn and diffuse into the Nb sample.
In the case of studies of nucleation of Nb 3 Sn, only a SnCl 2 nucleation agent was placed in the furnace without Sn and then heated to 500 ˚C to induce nucleation. Next, the temperature was increased to 1100 ˚C and then cooled immediately after reaching 1100 ˚C.
The samples were systematically characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). A 600i nanolab Helios Focused Ion Beam (FIB) was employed to prepare cross-section samples for TEM. The samples were thinned by a 30kV Ga+ ion beam with 27 pA, and fine-polished by 5kV Ga+ ions with 47 pA. A Hitachi HD-8100 was used for the Bright Field (BF) TEM imaging and electron diffraction analysis, and a Hitachi HD-2300 for scanning transmission electron microscopy (STEM) and energy dispersive spectroscopy (EDS). High-resolution TEM images were taken by JEOL Grand ARM-300 and high-resolution STEM images by JEOL aberration-corrected Grand ARM-200. Gatan Micrograph Suite was used to analyze and process the images.  [1,20]. (b) Qualify factor (Q) vs electric field (E) curve of various ~2 μm thick Nb 3 Sn coated SRF cavities [14]. Nb 3 Sn coated SRF cavity of ERL 1-4 displays high Q-factor up to 15-17 MV/m, which is close to state-of-art performance for a Nb 3 Sn SRF cavity.  showed low Q-factor, ie, high surface resistance. Thin grain regions were widely observed in the Nb 3 Sn SRF cavity of ERL 1-5 with a strong correlation observed between the surface resistance of Nb 3 Sn and microstructures. (c) Temperature profile of substrate and tin source during the coating [9,18].

Computational details
The first-principles calculations in this work employed the plane wave pseudopotential total energy method as implemented in the Vienna ab initio simulation package (VASP) [30]. We used projector augmented wave (PAW) potentials [31] and the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) [32] for exchange-correlation. Unless otherwise specified, all structures are fully relaxed with respect to volume, as well as all cell-internal atomic coordinates. We carefully considered the convergence of results with respect to energy cutoff and k-points. A plane-wave basis set was used with an energy cutoff of 600 eV to represent the Kohn-Sham wave functions. A summation over the Brillouin zone for the bulk structures was performed on a 12x12x12Monkhorst-pack k-point mesh for all calculations and a magnetic spin-polarized method was applied in all the calculations. The calculated lattice parameters of Nb and Nb 3 Sn were 3.324 and 5.332 Å respectively, which are in excellent agreement with the experimental results, 3.300 Å for Nb [33] and 5.289 Å for Nb 3 Sn [34]. Both 2x2x2 and 3x3x3 supercells were used to determine the vacancy formation, antisite, and lattice substitution calculations.

TEM analysis of nucleated Nb 3 Sn grains
As a first step, we characterized nucleated Nb 3 Sn grains in the early stages of Nb 3 Sn coating in order to see details of the initial grain growth. The SEM image in Fig. 2 shows nucleated Nb 3 Sn grains on the Nb surface with some displaying lateral growth with a flat morphology. Figure 2 shows three connected nucleated Nb 3 Sn grains with diameters of ~500 nm (n1), ~200 nm (n2), and ~100 nm (n3), respectively.
Two of these nucleated Nb 3 Sn grains were selected and cross-section TEM samples were prepared using FIB. HAADF-STEM images in Fig.2 revealed that the thickness of nucleated grain, n1 was ~100 nm and that of n2 was ~60 nm. EDS Nb Lα (2.17 keV) and Sn Lα (3.44 keV) mapping performed in STEM mode suggested that the composition of the nucleated Nb 3 Sn grain was 16-19 at.%, which is Sn-deficient compared to the nominal composition of 25 at.%Sn in Nb 3 Sn.

TEM analysis of Nb 3 Sn grains
The microstructure of the Nb 3 Sn coating and the Nb 3 Sn/Nb interfaces were analyzed by BF-TEM, HAADF-STEM, EDS, and HR-S/TEM after the coating process was completed. The results showed significant variation of the microstructures with respect to Sn-flux, i,e, growth rate. Due to the difficulties of measuring the actual Sn-flux on the surface of Nb during the coating process, we used net Sn-flux estimated by taking the average thickness of the Nb 3 Sn coating and the coating process time. It was possible to distinguish three different types of regions: high Sn-flux regions with abnormally large grains, medium Sn-flux regions with normal grains, and low Sn-flux regions with thin grains, see Table 1.

Normal Nb 3 Sn grain regions (average growth rate: 12 nm/min)
The HAADF-STEM image in Fig. 4(c) shows that the Nb 3 Sn coatings formed on Nb were ~2.5 um thick with surface features shown in the SE (secondary electron)-SEM image in Fig. 4(a). The sample in the SEM image was tilted by 52˚ against the SEM optic axis, in order to display the granular roughness of the surface. From the SEM imaging, the average grain size for two samples, A5 and As the next step, we analyzed the Nb 3 Sn/Nb interfaces by BF-TEM, HR-TEM and electron diffraction.
The results revealed orientation relationships (ORs) between Nb 3 Sn and Nb at the Nb 3 Sn/Nb interface.

Thin Nb 3 Sn grain regions (average growth rate: 5 nm/min)
As previously reported [9,14,35], thin grains with a large lateral grain size of up to tens of microns were  Fig. 8 (b) shows that, indeed, the Nb 3 Sn grains formed 8.9 o [12 ̅ 0] tilt grain boundary.
Grain number 5 was analyzed as a representative of the thin grains. HR-STEM imaging of the Nb 3 Sn/Nb interface with the thin grain number 5 is shown in Fig. 9(a) and proved to possess Orientation C, Nb 3 Sn

Vacancy formation and antisite substitutional behaviors in Nb 3 Sn
We used first-principle calculations to understand the formation of Nb and Sn antisite defects and vacancies. The vacancy formation energies in both Nb and Nb 3 Sn can be described using a 2x2x2 supercell according to the following equation:

Effect of Sn-flux (growth rate) on the microstructure of Nb 3 Sn on Nb
This study described the microstructure of three regions of Nb 3 Sn coatings on Nb formed by different rates of Sn flux. As seen in Table 1, the microstructure of Nb 3 Sn coating is strongly affected by the net Sn-flux during formation. This is important because a homogeneous high-quality Nb 3 Sn coating on Nb with a reasonably smooth surface, no uncoated regions or thin grains, and less composition variation is critical for the performance of Nb 3 Sn SRF cavities in order to avoid heating at microstructural defects. A uniform Nb 3 Sn coating with an average grain size of 2 ± 0.6 μm and thickness of ~2.5 μm was only obtained with a medium Sn flux with a value around 161 Sn atoms/nm 2 min, see Fig. 4 and Table 1. Our results indicate that the Sn-flux has a strong influence on the kinetics of Nb 3 Sn nucleation and growth during the coating process. A large net Sn-flux (322 Sn atoms/nm 2 min), and growth rate of 24 nm/min were associated with the formation of abnormally large grains (more than 5 μm) and a bulky and rough surface topology of Nb 3 Sn coating (see Fig. 3). This is probably due to an abrupt formation of Based on our observations and previous studies [18,19,35], we propose the scheme as summarized in

Orientation relationships at Nb 3 Sn/Nb
In addition to the effect of Sn-flux on the microstructure of Nb 3 Sn, the primary finding of the current study is that Nb 3 Sn/Nb interfaces play a critical role on the formation of defects in Nb 3 Sn coatings, such as thin grains and Sn-deficient regions. A strong correlation was found between the formation of thin grains and Orientation C, see Fig. 9. The correlation between the distribution of Sn-deficient regions and orientation relationships (ORs) is discussed below.
The four types of orientation relationships at the Nb 3 Sn/Nb interface with lattice mismatch of Nb 3 Sn and Nb planes, and planar distortions of each interface described in this study are summarized in Table 3.
Three of these ORs were frequently observed on the zone axis of Nb [1 ̅ 11] with Nb 3 Sn [12 ̅ 0], which suggests that these interfaces have lower interfacial energies than other alternatives. Epitaxial growth of thin films on the substrate is commonly observed [37,38] and it is not surprising that Nb 3 Sn films grow epitaxially on Nb with certain orientation relationships as previously indicated for the formation of thin grain on Nb [111] substrate [15]. Additional studies on the textures of solid-diffusion processed Nb 3 Sn on Nb for high-power applications, have also reported indications for orientation relationships [39][40][41]. Here we first describe clear orientation relationships at the Nb 3 Sn/Nb interface of Nb 3 Sn samples in vapor diffusion or solid diffusion process. It is also noteworthy that the orientation relationships, in particular, Orientation A, B and C, were more frequently observed in the case of low Sn-flux. This may be because the low Sn-flux results in slow growth of Nb 3 Sn grains, providing enough time for the Sn atoms to diffuse into the Nb substrate and form a stable interface at Nb 3 Sn/Nb.

Origin of the formation of thin grains
Concerning the origin of the formation of thin grains, we found a strong correlation between thin Nb 3 Sn grains and Orientation C, Nb 3 Sn (12 ̅ 0)//Nb (1 ̅ 11) and Nb 3 Sn (002)//Nb (01 ̅ 1) (Fig. 9). The first feature of grains with Orientation C is the large lateral grain size. A general analytical model employed to understand the fast lateral growth of thin grains with Orientation C on substrate [42], can be described by Where M represents a mobility term of grain boundary, γ s represents the average surface energy in the films, γ s represents the surface energy of the grain, γ i represents the average interfacial energy in the films, γ s represents the interfacial energy of the grain. γ gb is grain boundary energy, ̿ and are the average radius of grains in the film, and a radius of the grain, respectively, and h is the thickness of the film at a given time. This equation assumes that films grow purely by deposition or with the same interfacial reaction rate so that the resulting grains have identical thickness. Since the grain boundary energy at GB (γ gb ) is expected to be smaller than the surface energy and interfacial energy at Nb 3 Sn/Nb, the equation can be simplified as a function of surface energy, interfacial energy. According to the equation, grain growth rate is faster as the surface energy and interfacial energy is low. Firstly, it is noteworthy that the surface of thin grains is often close to the (210) plane, which is the most densely packed plane that might leads to the lower surface energy [42][43][44]. However, some grains with the [210] surface do become thicker and no strong correlation between the orientation of surface and the grain growth was observed in previous EBSD studies [16]. In terms of interfacial energy (γ i ), the interfacial energy of thin grains is expected to be significantly higher than other grains due to the high strain energy and high density of misfit dislocation, which is a consequence of the large lattice misfit (12.3%), see Fig. 9. Therefore, it can be concluded that the formation of abnormal thin grain is not fully explained by either the surface energy or the interfacial energy of thin grains with Orientation C.
The second feature of grains with Orientation C is that they are significantly thinner than other grains.
The influence of orientation relationships on the interfacial reaction rate during a solid-state reaction has been reported in other systems and the low interfacial mobility was attributed to the misfit dislocations at the interfaces [43,[45][46][47][48][49]. Interfacial migration requires climb of the misfit dislocations at the interface and it play as rate-limiting step [48,50]. In this case, the nucleated Nb 3 Sn grains with Orientation C might preferentially spread in the lateral direction rather than increasing the thickness. This gives rise to the formation of abnormally large thin grains during the early stage of Nb 3 Sn growth. The formation of large thin grains significantly reduces the Sn supply across the grain boundary by the square of the size of the large thin grain. As a result, the interfacial reaction rate at Nb 3 Sn/Nb becomes even slower.
Another factor that influences the formation of thin Nb 3 Sn grains is the Sn-flux, i.e. growth rate [51].
Large thin grains appeared when the growth rate was slow (3.5 nm/min) as a consequence of a low net Sn flux (47 Sn atoms/nm 2 min), and they were not observed in medium and high Sn-flux regions. It can be rationalized by that when the Sn flux and growth rate are high, the density of nucleation site increases and therefore, the lateral growth of the thin grains is limited due to the competition with neighboring Nb 3 Sn grains. Indeed, the grains with Orientation C that were found in the normal grain region were similar in grain size (~ 2 μm) to other neighboring grains even though the thickness of the grain (~700nm) was still thinner than the others (~2 μm) as seen in Fig. 11. This provides additional strong evidence that the interfacial reaction rate at Nb 3 Sn/Nb is slower with orientation relationship C than for other grains. Since the Sn supply through the grain boundary should not be significantly different, the slow reaction rate (roughly 2~3-fold slower) with orientation relationship C is the only possible explanation for the lower thickness of the grain with Orientation C compared to other grains.

Formation of Sn-deficient regions: nucleation and their evolution
In the Nb-Sn binary phase diagram in Fig.1, the composition of Nb 3 Sn in two phase equilibrium regions (Nb + Nb 3 Sn) is ~17at% at 1100 o C, and it is reasonable that the nucleated Nb 3 Sn grains at Nb 3 Sn/Nb interface have low Sn composition as seen in Fig. 2. As already discussed, the Sn-deficient regions were probably initially formed at the Nb 3 Sn/Nb interface and the deficiency of Sn in the middle of the grains is a consequence of the slow Sn diffusion, ~100nm/h, in Nb 3 Sn [52]. First-principle calculations revealed that the Nb anti-site defect has low formation energy, ~0.3 eV-see Table 2-and the formation of Sndeficient regions might be assisted by the low formation energy of Nb anti-site defects [26,34,52]. The   generate about 6% more strain energy compared with perfect Nb 3 Sn in the selected interfaces. Overall, we conclude that Sn-deficient Nb 3 Sn has similar lattice misfits to perfect Nb 3 Sn and the slight change of lattice misfit cause some variation of strain energies of Nb 3 Sn. Also, planar lattice match between Nb 3 Sn and Nb is more energetic favorable than volume match during the early stage when Nb 3 Sn forms from Nb subtract.

Correlation between microstructures and superconductivity of Nb 3 Sn SRF cavity
We directly cut out the degraded region of superconductivity of the Nb 3 Sn superconducting radiofrequency (SRF) cavity, ERL 1-5 in Fig. 1 [14], and analyzed one of the thin grains. It also revealed Orientation C in the electron diffraction Fig. 11 (c,d) and provides another strong evidence that the degradation of superconductivity in Nb 3 Sn cavity due to thin grains can be caused by specific orientation relationship at Nb 3 Sn accompanied by low Sn-flux. Therefore, it is suggested that proper amount of Sn need to be supplied to avoid the formation of thin grains due to Orientation C. Also, pre-anodization of Nb substrates can be employed to induce higher density and more homogeneous nucleation of Nb 3 Sn, and it significantly reduce the large lateral growth of the thin grain with Orientation C as seen in Fig. 11(a,b) [18,35]. The relatively thin grain in Fig. 11 is observed in the cavity showing no degradation of superconductivity till 17 MV/m similar to ERL 1-4 in Fig. 1(b), and this demonstrates that detrimental effects of thin grains on Nb 3 Sn SRF cavities can be prevented by proper amount of Sn-supply and inducing homogeneous nucleation of Nb 3 Sn using pre-anodization of Nb substrates. It is possible that Nb oxide layers on the surface may affect the epitaxial growth of Nb 3 Sn on Nb and orientation relationships between Nb 3 Sn/Nb, and it requires further investigation to understand clearly. The effect of Sn-deficient Nb 3 Sn on the superconductivity of Nb 3 Sn SRF cavity is anticipated as obviously unfavorable since T c of Sn-deficient Nb 3 Sn (17 at.%Sn) decrease from 18.3 K of perfect Nb 3 Sn to 6 K, which is even less than T c of Nb (9.2 K). Distribution of Sn-deficient regions in the Nb 3 Sn coatings and the detailed correlation between Sn-deficient regions and SRF cavity performance may need further studies.