We have shown recently that the addition of rare-earth (RE) elements can significantly enhance the critical current density ($J_c$) of V_0.6Ti_0.4 alloy [1], [2]. This is due to the fact that RE elements are immiscible in the body centred cubic (bcc) V-Ti phase and form precipitates. The RE-rich precipitates act as barrier to the growth of grains, which results in the increase of grain boundary density. Since, the grain boundaries are effective flux line pinning centres in V-Ti alloys, the $J_c$ is enhanced considerably. The increase in $J_c$ is found to depend on the RE element introduced as well as its concentration. Among all the RE elements, we found that the addition of 1 at.% ferromagnetic Gd produces maximum $J_c$ enhancement. The superconducting critical temperature ($T_c$) is also observed to increase slightly with Gd addition [3].

The solubility of RE elements in the bcc materials like Ta and Nb is also very low (< 0.5 at.%) [4], [5], [6]. Koch and Love showed that the $J_c$ of Nb can be enhanced by the addition Y and Gd [7]. The above studies suggest that the $J_c$ of Ta-Ti and Nb-Ti superconducting alloys might also be improved by Gd addition. The Ta_0.4Ti_0.6 and Nb_0.6Ti_0.4 alloys crystallize in bcc structure, similar to that of V_0.6Ti_0.4 [8], [9]. Therefore, we compare here the $J_c$ of Ta_0.4Ti_0.6 and Nb_0.6Ti_0.4 alloys before and after the addition of Gd.

We observe that Gd precipitates in the Ta-Ti and Nb-Ti alloys, as observed in the case of V-Ti. Gd addition to Nb_0.6Ti_0.4 results in the reduction of grain size by 3 times, while a slight reduction was observed in the Ta_0.4Ti_0.6 alloy. The Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6 alloys continue to superconduct even after Gd addition, with the lowering of $T_c$ in Nb_0.6Ti_0.4 and increase in Ta_0.4Ti_0.6. The $J_c$ increases substantially with Gd addition to Nb_0.6Ti_0.4, whereas a very small increase in $J_c$ was found in the case of Ta_0.4Ti_0.6 below 5 T.

The polycrystalline samples used in this study were synthesized by arc melting appropriate amounts of pure (>99.9%) constituents elements in high purity Ar (>99.99%) atmosphere. The nominal elemental composition (in at.%) of the samples used in this study are shown in Table 1. The Ta-Ti and Ta-Ti-Gd alloys were annealed at 1000 °C for 12 h in a vacuum better than 10^-5 Torr, to improve the homogeneity. A portion of each sample was well polished, before the microstructural characterisation using scanning electron microscope (SEM, Carl Zeiss, Germany) coupled with energy dispersive analysis of x-rays (EDAX). The polished samples were chemically etched with Kroll’s reagent (2 ml HF, 3 ml HNO₃ in 100 ml distilled water) to reveal the grain boundaries. The resistivity measurements were performed in 9 T Physical Property Measurement System (PPMS, Quantum Design, USA). The magnetisation of the samples were measured using Superconducting Quantum Interference Device based Vibrating Sample Magnetometer (MPMS-3 SQUID-VSM, Quantum Design, USA).

The results of microstructural characterisation for V-Ti and V-Ti-Gd alloys can be found elsewhere [1], [10]. Gd precipitates in clusters with an average size of 2 μm in the V-Ti matrix, mostly along the grain boundaries. Moreover, addition of Gd results in the reduction of grain size by an order of magnitude in the V-Ti alloy [1]. The reduction in grain size results in the increase in grain boundary density. The optical images of R-Ti and R-Ti-Gd (R = Ta, Nb) alloys are shown in Fig. 1. The grain size reduces with Gd addition in Nb-Ti alloy. The average grain sizes of the alloys were estimated by taking the square root of the average grain area. The average grain area was obtained after computing the grain areas of a large number of grains using the imageJ software. The average grain size of the Nb-Ti alloy is 63 μm. The average grain size estimated in the Nb-Ti-Gd alloy is 22 μm, which is considerably lower than the parent alloy. However, no significant reduction of grain size is observed with Gd addition to the Ta-Ti alloy. The estimated grain size in Ta-Ti and Ta-Ti-Gd alloys are 120 μm and and 108 μm respectively. Comparing the R-Ti and V-Ti alloys, the maximum reduction of grain size with Gd addition is observed in V-Ti and the least reduction is seen in Ta-Ti. The SEM images of Nb-Ti-Gd and Ta-Ti-Gd alloys are presented in the top panels of Fig. 2(a) and (b) respectively. The elemental mapping of both the alloys are then shown in the lower panels. Nb (Ta) and Ti are uniformly distributed through out the whole sample in Nb-Ti-Gd (Ta-Ti-Gd). Gd is immiscible in both the Nb-Ti and Ta-Ti matrix and form precipitates, which can be inferred from the lower panels in both the figures. The results are similar to that observed in V-Ti-Gd alloy [1]. The presence of Gd-rich clusters in Ta-Ti-Gd and Nb-Ti-Gd were further confirmed using point analysis EDAX. The Gd-clusters have Gd conc. above 85 at.% in both the alloys. The distribution of Gd-clusters in Nb-Ti-Gd seems to follow a pattern similar to the distribution of Y in V-Ti-Y alloys [2] and Gd in V-Ti-Gd alloys [1]. Connecting the Gd-rich precipitates (see lower panel of Fig. 2(a)), an indication is obtained they lie on the grain boundaries. The grain size obtained in this case is 20μm which is approximately the same as obtained from optical images. One of the grain boundaries in Ta-Ti-Gd alloy is marked in the top panel of Fig. 2(b). Since the grain size is around 85μm, one can conclude from Fig. 2(b) that Gd is present along the grain boundary as well as inside the grains. The average size of Gd precipitates in the Ta-Ti-Gd and Nb-Ti-Gd alloys are approximately 1.2 μm and 2 μm respectively.

The temperature dependence of magnetisation ($M(T)$) of R-Ti and R-Ti-Gd (R = V, Nb, Ta) alloys in the temperature range 4–10 K is shown in Fig. 3(a). All the alloys are superconducting, which can be inferred from the sharp drop in ($M(T)$ below the transition temperature ($T_c$). A slight increase in $T_c$ after Gd addition has been reported in the V-Ti alloy. The addition of Gd to Ta-Ti alloy resulted in an increase in $T_c$ from 6.7 K to 7 K. However, the $T_c$ dropped by 0.15 K when Gd was added to the Nb-Ti alloy. Similar drop in $T_c$ was observed when Gd (2 at.%) was added to pure Nb [11]. The $M(T)$ for the Gd containing alloys in the range 10–320 K is shown in Fig. 3(b). The most striking observation is the presence of paramagnetic to ferromagnetic transition around 295 K in the V-Ti-Gd alloy, but the absence of the same in the Nb-Ti-Gd and Ta-Ti-Gd alloys. The inset to Fig. 3(b) shows the normal state $M(H)$ for the Gd containing alloys. The saturation of magnetisation is observed for the V-Ti-Gd alloy near 1 T, indicating the presence of ferromagnetic order. On the contrary, the $M(H)$ curve is almost linear for the R-Ti-Gd (R = Ta, Nb) alloys, with slight non linearity in low fields. This indicates the absence of long range ferromagnetic order in the Ta-Ti-Gd and Nb-Ti-Gd alloys. A detailed analysis on the above aspect is currently in progress.

In order to study the effect of adding small amounts of Gd on the $J_c$ of the R-Ti alloys, the field dependence of magnetisation at 4 K were measured for all the alloys with and without Gd. The $M(H)$ at 4 K for R-Ti and R-Ti-Gd (R = Nb, Ta) is shown in Fig. 4. The width of the hysteresis increases significantly in the entire field regime with Gd addition to Nb-Ti alloy. In contrast, a very small increase in hysteresis is observed only at low and intermediate fields in case of Ta-Ti alloy. The irreversibility field ($H_{i r r}$) increases with Gd addition to Nb-Ti alloy and no change in $H_{i r r}$ is observed in case of Ta-Ti. The $J_c$ (shown in Fig. 5(a)) is estimated from M-H hysteresis loop using Bean’s critical state model, where $J_c$ is given by the expression [12]:

Here w and t (w>t) are the width and thickness of the sample normal to the applied field and ΔM is the difference in M (at a particular H) obtained during increasing and decreasing H cycles. The addition of Gd enhanced the $J_c$ in each of R-Ti alloys in the entire measured field region (see Fig. 5(a)). The only exception is the Ta-Ti-Gd alloy, where $J_c$ is lower than the parent alloy for H > 5 T. The maximum increase (by 20 times in 1 T) in $J_c$ is observed for the V-Ti-Gd alloy. A 5-fold increase in $J_c$ is observed in 2 T and 5 T, in the case of Nb-Ti alloy with Gd addition. The minimal increase in $J_c$ (by 1.3 times in 2 T) is observed for Ta-Ti alloys. The influence on $J_c$ can be correlated with flux line pinning properties by estimating the pinning force density($F_p$) as $F_{p}=J_{c} \times H$. The $F_{p}(H)$ curves for all the alloys are shown in Fig. 5(b). The maximum value of Fp ($F_{\text {pmax }}$) observed in V-Ti-Gd is 1.54×10⁸N/m³, which is the highest among all the alloys. The $F_{\text {pmax }}$ increases from 1.9×10⁷N/m³ to 6.4×10⁷N/m³ and from 4×10⁷N/m³ to 7.6×10⁷N/m³ with Gd addition in the Nb-Ti and Ta-Ti alloy, respectively. Though V-Ti-Gd has the highest $F_{\text {pmax }}$, the $F_p$ value drops by two orders of magnitude in 7 T. However, a significant amount of $F_p$ is still observed for Nb-Ti-Gd in 7 T field.

In order to get insight into the pinning mechanisms in the Ta-Ti and Ta-Ti-Gd alloys, we have used the Dew-Hughes scaling procedure [13]. According to Dew-Hughes flux pinning model, the normalised flux pinning density $f_{p}=F_{p} / F_{p \max }$ is proportional to $h^{p}(1-h)^{q}$, where $h=H / H_{i r r}$. The field at which the irreversibility vanishes and $F_p$=0, is considered as Hirr. The set of parameters p,q and the peak position $h_{\max }=p /(p+q)$, uniquely identifies the dominant pinning mechanism. For instance, p=0.5,q=2 with $h_{\max }=0.2$ indicate that flux pinning is by surface pinning centres (grain boundaries). The $F_p(H)$ analysis of V-Ti-Gd alloys using Dew-Hughes model indicates that the larger grain boundary density (relative to V-Ti alloy) is responsible for enhanced flux line pinning [1]. Fig. 5(a) shows the $f(h)$ curve obtained for the Ta-Ti alloy at 4 K. The solid line (orange color) shows the fit using the scaling law $h^{p}(1-h)^{q}$. For h<0.7 (excluding the peak effect [14] region), the experimental curve is well fitted with the parameters p=0.4 and q=1.79. The peak position ($h_{max}$=0.18) along with the values of p and q, indicate pinning is mainly due to the grain boundaries (normal surface pinning centres [13]). The slight deviation in the parameters from the theoretical values may be due to the presence of dislocation pinning (p=1.5,q=1), which tends to shift the value of q towards 0.6 [13]. The f(h) curve for Ta-Ti-Gd alloy (Fig. 6(b)) shows a sharp peak at h=0.06, followed by a hump around 0.25. For h>0.25 (ignoring the peak effect region) the experimental curve exactly follows the theoretical curve predicted for normal surface pinning (grain boundaries). However, the peak at 0.06 cannot be explained by using Dew-Hughes model. A reasonable fit could be achieved considering an additional normal surface pinning contribution $h^{0.5}\left(1-h^{\prime}\right)^{2}$ (where $h^{\prime}=0.21 h$), which contributes only at low fields. Such contribution can arise due to pinning by regions which are superconducting only at low fields due to proximity effect [2], [15]. Moreover, a common feature observed in both these alloys is the presence of peak effect around 6.15 T (see Fig. 5(a) and (b)). The peak effect is characterised by a maximum in the $J_c$ and $F_p$ in the vicinity of $H_{irr}$ [14], [16], [17]. The peak effect can arise due to softening of elastic modulus of a vortex lattice [18], crossover from weak collective pinning to strong pinning [19], Bragg-glass disordering transition or order–disorder transition [20] or the presence of multiple superconducting phases [21]. A recent report suggest that Ta-Ti alloys can form in two different bcc phases [22], [8]. Moreover it has also been reported that the Ta-Ti samples needs to be melted several times and then annealed, in order to obtain a perfectly homogeneous matrix [8]. Hence, the peak effect in these alloys may be due to the difference in $T_{c}^{\prime} s$ of various phases. The exact origin of peak effect in these alloys will be explored and published elsewhere.

The $H_{irr}$ of the Nb-Ti and Nb-Ti-Gd alloys is above 7 T at 4 K. We tried fitting the $f(h)$ curves using extrapolated $H_{irr}$ values. However, the parameters p and q obtained could not be associated with any of the functions derived by Dew-Hughes. Hence, we have used two different scaling procedures where H is normalised by $H_{max}$ ($H=H_{\max } $, when $ F_{p}=F_{p \max } $) [23], [24] and $H_n$ ($H=H_n$, when $ F_{p}=F_{p \max } / 2 $ in the high field regime) [25]. The f vs $ h_{m}\left(=H / H_{\max }\right) $ curves for Nb-Ti and Nb-Ti-Gd alloys is presented in Fig. 7(a). The solid lines are the theoretical curves expected for pinning by normal point (green) and normal surface (orange) pinning centres, when hm scaling is used [23], [24]. The comparison with the curves obtained for Nb-Ti and Nb-Ti-Gd alloys, shows that pinning is due to the surface like pinning centres (in low and intermediate fields). A close inspection of the experimental curves reveals that the deviation from surface pinning curve occurs at a higher field for the Nb-Ti-Gd alloys, than in Nb-Ti alloys. This is expected, since Nb-Ti-Gd has larger grain boundary density. Moreover, the $h_m$ scaling procedure indicates that both the alloys have a deficit of high field surface and normal point pinning centres. The other scaling procedure based on $h_n$ scaling has been used to explain the pinning behavior in MgB₂ superconductor [25]. The solid curves shown in Fig. 7(b) represents the behavior of normal surface and point like pinning centres, for the special case of a low anisotropic dirty MgB₂ superconductor. According to this scaling, the peak is observed at 0.34 and 0.47 for normal surface and point pinning centres, respectively [25]. The $f(h_n)$ curves for Nb-Ti and Nb-Ti-Gd are roughly similar to the surface pinning curve (for $h_n$<1) and show a peak at 0.34. This indicates that grain boundary pinning is dominant in both these alloys. For $h_n$>1, the curve for Nb-Ti-Gd alloy matches roughly with the point pinning curve. This indicates that additional point pinning centres are created due to Gd addition to Nb-Ti alloys, which enhances the high field Jc. The presence of very small clusters of Gd can act as a point defect. Pinning in Nb-Ti-Gd is best explained by $h_n$ scaling.

The results presented so far show that the $J_c$ of Nb and Ta based Ti alloys can be enhanced by adding 1 at.% Gd. This encouraged us to check whether similar enhancement could be obtained in commercial Nb-Ti alloy compositions. The Nb-Ti alloys generally used for commercial purpose have Ti concentration between 60-66 at.% [26], [27], [28], [29]. Hence, we chose Nb_0.37Ti_0.63 and the effect of adding 1 at.% Gd to it is shown in Fig. 8. The $J_c$ at 4 K increases in the entire field regime and an order of magnitude increase is observed in 1 T (see Fig. 7(a)). The $F_{pmax}$ of Nb_0.36Ti_0.63Gd_0.01 is 9 times greater than that of the parent Nb_0.37Ti_0.63. Additionally, the $T_c$ increases by 0.5 K with 1 at.% Gd addition to Nb_0.37Ti_0.63, as shown in the inset to Fig. 8(b). The production of commercial Nb-Ti alloys involves repeated cold working followed by annealing at 350-500 °C [28], [29]. Annealing at these temperatures results in formation of α-Ti precipitates which are one of the dominant flux pinning centres in the those alloys [26], [27], [28], [29]. The field dependence of $J_c$ and $F_p$ of the ANN samples are shown in Fig. 8(a) and (b), respectively. Here ANN indicates that the as cast (AC) samples were cold rolled to achieve a thickness reduction of 50%, followed by annealing at 450 °C for 5 hours. The $J_c$ increases drastically in both these alloys due to cold rolling followed by annealing, as expected due to the formation of α-Ti precipitates. The $J_c$ (H = 5 T, T = 4 K) of ANN Nb_0.36Ti_0.63Gd_0.01 is approximately 5 times greater than that of the ANN Nb_0.37Ti_0.63. The $F_{p}(H=6.5T)$ of ANN Nb_0.36Ti_0.63Gd_0.01 reaches a value of 4.34×109N/m³, which is 4 times higher than that of ANN Nb_0.37Ti_0.63. Further studies and cold rolling and heat treatment protocols to increase the $J_c$ in Nb_0.36Ti_0.63Gd_0.01 are currently being made, and will be presented elsewhere.

The present study indicates that while Gd has low solubility in both Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6 alloys, the grain refinement due to Gd addition is more effective in Nb_0.6Ti_0.4, as compared to Ta_0.4Ti_0.6. The maximum value of flux pinning force density increases by 350% and 170% at 4 K after Gd addition to Nb_0.6Ti_0.4 and Ta_0.4Ti_0.6 alloys respectively. The creation of additional grain boundaries and point defects, which act as pinning centres is responsible for improving the flux pinning characteristics in Nb_0.6Ti_0.4. The presence of some additional normal surface pinning mechanism that is active only at low fields, as well as an increase in grain boundary pinning, are responsible for increase in the flux pinning density in Ta_0.4Ti_0.6-Gd. Preliminary results on the effect of Gd addition to commercial Nb-Ti alloys (for eg. Nb_0.37Ti_0.63) suggest that Gd addition can be used to boost the $J_c$ of commercial Nb-Ti alloys.

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.