Nonsaturated pinning characteristics by normal precipitates in superconducting NbTa

Nonsaturated pinning characteristics by normal precipitates in superconducting Nb-Ta* T. M a t s u s h i t a , N. Harada and K. Y a m a f u j i Department of Electronics, Kyushu University 36, Fukuoka 812, Japan Nonsaturated pinning characteristics and elastic and plastic properties of a fluxoid lattice were measured by an a.c. inductive method for superconducting Nb-Ta tapes with normal Nb2N precipitates. The Labusch parameter characterizing an elastic constant of the pinned fluxoid lattice decreased fairly linearly with increasing magnetic field, and increased with increasing volume fraction of normal precipitates. The interaction distance, the maximum reversible displacement at the yield point, was kept nearly constant or increased up to a vicinity of the upper critical field for strongly pinned specimens. This behaviour in the interaction distance, which is quite different from the case of saturation, suggests that the defective fluxoid lattice is stabilized by strong pinning interactions. The dependence of the macroscopic pinning force on the pinning parameters estimated from electron micrographs was also investigated. It seems to agree with the linear summation theory better than the Larkin-Ovchinnikov theory.

Keywords: superconductor; pinning force density; normal precipitate; a.c. inductive measurement; summation problem; nonsaturation

Critical current density is one of the most important parameters for the application of superconductors to power systems. It is desirable to increase the critical current density by manipulating the pinning structure. An improvement from saturated characteristic in Nb3Sn to nonsaturated characteristic with a superior pinning property at high fields is particularly required. For this purpose, it is necessary to understand the pinning characteristic in saturation and nonsaturation regions. The former has been investigated in detail by an a.c. inductive method and it has been elucidated 1'2 that the fluxoid lattice becomes harder and more brittle with increasing pinning strength, resulting in almost no variation in the yield strain, the macroscopic pinning force. This behaviour contradicts the models 3 - 5 of simple shearing flow but is explainable by the avalanching depinning model 1'2. The pinning behaviour in the nonsaturation regime has also been investigated 6-8. However, the relation between saturation and nonsaturation has not yet been clarified. It has recently been shown 1 that the interaction distance, the maximum reversible displacement of the fluxoids, was increased at the transition from saturation to nonsaturation, suggesting that the brittle fluxoid lattice was stabilized by strong pinning centres. The stability of the fluxoid lattice in the nonsaturation regime was assured again 9 in Nb-Ta, which contained Nb2N precipitates as strong pinning centres. *Paper presented at The International Conference on Critical Currents in High-Temperature Superconductors, Snowmass Village, Colorado, USA, 1 6-1 9 August 1 988 0 0 1 1 - 2 2 7 5 / 8 9 / 0 3 0 3 2 8 ~ 6 $03.00 ~ 1989 Butterworth & Co (Publishers) Ltd

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Cryogenics 1989 Vol 29 March supplement

In this paper, elastic and plastic properties of the fluxoid lattice pinned by normal precipitates with large interaction forces are investigated in detail. The result is compared with the avalanching depinning model. As for the summation problem in the strongly pinned nonsaturation regime, the Larkin-Ovchinnikov theory TM and the linear summation theory ~ were proposed, and predicted dependences of the pinning force density on the pinning parameters, the elementary pinning force fp and the pin concentration Np are different in respective theories. The pinning-parameter dependence is a fairly important factor in designing a strong pinning structure in superconducting wires. Hence, it is necessary to clarify the dependence so that the critical current density can be estimated. For this purpose, the pinning-parameter dependence is also investigated for the present system.

Experimental details Specimens were Nb-50 at% Ta tapes, 0.5 mm thick, 5 mm wide and 50 mm long. The tapes of specimens 1-8 (group I) were prepared by Kobe Steel Ltd, and in the case of the other tapes of specimens 11-18 (group II), a rod of the alloy was provided by Showa Electric Wire & Cable Co. Ltd and was cold rolled into tapes. These tapes were heat treated at a temperature higher than 1900°C for group I and at 1900°C for group II for 10 h in a vacuum higher than 7 x 1 0 - S P a (5 x 10 -~ torr) to outgas and remove dislocations. The specimens were put in nitrogen atmosphere of 1800°C and 1.3 x 10 -z Pa (1 × 10 -4 torr) for 100 h so that nitrogen completely diffused into the specimens. These were then quenched

Nonsaturated pinning characteristics in Nb-Ta: T. Matsushita

et al.

T a b l e 1 The condition of heat treatment, the upper critical field and the pinning parameters of the specimens. Specimen 11 contains two types of precipitates and the parameters are not given in the table Heat treatment Group

Specimen Temperature (°C)

Time (h)

Bc2 (T)

No (1018 m -3)

1 2 3 4 5 6 7 8

550 600 650 700 750 850 900 1000

50 1 O0 1 O0 1O0 1O0 110 80 40

0.27 0.31 0.26 0.26 0.25 0.25 0.23 0.20

0.86-1.7 0.19-0.39 0.40-0.81 0.35-0.71 0.84-1.7 0.41-0.82 -

11 12 13 15 t6 17 18

500 500 500 550 550 550 550

1O0 50 20 1 O0 50 5 0.5

0.465 0.453 0.449 0.463 0.447 0.450 0.448

5.2-10 ', 0.23-0.46 " 2,9-5.8 0.27-0.53 0.25-0.50 -

and annealed at temperatures ranging between 500 and 1000°C in order to form normal NbEN precipitates. Conditions of annealing are given in Table 1. Figure la, b and c shows examples of transmission electron micrographs. Precipitate particles had the shape of a long ellipsoid or cylinder. From observed diffraction patterns of the electron beam, the precipitates were identified as normal NbzN phase with a hexagonal close-packed structure (fl phase). Thickness of the observed region in specimens could not be exactly determined, and the density Np of the precipitates estimated from micrographs had an uncertainty of factor 2, at most. The elementary pinning force fp of the precipitates was theoretically estimated from a shape and size for a given magnetic field. The method of estimation is explained in detail in Reference 9. Obtained pinning parameters in each specimen are given in Table 1. A.c. inductive measurement 12 was carried out on each specimen at 4.2 K; d.c. and superposed a.c. magnetic fields were applied parallel to a long axis of the specimen. The frequency of the a,c. magnetic field was 40.2 Hz. From the measurement, critical current density and force~lisplacement characteristics were obtained. The upper critical field B¢2 was defined by the magnetic field at which extrapolation of the obtained pinning force density from a proper level reaches zero. The results of Bc2 are given in Table 1. The Ginzburg-Landau parameter x obtained from the d.c. magnetization measurement was 3.8 for specimen 2 and 3.9 for specimen 11.

Results Observed pinning force density is shown in Figure 2a and b. Residual pinning force density in an outgassed specimen was 4 × 104 N m -3 at b = 0.7, where b = B/B~2 is a reduced field. The pinning force density shown in Figure 2a and b is much larger than this value and can be attributed to the pinning by the normal precipitates.

fp at b = 0.65 (10 -10 N) 0.25 0.70 0.43 0.65 0,27 0.31

0.14 1.2 0.22 1.1 1.3

It decreases fairly linearly with an increasing magnetic field except in the vicinity of the upper critical field for the specimens heat treated at lower temperatures, and is not saturated to a certain value. Hence, it is concluded that the present specimens have nonsaturation characteristics due to the normal precipitates with strong interactions. For the specimens heat treated at higher temperatures, the pinning force density decreases more rapidly with an increasing field. The region of pronounced curvature in the vicinity of the upper critical field increases systematically with a decreasing pinning force density. This curvature exists even in the case of strongly pinned nonsaturation. This behaviour is considered to come from a brittleness of the fluxoid lattice due to a large inhomogeneity in the vicinity of the upper critical field. More detailed discussion of this point is given in Reference 9. Figure 3 represents an example of obtained forcedisplacement characteristic. The Labusch parameter and the interaction distance, which characterize an elastic and plastic property of the fluxoid lattice, are obtained from this curve 9. The Labusch parameter e L, which is a spring constant per unit length of the fluxoid, is depicted in Figure 4a and b. It decreases fairly linearly with an increasing field at high fields and decreases systematically with a decreasing pinning force density. This result is understandable, since the fluxoids are considered to be directly pinned by the normal precipitates. The interaction distance di, which gives a maximum reversible displacement of the fluxoids at the yield point, is shown in Figure 5a and b. For the strongly pinned specimens which were heat treated at lower temperatures (except for specimens 7 and 8), the interaction distance is almost constant or increases up to a certain value of the magnetic field, and then decreases drastically. For weakly pinned specimens 7 and 8, the region in which the interaction distance decreases widens. The decrease in di in this region is associated with a concave curvature in Fp shown in Figure 2a and b and shows 9 that the fluxoid lattice becomes brittle.

Cryogenics

1989

Vol 29 March supplement

329

Nonsaturated pinning characteristics in Nb-Ta." T. Matsushita et al.

o

2

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2 F i g u r e I Transmission electron micrographs ofthe pinning centres on (a) specimen 7, (b) specimen 12 and (c) specimen 17 B

Discussion

E

The interaction distance, which gives the critical displacement at the yield point, takes approximately a constant value or gradually increases, except in the vicinity of Bcz. This behaviour is quite different from the case of saturation 1'2, where the interaction distance decreases drastically, showing that the fluxoid lattice becomes brittle with an increasing field. It means that the fluxoid lattice is stabilized without becoming brittle in the nonsaturation regime. This stability in the defective fluxoid lattice is considered to be attained by strong pinning interactions. That is, the strong pinning interactions will prevent a local plastic deformation from developing to a cata-

330

Cryogenics 1989 Vol 29 March supplement

Z

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Force-displacement curve observed for specimen 1 5 at b

Nonsaturated

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c h a r a c t e r i s t i c s in N b - T a :

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I 0.8

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Interaction distance on the specimens of (a) group I and

11; ~, 12; [3, 13; O, 15; A, 16; i , 17;V, 18

(b) group I1. (a): O, 1 ; ,~, 2; O, 3; ~7, 4; Q, 5; A, 6 ; . , 7; V, 8. (b): ©, 11; A, 12; I~, 13; O, 15; A, 16; m, 17;V, 18

strophic instability on a global scale, the flux flow. The correlation length is known to have a large value near the bifurcation point at which a catastrophic phenomenon such as the avalanching depinning occurs. The transition from saturation to nonsaturation seems to be explained by a reduction of elastic correlation length due to a stronger restraint by pins. A smaller elasticity of the highly disordered fluxoid lattice will also contribute to a smaller correlation length. Here we discuss the summation problem, i.e., the dependence of the pinning force density on the elementary pinning forceJ~ and the pin concentration Np. As for the theory which describes the pinning force density proportional to ( 1 - b) in nonsaturation regime, the Larkin-Ovchinnikov theory 1° and the linear summation theory 11 were proposed. According to the Larkin-Ovchinnikov theory, the pinning force density is given by Fp = (,uo Nvf;/4zr 2 4 1/2 B 2 k h2 af6 ~) 1 / 3 (1)

provides

where k2 = ( I - b ) / ) . 2 with ). denoting the penetration depth. On the other hand, the linear summation theory

Fp = ¢Npfp

(2)

where ( represents a pinning efficiency and is given by ¢ = (dp - aO/(dp + aO

(3)

with dp = N~- 1/3 denoting a mean spacing of the pinning centres. For the present specimens dp is much larger than the fluxoid spacing af and ( can be approximately regarded as a constant except in the low field region. Figures 6 and 7 are plots of the pinning force density at b = 0 . 6 5 versus the theoretical pinning-parameter dependences, -N- p 2/3 . f413 and Npfp, respectively. The /p hatched region in Figure 6 represents the theoretical expression of Equation (1). The line in Figure 7 shows Equation (2) with substitution of ~ = 0.17 in order to obtain a good fit, while Equation (3) leads to ~ -~ 0.8. That is, the estimate from the linear summation theory is approximately larger by a factor 5 than the experimental results. In these figures, the experimental results of Antesberger and Ullmaier 6, labelled A8, A18, and A20,

C r y o g e n i c s 1 9 8 9 Vol 29 M a r c h s u p p l e m e n t

331

Nonsaturated pinning characteristics in Nb-Ta." T. Matsushita et al. 108

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A~fp (Nm -3 ) F i g u r e 7 Pinning force density versus the function Npfp predicted by the linear summation theory 11 at b = 0.65. The solid line represents Equation (2) with ( = 0.1 7. Data from Antesberger and Ullmaier s are also shown

are also shown. For these results, the elementary pinning force of a platelike precipitate is recalculated by taking account of simultaneous interactions with many fluxoids (see Reference 9). It can be said from Figure 6 that the Larkin-Ovchinnikov theory neither explains the experimental results quantitatively nor qualitatively. For the present specimens, particularly, the Larkin-Ovchinnikov theory derives very large values: these are even larger than the direct summation. One reason for such a large value of the Larkin-Ovchinnikov theory is found in the fact that the pin concentration in the present specimens is too low: it is not realistic to assume that many pinning centres are contained within the transverse coherent area of Ra~, ~- a~, since the size of the precipitates is much larger than af. A use of nonlocal theory on the tilt modulus of the fluxoid lattice is also responsible for the too-large pinning force density. It has been recently pointed out 13 that the local modulus 14 should be used instead of the nonlocal one. Use of the local modulus with a larger value reduces the pinning force density. It is concluded from Figure 7 that the linear summation theory is qualitatively satisfactory. The result of this theory is larger by a factor 5 than the experimental result.

332

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e L = 2 x 3+afNpfp

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161

This deviation seems to be caused by too-simplified treatment, and more exact theoretical treatment is needed. As for the Labusch parameter, the linear summation theory11 predicts that

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F i g u r e 6 Pinning force density versus the function N2/3 f4/3 predicted by the Larkin-Ovchinnikov theory 10 at b = 0.65.

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Cryogenics 1989 Vol 29 March supplement

(4)

which suggests that the field dependence of % is approximately expressed as eL oc b-I/Z(l - b ) , with substitution offp oc (1 - b). This field dependence agrees fairly well with the present experimental result. Equation (4) insists that the pinning parameter dependence of e L is the same as that of Fp. Figure 8 represents plots of e L versus Npfp predicted from the theory. However, the present experimental result shows that eL has a stronger pinning-parameter dependence than expected. This is coupled with a decrease in the interaction distance d i with an increase in the pinning parameters. The above results for e L and d i imply that the flux pinning phenomena in the nonsaturation region are not simply described by the linear summation theory, although the resultant global pinning force agrees qualitatively with its expectation. In specimens containing precipitates of large concentration, e L and d i are likely to have larger and smaller values than expected, respectively. The quantitative disagreement in Fp shown in the above seems to be mainly caused by the disagreement in e L shown in Figure 8. In summary, the force~lisplacement curve which characterizes the elastic and plastic properties of the pinned fluxoid lattice has been found to vary, as shown in Figure 9a and b, with an increase of some pinning function such a s Npfp in the regions of saturation and nonsaturation, respectively. Conclusion

The pinning characteristic and the elastic and plastic property of the fluxoid lattice in the nonsaturation regime were investigated for N b - T a alloys with normal Nb2N precipitates and the following results were obtained. First, the interaction distance dt which is proportional to the yield strain of the fiuxoid lattice does not decrease with an increasing field except near Be2. Nonsaturation is expected to be attained, since the fluxoid lattice can endure the Lorentz force up to a large strain without yielding. Such a ductile property of the fluxoid lattice

Nonsaturated pinning characteristics in Nb-Ta: 7-. Matsushita et al. Larkin-Ovchinnikov theory (Fpoc N2p/3f~13). However, the elastic and plastic property of the pinned fluxoid lattice cannot be described by the linear summation theory.

Acknowledgement The electron microscope JEM-1000 in Research Laboratory of High Voltage Electron Microscope, Kyushu University was used for observation of microstructures of pinning centres.

References (a)

F,

i (b) Figure 9 Variation of force-displacement curve with an increaseof the pinning parameters in (a) saturation region and (b) nonsaturation region

seems to be caused by strong pinning interactions which stabilize the brittle fluxoid lattice. Secondly, the dependence of the pinning force density on the pinning parameters, fp and Np, is better explained by the linear summation theory (Fp oc Npfp) than by the

1 Matsushita, T., Itoh, M., Kikitsu, A. and Miyamoto, Y. Elastic and plastic behaviour of a fluxoid lattice in the saturation region of the global pinning force in super-conducting Nb-Ta Phys Rev B (1986) 33 3134-3138 :2 Matsushita, T. and Kiipfer, H. Enhancement of the super conducting critical current from saturation in Nb-Ti wire. I. J Appl Phys (1988) 63 5048-5059 3 Kramer, E.J. Scaling laws for flux pinning in hard superconductors J Appl Phys (1973) 44 1360-1370 , 4 Evetts, J.E. and Plummet, C.J.G. Flux pinning in polycrystalline AI5 bronze route filaments Proc lnt Symp on Flux Pinning and Electromagnetic Properties in Superconductors Matsukuma, Fukuoka (1985) 146-151 5 Dew-Hughes, D. The role of grain boundaries in determining Jc in high-field high-current superconductors Philos Mag (1987) 55 459-479 6 Antesberger, G. and UIImaier, H. Pinning of vortices in superconducting NbTa alloys due to normal conducting precipitates Philos Mag (1974) 29 1101-1124 7 Freyhardt, H.C. Radiation-induced flux pinning in type II superconductors J Low Temp Phys (1978) 32 101-129 8 Van der Meij, G.P. and Kes, P.H. Effective volume of voids for flux pinning in superconductors Phys Rev B (1984) 29 6233-6243 9 Harada, N., Miyamoto, Y., Matsushita, T. and Yamafuji, K. Nonsaturated global pinning fi)rce in superconducting Nb-Ta with normal precipitates J Phys Soc Jpn (1988) 57 3910-3919 10 Larkin, A.I. and Ovchinnikov, Yu. N. Pinning in type II superconductors J Low Temp Phys (1979) 34 409-428 11 Matsushita, T. Pinning force of nonideal superconductor containing pins with large interaction forces. I1. Low pin density Jpn J Appl Phys (1981) 20 1955-1966 12 Campbell, A.M. The interaction distance between flux lines and pinning centres J Phys C (1971) 4 3186-3198 13 Matsushita, T. On the elasticity of fluxoid lattice in type II superconductors J Phys Soc Jpn (1988) 57 1037-1043 14 Labusch, R. Elastische Konstanten des Flu,Ofadengitters in Supraleitern zweiter Art Phys Stat Sol (1967) 19 715-719

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