Critical currents, I_c-anisotropy and stress tolerance of MgB₂ wires made by internal magnesium diffusion

Critical current densities (J_cm) at variable temperatures (4.2–25 K) and external fields (up to 9 T) obtained by VSM measurements are shown by figure 2 together with J_ct (4.2 K) from the DC transport measurement between 4 and 8 T.

Zoom In Zoom Out Reset image size

One can see very good agreement between the J_cm(B) and J_ct(B) measured at 4.2 K, which was not observed for the PIT in situ made MgB₂. Usually, the in situ MgB₂ wire shows different field dependences for J_cm and J_ct. A relatively good agreement of J_cm and J_ct was obtained at a low field, but as the field increased to around 8 T (at 4.2 K) the J_cm began to drop much faster than the J_ct due to the different current paths for the magnetic and transport current measurements [17]. Consequently, different J_cm(B) are measured when the field direction is parallel or perpendicular to the wire axis due to anisotropic structure of the in situ MgB₂ wires [18].

The estimation of induced electric field during the magnetization was performed for IM1Cu wire by equationE ≈ (d/2)dB/dt, where d is the outer diameter of MgB₂ core and dB/dt is the applied sweep rate (6 mT s⁻¹) [19]. The estimated electric field of 1.8 × 10⁻⁸ V cm⁻¹ correlates well with the E ≈ values calculated for variable dB/dt, ranging from 1 to 18 mT s⁻¹ [19], but it is much lower than the electric field criterion applied for transport measurement (10⁻⁶ V cm⁻¹). Taking into account the large n index of IM1Cu wire (∼40 at 6 T), the comparison of transport and magnetization J_c is reasonable. Identical J_cm(B) and J_ct(B) dependences measured at 4.2 K for IM1Cu wire (shown in figure 2) demonstrate the isotropic character of MgB₂ made by IMD.

Figure 3(a) shows broken IM1Cu wire with clearly visible central hole, MgB₂ area and Ti barrier, and figure 3(b) shows a metallographic view with a compact and hard MgB₂ layer of average thickness ∼70 μm. Average microhardness of HV 0.05 = 1600 MPa was measured in this layer after HT at 640 °C/1 h, which is considerably higher in comparison to in situ MgB₂ with HV 0.05 = 350−500 MPa HT at 650–800 °C/0.5 h [20].

Zoom In Zoom Out Reset image size

Figure 4(a) compares the critical current densities at 4.2 K for undoped MgB₂ (extrapolated to zero field) obtained by the presented IMD process with PIT: I in situ,  E ex situ, M mechanical alloying [21] and also with thin MgB₂ film made by molecular beam epitaxy (MBE) [22]. More than one order of magnitude higher J_c are obtained by IMD in comparison to the in situ PIT process. IMD wire IM1Cu subjected to pressing by 1.9 GPa shows an additional J_c increase of 40%, which correlates with the increased core hardness HV0.05 of the MgB₂ layer from 1600 to 1750 MPa. This confirms the importance of boron powder density for the final current carrying capacity of the MgB₂ compound made by IMD. Also of interest is the identical slope of J_c(B) for I and IM1Cu, which is different in comparison to E, M and MBE. The best J_c(B) dependence is obtained for well textured 200 nm thin MgB₂ film made by MBE with larger J_c for the B direction in the c-axis of MgB₂ grains (perpendicular to MgB₂ film) and a lower one for B perpendicular to the c-axis [22]. J_c extrapolated to low field region (B < 2 T) indicates comparable current densities for E, IM1Cu and MBE approaching 10⁷ A cm⁻² at self-field and ∼10⁶ A cm⁻² at 2 T. Therefore, these three techniques seem to be promising for the low field application of MgB₂. Figure 4(b) compares the engineering current densities (J_e) measured for IM1Cu,  IM4Inc and IM4Gli wire at 4.2 K. Although the fill factors of these wires are quite low (5.7–9.4%), J_e values (10⁴ A cm⁻² at 3.5–5 T) are high enough to be interesting for possible medium field generation at 4.2 K. Further optimization of IMD wire composition (e.g. increased MgB₂ content) is able to increase J_e to higher values.

Zoom In Zoom Out Reset image size

Figure 5(a) shows the critical currents for  IM4Gli wire measured by pulse currents (PCs) between 4.2 and 20 K and external fields of 1–9 T [13]. Comparison of I_c obtained by DC and by PC measurement at 4.2 K and B = 4−8 T (see figure 5(a)) shows good agreement. The corresponding engineering current densities are plotted by figure 5(b):J_e = 10⁴ A cm⁻² measured at magnetic fields between 2.5 and 5 T for the temperature range of 4.2–20 K makes this conductor suitable for cryogen-free applications and for generating low magnetic fields 0.5–3 T, for example in MRI systems [23] or for large wind power generators [24].

Zoom In Zoom Out Reset image size

Critical currents of IM1Cu tapes with thickness 0.69 and 0.48 mm were measured in the parallel and the perpendicular field direction. Figure 6(a) presents the ratio k_a = I_c−par/I_c−perp for these tapes having aspect ratio (width to thickness) b/a = 2 and 3. It is apparent that the current anisotropy of IMD tape increases with the field magnitude and also with b/a ratio.

Zoom In Zoom Out Reset image size

This indicates that some preferential orientation of MgB₂ grains was formed during the Mg-diffusion into the boron layer. The texture of rolled Mg particles and consequent I_c-anisotropy affected by the additions into the Mg + B mixture has been already shown for in situ MgB₂ tapes [25, 26]. Figure 6(a) shows a similar behaviour for flattened Mg core surrounded by boron powder. The anisotropy of the in situ MgB₂ and IMD is compared in figure 6(b), where the k_a ratio at 8 T is plotted versus the aspect ratio b/a. In the case of no addition into MgB₂, the k_a is increasing linearly with b/a for IMD tapes and likewise for in situ tape with b/a = 5 [25], which follows the same tendency. Carbon addition through SiC particles increases the upper critical field of MgB₂ apparently [27]. At fixed intrinsic anisotropy $\gamma =B^{\mathrm {ab}}_{\mathrm {c}2}/B^{\mathrm {c}}_{\mathrm {c}2}$, the current anisotropy k_a is a function of the reduced magnetic field b = B/B_c2 [28] and is also affected by the texture induced by rolling deformation. An increase of B_c2 reduces b = B/B_c2 and consequently a decreased k_a(B) is measured at the given scale of external field [26]. Figure 6(b) confirms the same mechanism of I_c-anisotropy for the rolled in situ and for IMD MgB₂ tapes. This is explained by the preferred orientation of MgB₂ caused by axially unsymmetric Mg-diffusion into boron from the flat Mg core and/or flat Mg particles.

In relation to possible AC applications, the low loss of MgB₂ is an important issue. This could be decreased effectively by a proper twisting of MgB₂ filaments reducing the filament's coupling. But the twisting process introduces torsion stress into composite wire and it may reduce the critical current considerably [29]. Therefore, IM4Gli wire of 0.86 mm has been twisted with variable twist pitches L_t = 2.5−50 mm, heat treated and measured at 4.2 K. Figure 7(a) shows the J_c(B) characteristics of twisted wires compared to untwisted wires. The small J_c degradation caused by twisting up to short twist (2.5 mm) is surprising. Consequently, J_c = 10⁴ A cm⁻² measured at B = 7.6 T in untwisted wire is shifted only slightly to B = 7 T for L_t = 2.5 mm. Figure 7(b) compares the normalized critical currents versus the L_t/d_w ratio (d_w is the wire diameter) for two different in situ samples and IM4Gli wire.

Zoom In Zoom Out Reset image size

It has been already shown that critical degradation by twisting depends on the wire composition, filament structure and heat treatment conditions [29]. Reduction of the current carrying capability in twisted in situ wires is attributed to the reduced filament's density prior to final heat treatment [29]. Figure 7(b) shows the corresponding critical current degradation for in situ 4- and 30-filaments wires sheathed by AgMg and GlidCop, respectively. The mechanically stronger GlidCop sheath makes it possible to apply shorter L_t than the softer AgMg one. The IM4Gli wire shows 90% of the original I_c for L_t/d_w = 10 (L_t = 8.6 mm). The smaller sensitivity of IMD wire to twisting can be attributed to the lower sensitivity of boron powder density reduced by torsion stress in comparison to the Mg + B powder mixture used for the in situ process. Figure 7(c) presents the measured magnetization AC losses versus temperature for twisted IM4Gli wires at frequency 72 Hz and external field 37 mT. The plateau of losses at temperatures near to 18 K indicates the presence of coupling currents. AC magnetization losses of all samples increase with the temperature from 18 K up to a maximum at 32 K. This is caused by decreased critical current density J_c and subsequent penetration of the magnetic flux deeper into the filaments at the AC field of 37 mT, which results in a hysteresis loss addition to the coupling ones. The maximum of the AC loss represents full penetration of the magnetic flux at given temperature and AC field. One can see that the AC loss due to coupling current is considerably decreased by the applied twisting to L_t = 10 and 5 mm. The AC loss of this wire at 20 K is reduced by ∼60% for L_t = 10 mm (∼90% I_c) and by one order of magnitude in comparison to the untwisted one with L_t = 5 mm (∼80% I_c). Consequently, low critical current reduction by twisting and effective reduction of AC losses can be utilized for future filamentary IMD wires.

Practical superconducting wires are usually tested by axial tension to unveil their strain tolerance, which is important for possible coil applications. Figure 8 shows normalized I_c(ε) dependences for the two presented IMD wires (IM4Inc and IM4Gli) and for one in situ four-filament wire sheathed by Inconel [30]. A nearly identical increase of critical current with the tensile strain has been measured for both  IM4Inc and IM4Gli wires at ε < ε_irr. The less gradual I_c degradation of the in situ wire above ε_irr in comparison to IM4Inc and IM4Gli wires can be explained by the different MgB₂ cores densities (HV 0.05 ∼ 1600 MPa for IMD, and ∼400 MPa for in situ [20]). A similar difference has been observed between in situ and ex situ MgB₂ wires subjected to tensile stress, where better connected grains of the in situ wire showed more radical I_c decrease above ε_irr.

Zoom In Zoom Out Reset image size

Comparably designed in situ wire with Inconel sheath also shows less steep I_c increase below ε_irr than does IM4Inc. The  IM4Inc wire also has higher irreversible strain of 0.43% in comparison to the in situ one of ε_irr = 0.38%. Nishijima et al have compared the strain tolerance of two MgB₂/Fe wires made by in situ PIT and IMD processes [31]. The IMD-processed wire showed larger irreversible strain and smaller strain sensitivity than the PIT-processed one (ε_irr is 0.67% and 0.54% for IMD and PIT wires, respectively), which has been explained by a porous structure of the MgB₂ made by the PIT process. It should be noted that different HTs have been used (670 and 800 °C) for the compared wires [31], which also influences the mechanical strength of the iron sheath. Similarly, in our case HTs at 640 and 850 °C have been applied for IMD and PIT, which affect the strain tolerances of the compared conductors as already shown for filamentary MgB₂ wires with variable sheaths and HT conditions [32].